GRADE 5 SUPPLEMENT

1 GRADE 5 SUPPLEMENTSet A11 Number & Operations: Multiplying & Dividing DecimalsIncludes HActivity 1: Multiplying by Powers of Ten HActivity 2: Dividing by Powers of Ten HActivity 3: Using Decimals to Calculate Sale Prices HActivity 4: Multiplying Decimals HActivity 5: Building a Deck, Using Partial Products & Arrays for Decimal Multiplication HActivity 6: Multiplying Decimals, More/Less HActivity 7: Dividing Decimals with Money & Menus HActivity 8: Using Models & Strategies to Divide with Decimals HIndependent Worksheet 1: Thinking about Tenths, Hundredths & Thousandths HIndependent Worksheet 2: Very Large & Very Small Numbers in Context HIndependent Worksheet 3: Multiplying & Dividing by Powers of Ten HIndependent Worksheet 4: Using Landmark Fractions & Percents to multiply by Decimals HIndependent Worksheet 5: Multiplying Two Decimal Numbers HIndependent Worksheet 6: Comparing & Multiplying Fractions & Decimals HIndependent Worksheet 7: Olympic Swimmers HIndependent Worksheet 8: Olympic Track Star Skills & Concepts Hround numbers to the nearest , , and Hmultiply and divide by powers of 10, including , , 1, 10, 100, and 1,000 Hmultiply whole numbers and decimal numbers by decimal numbers Happly fraction, decimal, and percent equivalencies to solve problems Hdescribe the effect of place value when multiplying whole numbers and decimals Hmultiply decimal using concrete models, drawing and strategies Hestimate solutions to arithmetic problems in order to assess reasonableness of results Hdivide decimals using concrete models or drawings and strategies based on place value, properties of operations.

2 Hrelate the strategy to a written method and explain the reasoning in Mathematics GRADE 5 SupplementSet A11 Number & Operations: Multiplying & Dividing DecimalsThe Math Learning Center, PO Box 12929, Salem, Oregon 97309. Tel. 1 800 575 8130. 2013 by The Math Learning Center All rights for publication on Macintosh Desktop Publishing in the United States of Math Learning Center grants permission to classroom teachers to reproduce blackline masters in appropriate quantities for their classroom in Mathematics is a standards-based K 5 curriculum that provides a unique blend of concept development and skills practice in the context of problem solving. It incorpo-rates the Number Corner, a collection of daily skill-building activities for Math Learning Center is a nonprofit organization serving the education community. Our mission is to inspire and enable individuals to discover and develop their mathematical confidence and ability.

3 We offer innovative and standards-based professional development, curriculum, materials, and resources to support learning and teaching. To find out more, visit us at A11 Number & Operations: Multiplying & Dividing Decimals The Math Learning Center Bridges in Mathematics GRADE 5 SUPPLEMENT Set A11 H Activity 1 ACTIVITYM ultiplying by Powers of TenOverviewStudents complete a string of calculations with fractions and decimals and then discuss the relationships among those calculations to build greater computational fluency and a stronger number sense with decimals. Then they explore what happens, and why, when they multiply by powers of 10 ( , , 1, 10, etc.).Skills & Concepts Hmultiply by powers of 10, including , , 1, 10, 100, and 1,000 Hdescribe the effect of place value when multiplying whole numbers and decimals by , , 1, 10, 100, and 1,000 Happly fraction and decimal equivalencies to solve problemsYou ll need HPatterns in Multiplying by Powers of Ten (pages and , run 1 copy for display, plus a class set) HMultiplying by Powers of Ten Practice (page , run 1 copy for display, plus a class set) Hbase ten pieces for each pair of students, plus a set for display HGreat Wall of Base Ten saved from Unit SixAdvance Preparation Try to find some copies of Bridges Student Book pages 160 and 161, Fraction & Deci-mal Equivalents, which students completed in Unit Six, Session 10.

4 You might also fill in Display Master , Frac-tion & Decimal Equivalencies, which you used in Session 12. Both of these resources may jog students memory of the fraction equivalents of common decimals in steps 1 and 3 for Multiplying by Powers of Ten1. Explain to students that they re going to be multiplying decimal numbers in the next few days and that they ll begin with powers of 10, like , 10, and 100. Write the following problems one at a time where students can see them (answers included in parentheses for your reference). Ask students to work in pairs for a minute or two to solve one problem at a time, and then have students share their an-swers and strategies as a whole group. 1 2 10 (5) 10 (5) 1 4 10 ( ) 10 ( ) 10 ( 7. 5 )When they have solved all five problems, ask students to discuss the relationships they noticed among the problems. Students are likely to note equivalencies between 1 2 and , and between 1 4 and They may also have noticed that they could halve half of 10 to find one-fourth of 10, and that three-fourths ( ) is three times one-fourth.

5 They might also notice that when multiplying a decimal num-ber by 10, you move the decimal point one place to the right ( , 10 = ).Set A11 Number & Operations: Multiplying & Dividing Bridges in Mathematics GRADE 5 SUPPLEMENT The Math Learning CenterDescribing the relationships among the problems should help students begin to develop efficient strate-gies for computing with decimal numbers. Students will solve similar sets of problems at the beginning of each activity in this Place Patterns in Multiplying by Powers of Ten on display and give each student a copy. Review the sheet with the class. Discuss the sample equations in each table and have students connect the elements of each equation to the problem situation. Also be sure students remember how to write each decimal ( and ) as a fraction. Invite them to refer to Bridges Student Book pages 160 and 161, Fraction and Decimal Equivalents, or a filled in copy of Display Master , Fraction and Decimal Equivalencies, if you were able to retrieve these resources from Unit DATE Set A11 Number & Operations: Mu t p ying & Div ding Dec ma s Blackl ne Run 1 copy for d sp ay, plus a class set Patterns in Multiplying by Powers of Ten, page 1 of 2 1a The post office sells one-cent stamps.

