Transcript Content Session # 7 & 8 - Kennesaw State University

Content Session # 7 & 8
July 9, 2009
Which problem can we use our whole
number multiplication knowledge to solve?
• 1m of wire weighs 1.4 lb. How much will 6m
of the same wire weigh?
• 1m of wire weighs 6 grams. How much will
1.4 m of the sa,e wore weigh?
Double Number Line
0
0
1.4
1
?
Weight (in grams)
Length (in meters)
6
Unitary Perspective of Numbers
0
14
1.4
?
0
1
6
•
•
•
•
weight (in 0.1 grams)
weight (in grams)
length (in meters)
We have 6 groups of 14 0.1 grams.
14 x 6 = 84; Altogether, we have 84 0.1 grams.
84 0.1 grams  8.4 grams
1.4 x 6 = 8.4
Which problem can we use our whole
number division knowledge to solve?
• 4 m of iron pipe weighs 3.6 kg. How much will
1m of the same pipe weigh?
• 3.6 m of iron pipe weighs 9 kg. How much will
1m of the same pipe weigh?
Double Number Line
0
0
?
3.6
Weight (in kg)
Length (in meters)
1
4
Unitary Perspective of Numbers
0
?
36
3.6
0
1
4
•
•
•
•
weight (in 0.1 grams)
weight (in grams)
length (in meters)
Divide 36 0.1-kg to make 4 equal groups.
36 ÷ 4 = 9; Each group will have 9 0.1-kg.
9 0.1-kg = 0.9 kg.
3.6 ÷ 4 = 0.9
What if we had 3.7 ÷ 4 mean?
• 37 0.1-kg: make 4 equal groups
• BUT,
37 ÷ 4 = 9 rem. 1
• Each group will get 9 0.1-kg and there will
be 1 0.1-kg left over.
• 3.7 ÷ 4 = 0.9 rem. 0.1
Dividing on: 3.7 ÷ 4
• Model 3.7 ÷ 4 using base-10 blocks – use a
flat as 1.
• What will be left over?
• Can we trade it? With what?
What is 8 ÷ 5?
Multiplying by Decimal Numbers
• 1m of wire weighs 6 grams. How much will
1.4 m of the same wire weigh?
0
6
?
weight (in grams)
0
1
1.4
length (in meters)
Unit Approach
0
6
?
weight (in grams)
0 0.1
1
1.4
14
length (in meters)
1.4 meters means 14 0.1 meters.
So, we have 14 groups of weight of 0.1 meter.
Weight of 0.1 meter = 6 ÷ 10 = 0.6
Weight of 1.4 meters = 14 x 0.6
Make-It-Bigger Approach
What if we were looking for the weight of 14
meters of the wire?
Weight of 14 meters = 14 x 6 = 84 grams
14 meters are 10 times as long as 1.4 meters,
so it must also weigh 10 times as much as the
weight of 1.4 meters of the wire.
Weight of 1.4 meters = 84 ÷ 10 = 8.4 grams
0
6
?
0
1
1.4
weight (in grams)
14
length (in meters)
Dividing by Decimal Numbers
3.6 m of iron pipe weighs 9 kg. How
much will 1m of the same pipe weigh?
0
?
9
weight (in grams)
0
1
3.6
length (in meters)
Unit Approach
0
?
9
weight (in grams)
0 0.1
1
3.6
length (in meters)
3.6 meters means 36 0.1 meters. So, if we divide
9 by 36, we get the weight of 0.1 meter of the wire.
To get the weight f 1 meter of the wire, we have to
multiply by 10.
9 ÷ 36 = 0.25; 0.25 x 10 = 2.5 grams
Make-It-Bigger Approach
36 meters of the same wire will weigh 10x9=90
grams.
To find how much 1 meter will weigh, you just have
to divide 90 by 36.
0
?
9
0
1
3.6
weight (in grams)
36
length (in meters)
Area Model of Multiplication
• The two factors are represented by the two
dimensions of a rectangle.
• The product is represented by the area of the
rectangle.
• Represent 24 x 13 using base-10 blocks.
24 x 13 or 2.4 x 1.3
Multiplying Fractions by Whole #
You can paint 3/5 sq. feet with 1 pint of paint.
How much can you paint with 2 pints?
0
1
2
Multiplying Fractions by Whole #
You can paint 3/5 sq. feet with 1 pint of paint.
How much can you paint with 2 pints?
0
1
2
Dividing Fraction by Whole #
You can paint 4/5 sq. feet with 3 pints of
paint. How much can we paint with 1 pint?
0
1
2
3
Dividing Fraction by Whole #
You can paint 4/5 sq. feet with 3 pints of
paint. How much can we paint with 1 pint?
0
1
2
3
Multiplying by Fractions
With 1 pint of paint, you can paint 4/5 square
feet. How much can we paint with 2/3 pints?
0
2
3
1
Multiplying by Fractions
With 1 pint of paint, you can paint 4/5 square
feet. How much can we paint with 2/3 pints?
0
2
3
1
Dividing by Fractions
With 3/4 pints of paint we can paint 2/5 sq
feet. How much can we paint with 1 pint?
0
3
4
1
Dividing by Fractions
With 3/4 pints of paint we can paint 2/5 sq
feet. How much can we paint with 1 pint?
0
3
4
1
Area Model of Multiplication
3
4
Area Model of Multiplication
3
4
2
3
Area Model of Multiplication
3
4
2
3
Measurement Division
You need 2/3 cups of sugar to make 1 loaf of
bread. If you have 8 cups of sugar, how many
loaves of bread can you make?
Measurement Division
with Drawing
You need 2/3 cups of sugar to make 1 loaf of
bread. If you have 8 cups of sugar, how many
loaves of bread can you make?
Measurement Division
with Drawing
You need 2/3 cups of sugar to make 1 loaf of
bread. If you have 8 cups of sugar, how many
loaves of bread can you make?
Measurement Division
with Drawing
You need 2/3 cups of sugar to make 1 loaf of
bread. If you have 8 cups of sugar, how many
loaves of bread can you make?
Measurement Division
with Pattern Blocks
You need 2/3 cups of sugar to make 1 loaf of
bread. If you have 8 cups of sugar, how many
loaves of bread can you make?
Partitive Division
with Cubes and Drawing
3/4 pounds of coffee cost $6. How
much does a pound of the same coffee
cost?
$6
Partitive Division
with Cubes and Drawing
3/4 pounds of coffee cost $6. How
much does a pound of the same coffee
cost?
$2
$2
$2
Multiplication Makes Bigger?
1yd of cloth costs $3. What is the price of
11/3 yd of the same cloth? What is the price
of 2/3 yd?
0
?
0
2
3
?
1
1
1
3
Division Makes Smaller?
1 1/3m of thin wire weighs 12 g and 2/3m of thick wire
weighs 12g. How many g does 1m of each weigh?
0
?
12
0
1
1
3
0
12
?
0
2
3
1