Problem
Cut a rectangle into a grid of cards
A 30 cm by 20 cm rectangular sheet is cut into identical 5 cm squares. We need the total number of squares.
GeometryMeasurement & data
Your answer
squares
Watch out A grid is counted by multiplying the across-count by the down-count, not by adding the two.
How to solve
Strategy Identify Subproblems — Break it into two subproblems: how many squares fit across the width, and how many fit down the height. Then a rows-times-columns array gives the total, matching the grid in the figure.
1STEP 1
Squares across the width
Split the 30 cm width into 5 cm pieces — that gives 6 squares across.
30 ÷ 5 = 6
Partitioning a length into equal 5 cm pieces is a Grade 2 measurement idea.
2.G.A.2Identify Subproblems2STEP 2
Squares down the height
Split the 20 cm height into 5 cm pieces — that gives 4 squares down.
20 ÷ 5 = 4
Same partitioning idea applied to the vertical side gives the number of rows.
2.G.A.2Identify Subproblems3STEP 3
Multiply rows by columns
The squares form a 6-by-4 array, so multiply across by down to get 24 in all.
6 × 4 = 24
An array of equal squares is counted by multiplication, just like finding area in unit squares.
3.MD.C.7Identify SubproblemsThe number of 5 cm squares in the sheet equals the 6 squares in one row multiplied by the 4 rows.
Why?
The 5 cm squares sit in a neat grid, so each of the 4 rows holds the very same 6 squares, and the total is those 4 equal groups of 6.
Why?
Taking the same group of 6 squares once for every one of the 4 rows is adding 6 over and over, which is exactly what multiplying 6 by 4 means.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Adding the rows really does account for every square, because the grid covers the whole sheet with none left out and none counted twice.
Why?
When a shape is split into pieces with no gaps and no overlaps, those pieces add back to exactly the whole shape.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Answer
24 squares
The figure shows exactly 6 columns and 4 rows; counting the grid cells gives 24, confirming the array. The unit (squares, a count) matches the question.
Takeaway
Count squares across and down, then multiply — the same row-by-column array thinking behind area!
- Squares across the width
- Squares down the height
- Multiply rows by columns
Where next?
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