Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.3

Lesson 3.5Comparing Rates with Benchmarks

Apply Day · Set BSecond form · new problems, same idea

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

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Learning target I can compare ratios by finding unit rates or using equivalent ratios.

Remember3.5 · Part II

Comparing Ratio Relationships

Convert each ratio to a unit rate (e.g. price per item or miles per gallon)
Alternatively, scale both ratios to a common term (like a common denominator)
Compare the resulting unit rates to identify the better buy or faster rate

Words: Unit rate (Tasa unitaria)Equivalent ratio (Razón equivalente)Compare (Comparar)Simplify (Simplificar)Common denominator (Denominador común)

1Complete each step, then write the final answer.

Pack A: first two columns. Pack B: last two.
Pack A has 2 apples for $1. Pack B has 5 apples for $3. What is the lower price for 1 apple?
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Final answer:
2Complete each step, then write the final answer.

Reyes: first two columns. Tran: last two.
Chef Reyes uses 2 tablespoons of cocoa for 3 ounces of milk. Chef Tran uses 3 tablespoons for 5 ounces of milk. Scale both to 15 ounces of milk. Whose cocoa is more chocolatey?
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Final answer:
3Complete each step, then write the final answer.

Mix A uses 4 cups of juice for 10 cups of water. Mix B uses 6 cups of juice for ? cups of water. The two mixes taste the same. Find the missing number.
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Final answer:
4Complete each step, then write the final answer.

Paint A: first two columns. Paint B: last two.
Paint A mixes 1 cup of red with 2 cups of white. Paint B mixes 2 cups of red with 5 cups of white. Which paint is more red?
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Final answer:
5Complete each step, then write the final answer.

Bird A: first two columns. Bird B: last two.
Bird A flies 54 miles in 3 hours. Bird B flies 75 miles in 5 hours. How many more miles per hour does the faster bird fly?
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Final answer:
6Complete each step, then write the final answer.

Columns in pairs: Shop A, Shop B, Shop C.
Shop A sells 6 pens for $4.50. Shop B sells 8 pens for $5.60. Shop C sells 10 pens for $7.20. What is the lowest price for 1 pen?
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Final answer:
7Circle the letter of the best answer. Show how you know.
Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?
1. AChef A
2. BChef B
3. CThey use the same amount
4. DCannot determine
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8Circle the letter of the best answer. Show how you know.
Which ratio is greater: 3:4 or 5:8?
1. A5:8
2. B3:4
3. CThey are equal
4. DCannot determine
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9Circle the letter of the best answer. Show how you know.
Which lemonade recipe is more lemony? Recipe A: 2 lemons for 6 cups of water. Recipe B: 3 lemons for 7 cups of water.
1. ARecipe B
2. BRecipe A
3. CThey are the same
4. DCannot determine
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