California State Standards - Mathematics
Grade Eight
Algebra I
Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
1.1 Students use properties of numbers to demonstrate whether assertions are true or false.
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
3.0 Students solve equations and inequalities involving absolute values.
4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < style="font-weight: bold;">
Geometry
The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
4.0 Students prove basic theorems involving congruence and similarity.
5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
6.0 Students know and are able to use the triangle inequality theorem.
7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.
10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.
13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
14.0 Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x)) 2 = 1.
19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
Algebra II
This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system.
1.0 Students solve equations and inequalities involving absolute value.
2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.
3.0 Students are adept at operations on polynomials, including long division.
4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
6.0 Students add, subtract, multiply, and divide complex numbers.
7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.
8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.
9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) 2+ c.
10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
11.0 Students prove simple laws of logarithms.
11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
11.2 Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.
13.0 Students use the definition of logarithms to translate between logarithms in any base.
14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.
15.0 Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.
16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.
17.0 Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.
18.0 Students use fundamental counting principles to compute combinations and permutations.
19.0 Students use combinations and permutations to compute probabilities.
20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
21.0 Students apply the method of mathematical induction to prove general statements about the positive integers.
22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
Probability and Statistics
This discipline is an introduction to the study of probability, interpretation of data, and fundamental statistical problem solving. Mastery of this academic content will provide students with a solid foundation in probability and facility in processing statistical information.
1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.
4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families.
5.0 Students determine the mean and the standard deviation of a normally distributed random variable.
6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.
7.0 Students compute the variance and the standard deviation of a distribution of data.
8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
Friday, September 12, 2008
Grade 7 - Mathematics
California State Standards - Mathematics
Grade Seven
Mathematics
By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
1.4 Differentiate between rational and irrational numbers.
1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
1.6 Calculate the percentage of increases and decreases of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
2.2 Add and subtract fractions by using factoring to find common denominators.
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x +25.)
1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
3.0 Students graph and interpret linear and some nonlinear functions:
3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.
4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
1.2 Construct and read drawings and models made to scale.
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.
2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in 3] = [16.38 cm3]).
3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
3.5 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.
3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).
Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and whisker plot; use the forms to display a single set of data or to compare two sets of data.
1.2 Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Make and test conjectures by using both inductive and deductive reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Grade Seven
Mathematics
By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
1.4 Differentiate between rational and irrational numbers.
1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
1.6 Calculate the percentage of increases and decreases of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
2.2 Add and subtract fractions by using factoring to find common denominators.
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x +25.)
1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
3.0 Students graph and interpret linear and some nonlinear functions:
3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.
4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
1.2 Construct and read drawings and models made to scale.
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.
2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in 3] = [16.38 cm3]).
3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
3.5 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.
3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).
Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and whisker plot; use the forms to display a single set of data or to compare two sets of data.
1.2 Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Make and test conjectures by using both inductive and deductive reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Grade 6 - Mathematics
California State Standards - Mathematics
Grade Six
Mathematics
By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (e.g., tax, tips, interest). Students know about π and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations.
Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions,
and percentages:
1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).
1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.
1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
2.2 Explain the meaning of multiplication and division of positive fractions and per 8 ÷ 158 × 16 form the calculations (e.g., 5⁄ ⁄16 = 5⁄ ⁄15 = 2⁄3).
2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
Algebra and Functions
1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:
1.1 Write and solve one-step linear equations in one variable.
1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
1.3 Apply algebraic order of operations and the commutative, associative, and distributive
properties to evaluate expressions; and justify each step in the process.
1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.
2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:
2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).
2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
2.3 Solve problems involving rates, average speed, distance, and time.
3.0 Students investigate geometric patterns and describe them algebraically:
3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A =⁄2 bh, C = π d—the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).
3.2 Express in symbolic form simple relationships arising from geometry.
Measurement and Geometry
1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
1.1 Understand the concept of a constant such as π; know the formulas for the circumference and area of a circle.
1.2 Know common estimates of π (3.14; 22⁄7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.
1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.
2.0 Students identify and describe the properties of two-dimensional figures:
2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.
2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).
Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.
1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.
1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.
1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.
2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:
2.1Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.
2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.
2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.
2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events:
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.
3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.
3.5 Understand the difference between independent and dependent events.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.7 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.
Grade Six
Mathematics
By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (e.g., tax, tips, interest). Students know about π and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations.
Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions,
and percentages:
1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.
1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).
1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.
1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
2.2 Explain the meaning of multiplication and division of positive fractions and per 8 ÷ 158 × 16 form the calculations (e.g., 5⁄ ⁄16 = 5⁄ ⁄15 = 2⁄3).
2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).
Algebra and Functions
1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:
1.1 Write and solve one-step linear equations in one variable.
1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
1.3 Apply algebraic order of operations and the commutative, associative, and distributive
properties to evaluate expressions; and justify each step in the process.
1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.
2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:
2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).
2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
2.3 Solve problems involving rates, average speed, distance, and time.
3.0 Students investigate geometric patterns and describe them algebraically:
3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A =⁄2 bh, C = π d—the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).
3.2 Express in symbolic form simple relationships arising from geometry.
Measurement and Geometry
1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
1.1 Understand the concept of a constant such as π; know the formulas for the circumference and area of a circle.
1.2 Know common estimates of π (3.14; 22⁄7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.
1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.
2.0 Students identify and describe the properties of two-dimensional figures:
2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.
2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).
Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.
1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.
1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.
1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.
2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:
2.1Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.
2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.
2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.
2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events:
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.
3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1-P is the probability of an event not occurring.
3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.
3.5 Understand the difference between independent and dependent events.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.7 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.
Wednesday, September 10, 2008
Grade 8 - Science
California State Standards - Science
Grade Eight
Focus on Physical Sciences
Motion
Periodic Table
7. The organization of the periodic table is based on the properties of the elements and reflects the structure of atoms. As a basis for understanding this concept:
8. All objects experience a buoyant force when immersed in a fluid. As a basis for understanding this concept:
Grade Eight
Focus on Physical Sciences
Motion
1. The velocity of an object is the rate of change of its position. As a basis for understanding this concept:
a. Students know position is defined in relation to some choice of a standard reference point and a set of reference directions.
b. Students know that average speed is the total distance traveled divided by the total time elapsed and that the speed of an object along the path traveled can vary.
c. Students know how to solve problems involving distance, time, and average speed.
b. Students know that average speed is the total distance traveled divided by the total time elapsed and that the speed of an object along the path traveled can vary.
c. Students know how to solve problems involving distance, time, and average speed.
d. Students know the velocity of an object must be described by specifying both the direction and the speed of the object.
e. Students know changes in velocity may be due to changes in speed, direction, or both.
f. Students know how to interpret graphs of position versus time and graphs of speed versus time for motion in a single direction.
Forces
2. Unbalanced forces cause changes in velocity. As a basis for understanding this concept:
a. Students know a force has both direction and magnitude.
b. Students know when an object is subject to two or more forces at once, the result is the cumulative effect of all the forces.
c. Students know when the forces on an object are balanced, the motion of the object does not change.
d. Students know how to identify separately the two or more forces that are acting on a single static object, including gravity, elastic forces due to tension or compression in matter, and friction.
e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction).
c. Students know when the forces on an object are balanced, the motion of the object does not change.
d. Students know how to identify separately the two or more forces that are acting on a single static object, including gravity, elastic forces due to tension or compression in matter, and friction.
e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction).
f. Students know the greater the mass of an object, the more force is needed to achieve the same rate of change in motion.
g. Students know the role of gravity in forming and maintaining the shapes of planets, stars, and the solar system.
Structure of Matter
3. Each of the more than 100 elements of matter has distinct properties and a distinct atomic structure. All forms of matter are composed of one or more of the elements. As a basis for understanding this concept:
a. Students know the structure of the atom and know it is composed of protons, neutrons, and electrons.
b. Students know that compounds are formed by combining two or more different elements and that compounds have properties that are different from their constituent elements.
c. Students know atoms and molecules form solids by building up repeating patterns, such as the crystal structure of NaCl or long-chain polymers.
d. Students know the states of matter (solid, liquid, gas) depend on molecular motion.
b. Students know that compounds are formed by combining two or more different elements and that compounds have properties that are different from their constituent elements.
c. Students know atoms and molecules form solids by building up repeating patterns, such as the crystal structure of NaCl or long-chain polymers.
d. Students know the states of matter (solid, liquid, gas) depend on molecular motion.
e. Students know that in solids the atoms are closely locked in position and can only vibrate; in liquids the atoms and molecules are more loosely connected and can collide with and move past one another; and in gases the atoms and molecules are free to move independently, colliding frequently.
f. Students know how to use the periodic table to identify elements in simple compounds.
f. Students know how to use the periodic table to identify elements in simple compounds.
Earth in the Solar System (Earth Sciences)
4. The structure and composition of the universe can be learned from studying stars and galaxies and their evolution. As a basis for understanding this concept:
a. Students know galaxies are clusters of billions of stars and may have different shapes.
b. Students know that the Sun is one of many stars in the Milky Way galaxy and that stars may differ in size, temperature, and color.
b. Students know that the Sun is one of many stars in the Milky Way galaxy and that stars may differ in size, temperature, and color.
c. Students know how to use astronomical units and light years as measures of distances between the Sun, stars, and Earth.
d. Students know that stars are the source of light for all bright objects in outer space and that the Moon and planets shine by reflected sunlight, not by their own light.
e. Students know the appearance, general composition, relative position and size, and motion of objects in the solar system, including planets, planetary satellites, comets, and asteroids.
e. Students know the appearance, general composition, relative position and size, and motion of objects in the solar system, including planets, planetary satellites, comets, and asteroids.
Reactions
5. Chemical reactions are processes in which atoms are rearranged into different combinations of molecules. As a basis for understanding this concept:
a. Students know reactant atoms and molecules interact to form products with different chemical properties.
b. Students know the idea of atoms explains the conservation of matter: In chemical reactions the number of atoms stays the same no matter how they are arranged, so their total mass stays the same.
c. Students know chemical reactions usually liberate heat or absorb heat.
d. Students know physical processes include freezing and boiling, in which a material changes form with no chemical reaction.
e. Students know how to determine whether a solution is acidic, basic, or neutral.
b. Students know the idea of atoms explains the conservation of matter: In chemical reactions the number of atoms stays the same no matter how they are arranged, so their total mass stays the same.
c. Students know chemical reactions usually liberate heat or absorb heat.
d. Students know physical processes include freezing and boiling, in which a material changes form with no chemical reaction.
e. Students know how to determine whether a solution is acidic, basic, or neutral.
Chemistry of Living Systems (Life Sciences)
6. Principles of chemistry underlie the functioning of biological systems. As a basis for understanding this concept:
a. Students know that carbon, because of its ability to combine in many ways with itself and other elements, has a central role in the chemistry of living organisms.
b. Students know that living organisms are made of molecules consisting largely of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur.
c. Students know that living organisms have many different kinds of molecules, including small ones, such as water and salt, and very large ones, such as carbohydrates, fats, proteins, and DNA.
c. Students know that living organisms have many different kinds of molecules, including small ones, such as water and salt, and very large ones, such as carbohydrates, fats, proteins, and DNA.
