USE ALL FOUR OPERATIONS TO SOLVE PROBLEMS INVOLVING PERIMETER AND UNKNOWN MEASUREMENTS MODULE 7 LESSON 17

FACTORS 8 x ____ = 8 Say the equation, filling in the unknown factor. 2 x _____ = 8 Say the equation, filling in the unknown factor. ___ x 2 = 8 Say the equation, filling in the unknown factor.

FACTORS 12 x ____ = 12 Say the equation, filling in the unknown factor. 2 x _____ = 12 Say the equation, filling in the unknown factor. ___ x 6 = 12 Say the equation, filling in the unknown factor.

EQUIVALENT COUNTING WITH UNITS OF 8 Count 8s to Eighth 2 Eighths 3 eighths 4 eighths 5 eighths 6 eighths7 eighths8 eighths9 eighths 10 eighths Count to 10 eights.

EQUIVALENT COUNTING WITH UNITS OF Eighth 2 Eighths 3 eighths 4 eighths 5 eighths 6 eighths7 eighths8 eighths9 eighths 10 eighths We’re going to count to 10 eights again. But this time when I say stop – say the multiplication sentence. 3 x 8 = 24 5 x 8 = 40 8 x 8 = 64

FIND THE PERIMETER Each shape that I will show you is a REGULAR polygon. You’re going to have to find the perimeter of each regular polygon. What is the given side length of the the triangle? 4 cm P = ___ × ___ cm. Fill in the factors. Then, write the perimeter of the triangle. 3 4 P = 12 cm

FIND THE PERIMETER Each shape that I will show you is a REGULAR polygon. You’re going to have to find the perimeter of each regular polygon. What is the given side length of the the square ? 7 in P = ___ × ___ in. Fill in the factors. Then, write the perimeter of the Square. 4 7 P = 28 in

FIND THE PERIMETER Each shape that I will show you is a REGULAR polygon. You’re going to have to find the perimeter of each regular polygon. What is the given side length of the the hexagon? 8 m P = ___ × ___ m. Fill in the factors. Then, write the perimeter of the hexagon. 6 8 P = 48 m

FIND THE PERIMETER Each shape that I will show you is a REGULAR polygon. You’re going to have to find the perimeter of each regular polygon. What is the given side length of the the octagon? 9 ft P = ___ × ___ ft. Fill in the factors. Then, write the perimeter of the octagon. 8 9 P = 72 ft

PROBLEM OF THE DAY Gil places two regular hexagons side by side as shown to make a new shape. Each side measures 6 centimeters. Find the perimeter of his new shape

CONCEPT DEVELOPMENT Can you visualize the rectangles that make up this shape? Tell some at your table about them. Let’s find the perimeter of the shape. Say the side length as I point to it. This side length isn’t labeled. Let’s call this side length “a” and label the unit with cm. This side length isn’t labeled either. Let’s call this side length “b” and label the unit with cm. a cm b cm

Think back to how you visualized rectangles fitting together to make this shape. How does the line help you find the unknown side lengths?

Work with a partner. Use the bottom rectangle to find the length of the dashed line. If the whole bottom is 5 centimeters, then we have to subtract the 2 centimeters that we know. 5 cm – 2 cm = 3 cm. The dashed line is 3 centimeters 3 cm How does this help us find the value of a? The dashed line is the side opposite of a, so a is 3 too! 3 cm Look at the side lengths for the top rectangle. We know that three side lengths are 3 centimeters. What does that tell us about the fourth side length? It has to be 3 centimeters, too! Does that mean the length of b is 3 cm? We have to add on the side length from the bottom rectangle to find the total length of b.

3 cm What is the value of b? 3 cm + 1 cm = 4 cm b = 4 cm 4 cm Write a number sentence, including units, that shows the perimeter of this shape. What is the perimeter of this shape? 18 cm!

Discuss with a partner how you would solve by visualizing the rectangles this way instead.

EXTRA PRACTICE

Students might find the perimeter of the shaded rectangle, the unshaded shape, and/or the large rectangle.

PROBLEM SET