LESSON 13OBJECTIVE: MULTIPLY MIXED NUMBER FACTORS, AND RELATE TO THE DISTRIBUTIVE PROPERTY AND AREA MODEL

By the end of the lesson you will be able to…

5th Grade Module 5Lesson 13K. Clauson

Multiplying FractionsUse Interwrite Tools

Finding the VolumeV = ____ units x ____ units x ____ units

How many layers of 6 cubes are in the prism?

How many layers of 8 cubes are there?

How many layers of 12 cubes are there?

Application ProblemThe Colliers want to put new flooring in a 6 ½ foot by

7 1/3 foot bathroom. The tiles they want come in 12-inch squares. What is the area of the bathroom floor? If the tiles cost $3.25 per square foot, how much will they spend on the flooring?

Let’s draw out what this problem is saying!

Application Problem ~ ANSWER!The Colliers want to put new flooring in a 6 ½ foot by 7 1/3 foot bathroom. The tiles they want come in 12-inch squares. What is the area of the bathroom floor? If the tiles cost $3.25 per square foot, how much will they spend on the flooring?

To review…. We have been finding area by….

Using Ms. Patty Paper to tile the area Using a ruler to measure the lengths

and widths Today, we are going to find the most

efficient strategy to use to multiply mixed numbersDistributing with the area modelMultiplying improper fractions

Concept Development

Problem 1Find the area of a rectangle 1 1/3 inches x 3 ¾ inches and discuss strategies for solving

Let’s break this up into partial products. This is the distributive property!

1 1/3 in

3 ¾ in

*Use interwrite tools to fill in each partial product and then add up!

Let’s find the area of this rectangle again. This time we will change the mixed numbers into improper fractions! Do you realize that a

mixed number is really an addition sentence?!

When we convert to an improper fraction, the whole number can be expressed in the unit of the fractional part and then both like fractions added.

1 1/3 in

3 ¾ in

*Use interwrite tools to convert to improper fractions

Which strategy did you find to be more efficient? Why?

Distributive property with partial products

Changing mixed numbers to improper fractions

Problem 2Determine when the distributive property or the multiplication of fractions (improper fractions) is more efficient to solve for area

Which strategy do you think might be more efficient to find the area of this rectangle? Turn and talk!

16 ½ in

4 ¼ in

Partner A find the area using the distributive property

Partner B find the area using improper fractions

What is the area?Which strategy was more efficient?

16 ½ in

4 ¼ in

33 X 17 = 561 = 70 1/8 in2

2 4 864 2

16/4 = 4 1/8

64 + 2 + 4 + 1/8 = 70 1/8 in2

** Does it matter which strategy you use to solve the problem?

Problem 2bFind the area of a square with side lengths 3 2/3 m ~ use whichever method you prefer

3 2/3m

3 2/3m

Problem 3An 8 inch by 10 inch picture is resting on a mat. Three-fourths inch of the mat shows around the entire edge of the picture. Find the area of the mat not covered by the picture.

Work with a partner and use RDW to solve!

¾ in

8 in

10 in

Problem 3 ~ ANSWER

Get Ready to Finish theProblem Set on Your Own!

You will have 10 minutes to complete work on the Problem Set.

-----------------------------------------------------------------Fast finishers:

- Math Center Activities- choice boards, extra Sprint challenge

- CML packets/ worksheets- Problem Solving pages 5th Grade Module 5– Lesson 13

K. Clauson

5th Grade Module 5- Lesson 13K. Clauson

LET’S DEBRIEF• Take 2 minutes to check your answers with your partner.• Let’s share any insights you had while solving these problems.

• What are the strategies that we have used to find the area of a rectangle? Which one do you find the easiest? The most difficult? How do you decide which strategy you will use for a given problem? What kinds of things do you think about when deciding?

• In the Problem Set, when did you use the distributive property and when did you multiply improper fractions?

• How did you solve Problem 3?• What are some situations in real life where finding the area of

something would be needed or useful?

5th Grade Module 5– Lesson 13K. Clauson

EXITTICKETLESSON 13