Periodic Table
7. The organization of the periodic table is based on the properties of the elements and reflects the structure of atoms. As a basis for understanding this concept:
a. Students know how to identify regions corresponding to metals, nonmetals, and inert gases.
b. Students know each element has a specific number of protons in the nucleus (the atomic number) and each isotope of the element has a different but specific number of neutrons in the nucleus.
c. Students know substances can be classified by their properties, including their melting temperature, density, hardness, and thermal and electrical conductivity.
b. Students know each element has a specific number of protons in the nucleus (the atomic number) and each isotope of the element has a different but specific number of neutrons in the nucleus.
c. Students know substances can be classified by their properties, including their melting temperature, density, hardness, and thermal and electrical conductivity.
Density and Buoyancy
8. All objects experience a buoyant force when immersed in a fluid. As a basis for understanding this concept:
a. Students know density is mass per unit volume.
b. Students know how to calculate the density of substances (regular and irregular solids and liquids) from measurements of mass and volume.
c. Students know the buoyant force on an object in a fluid is an upward force equal to the weight of the fluid the object has displaced.
d. Students know how to predict whether an object will float or sink.
c. Students know the buoyant force on an object in a fluid is an upward force equal to the weight of the fluid the object has displaced.
d. Students know how to predict whether an object will float or sink.
Investigation and Experimentation
9. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:
a. Plan and conduct a scientific investigation to test a hypothesis.
b. Evaluate the accuracy and reproducibility of data.
c. Distinguish between variable and controlled parameters in a test.
d. Recognize the slope of the linear graph as the constant in the relationship y=kx and apply this principle in interpreting graphs constructed from data.
e. Construct appropriate graphs from data and develop quantitative statements about the relationships between variables.
f. Apply simple mathematic relationships to determine a missing quantity in a mathematic expression, given the two remaining terms (including speed = distance/time, density = mass/volume, force = pressure × area, volume = area × height).
g. Distinguish between linear and nonlinear relationships on a graph of data.
b. Evaluate the accuracy and reproducibility of data.
c. Distinguish between variable and controlled parameters in a test.
d. Recognize the slope of the linear graph as the constant in the relationship y=kx and apply this principle in interpreting graphs constructed from data.
e. Construct appropriate graphs from data and develop quantitative statements about the relationships between variables.
f. Apply simple mathematic relationships to determine a missing quantity in a mathematic expression, given the two remaining terms (including speed = distance/time, density = mass/volume, force = pressure × area, volume = area × height).
g. Distinguish between linear and nonlinear relationships on a graph of data.
Grade 7 - Science
California State Standards - Science
Grade Seven
Focus on Life Sciences
Cell Biology
Grade Seven
Focus on Life Sciences
Cell Biology
1. All living organisms are composed of cells, from just one to many trillions, whose details usually are visible only through a microscope. As a basis for understanding this concept:
a. Students know cells function similarly in all living organisms.
b. Students know the characteristics that distinguish plant cells from animal cells, including chloroplasts and cell walls.
c. Students know the nucleus is the repository for genetic information in plant and animal cells. d. Students know that mitochondria liberate energy for the work that cells do and that chloroplasts capture sunlight energy for photosynthesis.
e. Students know cells divide to increase their numbers through a process of mitosis, which results in two daughter cells with identical sets of chromosomes.
f. Students know that as multicellular organisms develop, their cells differentiate.
e. Students know cells divide to increase their numbers through a process of mitosis, which results in two daughter cells with identical sets of chromosomes.
f. Students know that as multicellular organisms develop, their cells differentiate.
Genetics
2. A typical cell of any organism contains genetic instructions that specify its traits. Those traits may be modified by environmental influences. As a basis for understanding
this concept:
this concept:
a. Students know the differences between the life cycles and reproduction methods of sexual and asexual organisms.
b. Students know sexual reproduction produces offspring that inherit half their genes from each parent.
c. Students know an inherited trait can be determined by one or more genes.
d. Students know plant and animal cells contain many thousands of different genes and typically have two copies of every gene. The two copies (or alleles) of the gene may or may not be identical, and one may be dominant in determining the phenotype while the other is recessive.
e. Students know DNA (deoxyribonucleic acid) is the genetic material of living organisms and is located in the chromosomes of each cell.
c. Students know an inherited trait can be determined by one or more genes.
d. Students know plant and animal cells contain many thousands of different genes and typically have two copies of every gene. The two copies (or alleles) of the gene may or may not be identical, and one may be dominant in determining the phenotype while the other is recessive.
e. Students know DNA (deoxyribonucleic acid) is the genetic material of living organisms and is located in the chromosomes of each cell.
Evolution
3. Biological evolution accounts for the diversity of species developed through gradual processes over many generations. As a basis for understanding this concept:
a. Students know both genetic variation and environmental factors are causes of evolution and diversity of organisms.
b. Students know the reasoning used by Charles Darwin in reaching his conclusion that natural selection is the mechanism of evolution.
c. Students know how independent lines of evidence from geology, fossils, and comparative anatomy provide the bases for the theory of evolution.
d. Students know how to construct a simple branching diagram to classify living groups of organisms by shared derived characteristics and how to expand the diagram to include fossil organisms.
e. Students know that extinction of a species occurs when the environment changes and the adaptive characteristics of a species are insufficient for its survival.
d. Students know how to construct a simple branching diagram to classify living groups of organisms by shared derived characteristics and how to expand the diagram to include fossil organisms.
e. Students know that extinction of a species occurs when the environment changes and the adaptive characteristics of a species are insufficient for its survival.
Earth and Life History (Earth Sciences)
4. Evidence from rocks allows us to understand the evolution of life on Earth. As a basis for understanding this concept:
a. Students know Earth processes today are similar to those that occurred in the past and slow geologic processes have large cumulative effects over long periods of time.
b. Students know the history of life on Earth has been disrupted by major catastrophic events, such as major volcanic eruptions or the impacts of asteroids.
c. Students know that the rock cycle includes the formation of new sediment and rocks and that rocks are often found in layers, with the oldest generally on the bottom.
d. Students know that evidence from geologic layers and radioactive dating indicates Earth is approximately 4.6 billion years old and that life on this planet has existed for more than 3 billion years.
e. Students know fossils provide evidence of how life and environmental conditions have changed.
f. Students know how movements of Earth’s continental and oceanic plates through time, with associated changes in climate and geographic connections, have affected the past and present distribution of organisms.
g. Students know how to explain significant developments and extinctions of plant and animal life on the geologic time scale.
b. Students know the history of life on Earth has been disrupted by major catastrophic events, such as major volcanic eruptions or the impacts of asteroids.
c. Students know that the rock cycle includes the formation of new sediment and rocks and that rocks are often found in layers, with the oldest generally on the bottom.
d. Students know that evidence from geologic layers and radioactive dating indicates Earth is approximately 4.6 billion years old and that life on this planet has existed for more than 3 billion years.
e. Students know fossils provide evidence of how life and environmental conditions have changed.
f. Students know how movements of Earth’s continental and oceanic plates through time, with associated changes in climate and geographic connections, have affected the past and present distribution of organisms.
g. Students know how to explain significant developments and extinctions of plant and animal life on the geologic time scale.
Structure and Function in Living Systems
5. The anatomy and physiology of plants and animals illustrate the complementary nature of structure and function. As a basis for understanding this concept:
a. Students know plants and animals have levels of organization for structure and function, including cells, tissues, organs, organ systems, and the whole organism.
b. Students know organ systems function because of the contributions of individual organs, tissues, and cells. The failure of any part can affect the entire system.
c. Students know how bones and muscles work together to provide a structural framework for movement.
d. Students know how the reproductive organs of the human female and male generate eggs and sperm and how sexual activity may lead to fertilization and pregnancy.
e. Students know the function of the umbilicus and placenta during pregnancy.
f. Students know the structures and processes by which flowering plants generate pollen, ovules, seeds, and fruit.
g. Students know how to relate the structures of the eye and ear to their functions.
d. Students know how the reproductive organs of the human female and male generate eggs and sperm and how sexual activity may lead to fertilization and pregnancy.
e. Students know the function of the umbilicus and placenta during pregnancy.
f. Students know the structures and processes by which flowering plants generate pollen, ovules, seeds, and fruit.
g. Students know how to relate the structures of the eye and ear to their functions.
Physical Principles in Living Systems (Physical Sciences)
6. Physical principles underlie biological structures and functions. As a basis for understanding this concept:
a. Students know visible light is a small band within a very broad electromagnetic spectrum.
b. Students know that for an object to be seen, light emitted by or scattered from it must be detected by the eye.
c. Students know light travels in straight lines if the medium it travels through does not change.
d. Students know how simple lenses are used in a magnifying glass, the eye, a camera, a telescope, and a microscope.
e. Students know that white light is a mixture of many wavelengths (colors) and that retinal cells react differently to different wavelengths.
f. Students know light can be reflected, refracted, transmitted, and absorbed by matter.
g. Students know the angle of reflection of a light beam is equal to the angle of incidence.
h. Students know how to compare joints in the body (wrist, shoulder, thigh) with structures used in machines and simple devices (hinge, ball-and-socket, and sliding joints).
i. Students know how levers confer mechanical advantage and how the application of this principle applies to the musculoskeletal system.
j. Students know that contractions of the heart generate blood pressure and that heart valves prevent backflow of blood in the circulatory system.
d. Students know how simple lenses are used in a magnifying glass, the eye, a camera, a telescope, and a microscope.
e. Students know that white light is a mixture of many wavelengths (colors) and that retinal cells react differently to different wavelengths.
f. Students know light can be reflected, refracted, transmitted, and absorbed by matter.
g. Students know the angle of reflection of a light beam is equal to the angle of incidence.
h. Students know how to compare joints in the body (wrist, shoulder, thigh) with structures used in machines and simple devices (hinge, ball-and-socket, and sliding joints).
i. Students know how levers confer mechanical advantage and how the application of this principle applies to the musculoskeletal system.
j. Students know that contractions of the heart generate blood pressure and that heart valves prevent backflow of blood in the circulatory system.
Investigation and Experimentation
7. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:
a. Select and use appropriate tools and technology (including calculators, computers,
balances, spring scales, microscopes, and binoculars) to perform tests, collect data, and display data.
b. Use a variety of print and electronic resources (including the World Wide Web) to collect information and evidence as part of a research project.
balances, spring scales, microscopes, and binoculars) to perform tests, collect data, and display data.
b. Use a variety of print and electronic resources (including the World Wide Web) to collect information and evidence as part of a research project.
c. Communicate the logical connection among hypotheses, science concepts, tests conducted, data collected, and conclusions drawn from the scientific evidence.
d. Construct scale models, maps, and appropriately labeled diagrams to communicate scientific knowledge (e.g., motion of Earth’s plates and cell structure).
e. Communicate the steps and results from an investigation in written reports and oral presentations.
