Muskogee Public Schools Curriculum Map, Math, Grade 8

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1 Muskogee Public Schools Curriculum Map, Math, Grade 8 The Test Blueprint reflects the degree to which each PASS Standard and Objective is represented on the test. Page1

2 1 st Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations Equations 1.1a Model, write, and solve two-step linear equations using a variety of methods. Model, graphs, number lines, coordinate graphs, linear equation, balance scales, integers, common fractions, coefficients, constants, additive inverse, multiply by the reciprocal, slope intercept form 1.1b. Graph and interpret the solution to oneand two-step linear equations on a number line with one variable and on a coordinate plane with two variables. Interpret, graphs, number lines, coordinate graphs, linear equation, balance scales, integers, common fractions, coefficients, constants, additive inverse, multiply by the reciprocal, slope intercept form 1.1d Apply appropriate formulas to solve problems. (e.g., d=rt, I=prt) Distance, interest formulas, rate, velocity, time, speed, interest, principle, Page2

3 1 st Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations Inequalities: Model, write, solve, and graph 1-and 2-step linear inequalities with one variable. Inequalities, number line, variables, additive inverse, zero pair, reciprocal, constant, coefficients, common factors, integers, solution set, algebraic inequalities Standard 2: Number Sense and Operations The student will use numbers and number relationships to solve problems. 2.2 Number Operations 2.2a. Use the rules of exponents, including integer exponents to solve problems Exponents, integers, power, perfect square, real number, irrational number, rational number, square root, scientific notation, base, exponential form Page3

4 1 st Nine Standard 2: Number Sense and Operation The student will use numbers and number relationships to solve problems. 2.2c. Simplify numerical expressions with rational numbers, exponents, and parentheses using order of operations. Order of operation, Rational numbers, set of real numbers, integers, positive/negative, fractions, decimals, percent, equivalent, number line, compare, order, common denominator, commutative, associative, distributive, identity, multiplicative properties Standard 3: Geometry The student will use geometric properties to solve problems in a variety of contexts. 3.1 Construct models, sketch (from different perspectives), and classify solid figures such as rectangular solids, prisms, cones, cylinders, pyramids, and combined forms. Geometric solid, perspective, classify, prisms, cones, cylinders, pyramids, combined forms, face, edge, vertex, base, orthogonal views, hexagonal, rectangular, square, triangular, pentagonal, side, top, front, congruent, Page4

5 1 st Nine Standard 3: Geometry The student will use geometric properties to solve problems in a variety of contexts. 3.2 Develop the Pythagorean Theorem and apply the formula to find the length of missing sides of a right triangle, the shortest distance between two points on a graph, and the length of other line segments. Pythagorean Theorem, leg, hypotenuse, formula, square root, squared, right triangle, Pythagorean Triple Page5

6 1 st Nine Standard 4: Measurement--The student will use measurement to solve problems in a variety of contexts Develop and apply formulas to find the surface area and volume of rectangular prisms, triangular prisms, and cylinders (in terms of pi). Review 7 th 4.1a/b first 4.1a (7 th grade review to scaffold 8 th PASS) Develop area and perimeter concepts (e.g., Use grids to estimate the area of irregular shapes.) Area/perimeter formulas, grid, estimate, irregular shapes, polygons, circle 4.1b. (7 th grade review to scaffold 8 th PASS) Apply formulas to solve problems involving perimeter (circumference) and area of polygons and circles. Area/perimeter (circumference)formulas, grid, polygons, circle Page6

7 1 st Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. 5.1 Data Analysis: Select, analyze, and apply appropriate formats to draw conclusions. Data, statistics, analysis, line plots, bar graphs, stem-and- leaf plot, scatter plot, histogram, circle graph, display, box and whisker, frequency table Recommended Math resources: Math Tools, Grades 3-12, 64 Ways to differentiate Instruction and Increase Student Engagement, by Harvey F. Silver, 2008 (Excellent tool) tml sment_assistance/state_standards_tests_to _print_8th_eighth_grade.htm Probability: Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population (e.g., is the average height of a men s college basketball team a good representative sample for height predictions?) This is tested at the local level. Benchmark 1: Core/Released/Gr8Math04-05.pdf 50 question EOI practice test Also available to create test is the Test and Item Specification document for 8 th grade math: Core/Comb/Gr8Math.pdf Page7

