Consultant: Lynn T. Havens. Director of Project CRISS Kalispell, Montana


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1 Teacher Annotated Edition Study Notebook Consultant: Lynn T. Havens SM Director of Project CRISS Kalispell, Montana i_sn_c1fmtwe_ indd i 3/16/09 9:17:03 PM
2 Copyright by The McGrawHill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher. Send all inquiries to: Glencoe/McGrawHill 8787 Orion Place Columbus, OH ISBN: MHID: Printed in the United States of America Math Connects, Course 1 Study Notebook, TAE
3 Contents Chapter 1 Multiply and Divide Decimals Before You Read... 1 Key Concepts... 2 Lesson 11 Multiply Decimals... 3 Lesson 12 Divide Decimals... 9 Lesson 13 Powers of Tie It Together Before the Test Chapter 2 Multiply and Divide Fractions Before You Read Key Concepts Lesson 21 Multiply Fractions and Whole Numbers Lesson 22 Multiply Fractions Lesson 23 Divide Fractions Tie It Together Before the Test Chapter 5 Fractions, Decimals, and Percents Before You Read Key Concepts Lesson 51 Fractions and Decimals Lesson 52 Percents Lesson 53 Compare and Order Fractions, Decimals, and Percents Lesson 54 Apply Percents Tie It Together Before the Test Chapter 6 Algebraic Expressions Before You Read Key Concepts Lesson 61 Write and Evaluate Expressions Lesson 62 Properties Tie It Together Before the Test Chapter 3 Data Analysis Before You Read Key Concepts Lesson 31 Measures of Central Tendency Lesson 32 Data Displays Tie It Together Before the Test Chapter 4 Ratios and Rates Before You Read Key Concepts Lesson 41 Ratios and Rates Lesson 42 Ratio Tables Lesson 43 Solve Ratio and Rate Problems Tie It Together Before the Test Chapter 7 Solve Equations Before You Read Key Concepts Lesson 71 Addition and Subtraction Equations Lesson 72 Multiplication and Division Equations Lesson 73 TwoStep Equations Tie It Together Before the Test Chapter 8 Functions and Inequalities Before You Read Key Concepts Lesson 81 Relations and Functions Lesson 82 Inequalities Tie It Together Before the Test iii
4 Chapter 9 Use Formulas in Geometry Before You Read Key Concepts Lesson 91 Area Lesson 92 Circles Lesson 93 Composite Figures Lesson 94 Volume Tie It Together Before the Test Chapter 10 Measurement: Volume and Surface Area Before You Read Key Concepts Lesson 101 Volume of Prisms and Pyramids Lesson 102 Volume of Cones and Cylinders Lesson 103 Surface Area of Three Dimensional Figures Lesson 104 ThreeDimensional Composite Figures Tie It Together Before the Test Chapter 11 Integers Before You Read Key Concepts Lesson 111 Integers and the Coordinate Plane Lesson 112 Add and Subtract Integers Lesson 113 Multiply and Divide Integers Tie It Together Before the Test Chapter 12 Operations with Rational Numbers Before You Read Key Concepts Lesson 121 Rational Numbers Lesson 122 Add and Subtract Rational Numbers Lesson 123 Multiply and Divide Rational Numbers Tie It Together Before the Test iv
5 NoteTaking Tips Your notes are a reminder of what you learned in class. Taking good notes can help you succeed in mathematics. The following tips will help you take better classroom notes. Before class, ask what your teacher will be discussing in class. Review mentally what you already know about the concept. Be an active listener. Focus on what your teacher is saying. Listen for important concepts. Pay attention to words, examples, and/or diagrams your teacher emphasizes. Write your notes as clear and concise as possible. The following symbols and abbreviations may be helpful in your notetaking. Word or Phrase Symbol or Abbreviation Word or Phrase Symbol or Abbreviation for example e.g. not equal such as i.e. approximately with w/ therefore without w/o versus vs and + angle Use a symbol such as a star ( ) or an asterisk ( ) to emphasize important concepts. Place a question mark (?) next to anything that you do not understand. Ask questions and participate in class discussion. Draw and label pictures or diagrams to help clarify a concept. When working out an example, write what you are doing to solve the problem next to each step. Be sure to use your own words. Review your notes as soon as possible after class. During this time, organize and summarize new concepts and clarify misunderstandings. NoteTaking Don ts Don t write every word. Concentrate on the main ideas and concepts. Don t use someone else s notes as they may not make sense. Don t doodle. It distracts from listening activity. Don t lose focus or you will become lost in your notetaking. v
6 About the Student Edition Study Notebook This notetaking guide is designed to help your students succeed in your mathematics class. Each chapter includes: Chapter 1 Before You Read Multiply and Divide Decimals Before you read the chapter, respond to these statements. 1. Write an A if you agree with the statement. 2. Write a D if you disagree with the statement. Multiply and Divide Decimals When rounding decimals, you refer to the digit to the left of the place that you are rounding. The number of decimal places in the product of two decimals is the sum of the number of decimal places in both factors. To check your answer to a division problem, multiply the dividend by the divisor. When dividing by decimals, you change the divisor into a whole number. Before You Read Chapter 1 The Chapter Opener contains strategies that are designed to help students learn and retain new concepts. Multiplying by a power of 10 greater than 1 moves the decimal place to the right. CRISSSM Project _SN_C1_C1_ indd 1 A summary frame can help you organize information and summarize the steps in a process. Skim a lesson and then set up a frame that you can complete as you go. You can use a summary frame to take notes and review. An example of a summary frame for estimating products is shown below. Decimal(s) Process Summarize Steps in Process or 28 Round 3.6; The digit to the right of 3 is > 5. So round up. Round 7.4; The digit to the right of 7 is < 5. So leave 7. Multiply whole numbers. Write the estimated product. Chapter 1 1 Math Connects, Course 1 A Key Points table helps students organize chapter topics as they preview upcoming lessons. 