L T

Transcription

1 Grade 7 Reviewers Brent Angelo Chillicothe Elementary Center Chillicothe, IL John J. Higgins Jr. Frazier Elementary School Chicago, IL James Cooper Northwood Middle School Woodstock, IL Kelly Astrahan Albert Einstein Elementary School Hanover Park, IL John W. Britton St. Luke Lutheran School Itasca, IL Joel Knoblock C. F. Simmons Middle School Aurora, IL Pamela Helm Robertson Charter School Decatur, IL Jeanna Ivey Primary Academic Center Markham, IL 2006 Perfection Learning Corporation All rights reserved. No part of this book may be reproduced, stored in a retrie val system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the publisher. Printed in the United States of America L T For information, contact Perfection Learning Corporation 1000 North Second Avenue, P.O. Box 500 Logan, Iowa Phone: Fax: perfectionlearning.com #79857 ISBN

2 For the Student This book will help you review, practice, and master the Illinois Mathematics Assessment Framework. Here are the steps to follow to use this book. 1. Take the Tryout Test and check your answers. Use the chart at the bottom of this page to find out your strengths and weaknesses in the areas covered. Don t be discouraged if you don t get all the answers right or if you don t understand some questions. Remember the questions that are hard for you to answer. They will be the types of questions you need to work on the most. 2. Work through the lessons that follow the Tryout Test. Each lesson provides a review as well as practice questions based on the Assessment Framework. Each lesson ends with a short mastery test to reinforce your learning. As you go, complete the Charting Your Progress chart on page 123 of this book. 3. After completing all six lessons, take the Final Mastery Test. Your score on this test will show your understanding of the Assessment Framework. By following the steps outlined above, you will increase your mastery of the Illinois Mathematics Assessment Framework. Lesson Tryout Test Items Final Mastery Test Items 1 Number Sense 1, 3, 7, 31, 32, 36, 39 1, 3, 7, 30, 32, 36, 39, 40, 46 2 Operations 3 Measurements 4 Algebra 10, 13, 17, 18, 21, 33, 35, 40, 10, 13, 17, 18, 21, 33, 35, 41, 44, 45, 60 60, 61 2, 11, 19, 34, 41, 47, 48, 58 2, 11, 19, 34, 42, 45, 47, 49, 57, 58 4, 5, 6, 20, 22, 37, 38, 42, 43, 4, 5, 6, 20, 22, 37, 38, 43, 44, 51, 59 50, 59 5 Geometry 6 8, 12, 14, 23, 26, 27, 28, 30, 8, 12, 14, 23, 24, 25, 27, 51, 46, 52, 53, 54, 57 52, 53, 54 Data Analysis, Statistics, 9, 15, 16, 24, 25, 29, 49, 50, 9, 15, 16, 26, 28, 29, 31, 48, and Probability 55, 56 55, 56, 62

3 Table of Contents Tips for Taking Tests..Inside front cover For the Student Tryout Test, Part Tryout Test, Part Number Sense Using Number Properties Working with Integers Working with Rational Numbers..17 Comparing and Ordering Factors and Multiples Prime and Composite Numbers..22 Ratios, Proportions, and Percents Extended-Response Practice Mastery Test Operations Computing with Integers and Rational Numbers Estimating Exponents and Square Roots Order of Operations Computing with Percents Extended-Response Practice Mastery Test Measurements Appropriate Units of Measure...42 Converting Units of Measure Perimeter and Area Volume and Surface Area Solving Angle Problems Using Scale Drawings Extended-Response Practice Mastery Test Algebra Patterns and Sequences Writing and Simplifying Algebraic Expressions Evaluating Expressions Graphing Equations Graphing Inequalities Solving Equations and Inequalities Solving Word Problems Extended-Response Practice Mastery Test Geometry Two-Dimensional Shapes Triangles and Quadrilaterals...79 Circles Coordinate Geometry Transformations Angles Three-Dimensional Shapes Congruent and Similar Figures..88 Distance on a Number Line Extended-Response Practice Mastery Test Data Analysis, Statistics, and Probability Reading and Interpreting Graphs..96 Displaying Data Scatterplots Range, Mean, Median, and Mode..103 Probability and Outcomes Permutations and Combinations..107 Extended-Response Practice Mastery Test Final Mastery Test, Part Final Mastery Test, Part Charting Your Progress Math Chart......Inside back cover

