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Module 4 Lesson 13

Find areas by decomposing into rectangles or completing composite

figures to form rectangles.

YOUR NAME

1c

Skip countingLet’s skip count by 3s to 30.

36

9

1215

18

21

24

27

30

Skip countingLet’s skip count by 6s to 60.

612

18

2430

36

42

48

54

60

Skip countingLet’s skip count by 8s to 80.

816

24

3240

48

56

64

72

80

Skip countingLet’s skip count by 9s to 90.

918

27

3645

54

63

72

81

90

FIND THE COMMON PRODUCTS

1. FOLD YOUR PAPER IN HALF.

2. ON THE LEFT HALF, List the multiples of 4 t0 40. 3. ON THE RIGHT HALF, list the multiples of 8 to 80.

4. DRAW LINES TO MATCH MULTIPLES THAT APPEAR IN BOTH COLUMNS. `

LEFT SIDE RIGHT SIDE

__ X 4 =

__ X 4=

__ X 4 =

__ X 4 =

__ X 4=

2

4

6

8

10

= ___ X 8

= ___ X 8

= ___ X 8

= ___ X 8

= ___ X 8

1

2

3

4

5

THUMBS UP IF YOUR PAPER LOOKS LIKE THIS.

WRITE THE COMPLETEEQUATIONS NEXT TOTHEIR PRODUCTS

THUMBS UP WHEN YOU’RE DONE

2 X 4 = 1 X 8

4 X 4 = 2 X 8

6 X 4 = ____ X 8

WRITE THE REMAININGEQUALS FACTSAS FULL EQUATIONS

WRITE THE REMAININGEQUALS FACTSAS FULL EQUATIONS

8 X 4 = ____ X 8

10 X 4 = ___ X 8

DO FIVE JUMPINGJACKS WHEN YOU’REFINISHED

DO FIVE JUMPINGJACKS WHEN YOU’REFINISHED

3

4

5

WHAT PATTERNDO YOU NOTICE

IN YOUR EQUATIONS?

WHAT PATTERNDO YOU NOTICE

IN YOUR EQUATIONS?

Problem of the DayAndrew finds the area of a 5-inch by 17-inch rectangle by breaking it into two smaller rectangles. Show one way that he could have solved the problem. What is the area of the rectangle?

Concept Development Part 1: Add using the break apart strategy to find the area of a

composite shape. Give 1 large grid to each student.

How do you find the area ofa rectangle?

Can we find the area of this figure by multiplyingthe side lengths?

In the problem of the day, we used the break apartstrategy to find the area of the larger rectangle. Turn and talk to your neighbor, How many we use a strategy like that to find the area of the shaded figure?

We could break it into a square and a rectangle

Or we can break it into 3 squares.

What are the side lengths of the top square?What are the side lengths of the bottom rectangle?

What can we do with the areas of the two shapes to find the total area of thecomposite figure?

What is the total area?

We can also find the area of the shaded figureby thinking of it as a 4 x 4 square with missingunits.

How can we find the area of the shaded areausing the un-shaded square?

(4 x 4) – (2 x 2) = 16 – 4 = 12 square units!

Part 2: Subtract to find the area of a composite shape.

The figure shows a small rectangle cut out of a larger, shaded rectangle. How can we find the area of the shaded figure?

WE can break apart the shaded part. Or we can subtract the un-shaded area from the shaded square.

Pretend we shade in the white rectangle.

We now have a large, shaded square. Write a number sentence to find the area of the largesquare.

6 x 6 = 36 Beneath the number sentence you just wrote, write a number sentence for the shape (white rectangle) we cut out. 2 x 4= 8

The area of the square is 36 square centimeters. We cut out, or took away, 8 square centimeters of shading. How can we find the area of the shaded region?

The area of the square is 36 square centimeters. We cut out, or took away, 8 square centimeters of shading. How can we find the area of the shaded region?

Write a number sentence to find the area of the shaded region. Write a number sentence to find the area of the shaded region.

Problem 3: Subtract to find the area of a composite shape with unknown side lengths.

This figure also shows a small rectangle cut out of a larger, shaded rectangle, but what is unknown?

The side lengths of the smaller rectangle.

Do we have enough information to find the side lengths of the smaller rectangle?

Opposite sides of a rectangle are equal. Since we know the length of the rectangle is 9 feet, what is the opposite side length? 9 ft

You can find the unknown lengths, by subtracting the known four feetfrom the total 9 feet.

9 – 4 = 5 feet is the unknown side length!

Use the same strategy to find the unknown width.

11 – 5 = 6 feet! Can we now find the area of the shaded figure?

Talk with your table how we can now find the area for the shaded figure.

What is the area?

Problem Set