Grade 6 - Science
California State Standards - Science
Grade Six
Focus on Earth Sciences
Plate Tectonics and Earth’s Structure
a. Students know evidence of plate tectonics is derived from the fit of the continents; the location of earthquakes, volcanoes, and midocean ridges; and the distribution of fossils, rock types, and ancient climatic zones.
b. Students know Earth is composed of several layers: a cold, brittle lithosphere; a hot, convecting mantle; and a dense, metallic core.
2. Topography is reshaped by the weathering of rock and soil and by the transportation
and deposition of sediment. As a basis for understanding this concept:
7. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:
Grade Six
Focus on Earth Sciences
Plate Tectonics and Earth’s Structure
1. Plate tectonics accounts for important features of Earth’s surface and major geologic events. As a basis for understanding this concept:
a. Students know evidence of plate tectonics is derived from the fit of the continents; the location of earthquakes, volcanoes, and midocean ridges; and the distribution of fossils, rock types, and ancient climatic zones.
b. Students know Earth is composed of several layers: a cold, brittle lithosphere; a hot, convecting mantle; and a dense, metallic core.
c. Students know lithospheric plates the size of continents and oceans move at rates of centimeters per year in response to movements in the mantle.
d. Students know that earthquakes are sudden motions along breaks in the crust called faults and that volcanoes and fissures are locations where magma reaches the surface.
e. Students know major geologic events, such as earthquakes, volcanic eruptions, and mountain building, result from plate motions.
d. Students know that earthquakes are sudden motions along breaks in the crust called faults and that volcanoes and fissures are locations where magma reaches the surface.
e. Students know major geologic events, such as earthquakes, volcanic eruptions, and mountain building, result from plate motions.
f. Students know how to explain major features of California geology (including mountains, faults, volcanoes) in terms of plate tectonics.
g. Students know how to determine the epicenter of an earthquake and know that the effects of an earthquake on any region vary, depending on the size of the earthquake, the distance of the region from the epicenter, the local geology, and the type of construction in the region.
Shaping Earth’s Surface
g. Students know how to determine the epicenter of an earthquake and know that the effects of an earthquake on any region vary, depending on the size of the earthquake, the distance of the region from the epicenter, the local geology, and the type of construction in the region.
Shaping Earth’s Surface
2. Topography is reshaped by the weathering of rock and soil and by the transportation
and deposition of sediment. As a basis for understanding this concept:
a. Students know water running downhill is the dominant process in shaping the landscape, including California’s landscape.
b. Students know rivers and streams are dynamic systems that erode, transport sediment, change course, and flood their banks in natural and recurring patterns.
c. Students know beaches are dynamic systems in which the sand is supplied by rivers and moved along the coast by the action of waves.
d. Students know earthquakes, volcanic eruptions, landslides, and floods change human and wildlife habitats.
Heat (Thermal Energy) (Physical Sciences)
3. Heat moves in a predictable flow from warmer objects to cooler objects until all the objects are at the same temperature. As a basis for understanding this concept:
a. Students know energy can be carried from one place to another by heat flow or by waves, including water, light and sound waves, or by moving objects.
b. Students know that when fuel is consumed, most of the energy released becomes heat energy.
c. Students know heat flows in solids by conduction (which involves no flow of matter) and in fluids by conduction and by convection (which involves flow of matter).
d. Students know heat energy is also transferred between objects by radiation (radiation
can travel through space).
c. Students know heat flows in solids by conduction (which involves no flow of matter) and in fluids by conduction and by convection (which involves flow of matter).
d. Students know heat energy is also transferred between objects by radiation (radiation
can travel through space).
Energy in the Earth System
4. Many phenomena on Earth’s surface are affected by the transfer of energy through radiation and convection currents. As a basis for understanding this concept:
a. Students know the sun is the major source of energy for phenomena on Earth’s surface; it powers winds, ocean currents, and the water cycle.
b. Students know solar energy reaches Earth through radiation, mostly in the form of visible light.
c. Students know heat from Earth’s interior reaches the surface primarily through convection.
d. Students know convection currents distribute heat in the atmosphere and oceans.
e. Students know differences in pressure, heat, air movement, and humidity result in changes of weather.
c. Students know heat from Earth’s interior reaches the surface primarily through convection.
d. Students know convection currents distribute heat in the atmosphere and oceans.
e. Students know differences in pressure, heat, air movement, and humidity result in changes of weather.
Ecology (Life Sciences)
5. Organisms in ecosystems exchange energy and nutrients among themselves and with the environment. As a basis for understanding this concept:
a. Students know energy entering ecosystems as sunlight is transferred by producers into chemical energy through photosynthesis and then from organism to organism through food webs.
b. Students know matter is transferred over time from one organism to others in the food web and between organisms and the physical environment.
b. Students know matter is transferred over time from one organism to others in the food web and between organisms and the physical environment.
c. Students know populations of organisms can be categorized by the functions they serve in an ecosystem.
d. Students know different kinds of organisms may play similar ecological roles in similar biomes.
e. Students know the number and types of organisms an ecosystem can support depends on the resources available and on abiotic factors, such as quantities of light and water, a range of temperatures, and soil composition.
e. Students know the number and types of organisms an ecosystem can support depends on the resources available and on abiotic factors, such as quantities of light and water, a range of temperatures, and soil composition.
Resources
6. Sources of energy and materials differ in amounts, distribution, usefulness, and the time required for their formation. As a basis for understanding this concept:
a. Students know the utility of energy sources is determined by factors that are involved in converting these sources to useful forms and the consequences of the conversion process.
b. Students know different natural energy and material resources, including air, soil, rocks, minerals, petroleum, fresh water, wildlife, and forests, and know how to classify them as renewable or nonrenewable.
c. Students know the natural origin of the materials used to make common objects.
Investigation and Experimentation
b. Students know different natural energy and material resources, including air, soil, rocks, minerals, petroleum, fresh water, wildlife, and forests, and know how to classify them as renewable or nonrenewable.
c. Students know the natural origin of the materials used to make common objects.
Investigation and Experimentation
7. Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Students will:
a. Develop a hypothesis.
b. Select and use appropriate tools and technology (including calculators, computers, balances, spring scales, microscopes, and binoculars) to perform tests, collect data, and display data.
c. Construct appropriate graphs from data and develop qualitative statements about the relationships between variables.
d. Communicate the steps and results from an investigation in written reports and oral presentations.
e. Recognize whether evidence is consistent with a proposed explanation.
d. Communicate the steps and results from an investigation in written reports and oral presentations.
e. Recognize whether evidence is consistent with a proposed explanation.
f. Read a topographic map and a geologic map for evidence provided on the maps and construct and interpret a simple scale map.
g. Interpret events by sequence and time from natural phenomena (e.g., the relative ages of rocks and intrusions).
h. Identify changes in natural phenomena over time without manipulating the phenomena (e.g., a tree limb, a grove of trees, a stream, a hill slope).
h. Identify changes in natural phenomena over time without manipulating the phenomena (e.g., a tree limb, a grove of trees, a stream, a hill slope).
Tuesday, September 9, 2008
Grade 8 - World History and Geography
California State Standards - World History and Geography
Grade Eight
United States History and Geography: Growth and Conflict
Students in grade eight study the ideas, issues, and events from the framing of the Constitution up to World War I, with an emphasis on America’s role in the war. After reviewing the development of America’s democratic institutions founded on the Judeo-Christian heritage and English parliamentary traditions, particularly the shaping of the Constitution, students trace the development of American politics, society, culture, and economy and relate them to the emergence of major regional differences. They learn about the challenges facing the new nation, with an emphasis on the causes, course, and consequences of the Civil War. They make connections between the rise of industrialization and contemporary social and economic conditions.
8.1 Students understand the major events preceding the founding of the nation and relate their significance to the development of American constitutional democracy.
1. Describe the relationship between the moral and political ideas of the Great Awakening and the development of revolutionary fervor.
2. Analyze the philosophy of government expressed in the Declaration of Independence, with an emphasis on government as a means of securing individual rights (e.g., key phrases such as “all men are created equal, that they are endowed by their Creator with certain unalienable Rights”).
3. Analyze how the American Revolution affected other nations, especially France.
4. Describe the nation’s blend of civic republicanism, classical liberal principles, and English parliamentary traditions.
8.2 Students analyze the political principles underlying the U.S. Constitution and compare the enumerated and implied powers of the federal government.
1. Discuss the significance of the Magna Carta, the English Bill of Rights, and the Mayflower Compact.
2. Analyze the Articles of Confederation and the Constitution and the success of each in implementing the ideals of the Declaration of Independence.
3. Evaluate the major debates that occurred during the development of the Constitution and their ultimate resolutions in such areas as shared power among institutions, divided state-federal power, slavery, the rights of individuals and states (later addressed by the addition of the Bill of Rights), and the status of American Indian nations under the commerce clause.
4. Describe the political philosophy underpinning the Constitution as specified in the Federalist Papers (authored by James Madison, Alexander Hamilton, and John Jay) and the role of such leaders as Madison, George Washington, Roger Sherman, Gouverneur Morris, and James Wilson in the writing and ratification of the Constitution.
5. Understand the significance of Jefferson’s Statute for Religious Freedom as a forerunner of the First Amendment and the origins, purpose, and differing views of the founding fathers on the issue of the separation of church and state.
6. Enumerate the powers of government set forth in the Constitution and the fundamental liberties ensured by the Bill of Rights.
7. Describe the principles of federalism, dual sovereignty, separation of powers, checks and balances, the nature and purpose of majority rule, and the ways in which the American idea of constitutionalism preserves individual rights.
8.3 Students understand the foundation of the American political system and the ways in which citizens participate in it.
1. Analyze the principles and concepts codified in state constitutions between 1777 and 1781 that created the context out of which American political institutions and ideas developed.
2. Explain how the ordinances of 1785 and 1787 privatized national resources and transferred federally owned lands into private holdings, townships, and states.
3. Enumerate the advantages of a common market among the states as foreseen in and protected by the Constitution’s clauses on interstate commerce, common coinage, and full-faith and credit.
4. Understand how the conflicts between Thomas Jefferson and Alexander Hamilton resulted in the emergence of two political parties (e.g., view of foreign policy, Alien and Sedition Acts, economic policy, National Bank, funding and assumption of the revolutionary debt).
5. Know the significance of domestic resistance movements and ways in which the central government responded to such movements (e.g., Shays’ Rebellion, the Whiskey Rebellion).
6. Describe the basic law-making process and how the Constitution provides numerous opportunities for citizens to participate in the political process and to monitor and influence government (e.g., function of elections, political parties, interest groups).
7. Understand the functions and responsibilities of a free press.
8.4 Students analyze the aspirations and ideals of the people of the new nation.
1. Describe the country’s physical landscapes, political divisions, and territorial expansion during the terms of the first four presidents.
2. Explain the policy significance of famous speeches (e.g., Washington’s Farewell Address, Jefferson’s 1801 Inaugural Address, John Q. Adams’s Fourth of July 1821 Address).
3. Analyze the rise of capitalism and the economic problems and conflicts that accompanied it (e.g., Jackson’s opposition to the National Bank; early decisions of the U.S. Supreme Court that reinforced the sanctity of contracts and a capitalist economic system of law).
4. Discuss daily life, including traditions in art, music, and literature, of early national America (e.g., through writings by Washington Irving, James Fenimore Cooper).
