illinois math assessment framework, grade 7 - …€¦ · · 2005-01-11illinois math assessment...

correlated to

IllinoisMath Assessment Framework, Grade 7

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Illinois Math Assessment FrameworkGrade 7

correlated to

McDougal Littell Middle School Math, Course 3

McDougal Littell Middle School Math, Course 3Chapter 1

Variables and Equations (pp. 2–49)Illinois Math Assessment Framework

Lesson 1.1Interpreting Graphs (pp. 5–9)Use graphs to analyze data.

10.7.01 Read, interpret, and make predictions from datarepresented in a bar graph, line (dot) plot, Venn diagram(with two circles), chart/table, line graph, scatterplot, circlegraph, or histogram.

10.7.02 Compare different representations of the samedata.

10.7.03 Create a bar graph, chart/table, line graph, or circlegraph for a given setof data.

Lesson 1.2Order of Operations (pp. 10–13)Use the order of operations to evaluate numericalexpressions.

6.7.09 Identify and apply order of operations to simplifynumeric expressions involving whole numbers (includingexponents), fractions, and decimals.

Lesson 1.3Variables and Expressions (pp. 15–19)Write and evaluate variable expressions.

8.7.02 Write an expression using variables to representunknown quantities.

8.7.05 Evaluate or simplify algebraic expressions with oneor more integer variable values (e.g., a2 + b for a = 3 and b= –4).

Lesson 1.4Powers and Exponents (pp. 20–23)Evaluate expressions with powers.

6.7.04 Represent repeated factors using exponents.



Lesson 1.5Equations and Solutions (pp. 28–31)Write and solve equation using mental math.

8.7.10 Represent and analyze problems with linearequations and inequalities.

8.7.11 Solve linear equations in one variable (e.g., 2x + 3 =13) and inequalities involving < or > (e.g., 2x<6, x+7>10).

8.7.12 Solve word problems involving unknown quantities.

Illinois Math Assessment Framework: Grade 7 correlated toMcDougal Littell Middle School Math, Course 3

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Lesson 1.6Variables in Familiar Formulas (pp. 33–37)Use formulas to find unknown values.

7.7.02 Solve problems involving the perimeter and area ofpolygons and composite figures using diagrams, models,and grids or by measuring or using given formulas (mayinclude sketching a figure from its description).

8.7.12 Solve word problems involving unknown quantities.

Lesson 1.7A Problem Solving Plan (pp. 38–43)Use a problem solving plan to solve problems.


8.7.12 Solve word problems involving unknown quantities..


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Integer Operations (pp. 50–103)Illinois Math Assessment Framework

Lesson 2.1Integers and Absolute Value (pp. 53–56)Study integers.

6.7.02 Read, write, recognize, model, and interpretintegers, including translating numerical expressions.

6.7.05 Order and compare integers, terminating decimals,fractions, and mixed numbers.

6.7.06 Identify and locate integers, decimals, andfractions/mixed numbers on a number line, and estimatethe locations of square roots.

Lesson 2.2Adding Integers (pp. 58–62)Add integers.


6.7.08 Solve problems and number sentences involvingaddition, subtraction, multiplication, and division usingintegers, fractions, and decimals.


Lesson 2.3Subtracting Integers (pp. 63–67)Subtract integers.





Lesson 2.4Multiplying Integers (pp. 70–73)Multiply integers.





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Lesson 2.5Dividing Integers (pp. 74–77)Divide integers.





10.7.05 Determine and use the mode, range, median, andmean to interpret data.

Lesson 2.6Number Properties (pp. 80–84)Use properties to evaluate expressions.




6.7.10 Identify and apply the following properties ofoperations with rational numbers: • the commutative andassociative properties for addition and multiplication; • thedistributive property; • the additive and multiplicativeidentity properties; • the additive and multiplicativeinverse properties; and • the multiplicative property ofzero.


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Lesson 2.7The Distributive Property (pp. 85–89)Use the distributive property.





8.7.03 Simplify algebraic expressions by identifying andcombining like terms.

Lesson 2.8The Coordinate Plane (pp. 91–95)Identify and plot points in a coordinate plane.


9.7.05 Graph points and identify coordinates of points onthe Cartesian coordinate plane (all four quadrants).

9.7.06 Represent and identify geometric figures usingcoordinate geometry.


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Solving Equations and Inequalities (pp. 104–163)Illinois Math Assessment Framework

Lesson 3.1Solving Equations Using Addition orSubtraction (pp. 109–112)Solve equations using addition or subtraction.


