Unit 2, Lesson 14
Solving Equivalent Ratio Problems
Grade 6
14.1
Warm-up
A red car and a blue car enter the highway at the same time and travel at a constant speed. How far apart are they after 4 hours?
What specific information do you need to be able to solve the problem?
14.2
Activity
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
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Silently read your card and think about what information you need to answer the question.
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Ask your partner for the specific information that you need. “Can you tell me ?”
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Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem.
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Once you have enough information, share the problem card with your partner, and solve the problem independently.
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Read the data card, and discuss your reasoning.
If your teacher gives you the data card:
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Silently read your card. Wait for your partner to ask for information.
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Before telling your partner any information, ask, “Why do you need to know ?”
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Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
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Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
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Share the data card, and discuss your reasoning.
14.3
Activity
- Lin read the first 54 pages from a 270-page book in the last 3 days.
- Diego read the first 100 pages from a 325-page book in the last 4 days.
- Elena read the first 160 pages from a 480-page book in the last 5 days.
If they continue to read every day at these rates, who will finish first, second, and third? Explain or show your reasoning.
Student Lesson Summary
To solve problems about something happening at the same rate, we often need:
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Two pieces of information that allow us to write a ratio that describes the situation.
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A third piece of information that gives us one number of an equivalent ratio. Solving the problem often involves finding the other number in the equivalent ratio.
Suppose we are making a large batch of fizzy juice and the recipe says, “Mix 5 cups of cranberry juice with 2 cups of soda water.” We know that the ratio of cranberry juice to soda water is , and that we need 2.5 cups of cranberry juice per cup of soda water.
We still need to know something about the size of the large batch. If we use 16 cups of soda water, what number goes with 16 to make a ratio that is equivalent to ?
To make this large batch taste the same as the original recipe, we would need to use 40 cups of cranberry juice.
| cranberry juice (cups) | soda water (cups) |
|---|---|
| 5 | 2 |
| 2.5 | 1 |
| 40 | 16 |
None