Grade 6 Module 1 Lesson 3
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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 inches to 6 inches 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
= 6 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
= 620 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)Wrong
Right
= 8
= 36
Exercise 4(b)Wrong
Right
= 20
= ?
Exercise 4(b)Wrong
Right
= 20
= 90
Exercise 4(d)Wrong
Right
=
= ?
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.
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