Illinois Math Assessment Framework, Grade 7 correlated to
Grade 7 correlated to Chapter 1 Variables, Expressions, and Integers (pp. 1 61) Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate and write variable expressions Lesson 1.2 (pp. 10 15) Powers and Exponents Use powers to describe repeated multiplication Lesson 1.3 (pp.16 20) Order of Operations Use order of operations to evaluate expressions Lesson 1.4 (pp. 22 26) Comparing and Ordering Integers Compare and order integers Lesson 1.5 (pp. 29 33) Adding Integers Add integers 8.7.02 Write an expression using variables to represent unknown quantities. 8.7.05 Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 + b for a = 3 and b = 4). 6.7.04 Represent repeated factors using exponents. 6.7.09 Identify and apply order of operations to simplify numeric expressions involving whole numbers (including exponents), fractions, and decimals. 8.7.05 Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 + b for a = 3 and b = 4). 6.7.05 Order and compare integers, terminating decimals, fractions, and mixed numbers. 6.7.06 Identify and locate integers, decimals, and fractions/mixed numbers on a number line, and estimate the locations of square roots. 8.7.05 Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 + b for a = 3 and b = 4). Lesson 1.6 (pp. 34 40) Subtracting Integers Subtract integers 8.7.05 Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 + b for a = 3 and b = 4). 1
Lesson 1.7 (pp. 41 46) Multiplying and Dividing Integers Multiply and divide integers Lesson 1.8 (pp. 47 51) The Coordinate Plane Identify and plot points in a coordinate plane 9.7.05 Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants). 2
Chapter 2 Properties of Real Numbers (pp. 62 127) Lesson 2.1 (pp. 63 70) Properties and Operations Use properties of addition and multiplication 6.7.09 Identify and apply order of operations to simplify numeric expressions involving whole numbers (including exponents), fractions, and decimals. 6.7.10 Identify and apply the following properties of operations with rational numbers: the commutative and associative properties for addition and multiplication; the distributive property; the additive and multiplicative identity properties; the additive and multiplicative inverse properties; and the multiplicative property of zero. Lesson 2.2 (pp. 71 76) The Distributive Property Use the distributive property 6.7.09 Identify and apply order of operations to simplify numeric expressions involving whole numbers (including exponents), fractions, and decimals. 6.7.10 Identify and apply the following properties of operations with rational numbers: the commutative and associative properties for addition and multiplication; the distributive property; the additive and multiplicative identity properties; the additive and multiplicative inverse properties; and the multiplicative property of zero. Lesson 2.3 (pp. 78 83) Simplifying Variable Expressions Simplify variable expressions Lesson 2.4 (pp. 85 90) Variables and Equations Solve equations with variables Lesson 2.5 (pp. 91 96) Solving Equations Using Addition or Subtraction Solving Equations Using Addition or Subtraction 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 8.7.10 Represent and analyze problems with linear equations and inequalities. 3
Lesson 2.6 (pp. 97 101) Solving Equations Using Multiplication or Division Solving Equations Using Multiplication or Division Lesson 2.7 (pp. 102 107) Decimal Operations and Equations with Decimals Solve equations involving decimals 4
Chapter 3 Multi-Step Equations and Inequalities (pp. 128 199) Lesson 3.1 (pp. 120 124) Solving Two-Step Equations Solve two-step equations Lesson 3.2 (pp. 125 130) Solving Equations Having Like Terms and Parentheses Solving equations using the distributive property Lesson 3.3 (pp. 131 136) Solving Equations with Variables on Both Sides Solving equations with variables on both sides Lesson 3.4 (pp. 138 142) Solving Inequalities Using Addition or Subtraction Solving inequalities using addition or subtraction Lesson 3.5 (pp. 144 148) Solving inequalities Using Multiplication or Division Solve inequalities using multiplication or division Lesson 3.6 (pp. 149 155) Solving Multi-Step Inequalities Solve multi-step inequalities 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 8.7.09 Identify, graph, and interpret inequalities on a number line. 8.7.09 Identify, graph, and interpret inequalities on a number line. 5
Chapter 4 Factors, Fractions and Exponents (pp. 168 265) Lesson 4.1 (pp. 172 176) Factors and Prime Factorization Write the prime factorization of a number 6.7.07 Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple). Lesson 4.2 (pp. 177 181) Greatest Common Factor Find the GCF of two or more whole numbers 6.7.07 Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple). Lesson 4.3 (pp. 182 186) Equivalent Fractions Write equivalent fractions 6.7.03 Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%). 6.7.07 Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple). Lesson 4.4 (pp. 187 193) Least Common Multiple Find the least common multiple of two numbers 6.7.07 Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple). Lesson 4.5 (pp. 194 198) Rules of Exponents Multiply and divide powers Lesson 4.6 (pp. 199 203) Negative and Zero Exponents Work with negative and zero exponents Lesson 4.7 (pp. 204 208) Scientific Notation Write numbers using scientific notation 6.7.04 Represent repeated factors using exponents. 6.7.05 Order and compare integers, terminating decimals, fractions, and mixed numbers. 6
