Equivalent Ratios Have the Same Unit Rates: IM 6.3.7
[url=https://im.kendallhunt.com/MS/teachers/1/3/7/preparation.html]“Equivalent Ratios Have the Same Unit Rates”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 6.3.7
- IM 6.3.7 Lesson: Equivalent Ratios Have the Same Unit Rates
- Practice 6.3.7
- IM 6.3.7 Practice: Equivalent Ratios Have the Same Unit Rates
IM 6.3.7 Lesson: Equivalent Ratios Have the Same Unit Rates
Which one doesn’t belong? Explain your reasoning.
[list][*]5 miles in 15 minutes[/*][*]3 minutes per mile[/*][*]20 miles per hour[/*][*]32 kilometers per hour[/*][/list]
Two burritos cost $14. Complete the table to show the cost for 4, 5, and 10 burritos at that rate. Next, find the cost for a single burrito in each case.
What do you notice about the values in this table?
Noah bought [math]b[/math] burritos and paid [math]c[/math] dollars. Lin bought twice as many burritos as Noah and paid twice the cost he did. How much did Lin pay per burrito?[br][br][img]data:image/png;base64,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[/img]
Explain why, if you can buy [math]b[/math] burritos for [math]c[/math] dollars, or buy [math]2⋅b[/math] burritos for [math]2⋅c[/math] dollars, the cost per item is the same in either case.
Complete the table.
Explain the strategy you used to complete the table.[br]
Here is a partially filled table from an earlier activity. Use the same strategy you used for the bracelet problem to complete this table.
Next, compare your results with those in the first table in the previous activity. Do they match? Explain why or why not.
It takes 4 pounds of apples to make 6 cups of applesauce. Complete the table.
Jada eats 2 scoops of ice cream in 5 minutes. Noah eats 3 scoops of ice cream in 5 minutes. How long does it take them to eat 1 scoop of ice cream working together (if they continue eating ice cream at the same rate they do individually)?
The garden hose at Andre's house can fill a 5-gallon bucket in 2 minutes. The hose at his next-door neighbor’s house can fill a 10-gallon bucket in 8 minutes. If they use both their garden hoses at the same time, and the hoses continue working at the same rate they did when filling a bucket, how long will it take to fill a 750-gallon pool?
IM 6.3.7 Practice: Equivalent Ratios Have the Same Unit Rates
A car travels 55 miles per hour for 2 hours. Complete the table.
The table shows the amounts of onions and tomatoes in different-sized batches of a salsa recipe.
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[/img][br]Elena notices that if she takes the number in the tomatoes column and divides it by the corresponding number in the onions column, she always gets the same result.[br][br]What is the meaning of the number that Elena has calculated?
A restaurant is offering 2 specials: 10 burritos for $12, or 6 burritos for $7.50. Noah needs 60 burritos for his party. Should he buy 6 orders of the 10-burrito special or 10 orders of the 6-burrito special? Explain your reasoning.
Complete the table so that the cost per banana remains the same.
Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster? Explain your reasoning.
A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go 1 mile. How far can the car travel with 15 gallons? Show your reasoning.
A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go 1 mile. How much gas does the car use to go 100 miles? Show your reasoning.
A box of cereal weighs 600 grams. How much is this weight in pounds? Explain or show your reasoning. (Note: 1 kilogram = 2.2 pounds)