8.7.11 Solve linear equations in one variable (e.g., 2x + 3= 13) and inequalities involving < or > (e.g., 2x<6,x+7>10).

8.7.12 Solve word problems involving unknownquantities.

Lesson 3.2Solving Equations Using Multiplication orDivision (pp. 113–116)Solve equations using multiplication or division.




Lesson 3.3Solving Two–Step Equations (pp. 119–123)Solve two–step equations.




Lesson 3.4Writing Two–Step Equations (pp. 124–128)Solve problems by writing two–step equations.

8.7.02 Write an expression using variables to representunknown quantities.



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Lesson 3.5Applying Geometry Formulas (pp. 134–139)Use formulas for perimeter and area.



9.7.02 Solve problems involving two– and three–dimensional shapes.

Lesson 3.6Solving Inequalities Using Addition orSubtraction (pp. 140–145)Solve inequalities using addition or subtraction.

8.7.09 Identify, graph, and interpret inequalities on anumber line.



Lesson 3.7Solving Inequalities Using Multiplicationor Division (pp. 146–149)Solve inequalities using multiplication or division.

8.7.09 Identify, graph, and interpret inequalities on anumber line.




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Factors, Fractions, and Exponents (pp. 164–215)Illinois Math Assessment Framework

Lesson 4.1Factors and Prime Factorization(pp. 168–172)Write the prime factorization of numbers.


6.7.07 Solve problems involving descriptions of numbers,including characteristics and relationships (e.g., squarenumbers, prime/composite, prime factorization, greatestcommon factor, least common multiple).

Lesson 4.2Greatest Common Factor (pp. 173–177)Find the greatest common factor of two or morenumbers.



Lesson 4.3Simplifying Fractions (pp. 179–183)Simplify fractions.

6.7.03 Recognize, translate between, and apply multiplerepresentations of rational numbers (decimals, fractions,mixed numbers, and percents less than 100%).


Lesson 4.4Least Common Multiple (pp. 186–189)Find the least common multiple of two numbers.


Lesson 4.5Comparing Fractions and Mixed Numbers(pp. 192–195)Compare and order fractions and mixed numbers.


6.7.05 Order and compare integers, terminating decimals,fractions, and mixed numbers.

Lesson 4.6Rules of Exponents (pp. 196–200)Multiply and divide expressions with exponents.




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Lesson 4.7Negative and Zero Exponents (pp. 201–204)Simplify expressions with negative exponents.




Lesson 4.8Scientific Notation (pp. 205–208)Read and write numbers using scientific notation.




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Rational Number Operations (pp. 216–267)Illinois Math Assessment Framework

Lesson 5.1Fractions with Common Denominators(pp. 219–223)Add and subtract fractions with commondenominators.





Lesson 5.2Fractions with Different Denominators(pp. 224–227)Add and subtract fractions with differentdenominators.





Lesson 5.3Multiplying Fractions (pp. 230–233)Multiply fractions and mixed numbers.





Lesson 5.4Dividing Fractions (pp. 234–238)Divide fractions.

6.7.08 Solve problems and number sentences involvingaddition, subtraction, multiplication, and division usingintegers, fractions, and decimals. .


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Lesson 5.5Fractions and Decimals (pp. 242–246)Write fractions as decimals and decimals asfractions.


6.7.05 Order and compare integers, terminating decimals,fractions, and mixed numbers

Lesson 5.6Adding and Subtracting Decimals(pp. 247–250)Add and subtract decimals.


Lesson 5.7Multiplying and Dividing Decimals(pp. 251–254)Multiply and divide decimals.


Lesson 5.8Mean, Median, and Mode (pp. 257–261)Describe data sets using mean, median, mode, andrange.



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Multi–Step Equations and Inequalities(pp. 268–313)

Illinois Math Assessment Framework

Lesson 6.1Solving Multi–Step Equations (pp. 271–275)Solve equations that require using two or moresteps.





Lesson 6.2Solving Equations with Variables on BothSides (pp. 278–281)Solve equations that have variables on both sides.






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Lesson 6.3Solving Equations Involving Fractions andDecimals (pp. 282–285)Solve equations with fractions and decimals.





Lesson 6.4Solving Equations Involving Circumference(pp. 290–294)Solve equations involving the circumference of acircle.





Lesson 6.5Solving Multi–Step Inequalities(pp. 295–299)Use two or more steps to solve inequalities.