3/2/09 10:00:09 AM Chapter 1 Multiply and Divide Decimals Key Points Scan the pages in the chapter and write at least one specific fact concerning each lesson. For example, in the lesson on multiplying decimals by whole numbers, one fact is that the whole number represents the number of times the decimal is used as an addend. After completing the chapter, you can use this table to review for your chapter test. Lesson 11A Estimate Products 11B Explore: Multiply Decimals by Whole Numbers 11C Multiply Decimals by Whole Numbers 11D Explore: Multiply Decimals by Decimals 11E Multiply Decimals 12A Estimate Quotients 12B Explore: Divide Decimals by Whole Numbers 12C Divide Decimals by Whole Numbers 12D Explore: Divide by Decimals 12E Divide Decimals by Decimals 13A Multiply by Powers of B Divide by Powers of C ProblemSolving Investigation Fact Chapter 1 2 Math Connects, Course _SN_C1_C1_ indd 2 3/2/09 10:00:11 AM vi
7 11 A Estimate Products What You ll Learn Scan the text in Lesson 11A. Write two facts you learned about estimating products as you scanned the text Lesson 11 A Lessons cover the content of the lessons in the textbook, emphasizing Active Vocabulary. Active Vocabulary Review Vocabulary To estimate products of decimals, first round each number. (Prior Grade) _SN_C1_C1_ indd 3 Round to the nearest whole number: Round to the nearest ten: Round to the nearest hundred: ,309.1 Chapter 1 3 Math Connects, Course A Main Idea and Details features provide structures for students to focus on main ideas while providing 3/2/09 10:00:13 AM supporting details. continued Main Idea Estimate Products p. 27 Details Complete the following model to find the product of 8.2 and 6.5. Step 1: Round each decimal to the nearest whole number. Rewrite the multiplication problem Step 2: Find the product of the whole numbers to estimate Chapter 1 Multiply and Divide Decimals Tie It Together Show an example problem in each box below. Write any tips alongside each problem. Compute with Decimals Multiply Divide A Decimal by a Whole Number A Decimal by a Whole Number A Decimal by a Decimal A Decimal by a Decimal A Decimal by a Power of Ten A Decimal by a Power of Ten Chapter 1 x Estimate each product. Show your work Think of two decimals: one between 40 and 90 and one between 2 and 9. Round the first decimal to the nearest ten and round the second decimal to the nearest whole number. Multiply the rounded numbers to estimate the product of the decimals. Exchange your decimals with a partner and estimate your partner s product. Compare estimates. Chapter 1 4 Math Connects, Course _SN_C1_C1_ indd 4 Helping You Remember allows students to summarize main lesson ideas. Tie It Together and Before the Test summarize main chapter topics and provide guidance for students as they prepare for the Chapter Test. 3/2/09 10:00:14 AM Chapter 1 21 Math Connects, Course _SN_C1_C1_ indd 21 3/2/09 10:00:39 AM vii
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9 Chapter 1 Before You Read Multiply and Divide Decimals Chapter 1 Before you read the chapter, respond to these statements. 1. Write an A if you agree with the statement. 2. Write a D if you disagree with the statement. Multiply and Divide Decimals When rounding decimals, you refer to the digit to the left of the place that you are rounding. Before You Read See students work. The number of decimal places in the product of two decimals is the sum of the number of decimal places in both factors. To check your answer to a division problem, multiply the dividend by the divisor. When dividing by decimals, you change the divisor into a whole number. Multiplying by a power of 10 greater than 1 moves the decimal place to the right. CRISSSM Project A summary frame can help you organize information and summarize the steps in a process. Skim a lesson and then set up a frame that you can complete as you go. You can use a summary frame to take notes and review. An example of a summary frame for estimating products is shown below. Decimal(s) Process Summarize Steps in Process Round 3.6; The digit to the right of 3 is > 5. So round up. Round 7.4; The digit to the right of 7 is < 5. So leave or 28 Multiply whole numbers. Write the estimated product. Chapter 1 1 Math Connects, Course 1
10 Chapter 1 Multiply and Divide Decimals Key Points Scan the pages in the chapter and write at least one specific fact concerning each lesson. For example, in the lesson on multiplying decimals by whole numbers, one fact is that the whole number represents the number of times the decimal is used as an addend. After completing the chapter, you can use this table to review for your chapter test. Lesson Fact 11A Estimate Products See students work. 11B Explore: Multiply Decimals by Whole Numbers 11C Multiply Decimals by Whole Numbers 11D Explore: Multiply Decimals by Decimals 11E Multiply Decimals 12A Estimate Quotients 12B Explore: Divide Decimals by Whole Numbers 12C Divide Decimals by Whole Numbers 12D Explore: Divide by Decimals 12E Divide Decimals by Decimals 13A Multiply by Powers of B Divide by Powers of C ProblemSolving Investigation Chapter 1 2 Math Connects, Course 1
