modeling)decimals)) with)base)10)blocks) · pdf...
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Modeling Decimals with Base 10 Blocks
Joyce Bishop
Using Familiar Base 10 Blocks to Model Decimal Numbers
• flat = 1
• long = 0.1
• small cube = 0.01
• small flat = 0.001
RepresenCng Decimal Numbers
Base 10 blocks Decimal FracCon RepresentaCon RepresentaCon
2.6
€
2 610
RepresenCng Decimal Numbers
Base 10 blocks Decimal FracCon RepresentaCon RepresentaCon
3.217 €
1 27100
Comparing Decimals
Represent each of the following numbers with base 10 blocks and put them in order from smallest to greatest:
2.1
1.96
2
Comparing Decimals
1.96
2
2.1
Model Space Ship
Ethan is construcCng a model of a space ship. The first stage is 2.34 meter tall. The second stage is 1.031 meters tall. What is the total height?
Model the soluCon with base 10 blocks.
Model Space Ship -‐ AddiCon
Add 2.34 + 1.031:
2.34
1.031
= (3 x 1) + (3 x 0.1) + (7 x 0.01) + (1 x 0.001)= 3.371
RepresenCng Two Ways
Use your understanding of place value to show two ways to represent 0.18 with base 10 blocks.
RepresenCng Two Ways
Use your understanding of place value to show two ways to represent 0.18.
or
Storing a Model Space Ship
Ethan has another model space ship that is 1.62 meters tall. If he stores it in a cabinet that is 2.18 meters tall, how much taller is the cabinet than the model space ship?
Model your soluCon with base 10 blocks.
Storing a Model Space Ship -‐ SubtracCon
Subtract 2.18 – 1.62
2.18
Rename 1 as 10 x 0.1
Storing a Model Space Ship -‐ SubtracCon
Subtract 2.18 – 1.62
2.18
Storing a Model Space Ship -‐ SubtracCon
Subtract 2.18 – 1.62
2.18
2.18 m – 1.62 m = 0.56 m
MulCplying Decimals Using an Understanding of Place Value
Using Place Value Materials (With Renaming)
1.6
x 2
2 groups of 1.6
MulCplying Decimals Using an Understanding of Place Value
Using Place Value Materials (With Renaming)
1.6
x 2
Trade to make another unit.
1.6 x 2 = 3.2
MulCplying a Decimal by a Decimal
1.6
x .2
Find two tenths of each part.
MulCplying a Decimal by a Decimal
1.6
x .2
Find two tenths of each part (not drawn proporConally.)
MulCplying a Decimal by a Decimal
1.6 x 0.2
1.6 x 0.2 = (2 x 0.1) + (12 x 0.01)
MulCplying a Decimal by a Decimal
1.6 x 0.2
1.6 x 0.2 = (3 x 0.1) + (2 x 0.01) = 0.32
One MulCplicaCve SituaCon: Two Division Types
Aeisha is cubng ribbon for a hair bow. She has 1.2 meters of ribbon. Each piece of ribbon must be 0.3 meters long. She can cut 4 pieces of ribbon.
Two division quesCons: • You know how long each piece of ribbon must be. How many pieces can you cut? (Measurement Division)
• You know how many pieces of ribbon you need. How long is each piece? (ParCCve or Sharing Division)
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut?
Rename 1.0 as (10 x 0.1)
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut?
Count groups of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut?
One group of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut?
Two groups of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut?
Three groups of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut?
Four groups of (3 x 0.1).
1.2 meters ÷ by 0.3 = 4
ParCCve (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be?
Rename 1.0 as (10 x 0.1)
ParCCve (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be?
Arrange the blocks in four equal groups.
ParCCve (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be?
Four groups of 0.1 m with 0.8 m leg.
ParCCve (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be?
Four groups of 0.2 m with 0.4 m leg.
ParCCtve (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be?
There are four groups with 0.3 meter in each. 1.2 meters ÷ by 4 = 0.3
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