8.5 Students analyze U.S. foreign policy in the early Republic.
1. Understand the political and economic causes and consequences of the War of 1812 and know the major battles, leaders, and events that led to a final peace.
2. Know the changing boundaries of the United States and describe the relationships the country had with its neighbors (current Mexico and Canada) and Europe, including the influence of the Monroe Doctrine, and how those relationships influenced westward expansion and the Mexican-American War.
3. Outline the major treaties with American Indian nations during the administrations of the first four presidents and the varying outcomes of those treaties.
8.6 Students analyze the divergent paths of the American people from 1800 to the mid-1800s and the challenges they faced, with emphasis on the Northeast.
1. Discuss the influence of industrialization and technological developments on the region, including human modification of the landscape and how physical geography shaped human actions (e.g., growth of cities, deforestation, farming, mineral extraction).
2. Outline the physical obstacles to and the economic and political factors involved in building a network of roads, canals, and railroads (e.g., Henry Clay’s American System).
3. List the reasons for the wave of immigration from Northern Europe to the United States and describe the growth in the number, size, and spatial arrangements of cities (e.g., Irish immigrants and the Great Irish Famine).
4. Study the lives of black Americans who gained freedom in the North and founded schools and churches to advance their rights and communities.
5. Trace the development of the American education system from its earliest roots, including the roles of religious and private schools and Horace Mann’s campaign for free public education and its assimilating role in American culture.
6. Examine the women’s suffrage movement (e.g., biographies, writings, and speeches of Elizabeth Cady Stanton, Margaret Fuller, Lucretia Mott, Susan B. Anthony).
7. Identify common themes in American art as well as transcendentalism and individualism
(e.g., writings about and by Ralph Waldo Emerson, Henry David Thoreau, Herman Melville, Louisa May Alcott, Nathaniel Hawthorne, Henry Wadsworth Longfellow).
8.7 Students analyze the divergent paths of the American people in the South from 1800 to the mid-1800s and the challenges they faced.
1. Describe the development of the agrarian economy in the South, identify the locations of the cotton-producing states, and discuss the significance of cotton and the cotton gin.
2. Trace the origins and development of slavery; its effects on black Americans and on the region’s political, social, religious, economic, and cultural development; and identify the strategies that were tried to both overturn and preserve it (e.g., through the writings and historical documents on Nat Turner, Denmark Vesey).
3. Examine the characteristics of white Southern society and how the physical environment influenced events and conditions prior to the Civil War.
4. Compare the lives of and opportunities for free blacks in the North with those of free blacks in the South.
8.8 Students analyze the divergent paths of the American people in the West from 1800 to the mid-1800s and the challenges they faced.
1. Discuss the election of Andrew Jackson as president in 1828, the importance of Jacksonian democracy, and his actions as president (e.g., the spoils system, veto of the National Bank, policy of Indian removal, opposition to the Supreme Court).
2. Describe the purpose, challenges, and economic incentives associated with westward expansion, including the concept of Manifest Destiny (e.g., the Lewis and Clark expedition, accounts of the removal of Indians, the Cherokees’ “Trail of Tears,” settlement of the Great Plains) and the territorial acquisitions that spanned numerous decades.
3. Describe the role of pioneer women and the new status that western women achieved (e.g., Laura Ingalls Wilder, Annie Bidwell; slave women gaining freedom in the West; Wyoming granting suffrage to women in 1869).
4. Examine the importance of the great rivers and the struggle over water rights.
5. Discuss Mexican settlements and their locations, cultural traditions, attitudes toward slavery, land-grant system, and economies.
6. Describe the Texas War for Independence and the Mexican-American War, including territorial settlements, the aftermath of the wars, and the effects the wars had on the lives of Americans, including Mexican Americans today.
8.9 Students analyze the early and steady attempts to abolish slavery and to realize the ideals of the Declaration of Independence.
1. Describe the leaders of the movement (e.g., John Quincy Adams and his proposed constitutional amendment, John Brown and the armed resistance, Harriet Tubman and the Underground Railroad, Benjamin Franklin, Theodore Weld, William Lloyd Garrison, Frederick Douglass).
2. Discuss the abolition of slavery in early state constitutions.
3. Describe the significance of the Northwest Ordinance in education and in the banning of slavery in new states north of the Ohio River.
4. Discuss the importance of the slavery issue as raised by the annexation of Texas and California’s admission to the union as a free state under the Compromise of 1850.
5. Analyze the significance of the States’ Rights Doctrine, the Missouri Compromise (1820), the Wilmot Proviso (1846), the Compromise of 1850, Henry Clay’s role in the Missouri Compromise and the Compromise of 1850, the Kansas-Nebraska Act (1854), the Dred Scott v. Sandford decision (1857), and the Lincoln-Douglas debates (1858).
6. Describe the lives of free blacks and the laws that limited their freedom and economic opportunities.
8.10 Students analyze the multiple causes, key events, and complex consequences of the Civil War.
1. Compare the conflicting interpretations of state and federal authority as emphasized in the speeches and writings of statesmen such as Daniel Webster and John C. Calhoun.
2. Trace the boundaries constituting the North and the South, the geographical differences between the two regions, and the differences between agrarians and industrialists.
3. Identify the constitutional issues posed by the doctrine of nullification and secession and the earliest origins of that doctrine.
4. Discuss Abraham Lincoln’s presidency and his significant writings and speeches and their relationship to the Declaration of Independence, such as his “House Divided” speech (1858), Gettysburg Address (1863), Emancipation Proclamation (1863), and inaugural addresses (1861 and 1865).
5. Study the views and lives of leaders (e.g., Ulysses S. Grant, Jefferson Davis, Robert E. Lee) and soldiers on both sides of the war, including those of black soldiers and regiments.
6. Describe critical developments and events in the war, including the major battles, geographical advantages and obstacles, technological advances, and General Lee’s surrender at Appomattox.
7. Explain how the war affected combatants, civilians, the physical environment, and future warfare.
8.11 Students analyze the character and lasting consequences of Reconstruction.
1. List the original aims of Reconstruction and describe its effects on the political and social structures of different regions.
2. Identify the push-pull factors in the movement of former slaves to the cities in the North and to the West and their differing experiences in those regions (e.g., the experiences of Buffalo Soldiers).
3. Understand the effects of the Freedmen’s Bureau and the restrictions placed on the rights and opportunities of freedmen, including racial segregation and “Jim Crow” laws.
4. Trace the rise of the Ku Klux Klan and describe the Klan’s effects.
5. Understand the Thirteenth, Fourteenth, and Fifteenth Amendments to the Constitution and analyze their connection to Reconstruction.
8.12 Students analyze the transformation of the American economy and the changing social and political conditions in the United States in response to the Industrial Revolution.
1. Trace patterns of agricultural and industrial development as they relate to climate, use of natural resources, markets, and trade and locate such development on a map.
2. Identify the reasons for the development of federal Indian policy and the wars with American Indians and their relationship to agricultural development and industrialization.
3. Explain how states and the federal government encouraged business expansion through tariffs, banking, land grants, and subsidies.
4. Discuss entrepreneurs, industrialists, and bankers in politics, commerce, and industry (e.g., Andrew Carnegie, John D. Rockefeller, Leland Stanford).
5. Examine the location and effects of urbanization, renewed immigration, and industrialization
(e.g., the effects on social fabric of cities, wealth and economic opportunity, the conservation movement).
6. Discuss child labor, working conditions, and laissez-faire policies toward big business and examine the labor movement, including its leaders (e.g., Samuel Gompers), its demand for collective bargaining, and its strikes and protests over labor conditions.
7. Identify the new sources of large-scale immigration and the contributions of immigrants to the building of cities and the economy; explain the ways in which new social and economic patterns encouraged assimilation of newcomers into the mainstream amidst growing cultural diversity; and discuss the new wave of nativism.
8. Identify the characteristics and impact of Grangerism and Populism.
9. Name the significant inventors and their inventions and identify how they improved the quality of life (e.g., Thomas Edison, Alexander Graham Bell, Orville and Wilbur Wright).
Grade Eight
United States History and Geography: Growth and Conflict
Students in grade eight study the ideas, issues, and events from the framing of the Constitution up to World War I, with an emphasis on America’s role in the war. After reviewing the development of America’s democratic institutions founded on the Judeo-Christian heritage and English parliamentary traditions, particularly the shaping of the Constitution, students trace the development of American politics, society, culture, and economy and relate them to the emergence of major regional differences. They learn about the challenges facing the new nation, with an emphasis on the causes, course, and consequences of the Civil War. They make connections between the rise of industrialization and contemporary social and economic conditions.
8.1 Students understand the major events preceding the founding of the nation and relate their significance to the development of American constitutional democracy.
1. Describe the relationship between the moral and political ideas of the Great Awakening and the development of revolutionary fervor.
2. Analyze the philosophy of government expressed in the Declaration of Independence, with an emphasis on government as a means of securing individual rights (e.g., key phrases such as “all men are created equal, that they are endowed by their Creator with certain unalienable Rights”).
3. Analyze how the American Revolution affected other nations, especially France.
4. Describe the nation’s blend of civic republicanism, classical liberal principles, and English parliamentary traditions.
8.2 Students analyze the political principles underlying the U.S. Constitution and compare the enumerated and implied powers of the federal government.
1. Discuss the significance of the Magna Carta, the English Bill of Rights, and the Mayflower Compact.
2. Analyze the Articles of Confederation and the Constitution and the success of each in implementing the ideals of the Declaration of Independence.
3. Evaluate the major debates that occurred during the development of the Constitution and their ultimate resolutions in such areas as shared power among institutions, divided state-federal power, slavery, the rights of individuals and states (later addressed by the addition of the Bill of Rights), and the status of American Indian nations under the commerce clause.
4. Describe the political philosophy underpinning the Constitution as specified in the Federalist Papers (authored by James Madison, Alexander Hamilton, and John Jay) and the role of such leaders as Madison, George Washington, Roger Sherman, Gouverneur Morris, and James Wilson in the writing and ratification of the Constitution.
5. Understand the significance of Jefferson’s Statute for Religious Freedom as a forerunner of the First Amendment and the origins, purpose, and differing views of the founding fathers on the issue of the separation of church and state.
6. Enumerate the powers of government set forth in the Constitution and the fundamental liberties ensured by the Bill of Rights.
7. Describe the principles of federalism, dual sovereignty, separation of powers, checks and balances, the nature and purpose of majority rule, and the ways in which the American idea of constitutionalism preserves individual rights.
8.3 Students understand the foundation of the American political system and the ways in which citizens participate in it.
1. Analyze the principles and concepts codified in state constitutions between 1777 and 1781 that created the context out of which American political institutions and ideas developed.
2. Explain how the ordinances of 1785 and 1787 privatized national resources and transferred federally owned lands into private holdings, townships, and states.
3. Enumerate the advantages of a common market among the states as foreseen in and protected by the Constitution’s clauses on interstate commerce, common coinage, and full-faith and credit.
4. Understand how the conflicts between Thomas Jefferson and Alexander Hamilton resulted in the emergence of two political parties (e.g., view of foreign policy, Alien and Sedition Acts, economic policy, National Bank, funding and assumption of the revolutionary debt).