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Lesson 6.6Problem Solving and Inequalities(pp. 301–305)Use multi–step inequalities to solve real–worldproblems.





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Ratio, Proportion, and Percent (pp. 314–371)Illinois Math Assessment Framework

Lesson 7.1Ratios and Rates (pp. 317–320)Find ratios and unit rates.

6.7.14 Create and explain ratios that represent a givensituation.

6.7.15 Use proportional reasoning to model and solveproblems

Lesson 7.2Writing and Solving Proportions(pp. 322–326)Write and solve proportions.

6.7.14 Create and explain ratios that represent a givensituation.

6.7.15 Use proportional reasoning to model and solveproblems.

Lesson 7.3Solving Percent Problems (pp. 327–330)Solve percent problems using proportions.



6.7.16 Read, write, recognize, model, and interpretpercents from 0% to 100%.

6.7.17 Solve number sentences and problems involvingfractions, decimals, and percents (e.g., 50% of 10 is thesame as 1/2 of 10 is the same as 0.5x10, sales tax, tips,interest, discounts).

Lesson 7.4Fractions, Decimals, and Percents(pp. 331–335)Rewrite fractions, decimals, and percents.




Lesson 7.5Percent of Change (pp. 338–341)Solve problems with percent of increase or decrease.


8.7.06 Determine how a change in one variable relates to achange in a second variable.


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Lesson 7.6Percent Applications (pp. 342–346)Solve percent application problems.



Lesson 7.7Using the Percent Equation (pp. 347–350)Solve percent problems using the percent equation.


Lesson 7.8Simple Probability (pp. 354–357)Find probabilities of events.

10.7.06 Solve problems involving the probability of asimple or compound event, including representing theprobability as a fraction, decimal, or percent.


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Polygons and Transformations (pp. 372–427)Illinois Math Assessment Framework

Lesson 8.1Angle Pairs (pp. 375–379)Solve equations to find angle measures.

9.7.08 Identify or analyze relationships of angles formedby intersecting lines.

9.7.10 Solve problems involving complementary andsupplementary angles.

Lesson 8.2Angles and Triangles (pp. 382–385)Classify angles and triangles.

9.7.01 Classify, describe, and sketch regular and irregulartwo–dimensional shapes according to the number of sides,length of sides, number of vertices, and interior angles.

9.7.02 Solve problems involving two– andthree–dimensional shapes.

9.7.03 Solve problems using properties of triangles andquadrilaterals (e.g., opposite sides of a parallelogram arecongruent).

9.7.09 Identify and sketch acute, right, and obtuse angles.

Lesson 8.3Quadrilaterals (pp. 386–389)Classify quadrilaterals.




Lesson 8.4Polygons and Angles (pp. 390–393)Find angle measures in polygons.




Lesson 8.5Congruent Polygons (pp. 397–401)Identify and name congruent polygons.




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Lesson 8.6Reflections and Symmetry (pp. 404–408)Reflect figures and identify lines of symmetry.



Lesson 8.7Translations and Rotations (pp. 409–413)Translate or rotate figures in a coordinate plane.



Lesson 8.8Similarity and Dilations (pp. 416–421)Use similar polygons to find missing measures.

9.7.14 Determine if figures are similar, and identifyrelationships between corresponding parts of similarfigures.


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Real Numbers and Right Triangles (pp. 428–477)Illinois Math Assessment Framework

Lesson 9.1Square Roots (pp. 431–436)Find and approximate square roots of numbers


6.7.13 Estimate the square root of a number less than1,000 between two whole numbers (e.g., √ 41 is between 6and 7)

Lesson 9.2Rational and Irrational Numbers(pp. 437–441)Work with irrational numbers.


Lesson 9.3The Pythagorean Theorem (pp. 443–447)Use the Pythagorean theorem to solve problems.



Lesson 9.4Using the Pythagorean Theorem(pp. 450–453)Solve real–life problems using the Pythagoreantheorem.



Lesson 9.5Special Right Triangles (pp. 456–460)Use special right triangles to solve real–lifeproblems.



Lesson 9.6Using Trigonometric Ratios (pp. 463–468)Use trigonometric ratios to find the side lengths.




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Measurement, Area, and Volume (pp. 478–537)Illinois Math Assessment Framework

Lesson 10.1Areas of Parallelograms and Trapezoids(pp. 481–485)Find the areas of parallelograms and trapezoids.





Lesson 10.2Areas of Circles (pp. 486–490)Find the areas of circles.