11 11 A Estimate Products What You ll Learn Scan the text in Lesson 11A. Write two facts you learned about estimating products as you scanned the text. 1. Sample answer: You can estimate products by rounding decimals to whole numbers and 2. multiplying. Sample answer: Estimating products is a skill that Lesson 11 A can be used to solve realworld problems. Active Vocabulary Review Vocabulary To estimate products of decimals, first round each number. (Prior Grade) Round to the nearest whole number: Round to the nearest ten: Round to the nearest hundred: , ,300 Chapter 1 3 Math Connects, Course 1
12 11 A continued Main Idea Estimate Products p. 27 Details Complete the following model to find the product of 8.2 and 6.5. Step 1: Round each decimal to the nearest whole number. Rewrite the multiplication problem Step 2: Find the product of the whole numbers to estimate Estimate each product. Show your work Think of two decimals: one between 40 and 90 and one between 2 and 9. Round the first decimal to the nearest ten and round the second decimal to the nearest whole number. Multiply the rounded numbers to estimate the product of the decimals. Exchange your decimals with a partner and estimate your partner s product. Compare estimates. Answers will vary. See students work. Sample answer: 47.7 and 5.3; 50 5 = 250 Chapter 1 4 Math Connects, Course 1
13 11 C Multiply Decimals by Whole Numbers What You ll Learn Scan Lesson 11C. List two headings you would use to make an outline of this lesson. 1. Sample answer: Multiply Decimals 2. Sample answer: Annex Zeros in the Product Active Vocabulary Review Vocabulary Match each term with its definition by drawing a line to connect the two. (Prior Grade) product an arithmetical operation involving repeated addition quotient an arithmetical operation involving repeated subtraction factor the result obtained by dividing multiplication the result obtained by multiplying division tenths place hundredths place thousands place whole number a number that is multiplied by another number Label the diagram with the correct terms. hundredths place whole number tenths place thousandths place Lesson 11 C Chapter 1 5 Math Connects, Course 1
14 11 C continued Main Idea Multiply Decimals pp Details Use the model to find the product of 5 and groups of 0.75 = 3.75 Fill in the blanks to find each product = = = = = = Describe the product you obtain when you multiply a whole number by another whole number. Is it greater or less than the factors? Then describe the product you obtain when you multiply a whole number by a decimal less than one. Provide examples to show your reasoning. Sample answer: The product of 2 whole numbers is usually greater than both factors. For example, 5 5 = 25. When one of the factors is 1, the product is equal to the other factor. For example, 5 1 = 5. The product of a whole number and decimal can be less than the whole number. For example, = and = 4.5. Chapter 1 6 Math Connects, Course 1
15 11 E Multiply Decimals What You ll Learn Scan the text in Lesson 11E. Write two facts you learned about multiplying decimals as you scanned the text. 1. Sample answer: You should estimate the answer first. 2. Sample answer: The number of places in the product is the sum of the number of places in the two factors. Lesson 11 E Active Vocabulary place value round Review Vocabulary Write the correct term next to each definition. (Prior Grade) the value of a digit depending on its place in a number to approximate a number to the nearest place value operation decimal arithmetical operations performed on numbers, including addition, subtraction, multiplication, and division number with one or more numbers to the right of a decimal point Vocabulary Link Give two examples of how decimals are used in everyday life. Sample answer: When buying something with money, the change is a decimal. Distance is often measured in tenths of a mile. Chapter 1 7 Math Connects, Course 1
16 11 E continued Main Idea Multiply Decimals pp Details Fill in the blanks with the number of decimal places in each product. 1. The product of has four decimal place(s). 2. The product of has five decimal place(s). 3. The product of has three decimal place(s). 4. The product of has one decimal place(s). Complete the following model showing how to find the product of 2.1 and = 6 Step 1: Estimate the product: Step 2: Multiply just as you would whole numbers Step 3: The product has three decimal places = Look at your estimate. Is the answer reasonable? yes How would you use the decimal model below to show ? Sample answer: Shade 0.3 lengthwise and 0.5 across. The product is 0.15 because each square is Chapter 1 8 Math Connects, Course 1
17 12 A Estimate Quotients What You ll Learn Skim Lesson 12A. Predict two things that you expect to learn about estimating quotients. 1. Sample answer: how to use compatible numbers to estimate quotients Active Vocabulary 2. Sample answer: how to solve realworld problems by estimating quotients New Vocabulary Write the definition next to the term. Lesson 12 A compatible numbers numbers that are easy to divide mentally Vocabulary Link Look up the word compatible in a dictionary or using the Internet. List one or two of the definitions that support the idea of compatible numbers. Explain how these definitions of the word compatible make sense in the context of compatible numbers. Sample answer: Compatible is an adjective meaning things that combine well or work well together. Compatible numbers such as 45 and 9 work well together because it is easy to divide 45 by 9. Chapter 1 9 Math Connects, Course 1
