lesson 10: i can multiply decimal fractions with tenths by multi-digit whole numbers using place...
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5th Grade Module 2 – Lesson 10
Lesson 10: I can multiply decimal fractions with tenths by multi-digit whole numbers using
place value understanding to record partial products.
5th Grade Module 2 – Lesson 10
Get Your White Boards Ready!
3 X 2 is? 3 x 2 x 10 ÷ 10 is?
6 6
5 x 0.3 is?5 x 0.3 x 10 ÷ 10
is?1.5 1.5
3 x 2.5 is? 7.53 x 2.5 x 10 ÷ 10
is?7.5
2 x 3.4 is? 6.82 x 3.4 x 10 ÷ 10
is?6.8
Why are the products the same when we multiply by 10 and
then divide by 10?
5th Grade Module 2 – Lesson 10
Get Your White Board Ready!
7.463
Say the Number
Represent this number in a two-part number bond with ones as one part and thousandths as the other part.
Draw on your whiteboard.
7.463
__ones
______thousandths
Now represent this number in a two-part number bond withtenths and thousandths.
7.463
74tenths
63thousandths
7 463
Now represent this number in a two-part number bond withhundredths & thousandths.
7.463
746hundredths
3thousandths
5th Grade Module 2 – Lesson 10
Draw three different two-part number bonds for the number.
8.972 1. Using ones & thousandths.2. Using tenths & thousandths.3. Using hundredths & thousandths.
Volunteer to share their solutions below…
5th Grade Module 2 – Lesson 10
Draw three different two-part number bonds for the number.
6.849 1. Using ones & thousandths.2. Using tenths & thousandths.3. Using hundredths & thousandths.
Volunteer to share their solutions below…
5th Grade Module 2 – Lesson 10
Application Problem
The fifth-grade craft club is making aprons to sell. Each apron takes 1.25 yards of fabric that costs $3 per yard and 4.5 yards of trim that costs $2 per yard. What does it cost the club to make one apron?
If the club wants to make $1.75 profit on each apron, how much should they charge per apron?
Solution on next slide…
5th Grade Module 2 – Lesson 10
Solution to Application Problem
5th Grade Module 2 – Lesson 10
Concept Development
Round the factors to estimate the product
40 x 2 = 80
43 x 2.4
Predict whether our estimate is greater than or less than the actual product?
Turn & Talk
5th Grade Module 2 – Lesson 10
43 x 2.4Let’s solve the product by decomposing the factors and building an area model.
Record in your journal with me.
How can we rename 2.4 using only tenths? 24 tenths
Let’s decompose 24 tenths in expanded form along the length of our rectangle.
20 + 4 tenthsThe width is 43
whole units. Decompose 43 into expanded
form.
3
+
40
Find the partial products for each
section. Then add each row.
60 12
800 160
= 72
= 960
2 4 tenths x 4 3 7 2 9 6 010 3 2
Lets Build theAlgorithm
Don’t forget the unit!!
tenths
43 x 24 tenths = 1,032 tenths (unit form)43 x 2.4 = 103.2 (standard form)
5th Grade Module 2 – Lesson 10
We just used unit form to multiply a decimal by a double digit.Now let’s learn another strategy to make it a little quicker.
We can multiply one of the factors by 10 and then divide the product by 10. This is a simplifying short cut for multiplying by tenths.
2.4x 4 3
X 10 24x 43
7 2 9 6 01 0 3 2 ÷ 10 = 103.2
Why does that work?Turn & Talk
5th Grade Module 2 – Lesson 10
We estimated that 43 x 2.4is about
40 x 2 = 80The actual product is 103.2Is the actual a reasonable answer compared to our
estimate?Turn & Talk
5th Grade Module 2 – Lesson 10
Let’s Solve3.5 x 42
First, round the factors and estimate the product.Record your work in your journal.
4 x 40 = 160
Naming 3.5 using tenths, draw an area model to show 3.5 x 42.
Check your work with your partner.Remember to compare your answer with our estimate to
make sure it is reasonable.
5th Grade Module 2 – Lesson 10
Volunteers to share their solutions…Or click to view solution
Is 147 reasonable with our estimate of 160?
5th Grade Module 2 – Lesson 10
Let’s confirm this product using the standard algorithm!!
Partner A: Find the product naming 3.5 in tenths.
Partner B:Find the product multiplying 3.5 by 10 and then dividing the product by 10.
3.5x 4 2
3 5x 4 2
x 10 3 5 tenthsx 4 2
÷ 10
Volunteers to show their answers using ink tool.How are these two ways of thinking the same?
Turn & Talk
5th Grade Module 2 – Lesson 10
Let’s Try15.6 x 73
First, round the factors and estimate the product.Record your work in your journal.
20 x 70 = 1400
Naming 15.6 using tenths, draw an area model to show 15.6 x 73.
Check your work with your partner.Remember to compare your answer with our estimate to
make sure it is reasonable.
5th Grade Module 2 – Lesson 10
Volunteers to share their solutions…Or click to view solution
Is 1,138.8 reasonable with our estimate of 1,400?
100 50 6 tenths3
300 150 18 = 468
707000 3500 420 = 10,920
11,388 tenths = 1,138.8
5th Grade Module 2 – Lesson 10
Let’s confirm 15.6 x 73 using thestandard algorithm!!
Partner B: Find the product naming 15.6 in
tenths.
Partner A:Find the product multiplying 3.5 by 10 and then dividing the product by 10.
15.6x 7 3
1 5 6x 7 3
x 10 1 5 6 tenthsx 7 3
÷ 10
Volunteers to show their answers using ink tool.How are these two ways of thinking the same?
Turn & Talk
5th Grade Module 2 – Lesson 10
Get Ready to Complete theRest of the Problem Set
on Your Own!
Complete Page 2.C.8 & 2.C.9You will have 10-15 minutes to
work.Try your Best!
5th Grade Module 2 – Lesson 10
Debrief• Let’s discuss Michelle’s error in Problem 3.
• How does being fluent in whole number multi-digit multiplication help you multiply decimals?
5th Grade Module 2 – Lesson 2
EXITTICKET
Page 2.C.10