Chapter 5 Rational Numbers and Equations (pp. 216 265) Lesson 5.1 (pp. 219 224) Rational Numbers Write fractions as decimals and vice versa 6.7.03 Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%). Lesson 5.2 (pp. 225 230) Adding and Subtracting Like Fractions Add and subtract like fractions 8.7.03 Simplify algebraic expressions by identifying and combining like terms. Lesson 5.3 (pp. 231 236) Adding and Subtracting Unlike Fractions Add and subtract unlike fractions Lesson 5.4 (pp. 237 242) Multiplying Fractions Multiply fractions and mixed numbers Lesson 5.5 (pp. 243 246) Dividing Fractions Divide fractions and mixed numbers Lesson 5.6 (pp. 247 252) Using Multiplicative Inverses to Solve Equations Use multiplicative inverses to solve equations 6.7.03 Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%). 6.7.10 Identify and apply the following properties of operations with rational numbers: the commutative and associative properties for addition and multiplication; the distributive property; the additive and multiplicative identity properties; the additive and multiplicative inverse properties; and the multiplicative property of zero. Lesson 5.7 (pp. 253 257) Equations and Inequalities with Rational Numbers Use the LCD to solve equation and inequalities 6.7.07 Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple). 7
Chapter 6 Ratio, Proportion, and Probability (pp. 266 325) Lesson 6.1 (pp. 269 274) Ratios and Rates Find ratios and unit rates 6.7.05 Order and compare integers, terminating decimals, fractions, and mixed numbers. 6.7.14 Create and explain ratios that represent a given situation. Lesson 6.2 (pp. 275 279) Writing and Solving Proportions Write and solve proportions Lesson 6.3 (pp. 280 287) Solving Proportions Using Cross Products Solve proportions using cross products Lesson 6.4 (pp. 288 292) Similar and Congruent Figures Identify similar and congruent figures 6.7.15 Use proportional reasoning to model and solve problems. 6.7.15 Use proportional reasoning to model and solve problems. 9.7.14 Determine if figures are similar, and identify relationships between corresponding parts of similar figures. Lesson 6.5 (pp. 293 297) Similarity and Measurement Find unknown side lengths of similar figures Lesson 6.6 (pp. 300 305) Scale Drawings Use proportions with scale drawings Lesson 6.7 (pp. 306 312) Probability and Odds Find probabilities Lesson 6.8 (pp. 313 317) The Counting Principle Use the counting principle to find probabilities 8.7.05 Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 + b for a = 3 and b = 4). 9.7.14 Determine if figures are similar, and identify relationships between corresponding parts of similar figures. 7.7.06 Solve problems involving scale drawings and maps. 8.7.12 Solve word problems involving unknown quantities. 10.7.06 Solve problems involving the probability of a simple or compound event, including representing the probability as a fraction, decimal, or percent. 10.7.07 Represent all possible outcomes for simple events. 10.7.07 Represent all possible outcomes for simple events. 10.7.08 Solve simple problems involving the number of ways objects can be arranged (permutations and combinations). 8
Chapter 7 Percents (pp. 326 380) Lesson 7.1 (pp. 329 334) Percents and Fractions Use a fraction to find the percent of a number 6.7.03 Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%). 6.7.16 Read, write, recognize, model, and interpret percents from 0% to 100%. 6.7.17 Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5x10, sales tax, tips, interest, discounts). Lesson 7.2 (pp. 335 339) Percents and Proportions Use proportions to solve percent problems 6.7.15 Use proportional reasoning to model and solve problems. 6.7.16 Read, write, recognize, model, and interpret percents from 0% to 100%. Lesson 7.3 (pp. 340 344) Percents and Decimals Use decimals to solve percent problems 6.7.03 Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%). 6.7.16 Read, write, recognize, model, and interpret percents from 0% to 100%. 6.7.17 Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5x10, sales tax, tips, interest, discounts). Lesson 7.4 (pp. 345 350) The Percent Equation Use equations to solve percent problems 6.7.16 Read, write, recognize, model, and interpret percents from 0% to 100%. 6.7.17 Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5x10, sales tax, tips, interest, discounts). Lesson 7.5 (pp. 352 356) Percent of Change Find a percent of change in a quantity 6.7.16 Read, write, recognize, model, and interpret percents from 0% to 100%. 6.7.17 Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5x10, sales tax, tips, interest, discounts). 9
