Count sticks needed via multiplication

3.OA.A.13.OA.A.3 · take · grade 3

Archetype: Multiplication as Equal Groups · step in a 2-type progression

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?

One square and one triangle, each built from sticks, are drawn. The square uses $4$ sticks for its four sides, and the triangle uses $3$ sticks for its three sides.

Show solution

Understand

We build 5 squares and 4 triangles out of sticks, with no stick shared between shapes. We need the total number of sticks used.

Givens

Each square is built from 4 sticks (one per side).
Each triangle is built from 3 sticks (one per side).
We build 5 squares and 4 triangles.
No sticks are shared between shapes.

Unknowns

The total number of sticks needed for all the shapes.

Constraints

Shapes do not share sticks, so we can count each shape separately and add.

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

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.

Execute

#7 Identify Subproblems 3.OA.A.1

Each square needs 4 sticks, and there are 5 squares. That is 5 equal groups of 4.

5 \times 4 = 20

Equal-groups multiplication is just repeated addition (4+4+4+4+4), a Grade 3 skill.

#7 Identify Subproblems 3.OA.A.1

Each triangle needs 3 sticks, and there are 4 triangles. That is 4 equal groups of 3.

4 \times 3 = 12

Again equal groups: 3+3+3+3 counted as one multiplication.

#7 Identify Subproblems 3.OA.A.3

Since no sticks are shared, the total is the squares' sticks plus the triangles' sticks.

20 + 12 = 32

Combining the results of the two subproblems answers the original question.

Answer: 32 sticks

Review

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.

Guess and Check (tool 6): count each shape one stick at a time and tally, getting 4+4+4+4+4+3+3+3+3 = 32, confirming the multiplication.

Standards · min grade 3

3.OA.A.1 Interpret products of whole numbers as total number of objects in groups — Counting sticks as equal groups (5 groups of 4, 4 groups of 3).
3.OA.A.3 Solve multiplication and division word problems within 100 — Combining the two multiplication results into the total count.

💡 You don't have to count every stick — group them by shape and multiply, which is just Grade 3 equal-groups sense!