Problem
Count sticks needed via multiplication
We build 5 squares and 4 triangles out of sticks, with no stick shared between shapes. We need the total number of sticks used.
Operations
Your answer
sticks
Watch out Each triangle uses only 3 sticks, not the 4 a square uses — don't use the same number for both shapes.
How to solve
Strategy Identify Subproblems — Split the total into two easy multiplication subproblems: sticks for all squares and sticks for all triangles. Because shapes don't share sticks, count each group with equal-groups multiplication, then add.
1STEP 1
Sticks for the squares
5 squares, each made of 4 sticks — that's 5 equal groups of 4, giving 20 sticks.
5 × 4 = 20
Equal-groups multiplication is just repeated addition (4+4+4+4+4), a Grade 3 skill.
3.OA.A.1Identify SubproblemsBuilding the 5 squares uses 5 × 4 = 20 sticks in all.
Why?
The five squares split the sticks into five separate groups, each group holding the 4 sticks of one square.
Why?
One square needs exactly 4 sticks, one stick for each of its four sides.
Why?
Each side is matched with its own single stick, so four sides take four sticks.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
No sticks are shared between shapes, so the five groups never overlap and can be counted separately and added.
🧱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?
Five equal groups of 4 sticks are totaled by the multiplication 5 × 4.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
2STEP 2
Sticks for the triangles
4 triangles, each made of 3 sticks — that's 4 equal groups of 3, giving 12 sticks.
4 × 3 = 12
Again equal groups: 3+3+3+3 counted as one multiplication.
3.OA.A.1Identify Subproblems3STEP 3
Add the two groups
No sticks are shared, so add the two groups: 20 + 12 = 32 sticks in all.
20 + 12 = 32
Combining the results of the two subproblems answers the original question.
3.OA.A.3Identify SubproblemsAnswer
32 sticks
5 × 4 + 4 × 3 = 32
5 squares would alone use 20 sticks and 4 triangles 12 sticks; 32 is between 'a couple dozen' and feels right for 9 small shapes. The unit is sticks (a count), which matches the question.
Takeaway
You don't have to count every stick — group them by shape and multiply, which is just Grade 3 equal-groups sense!
- Sticks for the squares
- Sticks for the triangles
- Add the two groups
Where next?
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