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.
1.
2.
3.
4.
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?
1. Estimate the amount of flour needed for the modified
recipe.
»
»
1.45 is about 1.5
So 1.5 + 1.5 = 3
2. Write the horizontal multiplication sentence that
represents the problem.
»
1.45 x 2 = ?
3. 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.
1.
2.
3.
4.
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.