Lesson 7.6 (pp. 357 361) Percent Applications Find markups, discounts, sales tax, and tips Lesson 7.7 (pp. 362 366) Simple and Compound Interest Calculate interest earned and account balances 6.7.16 Read, write, recognize, model, and interpret percents from 0% to 100%. 6.7.17 Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5x10, sales tax, tips, interest, discounts). 6.7.17 Solve number sentences and problems involving fractions, decimals, and percents (e.g., 50% of 10 is the same as 1/2 of 10 is the same as 0.5x10, sales tax, tips, interest, discounts). 10
Chapter 8 Linear Functions (pp. 382 449) Lesson 8.1 (pp. 384 390) Relations and Functions Use graphs to represent relations and functions Lesson 8.2 (pp. 391 397) Linear Equations in Two Variables Find solution of equations in two variables Lesson 8.3 (pp. 398 403) Using Intercepts Use x- and y- intercepts to graph linear equations Lesson 8.4 (pp. 404 411) The Slope of a Line Find and interpret slopes of lines Lesson 8.5 (pp. 412 419) Slope-Intercept Form Graph linear equations in slope-intercept form Lesson 8.6 (pp. 419 425) Writing Linear Equations Write linear equations Lesson 8.7 (pp. 426 430) Function Notation Use function notation Lesson 8.8 (pp. 431 435) Systems of Linear Equations Graph and solve systems of linear equations 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. 8.7.08 Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions. 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. 8.7.10 Represent and analyze problems with linear equations and inequalities. 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. 8.7.10 Represent and analyze problems with linear equations and inequalities. 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. 8.7.08 Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions. 8.7.08 Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions. 8.7.08 Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions. 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph. 11
Lesson 8.9 (pp. 436 441) Graphs of Linear Inequalities Graph the inequalities in two variables 8.7.10 Represent and analyze problems with linear equations and inequalities. 12
Chapter 9 Real Numbers and Right Triangles (pp. 450 507) Lesson 9.1 (pp. 453 457) Square Roots Find and approximate square roots of numbers Lesson 9.2 (pp. 458 464) Simplifying Square Roots Simplify radical expressions Lesson 9.3 (pp. 465 469) The Pythagorean Theorem Use the Pythagorean Theorem to solve problems 6.7.13 Estimate the square root of a number less than 1,000 between two whole numbers (e.g., 41 is between 6 and 7) 8.7.05 Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 + b for a = 3 and b = 4). 8.7.04 Recognize equivalent forms of algebraic expressions. 9.7.03 Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent). Lesson 9.4 (pp. 470 474) Real Numbers Compare and order real numbers Lesson 9.5 (pp. 476 482) The Distance and Midpoint Formulas Use the distance, midpoint, and slope formulas Lesson 9.6 (pp. 483 488) Special Right Triangles Use special right triangles to solve problems Lesson 9.7 (pp. 489 493) The Tangent Ratio Use tangent to find side lengths of right triangles Lesson 9.8 (pp. 494 499) The Sine and Cosine Ratios Use sine and cosine to find triangle side lengths 6.7.05 Order and compare integers, terminating decimals, fractions, and mixed numbers. 6.7.06 Identify and locate integers, decimals, and fractions/mixed numbers on a number line, and estimate the locations of square roots. 9.7.15 Determine the distance between two points on a horizontal or vertical number line. 9.7.03 Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent). 9.7.03 Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent).. 9.7.03 Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent). 13
Chapter 10 Measurement, Area, and Volume (pp. 508 569) Lesson 10.1 (pp. 511 515) Triangles Solve problems involving triangles 9.7.01 Classify, describe, and sketch regular and irregular two dimensional shapes according to the number of sides, length of sides, number of vertices, and interior angles. 9.7.03 Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent). Lesson 10.2 (pp. 516 520) Polygons and Quadrilaterals Classify polygons and quadrilaterals 9.7.01 Classify, describe, and sketch regular and irregular two dimensional shapes according to the number of sides, length of sides, number of vertices, and interior angles. 9.7.03 Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent). Lesson 10.3 (pp. 521 527) Areas of Parallelograms and Trapezoids Find the areas of parallelograms and trapezoids Lesson 10.4 (pp. 528 537) Circumference and Area of a Circle Find circumferences and areas of circles Lesson 10.5 (pp. 538 543) Surface Areas of Prisms and Cylinders Find the surface areas of prisms and cylinders Lesson 10.6 (pp. 544 551) Surface Areas of Pyramids and Cones Find the surface areas of pyramids and cones Lesson 10.7 (pp. 552 557) Volumes of Prisms and Cylinders Find the volumes of prisms and cylinders Lesson 10.8 (pp. 558 567) Volumes of Pyramids and Cones Find the volumes of pyramids and cones 7.7.02 Solve problems involving the perimeter and area of polygons and composite figures using diagrams, models, and grids or by measuring or using given formulas (may include sketching a figure from its description). 9.7.04 Identify, describe, and determine the radius and diameter of a circle. 7.7.04 Determine the volume and surface area of a right rectangular prism using an appropriate formula or strategy. 9.7.02 Solve problems involving two and three dimensional shapes. 7.7.04 Determine the volume and surface area of a right rectangular prism using an appropriate formula or strategy. 9.7.02 Solve problems involving two and three dimensional shapes. 14
