LESSON 10OBJECTIVE: FIND THE AREA OF RECTANGLES WITH WHOLE-BY-MIXED AND WHOLE-BY-FRACTIONAL NUMBER SIDE LENGTHS BY TILING, RECORD BY DRAWING, AND RELATE TO FRACTION MULTIPLICATION

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

5th Grade Module 5Lesson 10K. Clauson

Multiply Decimals

Change Mixed Numbers to Fractions (*improper) Use Interwrite tools

Multiply Mixed Numbers and Fractions

Application ProblemHeidi and Andrew designed two raised flowerbeds for their garden. Heidi’s flowerbed was 5 feet long by 3 feet wide, and Andrew’s flowerbed was the same length, but twice as wide. Calculate how many cubic feet of soil they need to buy to have soil to a depth of 2 feet in both flowerbeds.

Let’s draw out what this problem is saying!

Application Problem ~ ANSWER!Heidi and Andrew designed two raised flowerbeds for their garden. Heidi’s flowerbed was 5 feet long by 3 feet wide, and Andrew’s flowerbed was the same length, but twice as wide. Calculate how many cubic feet of soil they need to buy to have soil to a depth of 2 feet in both flowerbeds.

Teacher notes

The following will need to be created ahead of time:

* Copies of Rectangles A to E for student groups

Students will need:

* Problem Set

* Patty paper units for tiling

* Mystery rectangles A - E

Concept Development

Breaking News!5 rectangles from the Eureka laboratory at FWES escaped early this morning. Luckily, your amazing teacher located those 5 rectangles hiding in the Star Lab just moments ago! The only problem now is that those rectangles are without their correct areas. Your mission, 5th grade, is to help determine those areas and make everything right again! Good luck!

Rectangle A Ms. Patty Paper is here to help you solve

the mystery! Can you remind her how to find the area of a rectangle?

That’s right!…. Area = length x width Ok, now that we have that stored in our

memory bank, we need to cover this first rectangle with Ms. Patty Paper so that there is no space between units and no overlaps. How many Ms. Patty Papers will cover Rectangle A?

Rectangle A – on your Problem Set How many square units covered the

rectangle? Let’s sketch a picture of what our tiling

looks like. Follow along with me as I draw it on the board here!

Rectangle B

Will its area be greater than or less than that of Rectangle A?

A and B have the same length, but what about the width?

Use Ms. Patty Paper to help you find the area. You must completely cover the rectangle!

Rectangle B- on your Problem Set How many square units covered the

rectangle? Let’s sketch a picture of what our tiling

looks like. Follow along with me as I draw it on the board here!

What is the area?

Take a closer look at what happened here!

When we record our tiling do we always have to write in the tile lines?

The width measurement was decomposed and partial products were calculated!

Ok detectives, you are prepared for the rest of the mission! Work with your group to find the length, width, and area of Rectangles C, D, and E using Ms. Patty paper to help you!

Record your findings on your Problem Set. Answer the last two questions in the time remaining. You may record your tiling without drawing each tile if you wish!

5th Grade Module 5- Lesson 10K. 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 relationship did you notice between the areas of Rectangle C and E? What accounts for this relationship?

• How was Rectangle E different from the other rectangles you tiled? Describe how you tiled it.

• How did you determine the area of the rectangle in Problem 6?

5th Grade Module 5– Lesson 10K. Clauson

EXITTICKETLESSON 10