# Math Scope & Sequence Grades 3-8

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2 Multiplication and Division Multiply using strategies based on place value and properties of operations Represent the product of two 2-digit numbers 3.4G 3.4K 3.5B 4.4(B) 4.4(C) Use strategies and algorithms to multiply up to a 4-digit by a 1-digit number and a 2-digit by a 2-digit number 5.3(C) Multiply 2-digit by 1-digit numbers using standard algorithm 3.4G Multiply 3-digit by 2-digit numbers using standard algorithm Estimate solutions to multiplication and division problems Represent the quotient of up to a 4-digit number by a 2-digit number Use strategies and algorithms to divide up to a 4-digit by a 1-digit number Solve one- and two-step problems involving multiplication and division Interpret remainders Relate language to multiplication in everyday situations 4.4(G) 4.4(E) 4.4(F) 3.4K 4.4(H) 4.4(H) 3.5C 5.3(B) 5.3(A) 2 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

3 Understand the reciprocal relationship of multiplication and division Understand division as partitioning into equal groups Represent multiplication using various approaches (arrays, repeated addition, area, etc.) 3.4F 3.4J 3.5D 3.4I 3.4H 3.4D 3.4E 3.6C Whole Numbers Prime and Composite Numbers 5.4(A) Integers Positive and negative numbers Opposite signs of numbers Graph integers on a number line Graph points with integer coordinates on a coordinate plane Order integers Absolute value Operations with integers 6.2(A) 6.2(B) 6.2(C) (C) 6.2(B) 6.3(C), 6.3(D) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 3

4 Rational Numbers Classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers Graph rational numbers on a number line Order rational numbers on a number line Write, interpret, and explain order of rational numbers Graph points with rational coordinates on a coordinate plane Solve real-world problems by graphing points in all 4 quadrants Add, subtract, multiply, and divide rational numbers Solve real-world problems using operations with rational numbers 6.2(A) (C) 6.2(D) 6.2(D) (A) 7.3(B) Irrational Numbers Approximate the value of an irrational number, including π and square roots of numbers less than 225 Locate rational number approximations of irrational numbers on a number line 8.2(B) 8.2(B) 4 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

5 Real Numbers Use a visual representation to describe relationships between sets of real numbers Order a set of real numbers 8.2(A) 8.2(D) Number and Operations Fractions, Decimals, and Percents Fractions Represent fractions on a number line 3.3A 3.3B 3.7A 4.3(G) Decompose fractions 3.3D 4.3(B) Equivalent fractions 3.3F 3.3G Unit fractions 3.3C 3.3D 3.6E 4.3(C) 4.3(A) Compare and order fractions 3.3H 4.3(D) Represent mixed numbers and write as improper fractions Add and subtract fractions with equal denominators Add and subtract fractions with unequal denominators 4.3(E) 5.3(K) 5.3(H), 5.3(K) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 5

6 Estimate sums and differences of fractions 4.3(F) 5.3(A) Multiply fractions with objects and models 5.3(I) Estimate products with fractions 5.3(A) 6.3(B) Multiply fractions Divide whole numbers by unit fractions and unit fractions by whole numbers with objects and models Divide whole numbers by unit fractions and unit fractions by whole numbers Interpret fractions as division of numerator by denominator Divide fractions 5.3(J) 5.3(L) 6.3(E) 6.3(E) 6.3(E) 6.2(E) 6.3(A), 6.3(E) Use pictorial models to partition objects 3.3E Decimals Represent decimals 4.2(E) 5.2(A) Relate fractions as decimals 4.2(G) Compare and order decimals 4.2(F) 5.2(B) Add and subtract decimals 4.4(A), 4.4(B) 5.3(K) Estimate sums and differences of decimals by rounding Multiply and divide decimals using models 5.3(A) 5.3(D), 5.3(F) 6 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