18 12 A continued Main Idea Compatible Numbers p. 44 Details For each pair of numbers, write two compatible numbers that could be used to divide mentally and and and 5 50 and and and and and 15 Estimate Quotients p. 44 Solve each problem. 1. Craig spent $59.52 on four DVDs. If he spent the same amount on each one, what is a reasonable estimate of the cost of each DVD? about $15 each 2. There are 29 students in Mrs. Lang s homeroom. The class collected 154 canned goods during a charity food drive. About how many canned goods were collected per student? about 5 per student Suppose a classmate is having difficulty estimating quotients with compatible numbers. Explain how you can use multiples of the divisor to help find compatible numbers. Sample answer: Compatible numbers are numbers that are easy to divide. So, begin by rounding the divisor to a whole number if necessary. Then round the dividend to a whole number that is a multiple of the divisor. Chapter 1 10 Math Connects, Course 1
19 12 C Divide Decimals by Whole Numbers What You ll Learn Skim Lesson 12C. Predict two things you expect to learn about dividing decimals by whole numbers. 1. Sample answer: how to divide decimals by whole numbers 2. Sample answer: where to place the decimal point Active Vocabulary Review Vocabulary Label the diagram with the correct terms. (Prior Grade) quotient dividend divisor 0.9 8)7.2 quotient divisor dividend Vocabulary Link Compare the quotient obtained when you divide a whole number by a whole number to the quotient obtained when you divide a decimal by a whole number. Can you find any exceptions to your observations? Sample answer: When you divide a whole number by a whole number, the quotient is always less than either the dividend or divisor. When you divide a decimal by a whole number, the same is true. The only exception Lesson 12 C is when the divisor is 1. Then the quotient is the same as the dividend. Chapter 1 11 Math Connects, Course 1
20 12 C continued Main Idea Divide a Decimal by a 1digit Number p. 51 Details Describe how you could use this model to find the quotient of Sample answer: To divide 2.1 by 7, separate 21 squares into 7 groups. There are 3 squares in each group, so 0.3 is the quotient. Divide a Decimal by a 2digit Number p. 52 Fill in the blanks to find each quotient = = = = = = 1.67 Explain how multiplying decimals by whole numbers is different than dividing decimals by whole numbers. Sample answer: When multiplying a decimal by a whole number, the product will have the same number of decimal places as the decimal factor. When dividing a decimal by a whole number, the number of decimal places can vary. For example, = 0.3 but = Chapter 1 12 Math Connects, Course 1
21 12 E Divide Decimals by Decimals What You ll Learn Skim the lesson. Write two things you already know about dividing decimals by decimals. 1. Sample answer: Sometimes you need to add zeros to line up place values. Active Vocabulary 2. Sample answer: You need to multiply the divisor by a power of 10 to make it a whole number. Review Vocabulary Write the definition next to each term. (Prior Grade) Lesson 12 E whole number estimate dividend a counting number or zero an approximation of a number the number that is being divided divisor quotient place value the number by which the dividend is divided the result of a division problem the value of a digit depending on its place in a number Vocabulary Link One example in which decimals are divided in everyday life is when using money. Write a realworld problem that involves the division of decimals. Make sure to explain how the problem can be solved. Sample answer: Roger has $5.95. He wants to buy some notebooks that cost $1.19 each. How many notebooks can he buy? Model with manipulatives, baseten blocks, or money. Make as many groups of 119 squares or $1.19 as possible. The answer is 5. Chapter 1 13 Math Connects, Course 1
22 12 E continued Main Idea Divide by Decimals pp Details Fill in the blanks with the power of ten by which you will multiply the divisor and dividend. Rewrite the problem in its new form. Then fill in the quotient. For , multiply the divisor and dividend by ) ) 0.16 Complete the following model to find the quotient of 5.67 and ) ) Describe how to divide a decimal by a decimal. Sample answer: Multiply the divisor by a power of ten. If the divisor is to hundredths, multiply by 100. If it is to tenths, multiply by 10. Next, multiply the dividend by the same power of ten. Then divide. Chapter 1 14 Math Connects, Course 1
23 13 A Multiply by Powers of 10 What You ll Learn Skim the lesson. Write two things you already know about multiplying by powers of ten. 1. Sample answer: When you multiply a decimal by a power of 10 greater than 1, you move the decimal 2. point to the right. Sample answer: Multiplying a decimal by a power Lesson 13 A of 10 less than 1 moves the decimal point to the left. Active Vocabulary Review Vocabulary Fill in the blank with the correct term or phrase. (Lesson 12A) compatible numbers Compatible numbers are numbers that are easy to divide mentally. Fill in the blanks with the number of and the direction to move the decimal point in each product place(s) to the place(s) to the place(s) to the place(s) to the right right left left Chapter 1 15 Math Connects, Course 1
24 13 A continued Main Idea Multiply by Powers of 10 pp Complete the table. Details Multiply by Powers of Ten Decimal Power of 10 Product , ,000 23,100 Find each product , Explain in your own words how to multiply a decimal by a power of 10 that is greater than 1. Give an example. Answers will vary. Sample answer: Count the number of zeros in the power of ten. Then move the decimal point that many places to the right. For example, to multiply 6.25 by 1,000, move the decimal point 3 places to the right. The product is 6,250. Chapter 1 16 Math Connects, Course 1