5. Know the significance of domestic resistance movements and ways in which the central government responded to such movements (e.g., Shays’ Rebellion, the Whiskey Rebellion).
6. Describe the basic law-making process and how the Constitution provides numerous opportunities for citizens to participate in the political process and to monitor and influence government (e.g., function of elections, political parties, interest groups).
7. Understand the functions and responsibilities of a free press.
8.4 Students analyze the aspirations and ideals of the people of the new nation.
1. Describe the country’s physical landscapes, political divisions, and territorial expansion during the terms of the first four presidents.
2. Explain the policy significance of famous speeches (e.g., Washington’s Farewell Address, Jefferson’s 1801 Inaugural Address, John Q. Adams’s Fourth of July 1821 Address).
3. Analyze the rise of capitalism and the economic problems and conflicts that accompanied it (e.g., Jackson’s opposition to the National Bank; early decisions of the U.S. Supreme Court that reinforced the sanctity of contracts and a capitalist economic system of law).
4. Discuss daily life, including traditions in art, music, and literature, of early national America (e.g., through writings by Washington Irving, James Fenimore Cooper).
8.5 Students analyze U.S. foreign policy in the early Republic.
1. Understand the political and economic causes and consequences of the War of 1812 and know the major battles, leaders, and events that led to a final peace.
2. Know the changing boundaries of the United States and describe the relationships the country had with its neighbors (current Mexico and Canada) and Europe, including the influence of the Monroe Doctrine, and how those relationships influenced westward expansion and the Mexican-American War.
3. Outline the major treaties with American Indian nations during the administrations of the first four presidents and the varying outcomes of those treaties.
8.6 Students analyze the divergent paths of the American people from 1800 to the mid-1800s and the challenges they faced, with emphasis on the Northeast.
1. Discuss the influence of industrialization and technological developments on the region, including human modification of the landscape and how physical geography shaped human actions (e.g., growth of cities, deforestation, farming, mineral extraction).
2. Outline the physical obstacles to and the economic and political factors involved in building a network of roads, canals, and railroads (e.g., Henry Clay’s American System).
3. List the reasons for the wave of immigration from Northern Europe to the United States and describe the growth in the number, size, and spatial arrangements of cities (e.g., Irish immigrants and the Great Irish Famine).
4. Study the lives of black Americans who gained freedom in the North and founded schools and churches to advance their rights and communities.
5. Trace the development of the American education system from its earliest roots, including the roles of religious and private schools and Horace Mann’s campaign for free public education and its assimilating role in American culture.
6. Examine the women’s suffrage movement (e.g., biographies, writings, and speeches of Elizabeth Cady Stanton, Margaret Fuller, Lucretia Mott, Susan B. Anthony).
7. Identify common themes in American art as well as transcendentalism and individualism
(e.g., writings about and by Ralph Waldo Emerson, Henry David Thoreau, Herman Melville, Louisa May Alcott, Nathaniel Hawthorne, Henry Wadsworth Longfellow).
8.7 Students analyze the divergent paths of the American people in the South from 1800 to the mid-1800s and the challenges they faced.
1. Describe the development of the agrarian economy in the South, identify the locations of the cotton-producing states, and discuss the significance of cotton and the cotton gin.
2. Trace the origins and development of slavery; its effects on black Americans and on the region’s political, social, religious, economic, and cultural development; and identify the strategies that were tried to both overturn and preserve it (e.g., through the writings and historical documents on Nat Turner, Denmark Vesey).
3. Examine the characteristics of white Southern society and how the physical environment influenced events and conditions prior to the Civil War.
4. Compare the lives of and opportunities for free blacks in the North with those of free blacks in the South.
8.8 Students analyze the divergent paths of the American people in the West from 1800 to the mid-1800s and the challenges they faced.
1. Discuss the election of Andrew Jackson as president in 1828, the importance of Jacksonian democracy, and his actions as president (e.g., the spoils system, veto of the National Bank, policy of Indian removal, opposition to the Supreme Court).
2. Describe the purpose, challenges, and economic incentives associated with westward expansion, including the concept of Manifest Destiny (e.g., the Lewis and Clark expedition, accounts of the removal of Indians, the Cherokees’ “Trail of Tears,” settlement of the Great Plains) and the territorial acquisitions that spanned numerous decades.
3. Describe the role of pioneer women and the new status that western women achieved (e.g., Laura Ingalls Wilder, Annie Bidwell; slave women gaining freedom in the West; Wyoming granting suffrage to women in 1869).
4. Examine the importance of the great rivers and the struggle over water rights.
5. Discuss Mexican settlements and their locations, cultural traditions, attitudes toward slavery, land-grant system, and economies.
6. Describe the Texas War for Independence and the Mexican-American War, including territorial settlements, the aftermath of the wars, and the effects the wars had on the lives of Americans, including Mexican Americans today.
8.9 Students analyze the early and steady attempts to abolish slavery and to realize the ideals of the Declaration of Independence.
1. Describe the leaders of the movement (e.g., John Quincy Adams and his proposed constitutional amendment, John Brown and the armed resistance, Harriet Tubman and the Underground Railroad, Benjamin Franklin, Theodore Weld, William Lloyd Garrison, Frederick Douglass).
2. Discuss the abolition of slavery in early state constitutions.
3. Describe the significance of the Northwest Ordinance in education and in the banning of slavery in new states north of the Ohio River.
4. Discuss the importance of the slavery issue as raised by the annexation of Texas and California’s admission to the union as a free state under the Compromise of 1850.
5. Analyze the significance of the States’ Rights Doctrine, the Missouri Compromise (1820), the Wilmot Proviso (1846), the Compromise of 1850, Henry Clay’s role in the Missouri Compromise and the Compromise of 1850, the Kansas-Nebraska Act (1854), the Dred Scott v. Sandford decision (1857), and the Lincoln-Douglas debates (1858).
6. Describe the lives of free blacks and the laws that limited their freedom and economic opportunities.
8.10 Students analyze the multiple causes, key events, and complex consequences of the Civil War.
1. Compare the conflicting interpretations of state and federal authority as emphasized in the speeches and writings of statesmen such as Daniel Webster and John C. Calhoun.
2. Trace the boundaries constituting the North and the South, the geographical differences between the two regions, and the differences between agrarians and industrialists.
3. Identify the constitutional issues posed by the doctrine of nullification and secession and the earliest origins of that doctrine.
4. Discuss Abraham Lincoln’s presidency and his significant writings and speeches and their relationship to the Declaration of Independence, such as his “House Divided” speech (1858), Gettysburg Address (1863), Emancipation Proclamation (1863), and inaugural addresses (1861 and 1865).
5. Study the views and lives of leaders (e.g., Ulysses S. Grant, Jefferson Davis, Robert E. Lee) and soldiers on both sides of the war, including those of black soldiers and regiments.
6. Describe critical developments and events in the war, including the major battles, geographical advantages and obstacles, technological advances, and General Lee’s surrender at Appomattox.
7. Explain how the war affected combatants, civilians, the physical environment, and future warfare.
8.11 Students analyze the character and lasting consequences of Reconstruction.
1. List the original aims of Reconstruction and describe its effects on the political and social structures of different regions.
2. Identify the push-pull factors in the movement of former slaves to the cities in the North and to the West and their differing experiences in those regions (e.g., the experiences of Buffalo Soldiers).
3. Understand the effects of the Freedmen’s Bureau and the restrictions placed on the rights and opportunities of freedmen, including racial segregation and “Jim Crow” laws.
4. Trace the rise of the Ku Klux Klan and describe the Klan’s effects.
5. Understand the Thirteenth, Fourteenth, and Fifteenth Amendments to the Constitution and analyze their connection to Reconstruction.
8.12 Students analyze the transformation of the American economy and the changing social and political conditions in the United States in response to the Industrial Revolution.
1. Trace patterns of agricultural and industrial development as they relate to climate, use of natural resources, markets, and trade and locate such development on a map.
2. Identify the reasons for the development of federal Indian policy and the wars with American Indians and their relationship to agricultural development and industrialization.
3. Explain how states and the federal government encouraged business expansion through tariffs, banking, land grants, and subsidies.
4. Discuss entrepreneurs, industrialists, and bankers in politics, commerce, and industry (e.g., Andrew Carnegie, John D. Rockefeller, Leland Stanford).
5. Examine the location and effects of urbanization, renewed immigration, and industrialization
(e.g., the effects on social fabric of cities, wealth and economic opportunity, the conservation movement).
6. Discuss child labor, working conditions, and laissez-faire policies toward big business and examine the labor movement, including its leaders (e.g., Samuel Gompers), its demand for collective bargaining, and its strikes and protests over labor conditions.
7. Identify the new sources of large-scale immigration and the contributions of immigrants to the building of cities and the economy; explain the ways in which new social and economic patterns encouraged assimilation of newcomers into the mainstream amidst growing cultural diversity; and discuss the new wave of nativism.
8. Identify the characteristics and impact of Grangerism and Populism.
9. Name the significant inventors and their inventions and identify how they improved the quality of life (e.g., Thomas Edison, Alexander Graham Bell, Orville and Wilbur Wright).
Grade 7 - World History and Geography
California State Standards - World History and Geography
Grade Seven
Medieval and Early Modern Times
Students in grade seven study the social, cultural, and technological changes that occurred in Europe, Africa, and Asia in the years A.D. 500–1789. After reviewing the ancient world and the ways in which archaeologists and historians uncover the past, students study the history and geography of great civilizations that were developing concurrently throughout the world during medieval and early modern times. They examine the growing economic interaction among civilizations as well as the exchange of ideas, beliefs, technologies, and commodities. They learn about the resulting growth of Enlightenment philosophy and the new examination of the concepts of reason and authority, the natural rights of human beings and the divine right of kings, experimentalism in science, and the dogma of belief. Finally, students assess the political forces let loose by the Enlightenment, particularly the rise of democratic ideas, and they learn about the continuing influence of these ideas in the world today.
7.1 Students analyze the causes and effects of the vast expansion and ultimate disintegration of the Roman Empire.
1. Study the early strengths and lasting contributions of Rome (e.g., significance of Roman citizenship; rights under Roman law; Roman art, architecture, engineering, and philosophy; preservation and transmission of Christianity) and its ultimate internal weaknesses (e.g., rise of autonomous military powers within the empire, undermining of citizenship by the growth of corruption and slavery, lack of education, and distribution of news).
2. Discuss the geographic borders of the empire at its height and the factors that threatened its territorial cohesion.
3. Describe the establishment by Constantine of the new capital in Constantinople and the development of the Byzantine Empire, with an emphasis on the consequences of the development of two distinct European civilizations, Eastern Orthodox and Roman Catholic, and their two distinct views on church-state relations.
7.2 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Islam in the Middle Ages.
1. Identify the physical features and describe the climate of the Arabian peninsula, its relationship to surrounding bodies of land and water, and nomadic and sedentary ways of life.
2. Trace the origins of Islam and the life and teachings of Muhammad, including Islamic teachings on the connection with Judaism and Christianity.