7 Multiply and divide decimals using strategies 5.3(E), 5.3(G) Represent decimals on a number line 4.2(H) Convert rational numbers to decimals 6.4(G) Terminating and repeating decimals 7.3(A) Percent Represent percents with concrete models, fractions, and decimals Represent benchmark fractions and percents using 10 by 10 grids, strip diagrams, number lines, and numbers; Generate equivalent forms of fractions, decimals, and percents to show equal parts of the same whole 6.4(E) 6.4(F) 6.4(G), 6.5(C) 7.4(D) Solve percent problems for part 6.5(B) 7.4(D) Solve percent problems for whole 6.5(B) 7.4(D) Solve percent problems for percent 6.5(B) 7.4(D) Percent proportion 6.5(B) 7.4(D) Percent equation 6.5(B) 7.4(D) Solve problems involving applications of percent Percent increase and decrease 7.4(D) 7.4(D) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 7

8 Percent error 7.4(D) Ratio and Proportional Relationships Ratios and Rates Understand the concepts of a ratio and rate Represent ratios with concrete models, fractions, and decimals Understand and use the concept of a unit rate Tables of equivalent ratios Graph ratio tables 6.4(C), 6.4(D) 6.4(E) 6.4(B), 6.4(D) 6.5(A) 6.5(A) 7.4(B) Solve Proportions 6.4(B), 6.4(H) 7.4(D) Solve real-world problems using ratios and rates Use proportions and unit rates to convert measurements Ratio and probability 6.4(B), 6.5(A) 6.4(H) 7.4(D) 7.4(E) Proportional Relationships Determine rate of change (constant of proportionality) in a proportional relationship Represent proportional relationships by equations 7.4(A), 7.4(C) 7.4(A) 8 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

9 Use proportional relationships to solve multistep ratio problems Graph proportional relationships 7.4(D) 7.4(A) Interpret the unit rate of the graph of a proportional relationship as the slope of the line that models the relationship 8.4(B) Scale drawings 7.5(C) 8.3(B) Algebra and Functions Algebraic Representation Identify/generate/explain number patterns using input/output tables and numerical expressions 3.5E 4.5(B) Write and solve number sentences/ equations 3.5A 3.5B 4.5(A) Write and evaluate numerical expressions using order of operations Generate equivalent expressions involving variables using properties of operations Generate equivalent numerical expressions using order of operations Prime Factorization Evaluate Exponents Distinguish between expressions and equations 5.4(E), 5.4(F) 6.7(A) 6.7(D) 6.7(A) 6.7(A) 6.7(A) 6.7(B) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 9

10 Identify equivalent expressions 6.7(C) Convert between standard decimal notation and scientific notation 8.2(C) Equations and Inequalities Identify values that make an equation or inequality true 6.10(B) 7.11(B) Use variables and expressions to solve real-world problems 3.5A 3.5B 5.4(B) Write, model, and solve one-variable, one-step equations 3.5A 3.5B 6.9(A), 6.10(A) Write, model, and solve one-variable, two-step equations 3.5A 3.5B 7.10(A), 7.11(A) Write, model, and solve one-variable, one-step inequalities 6.9(A), 6.10(A) Write, model, and solve one-variable, two-step inequalities 7.10(A), 7.11(A) Write, model, and solve one-variable equations with variables on both sides of the equal sign 8.8(A), 8.8(C) Represent solutions to equations and inequalities on number line. 6.9(B) 7.10(B) Write corresponding real-world problems to represent equations and inequalities 6.9(C) 7.10(C) 8.8(B) 10 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

11 Equations in Two Variables Dependent and independent variables Write equations using two variables 6.6(A) 6.6(B) Form ordered pairs 5.8(C) Tables of ordered pairs 6.EE.C.9 Describe key attributes of coordinate plane Graph ordered pairs in the first quadrant 5.8(A) 5.4(C), 5.8(B), 5.8(C) Graph ordered pairs in all four quadrants 6.EE.C Analyze patterns and relationships 7.7 Compare two rules in the form of y = ax or y = x + a 6.4(A) Generate numerical pattern for rule of form y = ax or y = x + a. 5.4(C) Represent situations using verbal descriptions, tables, graphs, and equations in the form y = kx or y = x + b. 6.4(B) Represent linear relationships using verbal descriptions, tables, graphs, and equations that simplify to the for y = mx + b. 7.7 Use similar triangles to explain slope of a line 8.4(A) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 11