25 13 B Divide by Powers of 10 What You ll Learn Skim the Examples for Lesson 13B. Predict two things you think you will learn about dividing by powers of Sample answer: how to divide decimals by powers of ten that are greater than 1 2. Sample answer: how to divide decimals by powers of ten that are less than 1 Active Vocabulary Review Vocabulary Match each number in the lefthand column with a compatible number in the righthand column by drawing a line to connect the two. (Lesson 12A) Lesson 13 B compatible numbers Fill in the blanks with the number of places and the direction to move the decimal in each quotient , place(s) to the place(s) to the left right place(s) to the left Chapter 1 17 Math Connects, Course 1
26 13 B continued Main Idea Divide by Powers of Ten pp Complete the table. Details Divide by Powers of Ten Decimal Power of 10 Quotient , , , Find each quotient Compare and contrast the process of multiplying by powers of 10 with the process of dividing by powers of 10. Give an example. Answers will vary. Sample answer: In both cases, you move the decimal point of the number to the left or right depending on the power of 10. When multiplying by a power of 10, you move the decimal point to the right when the power is greater than 1 and to the left when the power is less than 1. The opposite is true for dividing by powers of 10. Chapter 1 18 Math Connects, Course 1
27 13 C ProblemSolving Investigation Use the fourstep problemsolving plan to solve Exercise 3 on page 73. Use the determine a reasonable answer strategy. CLOTHES Annie wants to buy 2 pairs of capris for $34.99 each and 3 pairs of flipflops for $7.99 each. Does she need to save $100 or $150? UNDERSTAND Read the problem. What are you being asked to find? I need to determine if $100 or $150 the 2 pairs of capris and 3 pairs of flipsflops. is enough to buy Underline key words and values. What information do you know? Annie wants to buy 2 pairs of capris at $ pairs of flipflops at $7.99 each. each and Is there any information that you do not need to know? I do not need to know exactly what she is buying PLAN Choose a problemsolving strategy. I will use the determine a reasonable answer. strategy. SOLVE Use your problemsolving strategy to solve the problem. The cost of one pair of capris is about $35 and the cost of one pair of flipflops is about $ = $70 and 3 8 = $24; $70 + $24 = $94. So, $100 is enough for Annie to buy the capris and flipflops. CHECK Use information from the problem to check your answer. $ = $69.98 and $ = $23.97 $ $23.97 = $ $93.98 < $100, so Annie needs to save $100. Lesson 13 C Chapter 1 19 Math Connects, Course 1
28 13 C continued FourStep ProblemSolving Plan UNDERSTAND Read the problem. What are you being asked to find? Underline key words and values. What information do you know? Is there any information that you do not need to know? PLAN Choose a problemsolving strategy. SOLVE Use your problemsolving strategy to solve the problem. CHECK Use information from the problem to check your answer. Use the fourstep problemsolving plan to solve the following problem. SCHOOL At one middle school there are 8 seventhgrade classes. If each classroom has an average of 28 students, is a reasonable estimate of seventh graders closer to 200 or 230? 230 UNDERSTAND I need to find if 200 students or 230 students is a more reasonable estimate of the number of seventh graders. There is an average of 28 students in 8 classrooms. There is no unnecessary information. PLAN I will use mental math to determine a reasonable answer. SOLVE Because 28 is closer to 30, I can estimate by multiplying 30 times = is closer to 230 than to 200. CHECK I will check by finding the exact product = is closer to 230 than to 200. Chapter 1 20 Math Connects, Course 1
29 Chapter 1 Tie It Together Multiply and Divide Decimals Show an example problem in each box below. Write any tips alongside each problem. Chapter x 1 Compute with Decimals Multiply Divide A Decimal by a Whole Number See students work. Sample product: A Decimal by a Whole Number See students work. Sample quotient: A Decimal by a Decimal See students work. Sample product: A Decimal by a Power of Ten See students work. Sample product: A Decimal by a Decimal See students work. Sample quotient: A Decimal by a Power of Ten See students work. Sample quotient: Chapter 1 21 Math Connects, Course 1
30 Chapter 1 Multiply and Divide Decimals Before the Test Now that you have read and worked through the chapter, think about what you have learned and complete the table below. Compare your previous answers with these. 1. Write an A if you agree with the statement. 2. Write a D if you disagree with the statement. Multiply and Divide Decimals After You Read When rounding decimals, you refer to the digit to the left of the place that you are rounding. The number of decimal places in the product of two decimals is the sum of the number of decimal places in both factors. To check your answer to a division problem, multiply the dividend by the divisor. When dividing by decimals, you change the divisor into a whole number. D A D A Multiplying by a power of 10 greater than 1 moves the decimal place to the right. Visit glencoe.com to access your textbook, more examples, selfcheck quizzes, personal tutors, and practice tests to help you study concepts in Chapter 1. Are You Ready for the Chapter Test? Use this checklist to help you study. I used my Foldable to complete the review of all or most lessons. I completed the Chapter 1 Study Guide and Review in the textbook. I took the Chapter 1 Practice Test in the textbook. I used the online resources for additional review options. I reviewed my homework assignments and made corrections to incorrect problems. I reviewed all vocabulary and definitions from the chapter. A Study Tips Work with a study buddy. Review the concepts that you learned in class with a partner or small group. Discussing, rephrasing, and explaining new concepts will help both your understanding and recollection. Chapter 1 22 Math Connects, Course 1