4 LESSON 1 Number Sense Using Number Properties Working with Integers Working with Rational Numbers Comparing and Ordering Factors and Multiples Prime and Composite Numbers Ratios, Proportions, and Percents Using Number Properties Review the Standard The commutative, associative, and distributive properties allow you to perform computations in different orders. These properties can help you solve some problems mentally. Review the chart below. Commutative Property The order in which you add or multiply does not change the answer Associative Property You can group addends or factors in different ways. (14 7) 6 14 (7 6) (5 2) 8 5 (2 8) Distributive Property The product of a sum equals the sum of two products. 3(12 8) (3 12) (3 8) ( 14) ( 10) (14 10) Example A Which statement shows the associative property for multiplication? (14.5n) A 14.5n C ( )n 14.5 B ( 14.5)n D (14.5 n) The associative property states that you can group factors in different ways. Follow these steps to solve example A. 1 In the given statement, you multiply 14.5 times n, and then multiply the answer by. 2 Use parentheses to show multiplying times 14.5 before multiplying by n. 14 Using Number Properties Perfection Learning No reproduction permitted.

5 Lesson 1: Number Sense The inverse, identity, and zero properties help you simplify computations. Inverse Property Opposite numbers are additive inverses Reciprocals are multiplicative inverses. 1 Identity Property Zero is the identity element for addition. 0 One is the identity element for multiplication Zero Property of Multiplication The product of any number and zero is zero Example B Which number is the multiplicative inverse of? A B C D 8 1 Reciprocals have a product of 1. Find the reciprocal of by interchanging the numerator and the denominator. 2 Remember the product of two negative numbers is positive. Try It Now try these problems on your own. 1 Complete this equation to show an example of the commutative property of addition Which property justifies this statement? 14 (6 1.5) 14 (1.5 6) A commutative property of addition B commutative property of multiplication C associative property of addition D associative property of multiplication 3 Which is the missing number? 4 Which statement illustrates the distributive property of multiplication over addition? A ( 2)(6) (5)(6) 2(6 5) B ( 2)(6) (5)(6) 2(5 6) C ( 2)(6) (5)(6) ( 2 5)6 D ( 2)(6) (5)(6) (6)( 2) (6)(5) 5 Which is the missing number? A 1 B x x 1 C x D x 3 0 Answer: Perfection Learning No reproduction permitted. Using Number Properties 15

6 Lesson 1: Number Sense Working with Integers Review the Standard Integers are the set of numbers that include 0, the counting numbers, and their opposites. Integers are often used to show losses and temperatures below zero. {... 3, 2, 1, 0, 1, 2, 3,... } Example C Keith is playing a game. He started with zero points. He lost 2 points and then gained 6 points. Which expression shows how many points Keith has now? A C It may help to use a number line to answer example C. Start at zero. Then move two units to the left to represent the 2 points Keith lost. B D From 2, move 6 units to the right. 3 Look for the expression that shows the sum of 2 6. Try It Now try these problems on your own. 6 What temperature is shown on the thermometer? A 10 B 5 C 5 D F The Vikings football team lost 5 yards during one play and gained 12 yards in the next play. Which expression shows the combination of yards lost and gained? A 5 12 C 5 12 B 5 12 D 5 12 Questions 8 9: Use the number line below. Q Which point is at negative 2 on the number line? A Q B R R C S D T 9 Which number is represented by point Q? A 5 C 2 B 4 D 4 S T 5 16 Working with Integers Perfection Learning No reproduction permitted.