12 Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems Represent and distinguish between linear and nonlinear proportional situations using tables, graphs, and equations Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation Use a trend line that approximates the linear relationship between bivariate sets of data to make predictions Direct Variation Write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations Solve systems of linear equations by graphing Solve systems of linear equations algebraically Solve problems leading to two linear equations in two variables 8.4(C) 8.5(A), 8.5(B), 8.5(F) 8.5(C) 8.5(D) 8.5(E) 8.5(I) ) Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

13 Functions Identify functions using sets of ordered pairs, tables, mappings, and graphs Identify proportional and non-proportional functions 8.5(G) 8.5(H) Measurement Linear Measurement Choose appropriate customary or metric unit of length Convert customary and metric units of length Solve linear measurement word problems using the four operations 4.8(A) 4.8(B) (C) 5.7 Perimeter and Area Develop and apply the formula for perimeter 3.7B 4.5(C), 4.5(D) 5.4(H) Develop and apply the formula for area 3.6C 4.5(C), 4.5(D) 5.4(H) Relate area and perimeter Volume Choose appropriate customary or metric unit of capacity Convert customary or metric units of capacity 3.7D 3.7E 4.8(A) 4.8(B) 5.7 SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 13

14 Measure in unit cubes by counting Solve word problems involving volume using the four operations Weight and Mass 4.8(C) 5.4(G), 5.6(A) 5.6(B), 5.4(H) Choose appropriate metric unit of mass 3.7E 4.8(A) Solve word problems involving mass 4.8(C) 5.7 Choose appropriate customary unit of weight 3.7E 4.8(A) Convert customary units of weight 4.8(B) 5.7 Convert metric units of mass 4.8(B) 5.7 Solve word problems involving weight and mass using the four operations 4.8(C) 5.7 Time Convert units of time 4.8(B) 5.7 Solve word problems involving time using the four operations 3.7C 4.8(C) 5.7 Data Sets and Populations Organize, represent, and interpret data 3.8A 3.8B 4.9(A) Distinguish between situations that yield data with and without variability. 6.13(A) 14 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

15 Distribution of a set of data 6.12(B), 6.12(C), 6.12(D) Statistics and population samples Random sampling of populations Draw inferences from random samples Compare two groups of numeric data using comparative dot or box plots by comparing shapes, centers, and spread Comparative inferences between two populations Measures of Center and Variability 7.6(F) 7.6(F), 7.12(A) 7.6(F), 7.12(B) 7.12(A) 7.12(C) 8.11(C) Measures of center Median Mean Mode Measures of variation Range 6.12(B) 6.12(B) 6.12(B) 6.12(D) 6.12(B), 6.12(C) 6.12(B), 6.12(C) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 15

16 Outliers Interquartile range 6.12(B), 6.12(C) 6.12(C) Mean Absolute Deviation 8.11(B) Represent Data, Statistical Displays Frequency table 4.9(A), 4.9(B) 5.9(A), 5.9(C) Relative Frequency table 6.12(D) Bar graphs 3.8A 5.9(A), 5.9(C) 7.6(G) Percent bar graphs 6.12(D) 7.6(G) Dot plots 3.8A 4.9(A), 4.9(B) 5.9(A), 5.9(C) 6.12(A), 6.13(A) 7.6(G) Stem and leaf plots 4.9(A), 4.9(B) 5.9(A), 5.9(C) 6.12(A), 6.13(A) Histograms Box plots 6.12(A), 6.13(A) 6.12(A), 6.13(A) Circle Graphs 7.6(G) Scatter Plots 8.11(A) Probability Probability and chance events 7.6(D) 16 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

17 Complement of event Compare theoretical and experimental probability Compound events Sample spaces (lists and tree diagrams) 7.6(E) 7.6(C), 7.6(D), 7.6(I) 7.6(A), 7.6(B), 7.6(C), 7.6(D), 7.6(I) 7.6(A), 7.6(I) Simulations 7.6(B) 8.11(C) Geometry Two- and Three-Dimensional Shapes and Figures Classify angles by their attributes Classify two-dimensional figures by their properties 3.6A 3.6B 4.6(C) 4.6(D) 5.5 Know and solve problems using the sum of the measures of the angles of a triangle Know and solve problems using relationships between lengths of sides and measure of angles in a triangle. 6.8(A) (A) 7.11 Draw and identify points, lines, segments, rays, angles, and parallel and perpendicular lines in two-dimensional figures 4.6(A) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 17