31 Chapter 2 Before You Read Multiply and Divide Fractions Before you read the chapter, respond to these statements. 1. Write an A if you agree with the statement. 2. Write a D if you disagree with the statement. Chapter 2 Multiply and Divide Fractions Before You Read An addition sentence for is A whole number can be written as a fraction with a denominator of 1. To multiply two fractions, multiply only the denominators. When you multiply mixed numbers, multiply the whole numbers together and then multiply the fractions. Any two numbers with a sum of 1 are called reciprocals. To divide by a fraction, multiply by its reciprocal. CRISSSM Project Writing about a process in letter form to a classmate who was absent that day will help your understanding of a concept. Use your own words and practice writing the explanation until you do not have to refer to your textbook. An example of a letter about dividing whole numbers by fractions is shown below. Dear Katie, Today we learned about dividing whole numbers by fractions. To divide a whole number by a fraction, all you have to do is multiply the whole number by the reciprocal. The reciprocal of a number is easy to find because the product of a number and its reciprocal is one! So, the reciprocal of 3 4 is 4 3 because = 1. Here is an example: = = 16 3 or Sincerely, Yolanda Chapter 2 23 Math Connects, Course 1
32 Chapter 2 Multiply and Divide Fractions Key Points Scan the pages in the chapter and write at least one specific fact concerning each lesson. For example, in the lesson on dividing whole numbers by fractions, one fact is that to divide a whole number by a fraction, you multiply by its reciprocal. After completing the chapter, you can use this table to review for your chapter test. Lesson Fact 21A Explore: Part of a Number See students work. 21B Estimate Products of Fractions 21C Explore: Multiply Fractions and Whole Numbers 21D Multiply Fractions and Whole Numbers 21E ProblemSolving Investigation 22A Explore: Multiply Fractions 22B Multiply Fractions 22C Explore: Multiply Whole Numbers by Mixed Numbers 22D Multiply Mixed Numbers 23A Explore: Divide by Fractions 23B Divide Whole Numbers by Fractions 23C Explore: Divide Fractions 23D Divide Fractions 23E Divide Mixed Numbers Chapter 2 24 Math Connects, Course 1
33 21 B Estimate Products of Fractions What You ll Learn Scan Lesson 21B. List two headings you would use to make an outline of this lesson. 1. Sample answer: Estimate Products of Fractions Using Compatible Numbers 2. Sample answer: Estimate Products of Fractions Using Rounding Active Vocabulary New Vocabulary Round each fraction to 0, 1, or 1. Use the 2 number line to help you Lesson 21 B Chapter 2 25 Math Connects, Course 1
34 21 B continued Main Idea Estimate Using Compatible Numbers p. 90 Details Estimate 1 14 using compatible numbers. Sketch 3 a bar diagram in the space below. Sample model provided Estimate Using Rounding p. 91 Estimate each product Compare and contrast estimating products of fractions using compatible numbers and using rounding. Sample answer: Both methods use rounding to make finding a product easier to compute. With compatible numbers, you round to two numbers that are easy to divide mentally. With rounding, you round the fractions and compute the product. Chapter 2 26 Math Connects, Course 1
35 21 D Multiply Fractions and Whole Numbers What You ll Learn Skim the lesson. Write two things you already know about multiplying fractions and whole numbers. 1. Sample answer: When multiplying a fraction and a whole number, write the whole number as a fraction and multiply the numerators and denominators. 2. Sample answer: You can use bar diagrams to help you multiply fractions and whole numbers. Active Vocabulary Review Vocabulary Write each mixed number as an improper fraction, or each whole number as a fraction. (Prior Grade) Lesson 21 D Chapter 2 27 Math Connects, Course 1
36 21 D continued Main Idea Multiply Fractions and Whole Numbers pp Details Model 3 5 by shading the appropriate rectangles in 4 the figure below. Then, find the product. Sample model provided = 15 4 = Multiply. Write in simplest form = = In your own words, describe how to multiply a fraction and a whole number. Explain how you would find the product Sample answer: Write the whole number as a fraction. In this case, 3 = 3 1. Next, multiply the numerators and the denominators. Then, simplify The product is 6 5 or Chapter 2 28 Math Connects, Course 1
37 21 E ProblemSolving Investigation Use the fourstep problemsolving plan to solve Exercise 2 on page 101. Use the draw a diagram strategy. COLLECTIONS Jeremy has 3 as many 5 baseball cards as Ria. If Jeremy has 24 baseball cards, how many baseball cards do they have in all? 24 Jeremy Ria? UNDERSTAND Read the problem. What are you being asked to find? how many baseball cards Jeremy and Ria have in all I need to find Underline key words and values. What information do you know? 3 5 Jeremy has as many baseball cards as Ria. Jeremy has 24 baseball cards.. Lesson 21 E Is there any information that you do not need to know? I do not need to know what kinds of cards they have. PLAN Choose a problemsolving strategy. I will use the draw a diagram strategy. SOLVE Use your problemsolving strategy to solve the problem. Draw a bar diagram and divide it into fifths. This is Ria s card collection. Make another bar diagram like the first. Shade three fifths. The shaded fifths represent Jeremy s 24 baseball cards. threefifths = = 8, so each part is 8 cards. Ria 24 Ria has in all are 5 8 = So, Jeremy and Ria have CHECK cards and Jeremy has 24 = cards in all. 24 cards Use information from the problem to check your answer. Threefifths of 40 is 24.. The total cards Chapter 2 29 Math Connects, Course 1
