GRADE 7 MATH · LEARNING PATHWAYS 2.0
Learn what a unit rate means, how it connects to ratios and division, and how to use it to make smarter decisions. Then practice 12 questions with instant feedback.
01 · DISCOVER
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Which bag has the lower cost per ounce? Make a prediction before calculating. Predictions are not graded.
Choose a prediction. You will revisit it in the virtual store.
Imagine you’re shopping with a limited budget. You find two bags of popcorn. Which should you buy for the lowest price per ounce?
We cannot simply choose the lower total price. To compare fairly, both prices must be expressed for the same amount: one ounce.
By the end, you will explain unit rates, calculate them using division, check their accuracy, and use them in everyday situations.
02 · BUILD YOUR FOUNDATION
A ratio compares quantities, such as $4.50 to 6 ounces. A rate is a ratio between quantities measured in different units. A unit rate describes how much of one quantity corresponds to one unit of the other.
The word per means “for each one.” For example, $0.75 per ounce means that each ounce costs 75 cents.
Six ounces cost $4.50 in total. Each ounce accounts for an equal share of the cost. Divide the total cost into six equal parts.
$4.50 ÷ 6 = $0.75 per ounce. Multiplying $0.75 × 6 = $4.50 checks the result.
03 · EXPLORE
Suppose one ounce costs $0.75. Two ounces cost twice as much, and four ounces cost four times as much. Both the weight and the cost change together.
| Ounces | 1 | 2 | 4 | 6 |
|---|---|---|---|---|
| Cost | $0.75 | $1.50 | $3.00 | $4.50 |
Start with the original popcorn bags. Then change one price or size and watch the unit prices update. All prices are fictional.
These models show the equivalent cost at each bag’s current unit price. Points between package sizes are mathematical comparisons; the store sells whole bags.
| Ounces | Bag A rate | Bag B rate |
|---|
Blue line: Bag A. Gold dashed line: Bag B. Displayed prices are rounded to cents; comparisons use unrounded rates.
What about the other bag? $6.40 ÷ 8 = $0.80 per ounce. Bag A costs $0.75 per ounce, so it is cheaper by $0.05 per ounce.
04 · WATCH IT SOLVED
A cyclist rides 36 miles in 3 hours at a constant speed. What is the speed in miles per hour?
Five notebooks cost $12.50. Divide the total cost by the number of notebooks: $12.50 ÷ 5 = $2.50 per notebook. Check by multiplying $2.50 × 5 = $12.50.
05 · SOLVE TOGETHER
A student writes: “Bag A costs 6 ÷ 4.50 = about $1.33 per ounce.”
Which correction gives dollars per ounce?
Choose the operation, then read the explanation.
Four movie tickets cost $30. What is the price for one ticket?
First, decide which quantity you want for one unit. The question asks for dollars per ticket. Divide total dollars by the number of tickets.
06 · PRACTICE
Complete 12 varied questions. Each answer gets instant feedback. If you make an error, use the hint and revise your answer before going on.
07 · APPLY AND REFLECT
Water bottle A: 20 ounces for $2.40. Bottle B: 30 ounces for $3.30.
Bottle A costs $2.40 ÷ 20 = $0.12 per ounce. Bottle B costs $3.30 ÷ 30 = $0.11 per ounce. Bottle B is the better value per ounce, although a shopper might still choose the smaller container.
Why isn’t comparing only the total price a fair way to decide which package gives you the best value? Describe one time you could use unit rates outside school.
You need at least 24 ounces of popcorn and can spend at most $20. Buy whole bags. Bag A is 6 oz for $4.50; Bag B is 8 oz for $6.40. Find the least expensive purchase that meets both requirements.
Mission feedback is practice, separate from your 12-question score. Your written explanations are not automatically graded or sent to the dashboard. Copy your final explanation into your Google Classroom response if your teacher requests it.
08 · REFLECT
I can use unit prices to compare two deals fairly and explain why one is better.
I know I am successful when…Bag A costs $0.75 per ounce because $4.50 ÷ 6 = $0.75. Bag B costs $0.80 per ounce because $6.40 ÷ 8 = $0.80. Bag A has the lower unit price by $0.05 per ounce.
Copy your reflection to your assignment before leaving this page.
09 · RESULTS & EXTEND
You’ve completed the learning pathway. Here’s how you performed on your 12 independent practice problems.
This score measures independent-practice first attempts. Select Submit My Score below to save your results to the teacher dashboard. Google Classroom posting depends on your teacher’s sync setup.
Your score will be saved to the Learning Pathways teacher dashboard.
How would you represent a unit rate in a ratio table or a graph?
Continue to the Proportional Tables Lab →