3. Explain the significance of the Qur’an and the Sunnah as the primary sources of Islamic beliefs, practice, and law, and their influence in Muslims’ daily life.
4. Discuss the expansion of Muslim rule through military conquests and treaties, emphasizing the cultural blending within Muslim civilization and the spread and acceptance of Islam and the Arabic language.
5. Describe the growth of cities and the establishment of trade routes among Asia, Africa, and Europe, the products and inventions that traveled along these routes (e.g., spices, textiles, paper, steel, new crops), and the role of merchants in Arab society.
6. Understand the intellectual exchanges among Muslim scholars of Eurasia and Africa and the contributions Muslim scholars made to later civilizations in the areas of science, geography, mathematics, philosophy, medicine, art, and literature.
7.3 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of China in the Middle Ages.
1. Describe the reunification of China under the Tang Dynasty and reasons for the spread of Buddhism in Tang China, Korea, and Japan.
2. Describe agricultural, technological, and commercial developments during the Tang and Sung periods.
3. Analyze the influences of Confucianism and changes in Confucian thought during the Sung and Mongol periods.
4. Understand the importance of both overland trade and maritime expeditions between China and other civilizations in the Mongol Ascendancy and Ming Dynasty.
5. Trace the historic influence of such discoveries as tea, the manufacture of paper, woodblock printing, the compass, and gunpowder.
6. Describe the development of the imperial state and the scholar-official class.
7.4 Students analyze the geographic, political, economic, religious, and social structures of the sub-Saharan civilizations of Ghana and Mali in Medieval Africa.
1. Study the Niger River and the relationship of vegetation zones of forest, savannah, and desert to trade in gold, salt, food, and slaves; and the growth of the Ghana and Mali empires.
2. Analyze the importance of family, labor specialization, and regional commerce in the development of states and cities in West Africa.
3. Describe the role of the trans-Saharan caravan trade in the changing religious and cultural characteristics of West Africa and the influence of Islamic beliefs, ethics, and law.
4. Trace the growth of the Arabic language in government, trade, and Islamic scholarship in West Africa.
5. Describe the importance of written and oral traditions in the transmission of African history and culture.
7.5 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Japan.
1. Describe the significance of Japan’s proximity to China and Korea and the intellectual, linguistic, religious, and philosophical influence of those countries on Japan.
2. Discuss the reign of Prince Shotoku of Japan and the characteristics of Japanese society and family life during his reign.
3. Describe the values, social customs, and traditions prescribed by the lord-vassal system consisting of shogun, daimyo, and samurai and the lasting influence of the warrior code in the twentieth century.
4. Trace the development of distinctive forms of Japanese Buddhism.
5. Study the ninth and tenth centuries’ golden age of literature, art, and drama and its lasting effects on culture today, including Murasaki Shikibu’s Tale of Genji.
6. Analyze the rise of a military society in the late twelfth century and the role of the samurai in that society.
7.6 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Europe.
1. Study the geography of the Europe and the Eurasian land mass, including its location, topography, waterways, vegetation, and climate and their relationship to ways of life in Medieval Europe.
2. Describe the spread of Christianity north of the Alps and the roles played by the early church and by monasteries in its diffusion after the fall of the western half of the Roman Empire.
3. Understand the development of feudalism, its role in the medieval European economy, the way in which it was influenced by physical geography (the role of the manor and the growth of towns), and how feudal relationships provided the foundation of political order.
4. Demonstrate an understanding of the conflict and cooperation between the Papacy and European monarchs (e.g., Charlemagne, Gregory VII, Emperor Henry IV).
5. Know the significance of developments in medieval English legal and constitutional practices and their importance in the rise of modern democratic thought and representative institutions (e.g., Magna Carta, parliament, development of habeas corpus, an independent judiciary in England).
6. Discuss the causes and course of the religious Crusades and their effects on the Christian, Muslim, and Jewish populations in Europe, with emphasis on the increasing contact by Europeans with cultures of the Eastern Mediterranean world.
7. Map the spread of the bubonic plague from Central Asia to China, the Middle East, and Europe and describe its impact on global population.
8. Understand the importance of the Catholic church as a political, intellectual, and aesthetic institution (e.g., founding of universities, political and spiritual roles of the clergy, creation of monastic and mendicant religious orders, preservation of the Latin language and religious texts, St. Thomas Aquinas’s synthesis of classical philosophy with Christian theology, and the concept of “natural law”).
9. Know the history of the decline of Muslim rule in the Iberian Peninsula that culminated in the Reconquista and the rise of Spanish and Portuguese kingdoms.
7.7 Students compare and contrast the geographic, political, economic, religious, and social structures of the Meso-American and Andean civilizations.
1. Study the locations, landforms, and climates of Mexico, Central America, and South America and their effects on Mayan, Aztec, and Incan economies, trade, and development of urban societies.
2. Study the roles of people in each society, including class structures, family life, warfare, religious beliefs and practices, and slavery.
3. Explain how and where each empire arose and how the Aztec and Incan empires were defeated by the Spanish.
4. Describe the artistic and oral traditions and architecture in the three civilizations.
5. Describe the Meso-American achievements in astronomy and mathematics, including the development of the calendar and the Meso-American knowledge of seasonal changes to the civilizations’ agricultural systems.
7.8 Students analyze the origins, accomplishments, and geographic diffusion of the Renaissance.
1.Describe the way in which the revival of classical learning and the arts fostered a new interest in humanism (i.e., a balance between intellect and religious faith).
2. Explain the importance of Florence in the early stages of the Renaissance and the growth of independent trading cities (e.g., Venice), with emphasis on the cities’ importance in the spread of Renaissance ideas.
3. Understand the effects of the reopening of the ancient “Silk Road” between Europe and China, including Marco Polo’s travels and the location of his routes.
4. Describe the growth and effects of new ways of disseminating information (e.g., the ability to manufacture paper, translation of the Bible into the vernacular, printing).
5. Detail advances made in literature, the arts, science, mathematics, cartography, engineering, and the understanding of human anatomy and astronomy (e.g., by Dante Alighieri, Leonardo da Vinci, Michelangelo di Buonarroti Simoni, Johann Gutenberg, William Shakespeare).
7.9 Students analyze the historical developments of the Reformation.
1. List the causes for the internal turmoil in and weakening of the Catholic church (e.g., tax policies, selling of indulgences).
2. Describe the theological, political, and economic ideas of the major figures during the Reformation (e.g., Desiderius Erasmus, Martin Luther, John Calvin, William Tyndale).
3. Explain Protestants’ new practices of church self-government and the influence of those practices on the development of democratic practices and ideas of federalism.
4. Identify and locate the European regions that remained Catholic and those that became Protestant and explain how the division affected the distribution of religions in the New World.
5. Analyze how the Counter-Reformation revitalized the Catholic church and the forces that fostered the movement (e.g., St. Ignatius of Loyola and the Jesuits, the Council of Trent).
6. Understand the institution and impact of missionaries on Christianity and the diffusion of Christianity from Europe to other parts of the world in the medieval and early modern periods; locate missions on a world map.
7. Describe the Golden Age of cooperation between Jews and Muslims in medieval Spain that promoted creativity in art, literature, and science, including how that cooperation was terminated by the religious persecution of individuals and groups (e.g., the Spanish Inquisition and the expulsion of Jews and Muslims from Spain in 1492).
7.10 Students analyze the historical developments of the Scientific Revolution and its lasting effect on religious, political, and cultural institutions.
1. Discuss the roots of the Scientific Revolution (e.g., Greek rationalism; Jewish, Christian, and Muslim science; Renaissance humanism; new knowledge from global exploration).
2. Understand the significance of the new scientific theories (e.g., those of Copernicus, Galileo, Kepler, Newton) and the significance of new inventions (e.g., the telescope, microscope, thermometer, barometer).
3. Understand the scientific method advanced by Bacon and Descartes, the influence of new scientific rationalism on the growth of democratic ideas, and the coexistence of science with traditional religious beliefs.
7.11 Students analyze political and economic change in the sixteenth, seventeenth, and eighteenth centuries (the Age of Exploration, the Enlightenment, and the Age of Reason).
1. Know the great voyages of discovery, the locations of the routes, and the influence of cartography in the development of a new European worldview.
2. Discuss the exchanges of plants, animals, technology, culture, and ideas among Europe, Africa, Asia, and the Americas in the fifteenth and sixteenth centuries and the major economic and social effects on each continent.
3. Examine the origins of modern capitalism; the influence of mercantilism and cottage industry; the elements and importance of a market economy in seventeenth-century Europe; the changing international trading and marketing patterns, including their locations on a world map; and the influence of explorers and map makers.
4. Explain how the main ideas of the Enlightenment can be traced back to such movements as the Renaissance, the Reformation, and the Scientific Revolution and to the Greeks, Romans, and Christianity.
5. Describe how democratic thought and institutions were influenced by Enlightenment thinkers (e.g., John Locke, Charles-Louis Montesquieu, American founders).
6. Discuss how the principles in the Magna Carta were embodied in such documents as the English Bill of Rights and the American Declaration of Independence.
Grade Seven
Medieval and Early Modern Times
Students in grade seven study the social, cultural, and technological changes that occurred in Europe, Africa, and Asia in the years A.D. 500–1789. After reviewing the ancient world and the ways in which archaeologists and historians uncover the past, students study the history and geography of great civilizations that were developing concurrently throughout the world during medieval and early modern times. They examine the growing economic interaction among civilizations as well as the exchange of ideas, beliefs, technologies, and commodities. They learn about the resulting growth of Enlightenment philosophy and the new examination of the concepts of reason and authority, the natural rights of human beings and the divine right of kings, experimentalism in science, and the dogma of belief. Finally, students assess the political forces let loose by the Enlightenment, particularly the rise of democratic ideas, and they learn about the continuing influence of these ideas in the world today.
7.1 Students analyze the causes and effects of the vast expansion and ultimate disintegration of the Roman Empire.
1. Study the early strengths and lasting contributions of Rome (e.g., significance of Roman citizenship; rights under Roman law; Roman art, architecture, engineering, and philosophy; preservation and transmission of Christianity) and its ultimate internal weaknesses (e.g., rise of autonomous military powers within the empire, undermining of citizenship by the growth of corruption and slavery, lack of education, and distribution of news).
2. Discuss the geographic borders of the empire at its height and the factors that threatened its territorial cohesion.
3. Describe the establishment by Constantine of the new capital in Constantinople and the development of the Byzantine Empire, with an emphasis on the consequences of the development of two distinct European civilizations, Eastern Orthodox and Roman Catholic, and their two distinct views on church-state relations.
7.2 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Islam in the Middle Ages.
1. Identify the physical features and describe the climate of the Arabian peninsula, its relationship to surrounding bodies of land and water, and nomadic and sedentary ways of life.
2. Trace the origins of Islam and the life and teachings of Muhammad, including Islamic teachings on the connection with Judaism and Christianity.
3. Explain the significance of the Qur’an and the Sunnah as the primary sources of Islamic beliefs, practice, and law, and their influence in Muslims’ daily life.
4. Discuss the expansion of Muslim rule through military conquests and treaties, emphasizing the cultural blending within Muslim civilization and the spread and acceptance of Islam and the Arabic language.