38 21 E continued FourStep ProblemSolving Plan UNDERSTAND Read the problem. What are you being asked to find? Underline key words and values. What information do you know? Is there any information that you do not need to know? PLAN Choose a problemsolving strategy. SOLVE Use your problemsolving strategy to solve the problem. CHECK Use information from the problem to check your answer. Use the fourstep problemsolving plan to solve the following problem. LANDSCAPING Melissa wants to plant trees in her rectangular backyard which measures 50 feet by 30 feet. Each tree requires a 10foot by 10foot area. What is the maximum number of trees that she can plant? 15 UNDERSTAND I need to determine how many trees will fit in a 50foot by 30foot area. The trees require a 10foot by 10foot area. I do not know need to know that the area is a backyard or what is being planted. PLAN I will draw a diagram that shows the area available and see how many will fit. SOLVE Use your problemsolving strategy to solve the problem. 50 ft ft So, a maximum of 15 trees can be planted. Because each tree requires a 100 square foot area, divide the back yard into 10foot by 10foot squares. CHECK Use information from the problem to check your answer. The area of the yard is = 1,500 square feet; the area needed for one tree is 100 square feet. 1, = 15; your answer is correct. Chapter 2 30 Math Connects, Course 1
39 22 B Multiply Fractions What You ll Learn Skim the Examples for Lesson 22B. Predict two things you think you will learn about multiplying fractions. 1. Sample answer: how to multiply fractions 2. Sample answer: how to solve realworld problems that involve multiplying fractions Active Vocabulary New Vocabulary Label each model with a fraction in simplest form. Vocabulary Link Give a reallife example of when you might need to multiply fractions. Sample answer: Your brother eats 1 4 of 2 of a pizza. 3 How much pizza did he eat? = 2 12 = Lesson 22 B Chapter 2 31 Math Connects, Course 1
40 22 B continued Main Idea Multiply Fractions pp Details Complete the model below to show = 3 20 Multiply. Write in simplest form Work with a partner. Look at each example on pages 104 and 105 in your textbook. Use a piece of paper to cover up the words that are beside the equations. Explain to your partner in your own words what is happening in each step. Then uncover the words and check your answers. See students work Chapter 2 32 Math Connects, Course 1
41 22 D Multiply Mixed Numbers What You ll Learn Skim Lesson 22D. Predict two things that you expect to learn about multiplying mixed numbers. 1. Sample answer: how to multiply mixed numbers by writing them as improper fractions 2. Sample answer: how to solve realworld problems that involve multiplying mixed numbers Active Vocabulary Review Vocabulary Write each mixed number as an improper fraction. (Prior Grade) Lesson 22 D Chapter 2 33 Math Connects, Course 1
42 22 D continued Main Idea Multiply Mixed Numbers pp Details Follow the steps below to find Step 1: Write both mixed numbers as improper fractions Step 2: Divide out any common factors to simplify before multiplying = Step 3: Multiply the numerators and denominators. Then simplify Multiply. Write in simplest form = or Describe the steps to multiply mixed numbers. Exchange descriptions with a partner. Follow your partner s explanation. Discuss and clarify the steps if needed. Answers will vary. Sample answer: Write all mixed numbers as improper fractions. Then multiply the numerators and denominators. Simplify the product. Chapter 2 34 Math Connects, Course 1
43 23 B Divide Whole Numbers by Fractions What You ll Learn Scan the text in Lesson 23B. Write two facts you learned about dividing whole numbers by fractions as you scanned the text. 1. Sample answer: Two numbers that have a product of 1 are called reciprocals. 2. Sample answer: To divide a whole number by a fraction, multiply by the reciprocal of the fraction. Active Vocabulary New Vocabulary Write the definition next to the term. reciprocals two numbers that have a product of 1 Match each number with its reciprocal by drawing a line to connect the two Lesson 23 B 7 3 Chapter 2 35 Math Connects, Course 1
44 23 B continued Reciprocals p. 118 Main Idea Details Write the reciprocal of each number Divide by a Fraction p. 119 Divide. Write in simplest form Explain to a friend who missed class how to divide a whole number by a fraction. List the steps involved, and show how you would find Sample answer: Write the whole number as a fraction. Then multiply by the reciprocal of the divisor. So can be rewritten as The quotient 3 is 20 3 or Chapter 2 36 Math Connects, Course 1
45 23 D Divide Fractions What You ll Learn Skim the lesson. Write two things you already know about dividing fractions. 1. Sample answer: Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction. 2. Sample answer: You can use multiplication to check your answer to a division problem involving fractions. Active Vocabulary Review Vocabulary Fill in the blank with the correct term or phrase. (Lesson 23B) reciprocals Any two numbers with a reciprocals. product of 1 Write the reciprocal of each number are called Lesson 23 D Chapter 2 37 Math Connects, Course 1
46 23 D continued Main Idea Divide Fractions pp Details Complete the table below illustrating how to divide fractions. Divide Fractions Words To divide by a fraction, multiply by its reciprocal. Example = Algebra a b c d = a b d c Divide. Write in simplest form Explain how you can use multiplication to check your result when you divide a fraction by a fraction. Find the quotient Show your work. Sample answer: Multiply the quotient by the divisor of the problem. The result should be the dividend ; = 5 18 ; Check: = Chapter 2 38 Math Connects, Course 1
