Testinar Grade 6 math

What Is a Rate?

Students will build Grade 6 mastery of what is a rate? using models, equations, and test-style reasoning.

CH01-03 Ratios, Rates, and Percents

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Date
Score: ____ / 8

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

A car travels $180$ miles in $3$ hours. Which of the following is the rate written in simplest form as miles per hour?
1. $60$ miles per hour
2. $90$ miles per hour
3. $180$ miles per hour
4. $540$ miles per hour
A recipe calls for $2$ cups of flour for every $3$ eggs. Is this a rate or a simple ratio? Explain.
1. It is a rate because the units are different
2. It is a simple ratio because we compare number to number
3. It is a rate because it involves two quantities
4. It is a simple ratio because the units are both measurements of quantity
Which of the following is a rate?
1. $3$ boys to $4$ girls
2. $60$ miles per hour
3. $5$ red marbles to $2$ blue marbles
4. $8$ pencils to $3$ pens
A factory makes $360$ toys in $6$ hours. What is the rate in toys per hour?
1. $60$ toys per hour
2. $54$ toys per hour
3. $80$ toys per hour
4. $360$ toys per hour
Based on the graph, what is the unit rate in miles per hour?
1. $\frac{1}{2}$ mile per hour
2. $2$ miles per hour
3. $1$ mile per hour
4. $\frac{2}{3}$ miles per hour
A painter paints $48$ square feet in $2$ hours. What is the rate in square feet per hour?
1. $20$ square feet per hour
2. $96$ square feet per hour
3. $50$ square feet per hour
4. $24$ square feet per hour
Based on the table, what is the rate in miles per gallon?
1. $20$ miles per gallon
2. $96$ miles per gallon
3. $48$ miles per gallon
4. $24$ miles per gallon
A store sells $8$ notebooks for $$6.40$. What is the unit price per notebook?
1. $$0.50$ per notebook
2. $$0.70$ per notebook
3. $$0.80$ per notebook
4. $$1.00$ per notebook

Teacher and parent reference

Answer key and explanations

A. $60$ miles per hour
A rate compares two quantities with different units. Divide the distance by the time: $180\div3=60$ miles per hour.
A. It is a rate because the units are different
A rate compares two quantities measured in different units. Here, cups of flour are compared to eggs, so the comparison is a rate: $2$ cups of flour for every $3$ eggs.
B. $60$ miles per hour
A rate compares quantities with different units. Option B compares distance (miles) to time (hours), which are different units. All other options compare quantities in the same category.
A. $60$ toys per hour
Divide toys by hours: $360 \div 6 = 60$ toys per hour.
D. $\frac{2}{3}$ miles per hour
From the graph, at 3 hours the distance is 2 miles. The unit rate is $2 \div 3 = \frac{2}{3}$ miles per hour.
D. $24$ square feet per hour
Divide area by time: $48 \div 2 = 24$ square feet per hour.
D. $24$ miles per gallon
Divide miles by gallons: $48 \div 2 = 24$ miles per gallon.
C. $$0.80$ per notebook
Divide total cost by number of notebooks: $6.40 \div 8 = 0.80$ dollars per notebook.