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Content Session # 7 & 8 July 9, 2009

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Page 1: 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

Content Session # 7 & 8

July 9, 2009

Page 2: 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

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?

Page 3: 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

Double Number Line

?

6

1.40

0 1Length (in meters)

Weight (in grams)

Page 4: 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

Unitary Perspective of Numbers

• 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

weight (in 0.1 grams)14

weight (in grams)

length (in meters)

?

6

1.4

10

0

Page 5: 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

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?

Page 6: 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

Double Number Line

? 3.6

4

Weight (in kg)

Length (in meters)

10

0

Page 7: 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

Unitary Perspective of Numbers

• 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

weight (in 0.1 grams)36

weight (in grams)

length (in meters)

3.6

4

?

10

0

Page 8: 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

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

Page 9: 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

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?

Page 10: 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

What is 8 ÷ 5?

Page 11: 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

Multiplying by Decimal Numbers

• 1m of wire weighs 6 grams. How much will 1.4 m of the same wire weigh?

weight (in grams)

length (in meters)

?

1.4

6

10

0

Page 12: 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

Unit Approach

0.114

weight (in grams)

length (in meters)

?

1.4

6

10

0

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 = 0.6Weight of 1.4 meters = 14 x 0.6

Page 13: 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

Make-It-Bigger ApproachWhat if we were looking for the weight of 14 meters of the wire?Weight of 14 meters = 14 x 6 = 84 grams14 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

14

weight (in grams)

length (in meters)

?

1.4

6

10

0

Page 14: 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

Dividing by Decimal Numbers3.6 m of iron pipe weighs 9 kg. How much will 1m of the same pipe weigh?

weight (in grams)

length (in meters)

?

3.6

9

10

0

Page 15: 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

Unit Approach

0.1

weight (in grams)

length (in meters)

?

3.6

9

10

0

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

Page 16: 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

Make-It-Bigger Approach

36

weight (in grams)

length (in meters)

?

3.6

9

10

0

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.

Page 17: 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

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.

Page 18: 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
Page 19: 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

24 x 13 or 2.4 x 1.3

Page 20: 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

Multiplying Fractions by Whole #

You can paint 3/5 sq. feet with 1 pint of paint. How much can you paint with 2 pints?

210

Page 21: 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

Multiplying Fractions by Whole #

You can paint 3/5 sq. feet with 1 pint of paint. How much can you paint with 2 pints?

210

Page 22: 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

Dividing Fraction by Whole #You can paint 4/5 sq. feet with 3 pints of paint. How much can we paint with 1 pint?

3210

Page 23: 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

Dividing Fraction by Whole #You can paint 4/5 sq. feet with 3 pints of paint. How much can we paint with 1 pint?

3210

Page 24: 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

Multiplying by FractionsWith 1 pint of paint, you can paint 4/5 square feet. How much can we paint with 2/3 pints?

12

30

Page 25: 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

Multiplying by FractionsWith 1 pint of paint, you can paint 4/5 square feet. How much can we paint with 2/3 pints?

12

30

Page 26: 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

Dividing by FractionsWith 3/4 pints of paint we can paint 2/5 sq feet. How much can we paint with 1 pint?

13

40

Page 27: 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

Dividing by FractionsWith 3/4 pints of paint we can paint 2/5 sq feet. How much can we paint with 1 pint?

13

40

Page 28: 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

Area Model of Multiplication

3

4

Page 29: 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

Area Model of Multiplication

2

3

3

4

Page 30: 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

Area Model of Multiplication

2

3

3

4

Page 31: 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

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?

Page 32: 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

Measurement Divisionwith 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?

Page 33: 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

Measurement Divisionwith 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?

Page 34: 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

Measurement Divisionwith 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?

Page 35: 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

Measurement Divisionwith 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?

Page 36: 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

Partitive Divisionwith Cubes and Drawing

3/4 pounds of coffee cost $6. How much does a pound of the same coffee cost?

$ 6

Page 37: 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

Partitive Divisionwith Cubes and Drawing

3/4 pounds of coffee cost $6. How much does a pound of the same coffee cost?

$ 2$ 2$ 2

Page 38: 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

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?

? ?

11

32

3

10

0

Page 39: 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

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?

12

0

01

1

3

12?

?

2

310

0