6 Fill out the table below to show how much it would cost to buy different quantities of one-cent of StampsDecimal EquationFraction EquationTotal Cost1 stamp1 = 1/100 = 1/100$ stamps2 = 2/100 = 2/100$ stamps20 stamps45 stamps321 stamps404 stampsb What do you notice about multiplying by 3. Give students time to complete the sheet in pairs. Then reconvene the class as a whole group and open the discussion by asking what they noticed about multiplying by , , and 10. Discuss each multiplier one at a time, and encourage students to explain why the patterns they see ( , When you multiply by , the decimal point moves two places to the left ) make sense. Encourage students to re-fer to the Great Wall of Base Ten and to use the base ten pieces to explain the patterns they see.

7 Remem-ber that when modeling decimals, the mat represents 1, the strip , and the unit I saw when you multiply a number by , like in the first problem, you can just move the decimal point two places to the left like this. It works every = becomes Why does it work? Can you use the Great Wall of Base Ten or these base ten pieces to explain?Josie Well, 45 times one-hundredth is 45 hundredths. 40 hundredths is the same as four-tenths. That s the .4 part of the answer. And 5 hundredths is just 5 hundredths. So it s like each part of the first number gets a hundred times smaller: 40 becomes four-tenths and 5 becomes five-hundredths. Or you could just think 45 hundredths, really. That s a hundred times smaller than 1 Multiplying by Powers of Ten (cont.)Set A11 Number & Operations: Multiplying & Dividing Decimals The Math Learning Center Bridges in Mathematics GRADE 5 SUPPLEMENT 40 hundredths is 4 tenths5 hundredths is just 5 hundredths4.

8 After students have discussed the patterns that emerged when multiplying by , , and 10, give each student a copy of Multiplying by Powers of Ten Practice. Explain that they ll complete it indepen-dently, and then select a couple of problems from the sheet to do together before asking students to work on their If students finish early, ask them to turn their papers over and write problems for each other in this form:45 _____ = 45 _____ = 4,500 45 _____ = Then they can trade papers and fill in the missing powers of 10 in each equation. Clarify the term power of ten using the Great Wall of Base Ten, and introduce exponent notation. A power of ten is a number resulting from multiplying 10 by itself any number of times. We use expo-nents to show how many times a number, in this case 10, is multiplied by itself. A negative exponent indicates a number less than 1 (a fraction or a decimal).

9 1000 = 103 100 = 102 10 = 101 1 = 100 = 10 1 = 10 2 Actvity 1 Multiplying by Powers of Ten (cont.) Bridges in Mathematics GRADE 5 SUPPLEMENT The Math Learning CenterNAME DATESet A11 Number & Operations: Multiplying & Dividing Decimals Blackline Run 1 copy for display, plus a class set. Patterns in Multiplying by Powers of Ten, page 1 of 21a The post office sells one-cent stamps. Fill out the table below to show how much it would cost to buy different quantities of one-cent of StampsDecimal EquationFraction EquationTotal Cost1 stamp1 = 1 100 = 1 100$ stamps2 = 1 100 = 2 100$ st a mps20 stamps45 stamps321 stamps404 stampsb What do you notice about multiplying by Amelia feeds her pet lizard crickets. The pet store sells crickets for ten cents each. Fill out the table below to show how much it would cost to buy different quantities of of CricketsDecimal EquationFraction EquationTotal Cost1 cricket1 = 1 10 = 1 10$ crickets2 = 1 10 = 2 10$ cr icket s20 crickets(Continued on next page.)

10 The Math Learning Center Bridges in Mathematics GRADE 5 SUPPLEMENT NAME DATESet A11 Number & Operations: Multiplying & Dividing Decimals Blackline Run 1 copy for display, plus a class set. Number of CricketsDecimal EquationFraction EquationTotal Cost45 crickets321 crickets404 cricketsb What do you notice about multiplying by Alfonso s company sells T-shirts to soccer teams. Each T-shirt costs ten dol-lars. Fill out the table below to show how much it would cost to buy different quantities of of ShirtsEquationTotal Cost1 shirt1 10 = 10$102 shirts2 10 = 20$2010 shirts20 shirts45 shirts321 shirts404 shirtsb What do you notice about multiplying by 10?2a (cont.)Patterns in Multiplying by Powers of Ten, page 2 of 2 (cont.) Bridges in Mathematics GRADE 5 SUPPLEMENT The Math Learning CenterNAME DATESet A11 Number & Operations: Multiplying & Dividing Decimals Blackline Run 1 copy for display, plus a class by Powers of Ten PracticeComplete the following = _____ 47 = _____ 3 = = _____ = _____ = _____10 = _____452 = _____ 302 = _____ 64 = _____ = _____ = _____ = = _____360 10 = _____ 23 10 = _____ 4 10 = _____ 10 = _____ 10 = _____ 10 = _____ 100 = _____ 100 = _____ 4 100 = _____ 45 100 = _____ 309 100 = _____ 100 = _____ 1,000 = _____ 1,000 = _____ 1,000 = _____ 603 1,000 = _____ 1,000 = _____Set A11 Number & Operations.