8 2 nd Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations. 1.1 Equations 1.1a Model, write, and solve multi-step linear equations using a variety of methods. Graphs, number lines, coordinate graphs, linear equation, balance scales, integers, common fractions, coefficients, constants, additive inverse, multiply by the reciprocal, 1.1b. Graph and interpret the solution to oneand two-step linear equations on a number line with one variable and on a coordinate plane with two variables. Graph, number line, coordinate graph, x-/yintercept, standard form, slope intercept form, variable, positive/negative slope, linear equation, x/ y axis, Page8

9 2 nd Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations. 1.1c. Predict the effect on the graph of a linear equation when the slope or the y- intercept changes (e.g. Make predictions from graphs, identify the slope or y- intercept in the equation y= mx + b and relate to a graph). Predict, linear equation, zero property of multiplication, slope, Graph, coordinate graph, x-/y- intercept, standard form, slope intercept form, variable, positive/negative slope, linear equation, x/ y axis, 1.1d. Apply appropriate formulas to solve problems (e.g., d = rt, I =prt). Distance, interest formulas, rate, velocity, time, speed, interest, principle, Page9

10 2 nd Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations Inequalities: Model, write, solve, and graph 1-and 2-step linear inequalities with one variable. Inequalities, number line, variables, additive inverse, zero pair, reciprocal, constant, coefficients, common factors, integers, solution set, algebraic inequalities Page10

11 2 nd Nine Standard 2: Number Sense and Operation The student will use numbers and number relationships to solve problems Number Sense: Represent and interpret large numbers and numbers less than one in exponential and scientific notation. Exponents, integers, power, perfect square, real number, irrational number, rational number, square root, scientific notation, base, exponential form 2.2 Number Operations 2.2a. Use the rules of exponents, including integer exponents to solve problems Exponents, integers, power, perfect square, real number, irrational number, rational number, square root, scientific notation, base, exponential form Page11

12 2 nd Nine Standard 2: Number Sense and Operation The student will use numbers and number relationships to solve problems. 2.2b. Solve problems using scientific notation. New skill Scientific notation, base ten, exponents, standard notation Page12

13 2 nd Nine Standard 2: Number Sense and Operation The student will use numbers and number relationships to solve problems. 2.2c. Simplify numerical expressions with rational numbers, exponents, and parentheses using order of operations. Order of operation, Rational numbers, set of real numbers, integers, positive/negative, fractions, decimals, percent, equivalent, number line, compare, order, common denominator, commutative, associative, distributive, identity, multiplicative properties Standard 3: Geometry The student will use geometric properties to solve problems in a variety of contexts. 3.1 Construct models, sketch (from different perspectives), and classify solid figures such as rectangular solids, prisms, cones, cylinders, pyramids, and combined forms. Geometric solid, perspective, classify, prisms, cones, cylinders, pyramids, combined forms, face, edge, vertex, base, orthogonal views, hexagonal, rectangular, square, triangular, pentagonal, side, top, front, congruent, Page13

14 2 nd Nine Standard 3: Geometry The student will use geometric properties to solve problems in a variety of contexts. 3.2 Develop the Pythagorean Theorem and apply the formula to find the length of missing sides of a right triangle and the length of other line segments. Pythagorean Theorem, leg, hypotenuse, formula, square root, squared, right triangle, Pythagorean Triple Standard 4: Measurement--The student will use measurement to solve problems in a variety of contexts. 4.1 Develop and apply formulas to find the surface area and volume of rectangular prisms, triangular prisms, and cylinders (in terms of pi). Build toward this skill 4.1a (7 th grade review to scaffold 8 th PASS) Develop area and perimeter concepts (e.g., Use grids to estimate the area of irregular shapes.) Area/perimeter formulas, grid, estimate, irregular shapes, polygons, circle Page14

15 2 nd Nine Standard 4: Measurement--The student will use measurement to solve problems in a variety of contexts. 4.1b (7 th grade review to scaffold 8 th PASS) Apply formulas to solve problems involving perimeter (circumference) and area of polygons and circles. Area/perimeter formulas, grid, estimate, irregular shapes, polygons, circle 4.2. Apply knowledge of ratio and proportion to solve relationships between similar geometric figures. Similar figures, ratio, proportion, height, base, length, width, depth, scale factor, scale drawings, corresponding sides/angles Page15

