Multiplying Decimals Using Models Alignment Lesson Day 56

Objectives for Today’s Lesson Students will be able to: discuss how to use base ten blocks to multiply a decimal by a whole number with a partner. explain how to use base ten grids to multiply a decimal by a whole number.

First Let’s Review Base Ten Pieces Units = ones Rods = tens Flat = hundreds

Using rods to cover a flat How many rods does it take to cover the flat? If a flat represents 1 whole, then what fraction does one rod represent? What fraction of the flat is 7 rods? What fraction of the flat is 4 rods?

Which base ten piece would you use to show one hundredth? Why? How many hundredths does a rod represent? How would you write 10 hundredths using decimal notation? Do 0.10 and 0.1 represent the same number? Explain why 0.10 and 0.1 represent the same number using the base ten blocks.

What number represents 3 flats, 5 rods, and 7 units using decimal notation. 3.57 What number represents 2 flats, 4 rods, and 1 unit using decimal notation. 2.41

Find Day 56, “Multiplying Decimals Using Models” Scenario 1   A lollipop costs $0.22. How much do 5 lollipops cost? Use what you know about decimals to estimate the cost of 5 lollipops. $0.22 is about $0.20 $0.20 + $0.20 + $0.20 + $0.20 + $0.20 = $1.00 What multiplication sentence is represented by the problem. $0.22 x 5 = ? (Write the problem horizontal.) How might you use base ten blocks to find the solution.

Model with Base Ten Blocks Create five sets of 0.22 (2 rods and 2 units) Put the rods together and count them 10 rods Put the units together and count them 10 units Trade 10 rods for 1 flat. Trade 10 units for 1 rod. Total is 1 flat and 1 rod. So how much do 5 lollipops cost? $1.10 Is this solution close to your estimated answer?

Let’s Look at Scenario 2 Roger and Becky both walk to school. Roger’s house is 0.54 miles from school. Becky’s house is 4 times farther from school than Roger’s house. How far is Becky’s house from school?  You will work in pairs to solve this problem. Remember to use the 4 steps below to guide you. Estimate the answer. Write a horizontal problem to represent the scenario. Use base ten blocks to find a solution. Compare your estimate with your actual answer.

Math Talk Share your solutions. Be sure to include discussion about place value and regrouping.

Find Day 56, “Multiplying Decimals Using Base Ten Grids 1” Scenario 3 Sydney is baking a cake for her sister’s birthday. The recipe makes two layers of cake, but Sydney wants to make four layers. The recipe requires 1.45 cups of flour. How much flour will Sydney need to make four layers of cake? Estimate the amount of flour needed for the modified recipe. 1.45 is about 1.5 So 1.5 + 1.5 = 3 Write the horizontal multiplication sentence that represents the problem. 1.45 x 2 = ? How might you use base ten grids to find the answer to the problem.

Using Base Ten Grids to Multiply Decimals Shade Base Ten Grids: Shade 1 whole, 4 columns, and 5 small squares. Then, shade 1 whole, 4 columns, and 5 small squares again. Count the total number of wholes 2 wholes Count the total number of columns or tenths 8 tenths Count the total number of small squares or hundredths 10 hundredths Regroup the 10 hundredths into 1 tenth. Total is 2 wholes and 9 tenths. So, how much flour will Sydney need to make four layers of cake? 2.9 pounds Is this solution close to your estimated answer?

Find Day 56, “Multiplying Decimals Using Base Ten Grids 2” Scenario 4 Mrs. Radford needs 9 pairs of scissors for her classroom. The best price she can find is $0.27 per pair. How much will she pay for 9 pairs of scissors at that price? You will work in pairs to solve this problem using base ten grids provided. Remember to use the 4 steps below to guide you. Estimate the answer. Write a horizontal problem to represent the scenario. Use base ten blocks to find a solution. Compare your estimate with your actual answer.

Math Talk Share your solutions. Be sure to include discussion about place value and regrouping.

Remaining Time… Day 56, “Multiplying Decimals with Base Ten Grids.” Finish any remaining problems and the journal prompt for homework.