7 Lesson 1: Number Sense Working with Rational Numbers Review the Standard Rational numbers are a set of numbers that can be written as a fraction. Percents, integers, and most decimals can be written as fractions. Number % 0.25 Fraction Form Example D Which shows that 0.78 is a rational number? A 78 B C D Use the word form to help you write the fraction in example D. Then reduce the fraction to simplest form. 78 hundredths Example E Complete the table. Show the decimal and fraction forms of the percent. Percent 54% Decimal Fraction Follow these steps to solve example E. 1 Write the percent as a decimal by moving the decimal point two places to the left. 54% Write the decimal as a fraction in simplest form. 54% 0.54 Try It Now try these problems on your own. 10 Which point has a value of 75%? 0 R S T V 1 A R C T B S D V 11 Which shows 1.5 as a mixed number? A C 1 B D 1 12 Which fraction is equivalent to 12%? A C B D 13 Which decimal has a value of? A C 0.45 B 0.8 D 0.4 Perfection Learning No reproduction permitted. Working with Rational Numbers 17

8 Lesson 1: Number Sense Comparing and Ordering Review the Standard When comparing or ordering numbers, convert them to the same type before comparing. By first converting the fraction and percent below to decimals, you can easily compare and order them. convert order 33% Example F Place the following points on the number line. A at 2.5 B at 75% C at Tip Memorize these common fractions, decimals, and percents % % % % To solve example F, first convert the percent and fraction into decimals. 1 Convert the percent by moving the decimal point two places to the left and dropping the percent sign. 75% Convert the mixed number by changing the fraction to a decimal. Hint: is a common fraction. 1 3 Place the points on the number line and label them. Remember to place the negative numbers to the left of zero on the number line. A has been placed for you as an example. Example G Which number is in the middle when the following numbers are ordered from least to greatest? 35% % A 45% C 35% B D 1 Write each number as a decimal. (Note: 0.2 is already a decimal.) 35% 45% 2 Order the numbers from least to greatest. Complete the list and then find the middle number. 45%, 0.2,,, 18 Comparing and Ordering Perfection Learning No reproduction permitted.

9 Lesson 1: Number Sense Try It Now try these problems on your own. 14 Which statement is true? You may want to draw a number line to help you compare. 19 Mark the following points on the number line below. W at 1.25; R at ; F at 50% A % B 15% C 0.8 D 29% 15 Which number is greater than 47%? A C 0.4 B D 0.74 Questions 16 18: Use the number line below. 1 K M P Q R Write these numbers from least to greatest. 1, 1.77, 4, 98% Answer: 21 Which fraction is less than? A C B D 16 Which point represents 95%? A M B P C Q D R 17 Between which pair of points on the number line would you place a point to represent? Questions 22 23: Write (greater than) or (less than) to complete each statement A K and M B M and P C P and Q D Q and R 18 Which is the least point represented on the number line? A B 0.95 C 8% D Remember... Add zeros to the right of decimals to make them easier to compare. 0.29? Perfection Learning No reproduction permitted. Comparing and Ordering 19

10 Lesson 1: Number Sense Factors and Multiples Review the Standard A factor is a number that divides another number evenly. 6 is a factor of 30 because 6 divides 30 evenly The greatest common factor (GCF) is the greatest factor two or more numbers have in common. Use prime factorization to help you find the GCF. Example H What is the greatest common factor of 8, 12, and 20? A 4 C 10 B 6 D 60 1 Draw a factor tree for each number Remember... Exponents show the number of times the base is a factor Record the numbers at the end of each branch of the factor trees. Use exponents to show the number of times a prime factor is repeated Find the least factor common to all numbers. This will be the GCF. 2 2 Example I What is the least common multiple of 8, 12, and 20? A 4 C 60 B 24 D 120 The least common multiple (LCM) of two or more numbers is the least multiple the numbers have in common. 1 Write the prime factorization of each number The numbers 2, 3, and 5 are factors. Multiply the greatest of each factor. The product is the LCM for the three numbers *Enter Factors text and here Multiples Perfection Learning No reproduction permitted.