16 2 nd Nine Standard 4: the student will use measurement to solve problems in a variety of contexts Find the area of a region of a region for simple composite figures (e.g., area of a rectangular picture frame. Composite figure, region in a region, area, formulas for areas of polygons/ circles Page16

17 2 nd Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. 5.1 Data Analysis: Select, analyze, and apply data displays in appropriate formats to draw conclusions. Data, statistics, analysis, line plots, bar graphs, stem-and- leaf plot, scatter plot, histogram, circle graph, display, box and whisker, frequency table, mean, median, mode, average Page17

18 2 nd Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts Central Tendency: Find the measure of central tendency (mean, median, and mode) of a set of data and understand why a specific measure provides the most useful information in a given context. Central tendency, mean, median, mode, range, weighted average, box-whisker plot, probability of distribution, expected value, variance, standard deviation, outlier, first/ third quartile Benchmark 2: Core/Released/Gr8Math04-05.pdf 50 question practice test Also available to create test is the Test and Item Specification document for 8 th grade Math: Core/Comb/Gr8Math.pdf Page18

19 3 rd Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations. 1.1 Equations 1.1a Model, write, and solve multi-step linear equations using a variety of methods. Graphs, number lines, coordinate graphs, linear equation, balance scales, integers, common fractions, coefficients, constants, additive inverse, multiply by the reciprocal, 1.1b. Graph and interpret the solution to oneand two-step linear equations on a number line with one variable and on a coordinate plane with two variables. Graph, number line, coordinate graph, x-/yintercept, standard form, slope intercept form, variable, positive/negative slope, slope intercept form, linear equation, x/ y axis, Page19

20 3 rd Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations. 1.1c. Predict the effect on the graph of a inear equation when the slope or the y- intercept changes (e.g., make predictions from graphs, indentify the slope or y- interecpt in the equation y+mx = b and relate to a graph) Graph, number line, coordinate graph, x-/yintercept, standard form, slope intercept form, variable, positive/negative slope, slope intercept form, linear equation, x/ y axis, Page20

21 3 rd Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations. 1.1d. Apply appropriate formulas to solve problems (e.g., d = rt, I =prt). Distance, interest formulas, rate, velocity, time, speed, interest, principle, 1.2. Inequalities: Model, write, solve, and graph 1-and 2-step linear inequalities with one variable. Inequalities, number line, variables, additive inverse, zero pair, reciprocal, constant, coefficients, common factors, integers, solution set, algebraic inequalities Page21

22 3 rd Nine Standard 2: Number Sense and Operation The student will use numbers and number relationships to solve problems Number Sense: Represent and interpret large numbers and numbers less than one in exponential and scientific notation. Exponents, integers, power, perfect square, real number, irrational number, rational number, square root, scientific notation, base, exponential form. 2.2 Number Operation 2.2b. Solve problems using scientific notation. New Skill! Scientific notation, exponents, base ten, standard form Page22

23 3 rd Nine Standard 2: Number Sense and Operation The student will use numbers and number relationships to solve problems. 2.2c Simplify numerical expressions with rational numbers, exponents, and parentheses using order of operations.. Order of operation, parentheses, Rational numbers, set of real numbers, integers, positive/negative, fractions, decimals, percent, equivalent, number line, compare, order, common denominator, commutative, associative, distributive, identity, multiplicative properties, Exponents, integers, power, scientific notation, base, exponential form Page23

24 3rd Nine Standard 3: Geometry The student will use geometric properties to solve problems in a variety of contexts. 3.2 Develop the Pythagorean Theorem and apply the formula to find the length of missing sides of a right triangle and the length of other line segments. Pythagorean Theorem, leg, hypotenuse, formula, square root, squared, right triangle, Pythagorean Triple Page24

25 3 rd Nine Standard 4: Measurement The student will use measurement to solve problems in a variety of contexts. 4.1 Develop and apply formulas to find the surface area and volume of rectangular prisms, triangular prisms, and cylinders (in terms of pi). Area/perimeter (circumference)formulas, volume, surface area, cubes, centimeter, faces, edges, vertex, length, width, depth, height, Page25

26 3 rd Nine Standard 4: Measurement The student will use measurement to solve problems in a variety of contexts Apply knowledge of ratio and proportion to solve relationships between similar geometric figures. Similar figures, ratio, proportion, height, base, length, width, depth, scale factor, scale drawings, corresponding sides/angles. Page26