5. Describe the growth of cities and the establishment of trade routes among Asia, Africa, and Europe, the products and inventions that traveled along these routes (e.g., spices, textiles, paper, steel, new crops), and the role of merchants in Arab society.
6. Understand the intellectual exchanges among Muslim scholars of Eurasia and Africa and the contributions Muslim scholars made to later civilizations in the areas of science, geography, mathematics, philosophy, medicine, art, and literature.
7.3 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of China in the Middle Ages.
1. Describe the reunification of China under the Tang Dynasty and reasons for the spread of Buddhism in Tang China, Korea, and Japan.
2. Describe agricultural, technological, and commercial developments during the Tang and Sung periods.
3. Analyze the influences of Confucianism and changes in Confucian thought during the Sung and Mongol periods.
4. Understand the importance of both overland trade and maritime expeditions between China and other civilizations in the Mongol Ascendancy and Ming Dynasty.
5. Trace the historic influence of such discoveries as tea, the manufacture of paper, woodblock printing, the compass, and gunpowder.
6. Describe the development of the imperial state and the scholar-official class.
7.4 Students analyze the geographic, political, economic, religious, and social structures of the sub-Saharan civilizations of Ghana and Mali in Medieval Africa.
1. Study the Niger River and the relationship of vegetation zones of forest, savannah, and desert to trade in gold, salt, food, and slaves; and the growth of the Ghana and Mali empires.
2. Analyze the importance of family, labor specialization, and regional commerce in the development of states and cities in West Africa.
3. Describe the role of the trans-Saharan caravan trade in the changing religious and cultural characteristics of West Africa and the influence of Islamic beliefs, ethics, and law.
4. Trace the growth of the Arabic language in government, trade, and Islamic scholarship in West Africa.
5. Describe the importance of written and oral traditions in the transmission of African history and culture.
7.5 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Japan.
1. Describe the significance of Japan’s proximity to China and Korea and the intellectual, linguistic, religious, and philosophical influence of those countries on Japan.
2. Discuss the reign of Prince Shotoku of Japan and the characteristics of Japanese society and family life during his reign.
3. Describe the values, social customs, and traditions prescribed by the lord-vassal system consisting of shogun, daimyo, and samurai and the lasting influence of the warrior code in the twentieth century.
4. Trace the development of distinctive forms of Japanese Buddhism.
5. Study the ninth and tenth centuries’ golden age of literature, art, and drama and its lasting effects on culture today, including Murasaki Shikibu’s Tale of Genji.
6. Analyze the rise of a military society in the late twelfth century and the role of the samurai in that society.
7.6 Students analyze the geographic, political, economic, religious, and social structures of the civilizations of Medieval Europe.
1. Study the geography of the Europe and the Eurasian land mass, including its location, topography, waterways, vegetation, and climate and their relationship to ways of life in Medieval Europe.
2. Describe the spread of Christianity north of the Alps and the roles played by the early church and by monasteries in its diffusion after the fall of the western half of the Roman Empire.
3. Understand the development of feudalism, its role in the medieval European economy, the way in which it was influenced by physical geography (the role of the manor and the growth of towns), and how feudal relationships provided the foundation of political order.
4. Demonstrate an understanding of the conflict and cooperation between the Papacy and European monarchs (e.g., Charlemagne, Gregory VII, Emperor Henry IV).
5. Know the significance of developments in medieval English legal and constitutional practices and their importance in the rise of modern democratic thought and representative institutions (e.g., Magna Carta, parliament, development of habeas corpus, an independent judiciary in England).
6. Discuss the causes and course of the religious Crusades and their effects on the Christian, Muslim, and Jewish populations in Europe, with emphasis on the increasing contact by Europeans with cultures of the Eastern Mediterranean world.
7. Map the spread of the bubonic plague from Central Asia to China, the Middle East, and Europe and describe its impact on global population.
8. Understand the importance of the Catholic church as a political, intellectual, and aesthetic institution (e.g., founding of universities, political and spiritual roles of the clergy, creation of monastic and mendicant religious orders, preservation of the Latin language and religious texts, St. Thomas Aquinas’s synthesis of classical philosophy with Christian theology, and the concept of “natural law”).
9. Know the history of the decline of Muslim rule in the Iberian Peninsula that culminated in the Reconquista and the rise of Spanish and Portuguese kingdoms.
7.7 Students compare and contrast the geographic, political, economic, religious, and social structures of the Meso-American and Andean civilizations.
1. Study the locations, landforms, and climates of Mexico, Central America, and South America and their effects on Mayan, Aztec, and Incan economies, trade, and development of urban societies.
2. Study the roles of people in each society, including class structures, family life, warfare, religious beliefs and practices, and slavery.
3. Explain how and where each empire arose and how the Aztec and Incan empires were defeated by the Spanish.
4. Describe the artistic and oral traditions and architecture in the three civilizations.
5. Describe the Meso-American achievements in astronomy and mathematics, including the development of the calendar and the Meso-American knowledge of seasonal changes to the civilizations’ agricultural systems.
7.8 Students analyze the origins, accomplishments, and geographic diffusion of the Renaissance.
1.Describe the way in which the revival of classical learning and the arts fostered a new interest in humanism (i.e., a balance between intellect and religious faith).
2. Explain the importance of Florence in the early stages of the Renaissance and the growth of independent trading cities (e.g., Venice), with emphasis on the cities’ importance in the spread of Renaissance ideas.
3. Understand the effects of the reopening of the ancient “Silk Road” between Europe and China, including Marco Polo’s travels and the location of his routes.
4. Describe the growth and effects of new ways of disseminating information (e.g., the ability to manufacture paper, translation of the Bible into the vernacular, printing).
5. Detail advances made in literature, the arts, science, mathematics, cartography, engineering, and the understanding of human anatomy and astronomy (e.g., by Dante Alighieri, Leonardo da Vinci, Michelangelo di Buonarroti Simoni, Johann Gutenberg, William Shakespeare).
7.9 Students analyze the historical developments of the Reformation.
1. List the causes for the internal turmoil in and weakening of the Catholic church (e.g., tax policies, selling of indulgences).
2. Describe the theological, political, and economic ideas of the major figures during the Reformation (e.g., Desiderius Erasmus, Martin Luther, John Calvin, William Tyndale).
3. Explain Protestants’ new practices of church self-government and the influence of those practices on the development of democratic practices and ideas of federalism.
4. Identify and locate the European regions that remained Catholic and those that became Protestant and explain how the division affected the distribution of religions in the New World.
5. Analyze how the Counter-Reformation revitalized the Catholic church and the forces that fostered the movement (e.g., St. Ignatius of Loyola and the Jesuits, the Council of Trent).
6. Understand the institution and impact of missionaries on Christianity and the diffusion of Christianity from Europe to other parts of the world in the medieval and early modern periods; locate missions on a world map.
7. Describe the Golden Age of cooperation between Jews and Muslims in medieval Spain that promoted creativity in art, literature, and science, including how that cooperation was terminated by the religious persecution of individuals and groups (e.g., the Spanish Inquisition and the expulsion of Jews and Muslims from Spain in 1492).
7.10 Students analyze the historical developments of the Scientific Revolution and its lasting effect on religious, political, and cultural institutions.
1. Discuss the roots of the Scientific Revolution (e.g., Greek rationalism; Jewish, Christian, and Muslim science; Renaissance humanism; new knowledge from global exploration).
2. Understand the significance of the new scientific theories (e.g., those of Copernicus, Galileo, Kepler, Newton) and the significance of new inventions (e.g., the telescope, microscope, thermometer, barometer).
3. Understand the scientific method advanced by Bacon and Descartes, the influence of new scientific rationalism on the growth of democratic ideas, and the coexistence of science with traditional religious beliefs.
7.11 Students analyze political and economic change in the sixteenth, seventeenth, and eighteenth centuries (the Age of Exploration, the Enlightenment, and the Age of Reason).
1. Know the great voyages of discovery, the locations of the routes, and the influence of cartography in the development of a new European worldview.
2. Discuss the exchanges of plants, animals, technology, culture, and ideas among Europe, Africa, Asia, and the Americas in the fifteenth and sixteenth centuries and the major economic and social effects on each continent.
3. Examine the origins of modern capitalism; the influence of mercantilism and cottage industry; the elements and importance of a market economy in seventeenth-century Europe; the changing international trading and marketing patterns, including their locations on a world map; and the influence of explorers and map makers.
4. Explain how the main ideas of the Enlightenment can be traced back to such movements as the Renaissance, the Reformation, and the Scientific Revolution and to the Greeks, Romans, and Christianity.
5. Describe how democratic thought and institutions were influenced by Enlightenment thinkers (e.g., John Locke, Charles-Louis Montesquieu, American founders).
6. Discuss how the principles in the Magna Carta were embodied in such documents as the English Bill of Rights and the American Declaration of Independence.
Grade 6 - World History and Geography
California State Standards - World History and Geography
Grade Six
Ancient Civilizations
Students in grade six expand their understanding of history by studying the people and events that ushered in the dawn of the major Western and non-Western ancient civilizations.
Geography is of special significance in the development of the human story. Continued emphasis is placed on the everyday lives, problems, and accomplishments of people, their role in developing social, economic, and political structures, as well as in establishing and spreading ideas that helped transform the world forever. Students develop higher levels of critical thinking by considering why civilizations developed where and when they did, why they became dominant, and why they declined. Students analyze the interactions among the various cultures, emphasizing their enduring contributions and the link, despite time, between the contemporary and ancient worlds.
6.1 Students describe what is known through archaeological studies of the early physical and cultural development of humankind from the Paleolithic era to the agricultural revolution.
1. Describe the hunter-gatherer societies, including the development of tools and the use of fire.
2. Identify the locations of human communities that populated the major regions of the world and describe how humans adapted to a variety of environments.
3. Discuss the climatic changes and human modifications of the physical environment that gave rise to the domestication of plants and animals and new sources of clothing and shelter.
6.2 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of Mesopotamia, Egypt, and Kush.
1. Locate and describe the major river systems and discuss the physical settings that supported permanent settlement and early civilizations.
2. Trace the development of agricultural techniques that permitted the production of economic surplus and the emergence of cities as centers of culture and power.
3. Understand the relationship between religion and the social and political order in Mesopotamia and Egypt.
4. Know the significance of Hammurabi’s Code.
5. Discuss the main features of Egyptian art and architecture.
6. Describe the role of Egyptian trade in the eastern Mediterranean and Nile valley.
7. Understand the significance of Queen Hatshepsut and Ramses the Great.
8. Identify the location of the Kush civilization and describe its political, commercial, and cultural relations with Egypt.
9. Trace the evolution of language and its written forms.
6.3 Students analyze the geographic, political, economic, religious, and social structures of the Ancient Hebrews.
1. Describe the origins and significance of Judaism as the first monotheistic religion based on the concept of one God who sets down moral laws for humanity.
2. Identify the sources of the ethical teachings and central beliefs of Judaism (the Hebrew Bible, the Commentaries): belief in God, observance of law, practice of the concepts of righteousness and justice, and importance of study; and describe how the ideas of the Hebrew traditions are reflected in the moral and ethical traditions of Western civilization.