11 Lesson 1: Number Sense Try It Now try these problems on your own. 24 Which numbers have 3 as a common factor? A 2, 24 C 12, 24 B 8, 12 D 10, Choose the GCF of 64, 40, and 88. A 2 C 8 B 4 D Choose the greatest common factor of 18 and 24. A 1 C 6 B 2 D 3 26 Choose the least common multiple of 6 and 4. A 12 C 27 B 18 D Which shows the prime factorization of 60? A C B D Which shows the factor expression used to find the LCM of 28 and 32? A C 2 7 B D Choose the LCM of 8, 6, and 3. A 18 C 30 B 24 D The GCF of 65 and some number is 13. Which number below could it be? A 5 C 156 B 15 D The LCM of 12 and some number is 48. Which number below could it be? A 4 C 8 B 6 D 16 Tip Think of opposites when looking for the GCF or LCM. To find the greatest common factor, take the least of each common factor. To find the least common multiple, multiply the greatest of each factor. Perfection Learning No reproduction permitted. Factors and Multiples 21

12 Lesson 1: Number Sense Prime and Composite Numbers Review the Standard A prime number has only two factors: 1 and itself. The number 17 is prime because it can be divided evenly only by 1 and 17. A composite number has more than two factors. 4 is a composite number because it can be divided evenly by 1, 2, and 4. Example J Which numbers in this list are prime numbers? 4, 7, 14, 11, 21, 33, 49 A 7, 11, and 21 C 7 and 11 B 7, 11, and 49 D 11 Tip 2 is the only even prime number. It can be divided evenly only by 1 and itself. 1 is neither prime nor composite. It only has 1 factor: itself. 1 Rule out all even numbers. Even numbers are always divisible by 2. Even numbers: 2 Rule out the composite numbers. These are numbers that can be divided evenly by another number. For example, 21 is divisible by 3 and 7. Composite numbers: 3 Which numbers are left? Try It Now try these problems on your own. 33 Which number is a prime number? A 26 C 57 B 42 D Which number is a composite number? A 37 C 73 B 61 D The prime factorization of a number includes only prime factors. Which of the following is NOT the prime factorization of a number? A C B D Questions 36 37: Use the numbers in the box below to answer the questions How many numbers in the box are prime numbers? A 1 C 3 B 2 D 4 37 How many numbers in the box are even composite numbers? A 0 C 2 B 1 D 3 22 Prime and Composite Numbers Perfection Learning No reproduction permitted.

13 Lesson 1: Number Sense Ratios, Proportions, and Percents Review the Standard A ratio shows the relative sizes of two groups of items. For example, if there are 8 boys and 9 girls in your class, the ratio of boys to girls is 8 to 9. Example K Gail is competing in a checkers tournament. She won 12 out of a total of 20 games. What is her ratio of wins to losses? A 3 : 5 C 5 : 3 B 3 : 2 D 2 : 3 Remember... Two ways of writing the ratio 4 to 3 are 4 : 3 and Simplify a ratio the same way you simplify a fraction divide both terms by the same factor. 8 : 12 In example K, you are to show the ratio of wins to losses. You know how many games Gail won, but you have to figure out the number of losses. 12 : wins losses 1 Notice that all the answer choices are written in simplest form. Simplify the ratio of wins to losses by dividing both terms by the largest common divisor. 2 Find the answer choice that matches the ratio. Be sure the wins and losses are in the same order. Two equal ratios form a proportion. When you write pairs of equivalent fractions, you are writing a proportion. Example L Find the missing number in the proportion below.? A 5 C 15 B 8 D 19 Tip You can check proportions using cross multiplication. If the two products are equal, the proportion is true True There are several ways to solve example L. Follow these steps for one solution. 1 Convert to a fraction with a denominator of 20 by multiplying the numerator and denominator by The numerator of the equivalent fraction is the solution. Go On Perfection Learning No reproduction permitted. Ratios, Proportions, and Percents 23

14 Lesson 1: Number Sense A percent is a ratio to 100. These visual models show how percents can be determined even when you aren t comparing 100 items. Ratio: 35 out of out of 10 3 out of 8 Percent: 35% 70% 37.5% Decimal: Fraction: Example M What percent of this rectangle is shaded? A 3% C 30% B 6% D 60% 1 Write a ratio to describe the portion of the rectangle that is shaded. Convert the ratio into a decimal by dividing the numerator by the denominator To find the solution, convert the decimal to a percent by moving the decimal point 2 places to the right. Try It Now try these problems on your own. 38 In Sharla s computer club, 4 out of every 7 members are girls. What is the ratio of boys to girls in the club? A 3 to 7 C 4 to 3 B 7 to 3 D 3 to 4 Questions 39 40: Complete each ratio so that it will be equivalent to a ratio of 3 : to 41 What is the missing term in this proportion? ? A 6 C 18 B 9 D Which model has 70% shaded? A B C D 40 to Ratios, Proportions, and Percents Perfection Learning No reproduction permitted.