27 3 rd Nine Standard 4: Measurement The student will use measurement to solve problems in a variety of contexts Find the area of a region of a region for simple composite figures (e.g. area of a rectangular picture frame) Composite figure, region in a region, area, formulas for areas of polygons/ circles Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. 5.1 Data Analysis: Select, analyze, and apply data displays in appropriate formats to draw conclusions. Data, statistics, analysis, line plots, bar graphs, stem-and- leaf plot, scatter plot, histogram, circle graph, display, box and whisker, frequency table Page27

28 3 rd Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts 5.3. Central Tendency: Find the measure of central tendency (mean, median, and mode) of a set of data and understand why a specific measure provides the most useful information in a given context. Central tendency, mean, median, mode, range, weighted average, box-whisker plot, probability of distribution, expected value, variance, standard deviation, outlier, first/ third quartile Benchmark 3: Core/Released/Gr8Math04-05.pdf 50 question practice test Also available to create test is the Test and Item Specification document for 8 th grade Math: Core/Comb/Gr8Math.pdf Page28

29 4th Nine Standard 1: Algebraic Reasoning: Patterns and Relationships The student will graph and solve linear equations and inequalities in problem-solving situations. 1.1c. Predict the effect on the graph of a inear equation when the slope or the y- intercept changes (e.g., make predictions from graphs, indentify the slope or y- interecpt in the equation y+mx = b and relate to a graph). Graph, number line, coordinate graph, x-/yintercept, standard form, slope intercept form, variable, positive/negative slope, slope intercept form, linear equation, x/ y axis, 1.2. Inequalities: Model, write, solve, and graph one-and two-step linear inequalities with one variable Inequalities, number line, variables, additive inverse, zero pair, reciprocal, constant, coefficients, common factors, integers, solution set, algebraic inequalities Page29

30 4th Nine Standard 3: Geometry The student will use geometric properties to solve problems in a variety of contexts. 3.2 Develop the Pythagorean Theorem and apply the formula to find the length of missing sides of a right triangle and the length of other line segments. Pythagorean Theorem, leg, hypotenuse, formula, square root, squared, right triangle, Pythagorean Triple Standard 4: Measurement The student will use measurement to solve problems in a variety of contexts. 4.1 Develop and apply formulas to find the surface area and volume of rectangular prisms, triangular prisms, and cylinders (in terms of pi). Area/perimeter (circumference)formulas, volume, surface area, cubes, centimeter, faces, edges, vertex, length, width, depth, height, Page30

31 4th Nine Standard 4: Measurement The student will use measurement to solve problems in a variety of contexts Apply knowledge of ratio and proportion to solve relationships between similar geometric figures. Similar figures, ratio, proportion, height, base, length, width, depth, scale factor, scale drawings, corresponding sides/angles Page31

32 4th Nine Standard 4: Measurement The student will use measurement to solve problems in a variety of contexts Find the area of a region of a region for simple composite figures (e.g. area of a rectangular picture frame) Composite figure, region in a region, area, formulas for areas of polygons/ circles Page32

33 4th Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. 5.1 Data Analysis: Select, analyze, and apply data displays in appropriate formats to draw conclusions. Data, statistics, analysis, line plots, bar graphs, stem-and- leaf plot, scatter plot, histogram, circle graph, display, box and whisker, frequency table Page33

34 4th Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts Central Tendency: Find the measure of central tendency (mean, median, and mode) of a set of data and understand why a specific measure provides the most useful information in a given context. Central tendency, mean, median, mode, range, weighted average, box-whisker plot, probability of distribution, expected value, variance, standard deviation, outlier, first/ third quartile Page34

35 4th Nine Standard 5: Data Analysis and Statistics The student will use data analysis, probability, and statistics to interpret data in a variety of contexts. Core/Released/Gr8Math04-05.pdf 50 question practice test Also available to create test is the Test and Item Specification document for 8 th grade Math: Core/Comb/Gr8Math.pdf Also available are EOC released tests from other state including but not limited to: Virginia: ased_tests/2008/released_tests2008.shtml North Carolina: ity/testing/releasedforms California: p Great Resource for numerous state released test items: sment_assistance/state_standards_tests_to _print_8th_eighth_grade.htm Page35

36 NOTES Page36

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