Problem
Count sticks needed via multiplication
You want to use sticks to build 5 squares and 4 triangles, like the ones shown, with no sticks shared between shapes. How many sticks are needed in all?
Operations
Your answer
sticks
Watch out Even though the shapes sit side by side in the picture, sticks are never shared between them. Count each of the 5 squares' 4 sticks and each of the 4 triangles' 3 sticks separately.
How to solve
Strategy Identify Subproblems — Split the total into two easy multiplication subproblems: sticks for the squares and sticks for the triangles. Since shapes don't share sticks, count each group with multiplication, then add.
1STEP 1
Find the sticks for the squares
5 squares, each needing 4 sticks — that's 5 × 4 = 20 sticks.
5 × 4 = 20
The 5 squares split the sticks into five separate groups, each holding the 4 sticks of one square — one stick per side, four sides, so exactly 4 sticks each. With five such equal groups, they're counted in one multiplication, 5 × 4.
Identify Subproblems3.OA.A.1Multiplication FactsBuilding 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
Find the sticks for the triangles
4 triangles, each needing 3 sticks — that's 4 × 3 = 12 sticks.
4 × 3 = 12
The 4 triangles split the sticks into four separate groups, each holding the 3 sticks of one triangle — one stick per side, three sides, so exactly 3 sticks each. With four such equal groups, they're counted in one multiplication, 4 × 3.
Identify Subproblems3.OA.A.13STEP 3
Add the two totals
No sticks are shared, so 20 and 12 add up to 32 sticks in all.
20 + 12 = 32
Squares and triangles never share sticks, so the two groups don't overlap. Since the whole equals the sum of its non-overlapping parts, adding the 20 sticks for squares and the 12 for triangles gives the total directly.
Identify Subproblems3.OA.A.3Answer
32 sticks
20 + 12 = 32
Check — 5 squares use 20 sticks and 4 triangles use 12, with none shared. 20 + 12 = 32 confirms it.
Takeaway
Count each shape with equal-groups multiplication, then add the totals — 5 × 4 for squares, 4 × 3 for triangles.
- Find the squares' sticks (5 × 4 = 20)
- Find the triangles' sticks (4 × 3 = 12)
- Add for the total → 32
Where next?
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