Problem
Find the value of one unit
A craft store sells 24 marbles for $8.40 and a supermarket sells 16 marbles for $4.80. Find which store sells marbles more cheaply by comparing the price of a single marble.
Base-ten numbersOperations
Your answer
Watch out Don't compare the total prices directly ($4.80 vs $8.40) — the bundles are different sizes, so compare the price per single marble instead.
How to solve
Strategy Analyze the Units — To compare bundles of different sizes fairly, reduce each to the same unit -- the price of one marble (dollars per marble) -- by dividing total price by count. The smaller per-marble price wins.
1STEP 1
Price per marble at the craft store
Divide the total by the number of marbles: $8.40 / 24 = $0.35 per marble.
8.40 ÷ 24 = 0.35
Splitting the total cost equally among 24 marbles gives the cost of just one.
4.NBT.B.6Analyze The UnitsDividing the craft store's 0.35.
Why?
The $8.40 total is nothing more than the 24 individual marble prices combined, because the bundle's price is made of exactly those 24 prices with no gaps or overlaps.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Every marble costs the same, so the total is that one price taken 24 equal times, and dividing by 24 pulls the single price back out.
Why?
Twenty-four marbles all at the same price is twenty-four equal groups of that price, which is exactly what multiplying that price by 24 means.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Because 24 equal prices multiply up to the total, dividing the total by 24 runs that multiplication backward to land on one price.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Price per marble at the supermarket
Divide the total by the number of marbles: $4.80 / 16 = $0.30 per marble.
4.80 ÷ 16 = 0.30
The same one-unit idea applied to the supermarket bundle.
4.NBT.B.6Analyze The Units3STEP 3
Compare the unit prices
Compare $0.35 and $0.30 per marble. Since $0.30 is less than $0.35, the supermarket sells marbles more cheaply.
0.30 less than 0.35
Once both are measured per single marble, the smaller number is the better deal.
4.OA.A.2Identify SubproblemsAnswer
The supermarket (at $0.30 per marble versus $0.35 at the craft store).
Cross-check with equal counts: 48 marbles cost 2 x $8.40 = $16.80 at the craft store but 3 x $4.80 = $14.40 at the supermarket, so the supermarket is cheaper, agreeing with the per-marble result.
Takeaway
This only needs Grade 4 dividing -- find the price of one marble at each store, and the smaller one is the better deal!
- Price per marble at the craft store
- Price per marble at the supermarket
- Compare the unit prices
Where next?
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