Chapter 11 Data Analysis and Probability (pp. 578 647) Lesson 11.1 (pp. 581 587) Stem-and-Leaf Plots and Histograms Make stem-and-leaf plots and histograms 10.7.01 Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, scatterplot, circle graph, or histogram Lesson 11.2 (pp. 588 595) Box-and-Whisker Plots Make and interpret box-and-whisker plots Lesson 11.3 (pp. 596 600) Using Data Displays Choose appropriate data displays Lesson 11.4 (pp. 601 608) Collecting Data Identify populations and sampling methods Lesson 11.5 (pp. 609 614) Interpreting Data Make conclusions about populations using surveys Lesson 11.6 (pp. 615 619) Permutations Use permutations to count possibilities Lesson 11.7 (pp. 620 626) Combinations Use combinations to count possibilities Lesson 11.8 (pp. 627 633) Probabilities of Disjoint and Overlapping Events Probabilities of disjoint and overlapping events Lesson 11.9 (pp. 634 643) Independent and Dependent Events Find the probability that event A and event B occur 8.7.08 Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions. 10.7.05 Determine and use the mode, range, median, and mean to interpret data. 10.7.02 Compare different representations of the same data. 10.7.01 Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, scatterplot, circle graph, or histogram. 10.7.01 Read, interpret, and make predictions from data represented in a bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph, scatterplot, circle graph, or histogram. 10.7.08 Solve simple problems involving the number of ways objects can be arranged (permutations and combinations). 10.7.08 Solve simple problems involving the number of ways objects can be arranged (permutations and combinations). 10.7.06 Solve problems involving the probability of a simple or compound event, including representing the probability as a fraction, decimal, or percent. 10.7.06 Solve problems involving the probability of a simple or compound event, including representing the probability as a fraction, decimal, or percent. 15
Chapter 12 Polynomials and Nonlinear Functions (pp. 648 705) Lesson 12.1 (pp. 651 656) Polynomials Classify and write polynomials in standard form Lesson 12.2 (pp. 657 661) Adding and subtracting Polynomials Add and subtract polynomials Lesson 12.3 (pp. 662 667) Multiplying Monomials and Polynomials Multiply polynomials and monomials Lesson 12.4 (pp. 668 673) Multiplying Binomials Multiply binomials Lesson 12.5 (pp. 674 678) Other Rules of Exponents Simplify powers of products Lesson 12.6 (pp. 679 685) Quadratic Functions Graph quadratic functions Lesson 12.7 (pp. 686 691) Exponential Growth and Decay Graph exponential functions Lesson 12.8 (pp. 692 697) Sequences Extend and graph sequences 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 8.7.03 Simplify algebraic expressions by identifying and combining like terms. 6.7.04 Represent repeated factors using exponents. 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph 8.7.07 Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph 8.7.01 Determine a missing term in a sequence, extend a sequence, and construct and identify a rule that can generate the terms of an arithmetic or geometric sequence. 16
Chapter 13 Angle Relationships and Transformations (pp. 706 768) Lesson 13.1 (pp. 709 715) Angle Relationships Classify special pairs of angles Lesson 13.2 (pp. 716 721) Angles and Parallel Lines Identify angles when a transversal intersects lines Lesson 13.3 (pp. 722 728) Angles and Polygons Find measures of interior and exterior angles Lesson 13.4 (pp. 729 733) Translations Translate figures in a coordinate plane Lesson 13.5 (pp. 734 740) Reflections and Symmetry Reflect figures and identify lines of symmetry Lesson 13.6 (pp. 741 746) Rotations and Symmetry Rotate figures and identify rotational symmetry Lesson 13.7 (pp. 747 751) Dilations Dilate figures in a coordinate plane 9.7.08 Identify or analyze relationships of angles formed by intersecting lines. 9.7.10 Solve problems involving complementary and supplementary angles. 9.7.08 Identify or analyze relationships of angles formed by intersecting lines. 9.7.02 Solve problems involving two and three dimensional shapes. 9.7.07 Analyze the results of a combination of transformations. 9.7.07 Analyze the results of a combination of transformations. 9.7.07 Analyze the results of a combination of transformations. 9.7.07 Analyze the results of a combination of transformations. 17
IL 212 1/2005 2005 CC2