Grade 6 Module 1
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Transcript of Grade 6 Module 1
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Grade 6 Module 1
Lesson 3
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Equivalent Ratios•Understanding of equivalent
ratios.•Use tape diagrams• Formalize a definition of
equivalent ratios
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Exercise 1
•Write a one-sentence story problem about a ratio.
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Sample
The ratio of the number of sunny days to the number of cloudy days in this city is 3:1.
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Exercise 1
Write the ratio in two different forms
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Answers
•3:1 3 to 1
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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.
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Represent ratio in a table
Shanni’s Ribbon Mel’s Ribbon
7 3
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Represent ratio in a table
Shanni’s Ribbon Mel’s Ribbon
7 314 6
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Represent ratio in a table
Shanni’s Ribbon Mel’s Ribbon
7 314 621 9
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Tape DiagramShanni
Mel
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Tape Diagram
What does each unit on the tape diagram represent?
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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?
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Tape DiagramWhat if each unit on the tape diagrams represents 2 meters? What are the lengths of the ribbons?How did you find that?
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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
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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?
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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?
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Tape DiagramMathematicians call these ratios equivalent. What ratios can we say are equivalent to 7:3?
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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
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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
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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
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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
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Exercise 3 (a)Mason
Laney
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Exercise 3 (a)Mason
Laney
= 4 miles
= 6 miles
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Exercise 3 (a)2 mi 2 mi
2 mi 2 mi 2 mi
Mason
Laney
= 4 miles
= 6 miles
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Exercise 3 (b)Mason
Laney
= 620 m
= 930 m
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Exercise 3 (b)310m 310m
310m 310m 310m
Mason
Laney
= 620 m
= 930 m
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Exercise 3(c)
What ratios can we say are equivalent to 2:3?
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Exercise 3(c)
4:6 and 620:930
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Exercise 4(a)Wrong
Right
= 8
= ?
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Exercise 4(a)Wrong
Right
= 8
= 36
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Exercise 4(b)Wrong
Right
= 20
= ?
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Exercise 4(b)Wrong
Right
= 20
= 90
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Exercise 4(d)Wrong
Right
=
= ?
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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.