Download File - 5th Grade Lessons

Multiplying Decimals by Decimals
Alignment Lesson
Today’s Objective
Students will be able to:
explain how to multiply a decimal
by a decimal using an area model.
Multiplying Decimals by Decimals
• Let’s view a video showing how to multiply a
decimal by a decimal (2.4 x 1.3 = ?) using an
area model
• Multiplying whole numbers and decimalsusing-an-area-model
Let’s Review….
• Arrays
Rectangular Arrays
• Let’s say you have decided to create a
miniature movie theatre in your house. You
place 3 rows of chairs with 5 chairs in each
row. Use colored tiles to design your movie
theatre on your desk.
• How many people can your movie theatre
seat?
• What array have you created?
• Remember an array is items arranged in rows and
columns.
• 3 rows and 5 columns = 15
Use Rectangular Arrays to Help Solve…
• Create an array to solve 2 x 6.
• 2 rows and 6 columns = 12
• OR 6 rows and 2 columns = 12
• Create an array to solve 1 x 5
• 1 row and 5 columns = 5
• OR 5 rows and 1 column = 5
• We can use arrays to help use solve
multiplication problems. Today we will
use arrays to help us multiply decimals!
We are now going to use the
two strategies we have just
reviewed to solve some
multiplication problems.
Strategies:
»Rectangular Arrays
»Area Model
Find Day 60, “Multiplying Decimals by
Decimals”
Scenario 1
Kendall is filling 4.5 ounce bottles with a bubble
solution for her party. She was able to fill 3.5
bottles. How many ounces of bubble solution did
she make?
• Use what they know about decimals to estimate how
many ounces of bubble solution Kendall made.
• What multiplication sentence is represented by the
problem?
• Write the sentence horizontally on the your paper.
(4.5 x 3.5).
Solving using Rectangular Arrays – 1st
Strategy
• Create a 4.5 by 3.5 array (overlapping square is
purple because it is shared by 4.5 and 3.5)
Solving using Rectangular Arrays – 1st Strategy
• Next you are going to fill in the array with appropriate base ten pieces that
fit
• First, I will fill in the flats (or wholes)
• Second I will fill in the rods (or tenths) in appropriate spaces
• Third, I will fill in the bits (or hundredths)
Solving using Rectangular Arrays – 1st Strategy
• Lastly, you will count up the number of
wholes, tenths and hundredths you have to
find your answer.
12 wholes
35 tenths
25
hundredths
25
hundredths
= 2 tenths
and 5
hundredths
So now I have:
12 wholes
37 tenths
5 hundredths
37 tenths =
3 wholes
and 7 tenths
So now I have:
15 wholes
7 tenths
5 hundredths
Product:
15.75
Solve 4.5 x 3.5 Using Area Model
• First create 4.5 using base ten pieces
4.5
Solve 4.5 x 3.5 Using Area Model
• Next use base ten pieces to create 3.5 in the same box
3.5
4.5
Solve 4.5 x 3.5 Using Area Model
• Next use base ten pieces to create 3.5 in the same box
3
+
RED Square = 4 x 3 = 12
PURPLE = 0.5 x 3 =
1.5
4
4.5
0.5
BLUE = 4 x 0.5 =
2.0
YELLOW = 0.5 x 0.5
= 0.25
+
Add all products:
12 + 1.5 + 2.0 +
0.25 = 15.75
0.5
3.5
Continue with Scenarios
• Try to Solve Scenarios 2 and 3 using either the
Rectangular Array or Area Model Strategy
• Day 60, “Multiplying Decimal by Decimal
Using Area Model” can be used for more
practice problems