15 Extended-Response Practice Lesson 1: Number Sense Some tests include questions in which you must explain how you solved the problem. You may also be asked to show your work, draw graphs, or make diagrams. The example below will give practice answering such questions. Example N Karyl was given 12 numbers to sort in four categories. But Karyl has made 4 mistakes. Cross out the numbers she put in the wrong boxes and write them in the box where they belong. One of the numbers does not fit in any box. Write it on the line below the boxes. Odd Composite Numbers Rational Numbers Less than % Multiples of To solve extended-response items such as example N, first make a plan, either on paper or mentally. Label each step of your solution so that it is easy to follow. Help out with the solution below. My Plan: I will find the errors Karyl made. Then I will put the numbers in the right boxes. The remaining number should be the number that doesn t fit. Odd Composite Numbers: Number 17 is not composite. It is prime, since it is only evenly divisible by 1 and itself. Rational Numbers Less than : I found that is not less than by forming equivalent fractions with denominators of 6. ; Ratios Equivalent to 4 out of 6 Karyl should have put in the Ratios Equivalent to 4 out of 6 box. Multiples of 6: I mentally divided each number in the box by 6. The numbers 36 and 60 are each multiples of 6. But 49 is not. Karyl should have put 49 in the Odd Composite Numbers box, since 49 is evenly divisible by 7. Number that does not fit: Show your work in the space below. Ratios Equivalent to 4 out of 6: I could tell right away that is not equivalent to. She should have put in the Rational Numbers Less than box, since and. The number left over is 17. Perfection Learning No reproduction permitted. Extended-Response *Enter text Practice here 25

16 This test will tell you how well you understand the Illinois Assessment Framework after studying lesson 1. Mastery Test 1 Estimated time: 25 minutes Directions: For a multiple-choice question, choose the best answer. For a short-answer question, write your answer on the line. For an extended-response question, show all your work and explain your answer. Questions 1 2: Use this number line. H K P M 6 Find the missing number.? Answer: 1 Write the fraction shown at point K. Answer: 2 Which of these numbers is between points P and M? A 2.0 C 0.6 B 1.4 D Write these numbers from greatest to least. 3, 1, 84%, 5 Answer: 4 Choose the ratio that is equivalent to a speed of 4 miles in 2 hours. A 40 miles in 12 hours B 2 miles in 4 hours C 20 miles in 10 hours D 8 miles in 1 hour 5 Last week it rained 3 days and was sunny the rest of the week. Write the ratio of rainy days to sunny days. (1 week 7 days) Answer: 7 Which property tells you that you can change the order of the numbers you are adding without changing the sum? A identity property B associative property C distributive property D commutative property 8 Find the GCF of 45, 27, and 18. A 3 C 9 B 6 D 12 9 Find the LCM of 10, 12, and 5. A 30 C 100 B 60 D Which is a prime number? A 33 C 101 B 72 D Derek practiced free-throw shots today. He made 15 baskets and missed 25. Find the ratio of baskets made to baskets attempted. Then write this number as a decimal and as a percent. Ratio: Decimal: Percent: 26 Perfection Learning No reproduction permitted.

17 12 Rory has 15 fiction books and 12 nonfiction books on her bookshelf in her room. Her mom has a bookshelf in the living room with the same ratio of fiction to nonfiction books. a. There are 81 books in all on the bookshelf in the living room. How many books are fiction? b. Find the percent of nonfiction books Rory and her mom have in all. Mastery Test 1 Show your work in the space below. Write your explanation on the lines provided. Answer: a. b. Explain in words how you got your answer and why you took the steps you did to solve the problem. Points Earned / Total Possible /15 Perfection Learning No reproduction permitted. 27

