A focused Grade 7 learning session for Unit Rates with Fractions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving unit rates with fractions.
Unit Rates with Fractions is part of Grade 7 Ratios and Proportional Relationships. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of unit rates with fractions using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Unit Rates with Fractions, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving unit rates with fractions.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A runner covers \(\frac{3}{4}\) of a mile in \(\frac{1}{6}\) of an hour. What is the runner's speed in miles per hour?
Answer D: \(\frac{9}{2}\) mph
Unit rate \(=\frac{3/4}{1/6}=\frac{3}{4}\times 6=\frac{18}{4}=\frac{9}{2}=4.5\) mph.
A cyclist travels \(\frac{1}{2}\) mile in \(\frac{1}{8}\) hour. What is the cyclist's speed in miles per hour?
Answer D: 4 mph
Unit rate \(=\frac{1/2}{1/8}=\frac{1}{2}\times 8=4\) mph.
A store sells \(\frac{3}{5}\) pound of cheese for $6. What is the unit price per pound?
Answer D: $10
Unit rate \(=\frac{6}{3/5}=6\times\frac{5}{3}=10\) dollars per pound.
A painter completes \(\frac{2}{3}\) of a room in \(\frac{1}{5}\) hour. At this rate, how many rooms will the painter complete in 1 hour?
Answer D: \(\frac{10}{3}\) rooms
Unit rate \(=\frac{2/3}{1/5}=\frac{2}{3}\times 5=\frac{10}{3}\) rooms per hour.
A train travels \(3\frac{1}{2}\) miles in \(\frac{1}{4}\) hour. What is the train's speed in miles per hour?
Answer D: 14 mph
Convert \(3\frac{1}{2}=\frac{7}{2}\). Unit rate \(=\frac{7/2}{1/4}=\frac{7}{2}\times 4=14\) mph.
The table shows the relationship between pages read and time. Find the unit rate in pages per hour.
Answer D: 3 pages per hour
From the table, \(\frac{1}{2}\) page in \(\frac{1}{6}\) hour gives unit rate \(\frac{1/2}{1/6}=\frac{1}{2}\times 6=3\) pages per hour.
Runner A covers \(\frac{1}{3}\) mile in \(\frac{1}{20}\) hour. Runner B covers \(\frac{2}{5}\) mile in \(\frac{1}{12}\) hour. Which runner is faster?
Answer D: Runner A at \(\frac{20}{3}\) mph
Runner A: \(\frac{1/3}{1/20}=\frac{1}{3}\times 20=\frac{20}{3}\) mph. Runner B: \(\frac{2/5}{1/12}=\frac{2}{5}\times 12=\frac{24}{5}=4.8\) mph. Runner A is faster.
A recipe requires \(\frac{3}{4}\) cup of milk to make \(\frac{5}{8}\) of a batch. How much milk is needed per full batch?
Answer D: \(\frac{6}{5}\) cups
Unit rate: \(\frac{3/4}{5/8}=\frac{3}{4}\times\frac{8}{5}=\frac{24}{20}=\frac{6}{5}=1\frac{1}{5}\) cups per full batch.
Five erasers cost \(\frac{3}{4}\) dollar. What is the cost per eraser?
Answer D: $0.15
Unit rate \(=\frac{3/4}{5}=\frac{3}{4}\times\frac{1}{5}=\frac{3}{20}=0.15\) dollars per eraser.
A pool fills at a rate of \(\frac{5}{6}\) gallon in \(\frac{1}{3}\) minute. How many gallons per minute is this?
Answer D: \(\frac{5}{2}\) gal/min
Unit rate \(=\frac{5/6}{1/3}=\frac{5}{6}\times 3=\frac{15}{6}=\frac{5}{2}=2.5\) gal/min.
Two stores sell beans at different rates. Which store offers the better price?
Answer D: Store A at $4/lb
Store A: \(\frac{2}{1/2}=2\times 2=4\) dollars/lb. Store B: \(\frac{3}{2/3}=3\times\frac{3}{2}=4.5\) dollars/lb. Store A is cheaper.