3. Explain the significance of Abraham, Moses, Naomi, Ruth, David, and Yohanan ben Zaccai in the development of the Jewish religion.
4. Discuss the locations of the settlements and movements of Hebrew peoples, including the Exodus and their movement to and from Egypt, and outline the significance of the Exodus to the Jewish and other people.
5. Discuss how Judaism survived and developed despite the continuing dispersion of much of the Jewish population from Jerusalem and the rest of Israel after the destruction of the second Temple in A.D. 70.
6.4 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of Ancient Greece.
1. Discuss the connections between geography and the development of city-states in the region of the Aegean Sea, including patterns of trade and commerce among Greek city-states and within the wider Mediterranean region.
2. Trace the transition from tyranny and oligarchy to early democratic forms of government and back to dictatorship in ancient Greece, including the significance of the invention of the idea of citizenship (e.g., from Pericles’ Funeral Oration).
3. State the key differences between Athenian, or direct, democracy and representative democracy.
4. Explain the significance of Greek mythology to the everyday life of people in the region and how Greek literature continues to permeate our literature and language today, drawing from Greek mythology and epics, such as Homer’s Iliad and Odyssey, and from Aesop’s Fables.
5. Outline the founding, expansion, and political organization of the Persian Empire.
6. Compare and contrast life in Athens and Sparta, with emphasis on their roles in the Persian and Peloponnesian Wars.
7. Trace the rise of Alexander the Great and the spread of Greek culture eastward and into Egypt.
8. Describe the enduring contributions of important Greek figures in the arts and sciences
(e.g., Hypatia, Socrates, Plato, Aristotle, Euclid, Thucydides).
6.5 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of India.
1. Locate and describe the major river system and discuss the physical setting that supported the rise of this civilization.
2. Discuss the significance of the Aryan invasions.
3. Explain the major beliefs and practices of Brahmanism in India and how they evolved into early Hinduism.
4. Outline the social structure of the caste system.
5. Know the life and moral teachings of Buddha and how Buddhism spread in India, Ceylon, and Central Asia.
6. Describe the growth of the Maurya empire and the political and moral achievements of the emperor Asoka.
7. Discuss important aesthetic and intellectual traditions (e.g., Sanskrit literature, including the Bhagavad Gita; medicine; metallurgy; and mathematics, including Hindu-Arabic numerals and the zero).
6.6 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of China.
1. Locate and describe the origins of Chinese civilization in the Huang-He Valley during the Shang Dynasty.
2. Explain the geographic features of China that made governance and the spread of ideas and goods difficult and served to isolate the country from the rest of the world.
3. Know about the life of Confucius and the fundamental teachings of Confucianism and Taoism.
4. Identify the political and cultural problems prevalent in the time of Confucius and how he sought to solve them.
5. List the policies and achievements of the emperor Shi Huangdi in unifying northern China under the Qin Dynasty.
6. Detail the political contributions of the Han Dynasty to the development of the imperial bureaucratic state and the expansion of the empire.
7. Cite the significance of the trans-Eurasian “silk roads” in the period of the Han Dynasty and Roman Empire and their locations.
8. Describe the diffusion of Buddhism northward to China during the Han Dynasty.
6.7 Students analyze the geographic, political, economic, religious, and social structures during the development of Rome.
1. Identify the location and describe the rise of the Roman Republic, including the importance of such mythical and historical figures as Aeneas, Romulus and Remus, Cincinnatus, Julius Caesar, and Cicero.
2. Describe the government of the Roman Republic and its significance (e.g., written constitution and tripartite government, checks and balances, civic duty).
3. Identify the location of and the political and geographic reasons for the growth of Roman territories and expansion of the empire, including how the empire fostered economic growth through the use of currency and trade routes.
4. Discuss the influence of Julius Caesar and Augustus in Rome’s transition from republic to empire.
5. Trace the migration of Jews around the Mediterranean region and the effects of their conflict with the Romans, including the Romans’ restrictions on their right to live in Jerusalem.
6. Note the origins of Christianity in the Jewish Messianic prophecies, the life and teachings of Jesus of Nazareth as described in the New Testament, and the contribution of St. Paul the Apostle to the definition and spread of Christian beliefs (e.g., belief in the Trinity, resurrection, salvation).
7. Describe the circumstances that led to the spread of Christianity in Europe and other Roman territories.
8. Discuss the legacies of Roman art and architecture, technology and science, literature, language, and law.
Grade Six
Ancient Civilizations
Students in grade six expand their understanding of history by studying the people and events that ushered in the dawn of the major Western and non-Western ancient civilizations.
Geography is of special significance in the development of the human story. Continued emphasis is placed on the everyday lives, problems, and accomplishments of people, their role in developing social, economic, and political structures, as well as in establishing and spreading ideas that helped transform the world forever. Students develop higher levels of critical thinking by considering why civilizations developed where and when they did, why they became dominant, and why they declined. Students analyze the interactions among the various cultures, emphasizing their enduring contributions and the link, despite time, between the contemporary and ancient worlds.
6.1 Students describe what is known through archaeological studies of the early physical and cultural development of humankind from the Paleolithic era to the agricultural revolution.
1. Describe the hunter-gatherer societies, including the development of tools and the use of fire.
2. Identify the locations of human communities that populated the major regions of the world and describe how humans adapted to a variety of environments.
3. Discuss the climatic changes and human modifications of the physical environment that gave rise to the domestication of plants and animals and new sources of clothing and shelter.
6.2 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of Mesopotamia, Egypt, and Kush.
1. Locate and describe the major river systems and discuss the physical settings that supported permanent settlement and early civilizations.
2. Trace the development of agricultural techniques that permitted the production of economic surplus and the emergence of cities as centers of culture and power.
3. Understand the relationship between religion and the social and political order in Mesopotamia and Egypt.
4. Know the significance of Hammurabi’s Code.
5. Discuss the main features of Egyptian art and architecture.
6. Describe the role of Egyptian trade in the eastern Mediterranean and Nile valley.
7. Understand the significance of Queen Hatshepsut and Ramses the Great.
8. Identify the location of the Kush civilization and describe its political, commercial, and cultural relations with Egypt.
9. Trace the evolution of language and its written forms.
6.3 Students analyze the geographic, political, economic, religious, and social structures of the Ancient Hebrews.
1. Describe the origins and significance of Judaism as the first monotheistic religion based on the concept of one God who sets down moral laws for humanity.
2. Identify the sources of the ethical teachings and central beliefs of Judaism (the Hebrew Bible, the Commentaries): belief in God, observance of law, practice of the concepts of righteousness and justice, and importance of study; and describe how the ideas of the Hebrew traditions are reflected in the moral and ethical traditions of Western civilization.
3. Explain the significance of Abraham, Moses, Naomi, Ruth, David, and Yohanan ben Zaccai in the development of the Jewish religion.
4. Discuss the locations of the settlements and movements of Hebrew peoples, including the Exodus and their movement to and from Egypt, and outline the significance of the Exodus to the Jewish and other people.
5. Discuss how Judaism survived and developed despite the continuing dispersion of much of the Jewish population from Jerusalem and the rest of Israel after the destruction of the second Temple in A.D. 70.
6.4 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of Ancient Greece.
1. Discuss the connections between geography and the development of city-states in the region of the Aegean Sea, including patterns of trade and commerce among Greek city-states and within the wider Mediterranean region.
2. Trace the transition from tyranny and oligarchy to early democratic forms of government and back to dictatorship in ancient Greece, including the significance of the invention of the idea of citizenship (e.g., from Pericles’ Funeral Oration).
3. State the key differences between Athenian, or direct, democracy and representative democracy.
4. Explain the significance of Greek mythology to the everyday life of people in the region and how Greek literature continues to permeate our literature and language today, drawing from Greek mythology and epics, such as Homer’s Iliad and Odyssey, and from Aesop’s Fables.
5. Outline the founding, expansion, and political organization of the Persian Empire.
6. Compare and contrast life in Athens and Sparta, with emphasis on their roles in the Persian and Peloponnesian Wars.
7. Trace the rise of Alexander the Great and the spread of Greek culture eastward and into Egypt.
8. Describe the enduring contributions of important Greek figures in the arts and sciences
(e.g., Hypatia, Socrates, Plato, Aristotle, Euclid, Thucydides).
6.5 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of India.
1. Locate and describe the major river system and discuss the physical setting that supported the rise of this civilization.
2. Discuss the significance of the Aryan invasions.
3. Explain the major beliefs and practices of Brahmanism in India and how they evolved into early Hinduism.
4. Outline the social structure of the caste system.
5. Know the life and moral teachings of Buddha and how Buddhism spread in India, Ceylon, and Central Asia.
6. Describe the growth of the Maurya empire and the political and moral achievements of the emperor Asoka.
7. Discuss important aesthetic and intellectual traditions (e.g., Sanskrit literature, including the Bhagavad Gita; medicine; metallurgy; and mathematics, including Hindu-Arabic numerals and the zero).
6.6 Students analyze the geographic, political, economic, religious, and social structures of the early civilizations of China.
1. Locate and describe the origins of Chinese civilization in the Huang-He Valley during the Shang Dynasty.
2. Explain the geographic features of China that made governance and the spread of ideas and goods difficult and served to isolate the country from the rest of the world.
3. Know about the life of Confucius and the fundamental teachings of Confucianism and Taoism.
4. Identify the political and cultural problems prevalent in the time of Confucius and how he sought to solve them.
5. List the policies and achievements of the emperor Shi Huangdi in unifying northern China under the Qin Dynasty.
6. Detail the political contributions of the Han Dynasty to the development of the imperial bureaucratic state and the expansion of the empire.
7. Cite the significance of the trans-Eurasian “silk roads” in the period of the Han Dynasty and Roman Empire and their locations.
8. Describe the diffusion of Buddhism northward to China during the Han Dynasty.
6.7 Students analyze the geographic, political, economic, religious, and social structures during the development of Rome.
1. Identify the location and describe the rise of the Roman Republic, including the importance of such mythical and historical figures as Aeneas, Romulus and Remus, Cincinnatus, Julius Caesar, and Cicero.
2. Describe the government of the Roman Republic and its significance (e.g., written constitution and tripartite government, checks and balances, civic duty).
3. Identify the location of and the political and geographic reasons for the growth of Roman territories and expansion of the empire, including how the empire fostered economic growth through the use of currency and trade routes.
4. Discuss the influence of Julius Caesar and Augustus in Rome’s transition from republic to empire.
5. Trace the migration of Jews around the Mediterranean region and the effects of their conflict with the Romans, including the Romans’ restrictions on their right to live in Jerusalem.
6. Note the origins of Christianity in the Jewish Messianic prophecies, the life and teachings of Jesus of Nazareth as described in the New Testament, and the contribution of St. Paul the Apostle to the definition and spread of Christian beliefs (e.g., belief in the Trinity, resurrection, salvation).
7. Describe the circumstances that led to the spread of Christianity in Europe and other Roman territories.
8. Discuss the legacies of Roman art and architecture, technology and science, literature, language, and law.
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