47 23 E Divide Mixed Numbers What You ll Learn Skim the Examples for Lesson 23E. Predict two things you think you will learn about dividing mixed numbers. 1. Sample answer: The first step in dividing mixed numbers is to write the mixed numbers as improper 2. fractions. Sample answer: Once the divisor is written as an improper fraction, multiply the dividend by the Lesson 23 E reciprocal of the divisor. Active Vocabulary Review Vocabulary Write each mixed number as an improper fraction. Then find the reciprocal. (Lesson 23B) Improper Fraction Reciprocal Chapter 2 39 Math Connects, Course 1
48 23 E continued Main Idea Divide Mixed Numbers pp Details Follow the steps below to find Step 1: Write both mixed numbers as improper fractions Step 2: Rewrite the problem by multiplying by the reciprocal of the divisor = Step 3: Multiply the numerators and denominators. Simplify = Divide. Write in simplest form = Give an example of a reallife problem that could be represented by the expression, Then find the quotient. 4 Sample answer: Mr. Smith has 8 3 planks of wood to make shelves. If each 4 shelf requires planks, how many shelves can he make? = 7; 7 shelves or Chapter 2 40 Math Connects, Course 1
49 Chapter 2 Tie It Together Multiply and Divide Fractions Show an example problem in each box below. Write any tips alongside each problem. Chapter x 2 Computate with Fractions Multiply Divide A Fraction by a Whole Number Sample product: = 3 5 See students examples and work. A Whole Number by a Fraction Sample quotient: = 32 See students examples and work. A Fraction by a Fraction Sample product: = 2 5 See students examples and work. A Mixed Number by a Mixed Number Sample product: = See students examples and work. A Fraction by a Fraction Sample quotient: = See students examples and work. A Mixed Number by a Mixed Number Sample product: = See students examples and work. Chapter 2 41 Math Connects, Course 1
50 Chapter 2 Multiply and Divide Fractions Before the Test Now that you have read and worked through the chapter, think about what you have learned and complete the table below. Compare your previous answers with these. 1. Write an A if you agree with the statement. 2. Write a D if you disagree with the statement. Multiply and Divide Fractions After You Read An addition sentence for is A A whole number can be written as a fraction with a denominator of 1. A To multiply two fractions, multiply only the denominators. When you multiply mixed numbers, multiply the whole numbers together and then multiply the fractions. Any two numbers with a sum of 1 are called reciprocals. D D D To divide by a fraction, multiply by its reciprocal. Visit glencoe.com to access your textbook, more examples, selfcheck quizzes, personal tutors, and practice tests to help you study concepts in Chapter 2. Are You Ready for the Chapter Test? Use this checklist to help you study. I used my Foldable to complete the review of all or most lessons. I completed the Chapter 2 Study Guide and Review in the textbook. I took the Chapter 2 Practice Test in the textbook. I used the online resources for additional review options. I reviewed my homework assignments and made corrections to incorrect problems. I reviewed all vocabulary and definitions from the chapter. A Study Tips Use flash cards. Write a definition, concept, or problem on one side of an index card and the definition or solution on the other. Use flashcards to review your notes. Chapter 2 42 Math Connects, Course 1
51 Chapter 3 Before You Read Data Analysis Before you read the chapter, think about what you know about the topic. List three things you already know about data analysis in the first column. Then list three things you would like to learn about it in the second column. Chapter 3 K What I know W What I want to find out See students work. CRISSSM Project A way to test yourself to see how much you have learned about a concept is to do a quick write. A quick write is when you write down as much as you know about something. It is quick because it is timed; you only allow yourself 5 minutes or less to write as much as you can. Here is what a quick write on the Lesson 31D topics of median, mode, and range might look like. The median of a set of data is the middle number. To find the median of a set of data with an odd number of terms, put the numbers in order and the middle term is the median. If the number of terms is even, put the numbers in order and average the two middle numbers. Mode is the most often occurring number; there can be more than one mode or no mode at all. Range is the difference between the greatest and least value... it is not a measure of central tendency but a measure of variability or the distribution of the data... After you complete a quick write, look through your text and notes to make sure that what you wrote down was correct. Add details or examples and anything important you forgot. Chapter 3 43 Math Connects, Course 1
52 Chapter 3 Data Analysis Key Points Scan the pages in the chapter and write at least one specific fact concerning each lesson. For example, in the lesson on frequency tables, one fact might be that relative frequency is expressed as a fraction or a decimal. After completing the chapter, you can use this table to review for your chapter test. Lesson Fact 31A Explore: Find the Mean See students work. 31B Mean 31C Extend: Spreadsheets and Mean 31D Median, Mode, and Range 31E Extend: Mean, Median, and Mode 31F Appropriate Measures 32A ProblemSolving Investigation 32B Frequency Tables 32C Extend: Change Intervals 32D Line Plots 32E Select an Appropriate Display 32F Extend: Collect Data to Solve a Problem Chapter 3 44 Math Connects, Course 1
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