18 Teacher Guide Grade 7

19 For the Teacher The Review, Practice, and Mastery program is a refresher course. It provides a self-directed approach to reviewing and practicing the Illinois Mathematics Assessment Framework. Use the following steps to incorporate Review, Practice, and Mastery into your classroom. 1. Have students take the Tryout Test and check their answers. To provide practice in transferring answers to an answer sheet, you may wish to have students use the reproducible Student Information and Answer Sheets on pages of this teacher guide. Then have them use the reproducible Skills Chart on pages of this teacher guide to assess their strengths and weaknesses in the areas covered. (The chart below is also available in the student book.) 2. Have students work through the lessons, paying close attention to the areas in which they need improvement. You will see that each lesson page correlates to one or more of the skills on the Illinois Assessment Framework. Each lesson is followed by a Mastery Test that focuses on the skills covered in the lesson. 3. After completing all the lessons, have students take the Final Mastery Test. Reproducible Student Information and Answer Sheets are provided on pages of this teacher guide. On page 19 of this teacher guide is a rubric you can use to score the students extended-response answers. A reproducible student-friendly version is available on page 20. The chart that begins on page 29 of this teacher guide correlates the lessons in the student book to the Illinois Mathematics Assessment Framework. Lesson Tryout Test Items Final Mastery Test Items 1 Number Sense 1, 3, 7, 31, 32, 36, 39 1, 3, 7, 30, 32, 36, 39, 40, 46 2 Operations 3 Measurements 4 Algebra 10, 13, 17, 18, 21, 33, 35, 40, 10, 13, 17, 18, 21, 33, 35, 41, 44, 45, 60 60, 61 2, 11, 19, 34, 41, 47, 48, 58 2, 11, 19, 34, 42, 45, 47, 49, 57, 58 4, 5, 6, 20, 22, 37, 38, 42, 43, 4, 5, 6, 20, 22, 37, 38, 43, 44, 51, 59 50, 59 5 Geometry 6 8, 12, 14, 23, 26, 27, 28, 30, 8, 12, 14, 23, 24, 25, 27, 51, 46, 52, 53, 54, 57 52, 53, 54 Data Analysis, Statistics, 9, 15, 16, 24, 25, 29, 49, 50, 9, 15, 16, 26, 28, 29, 31, 48, and Probability 55, 56 55, 56, 62 2 Perfection Learning Review, Practice, and Mastery Illinois Mathematics Grade 7

20 Tryout Test, Part 1 Skills Chart Question Part Number Sense 2. Operations 3. Measurements 4. Algebra 5. Geometry 6. Data Analysis, Statistics, and Probability Subtotal, Part 1 /3 /5 /3 /6 /12 /6 /35 /2 /2 /4 Review, Practice, and Mastery Illinois Mathematics Grade 7 Perfection Learning 13

21 Tryout Test, Part 2 Skills Chart Question Part Subtotal, Part 2 1. Number Sense 2. Operations /4 3. Measurements 4. Algebra 5. Geometry 6. Data Analysis, Statistics, and Probability /4 /9 /5 /6 /6 /5 /35 /2 /2 14 Perfection Learning Review, Practice, and Mastery Illinois Mathematics Grade 7

22 Tryout Test, Total Skills Chart 1. Number Sense 2. Operations 3. Measurements 4. Algebra 5. Geometry 6. Data Analysis, Statistics, and Probability Subtotal, Part 1 /3 /5 /3 /6 /12 /6 Subtotal, Part 2 /4 /9 /5 /6 /6 /5 Total /7 /14 /8 /12 /18 /11 /70 Review, Practice, and Mastery Illinois Mathematics Grade 7 Perfection Learning 15

