Grade 6 Module 1

Lesson 3

Equivalent Ratios•Understanding of equivalent

ratios.•Use tape diagrams• Formalize a definition of

equivalent ratios

Exercise 1

•Write a one-sentence story problem about a ratio.

Sample

The ratio of the number of sunny days to the number of cloudy days in this city is 3:1.

Exercise 1

Write the ratio in two different forms

Answers

•3:1 3 to 1

Exercise 2• Shanni and Mel are using ribbon to

decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3. • Draw a tape diagram to represent

this ratio.

Represent ratio in a table

Shanni’s Ribbon Mel’s Ribbon

7 3

Represent ratio in a table

Shanni’s Ribbon Mel’s Ribbon

7 314 6

Represent ratio in a table

Shanni’s Ribbon Mel’s Ribbon

7 314 621 9

Tape DiagramShanni

Mel

Tape Diagram

What does each unit on the tape diagram represent?

Tape DiagramWhat if each unit on the tape diagrams represent 1 inch? What are the lengths of the ribbons?What is the ratio of the lengths of the ribbons?

Tape DiagramWhat if each unit on the tape diagrams represents 2 meters? What are the lengths of the ribbons?How did you find that?

Tape DiagramWhat is the ratio of the lengths of Shanni’s ribbon to the length of Mel’s ribbon now? What if each unit represents 3 inches? What are the lengths of the ribbons? Record

Tape Diagram

If each of the units represents 3 inches, what is the ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon?

Tape DiagramsWe just explored three different possibilities for the length of the ribbon; did the number of units in our tape diagrams ever change?What did these 3 ratios, 7:3, 14:6, 21:9, all have in common?

Tape DiagramMathematicians call these ratios equivalent. What ratios can we say are equivalent to 7:3?

Tape DiagramDraw a tape diagram to represent this ratio:

7:3 7 inches to 3 inches14:6 14 meters to 6 meters21:9 21 inches to 9 inches

Tape Diagram1 in 1 in 1 in 1 in 1 in 1 in 1 in

1 in 1 in 1 in

Shanni

Mel

7 inches to 3 inches 7:3

Tape Diagram2 m 2 m 2 m 2 m 2 m 2 m 2 m

2 m 2 m 2 m

Shanni

Mel

14 meters to 6 meters 14:6

Tape Diagram3 in 3 in 3 in 3 in 3 in 3 in 3 in

3 in 3 in 3 in

Shanni

Mel

21 inches to 9 inches 21:9

Exercise 3 (a)Mason

Laney

Exercise 3 (a)Mason

Laney

= 4 miles

= ? miles

Exercise 3 (a)2 mi 2 mi

2 mi 2 mi 2 mi

Mason

Laney

= 4 miles

= 6 miles

Exercise 3 (b)Mason

Laney

= ? m

= 930 m

Exercise 3 (b)310m 310m

310m 310m 310m

Mason

Laney

= 620 m

= 930 m

Exercise 3(c)

What ratios can we say are equivalent to 2:3?

Exercise 3(c)

4:6 and 620:930

Exercise 4(a)Wrong

Right

= 8

= ?

Exercise 4(a)r r

r r r r r r r r

Wrong

Right

= 8

= 36

Exercise 4(b)Wrong

Right

= 20

= ?

Exercise 4(b)Wrong

Right

= 20

= 90

Exercise 4(d)Wrong

Right

=

= ?

4(f)• 2:3 and 4:6 are equivalent

because they represent the same value. The diagram never changed, only the value of each unit in the diagram.

ClosingTwo ratios A:B and C:D are equivalent ratios if there is a positive number, c, such that C = cA and D = cB.Ratios are equivalent if there is a positive number that can be multiplied by both quantities in one ratio to equal the corresponding quantities in the second ratio.