9.7.04 Identify, describe, and determine the radius anddiameter of a circle.

Lesson 10.3Three–Dimensional Figures (pp. 492–495)Classify and sketch solids.


Lesson 10.4Surface Areas of Prisms and Cylinders(pp. 502–506)Find the surface areas of prisms and cylinders.

7.7.04 Determine the volume and surface area of a rightrectangular prism using an appropriate formula orstrategy.


9.7.11 Identify a three–dimensional object from its net.

Lesson 10.5Surface Areas of Pyramids and Cones(pp. 507–511)Find the surface areas of pyramids and cones.


Lesson 10.6Volumes of Prisms and Cylinders(pp. 513–517)Find the volumes of prisms and cylinders.

7.7.04 Determine the volume and surface area of a rightrectangular prism using an appropriate formula orstrategy.



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Lesson 10.7Volumes of Pyramids and Cones(pp. 519–523)Find volumes of pyramids and cones.



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Linear Equations and Graphs (pp. 538–593)Illinois Math Assessment Framework

Lesson 11.1Relations and Functions (pp. 541–544)Use tables to represent functions.

8.7.08 Translate between different representations (table,written, graphical, or pictorial) of whole numberrelationships and linear expressions.


Lesson 11.2Scatter Plots (pp. 545–548)Make and interpret scatter plots.

8.7.06 Determine how a change in one variable relates to achange in a second variable.



10.7.01 Read, interpret, and make predictions from datarepresented in a bar graph, line (dot) plot, Venn diagram(with two circles), chart/table, line graph, scatterplot,circle graph, or histogram.

Lesson 11.3Equations in Two Variables (pp. 549–553)Find solutions of equations in two variables.


8.7.12 Solve word problems involving unknown quantities

Lesson 11.4Graphs of Linear Equations (pp. 556–560)Learn to sketch the graph of a linear equation.




Lesson 11.5Using Intercepts (pp. 564–567)Find x– and y–intercepts of a line.

8.7.07 Represent linear equations and quantitativerelationships on a rectangular coordinate system, andinterpret the meaning of a specific part of a graph.



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Lesson 11.6Slope (pp. 570–574)Find and interpret slopes of lines.



Lesson 11.7Slope-Intercept Form (pp. 577–580)Write and graph equations in slope–intercept form.


Lesson 11.8Graphs of Linear Inequalities (pp. 583–587)Graph linear inequalities.




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Data Analysis and Probability (pp. 594–653)Illinois Math Assessment Framework

Lesson 12.1Stem–and–Leaf Plots (pp. 597–600)Make and interpret steam–and–leaf plots.


Lesson 12.2Box–and–Whisker Plots (pp. 601–604)Construct and interpret box–and–whisker plots.



Lesson 12.3Using Data Displays (pp. 605–609)Organize data using circle graphs and line graphs.


10.7.01 Read, interpret, and make predictions from datarepresented in a bar graph, line (dot) plot, Venn diagram(with two circles), chart/table, line graph, scatterplot,circle graph, or histogram.

Lesson 12.4Counting Methods (pp. 618–622)Use counting methods to count the number ofchoices.


10.7.07 Represent all possible outcomes for simple events.

10.7.08 Solve simple problems involving the number ofways objects can be arranged (permutations andcombinations).

Lesson 12.5Permutations (pp. 623–626)Use permutations to count possibilities.



Lesson 12.6Combinations (pp. 627–631)Use combinations to count possibilities.



Lesson 12.7Probability and Odds (pp. 632–636)Find the odds in favor of events.



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Lesson 12.8Independent and Dependent Events(pp. 639–643)Study independent and dependent events.



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Polynomials and Functions (pp. 654–703)Illinois Math Assessment Framework

Lesson 13.1Polynomials (pp. 657–660)Simplify polynomials by combining like terms.

8.7.03 Simplify algebraic expressions by identifying andcombining like terms..8.7.05 Evaluate or simplify algebraic expressions with oneor more integer variable values (e.g., a2 + b for a = 3 and b= –4).

Lesson 13.2Adding and Subtracting Polynomials(pp. 661–665)Add and subtract polynomials.


Lesson 13.3Monomials and Powers (pp. 666–670)Apply properties of exponents to monomials.


Lesson 13.4Multiplying Binomials (pp. 674–677)Multiply binomials.


Lesson 13.5Non-Linear Functions (pp. 680–684)Use function notation and graph non–linearfunctions.


IL 2101/2005

2005CC2

illinois math assessment framework, grade 7 - …€¦ · · 2005-01-11illinois math assessment...

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