23 Illinois Assessment Framework Standards This chart matches the Illinois Assessment Framework Standards to the lessons in Review, Practice, and Mastery for Illinois Mathematics, Grade 7. Illinois Assessment Framework Standards Math Goal 6: Number Sense Lesson 1 Number Sense Lesson 2 Operations Read, write, and recognize equivalent representations of positive powers of Read, write, recognize, model, and interpret integers, including translating numerical expressions Recognize, translate between, and apply multiple representations of rational numbers (decimals, fractions, mixed numbers, and percents less than 100%) Represent repeated factors using exponents Order and compare integers, terminating decimals, fractions, and mixed numbers Identify and locate integers, decimals, and fractions/mixed numbers on a number line, and estimate the locations of square roots Solve problems involving descriptions of numbers, including characteristics and relationships (e.g., square numbers, prime/composite, prime factorization, greatest common factor, least common multiple) Solve problems and number sentences involving addition, subtraction, multiplication, and division using integers, fractions, and decimals Identify and apply order of operations to simplify numeric expressions involving whole numbers (including exponents), fractions, and decimals 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 Demonstrate and apply the relationships between addition/subtraction and multiplication/division with rational numbers Make estimates appropriate to a given situation, and analyze what effect the estimation method used has on the accuracy of results Estimate the square root of a number less than 1,000 between two whole numbers (e.g., 41 is between 6 and 7) Create and explain ratios that represent a given situation Use proportional reasoning to model and solve problems Read, write, recognize, model, and interpret percents from 0% to 100% 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 , sales tax, tips, interest, discounts). Review, Practice, and Mastery Illinois Mathematics Grade 7 Perfection Learning 29

24 Illinois Assessment Framework Standards Math Goal 7: Measurements Lesson 3 Measurements Select and use appropriate standard units and tools to measure length, mass/weight, capacity, and angles. Sketch, with given specifications, line segments, angles, triangles, and quadrilaterals 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) Compare and estimate length (including perimeter), area, volume, weight/ mass, and angles (0 to 180 ) using referents Determine the volume and surface area of a right rectangular prism using an appropriate formula or strategy Solve problems involving unit conversions within the same measurement system for length, weight/mass, capacity, and square units (e.g., 1 ft in. 2 ) Solve problems involving scale drawings and maps. Math Goal 8: Algebra Lesson 4 Algebra 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 Write an expression using variables to represent unknown quantities Simplify algebraic expressions by identifying and combining like terms Recognize equivalent forms of algebraic expressions Evaluate or simplify algebraic expressions with one or more integer variable values (e.g., a 2 b for a 3 and b 4) Determine how a change in one variable relates to a change in a second variable Represent linear equations and quantitative relationships on a rectangular coordinate system, and interpret the meaning of a specific part of a graph Translate between different representations (table, written, graphical, or pictorial) of whole number relationships and linear expressions Identify, graph, and interpret inequalities on a number line Represent and analyze problems with linear equations and inequalities Solve linear equations in one variable (e.g., 2x 3 13) and inequalities involving or (e.g., 2x 6, x 7 10) Solve word problems involving unknown quantities. 30 Perfection Learning Review, Practice, and Mastery Illinois Mathematics Grade 7

25 Illinois Assessment Framework Standards Illinois Math Goal 9: Geometry Lesson 5 Geometry 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 Solve problems involving two- and three-dimensional shapes Solve problems using properties of triangles and quadrilaterals (e.g., opposite sides of a parallelogram are congruent) Identify, describe, and determine the radius and diameter of a circle Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants) Represent and identify geometric figures using coordinate geometry Analyze the results of a combination of transformations Identify or analyze relationships of angles formed by intersecting lines Identify and sketch acute, right, and obtuse angles Solve problems involving complementary and supplementary angles Identify a three-dimensional object from its net Recognize which attributes (such as shape, perimeter, and area) change or don t change when plane figures are composed, decomposed, or rearranged Describe the difference between congruence and similarity Determine if figures are similar, and identify relationships between corresponding parts of similar figures Determine the distance between two points on a horizontal or vertical number line. Illinois Math Goal 10: Data Analysis, Statistics, and Probability Lesson 6 Data Analysis, Statistics, and Probability 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 Compare different representations of the same data Create a bar graph, chart/table, line graph, or circle graph for a given set of data Identify a reasonable approximation of the line of best fit from a set of data or a scatter plot Determine and use the mode, range, median, and mean to interpret data Solve problems involving the probability of a simple or compound event, including representing the probability as a fraction, decimal, or percent Represent all possible outcomes for simple events Solve simple problems involving the number of ways objects can be arranged (permutations and combinations). Review, Practice, and Mastery Illinois Mathematics Grade 7 Perfection Learning 31