18 Identify and draw lines of symmetry in two-dimensional figures 4.6(B) Construct triangles from three lengths 6.8(A) Circles and circumference 7.5(B), 7.8(C), 7.9(B) Angle Measure and Relationships Measure and draw angles Solve addition and subtraction problems to determine measures of unknown angles 4.7(A), 4.7(B), 4.7(C), 4.7(D) 4.7(E) Sum of angles in a triangle 6.8(A) 8.8(D) Exterior angle of a triangle Parallel lines cut by a transversal Angle-angle criterion for similar triangles 8.8(D) 8.8(D) 8.8(D) Area and Surface Area Area of rectangle 3.6C 3.6D Area of triangles Area of parallelograms 4.5(C), 4.5(D) 6.8(C), 6.8(D) 6.8(B), 6.8(C), 6.8(D) 6.8(B), 6.8(C), 6.8(D) 18 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

19 Area of trapezoids 6.8(B), 6.8(C), 6.8(D) Area of a circle Area of composite figures Represent three-dimensional figures using nets Use nets to find surface area 7.9(C) 7.8(C), 7.9(B) 7.9(D) 7.9(D) Surface area of rectangular prisms 7.9(D) 8.7(B) Surface area of triangular prisms 7.9(D) 8.7(B) Surface area of pyramids 7.9(D) 8.7(B) Surface area of composite figures 7.9(D) 8.7(B) Surface area of cylinders 8.7(B) Volume Understand concepts of volume 5.4(G) Measure volume by counting cubes 5.4(G), 5.6(A) Volume of right rectangular prism 5.4(G), 6.8(C), 6.8(D) 7.8(A), 7.9(A) 5.4(H), 5.6(A) Volume of triangular prisms 7.8(B), 7.9(A) Volume of pyramids 7.8(A), 7.8(B), 7.9(A) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 19

20 Volume of a cylinder Describe the volume formula V = Bh of a cylinder in terms of its base area and its height and connect that relationship to the formulas Volume of a cone Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights Volume of a sphere 8.7(A) 8.6(A) 8.7(A) 8.6(B) 8.7(A) Scale Drawings Similar figures 7.5(A), 7.5(C) 8.3(A) Scale drawings 7.5(C) 8.3(A) Transformations Translations Reflections Rotations 8.10(A), 8.10(B), 8.10(C) 8.10(A), 8.10(B), 8.10(C) 8.10(A), 8.10(B), 8.10(C) 20 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

21 Dilations Effect of transformations using coordinates 8.3(A), 8.10(B), 8.10(C) 8.3(B), 8.3(C) Pythagorean Theorem Use the Pythagorean Theorem and its converse to solve problems Use models and diagrams to explain the Pythagorean theorem. Distance between two points in the coordinate plane 8.7(C) 8.6(C) 8.7(D) Personal Financial Literacy Fixed and variable expenses 4.10(B) 7.13(B) Compare savings options 4.10(C) Allocating money 3.9F 4.10(D) 7.13(B) Financial institutions 4.10(E) Taxes 5.10(A) 7.13(A) Gross vs. net income 5.10(B) 7.13(B) Payment methods 5.10(C) 8.12(E) Financial records Budgeting 3.9C 3.9F 5.10(D) 5.10(E), 5.10(F) 7.13(D) Checking accounts 6.14(A), 6.14(C) SCOPE & SEQUENCE MATH Texas Essential Knowledge and Skills State Standards 21

22 Credit cards 6.14(B), 6.14(D), 6.14(E), 6.13(F) Paying for college 3.9E 6.14(G) 8.12(G) Salaries 3.9A 6.14(H) Assets, liabilities, and net worth Simple and compound interest Analyze and compare monetary incentives 7.13(C) 7.13(E) 7.13(F) Interest rate and loan length 8.12(A) Total cost of repaying a loan 8.12(B) Simple and Compound Interest Financially responsible and irresponsible decisions 8.12(C), 8.12(D) 8.12(F) Understand supply and demand 3.9B Basic Interest and Credit 3.9D 22 Texas Essential Knowledge and Skills State Standards MATH SCOPE & SEQUENCE

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