Problem
Joining 9 cm four times makes a 36 cm wire in all.
Four equal 9 cm lengths are the same as adding 9 four times, so one multiplication, 9 × 4, gives the exact total.
Identify Subproblems3.OA.B.5A triangle with three 2 cm sides needs 6 cm of wire.
Since a triangle's three sides are each 2 cm, using that length three times is the same as adding 2 cm three times — one multiplication, 2 × 3, gives the wire it needs.
Analyze The Units3.OA.B.5Split 36 cm into 6 cm pieces and you get exactly 6 triangles.
How many triangles fit is the same question as how many equal groups of 6 make 36. Since dividing undoes multiplying, that means finding what number times 6 makes 36 — and 6 × 6 = 36, so there are exactly 6 groups, 6 triangles. Notice 9 × 4 = 36 and 6 × 6 = 36: different factors, the very same product.
Identify Subproblems4.OA.B.4Different Factor Pairs Same ProductThe 36 cm wire divides exactly into 6 cm triangle-lengths, with no wire left over.
Each triangle costs 6 cm of wire and the whole wire is 36 cm, so the number of triangles is just how many 6 cm lengths fit inside 36 cm.
Asking how many 6 cm lengths fit in 36 cm is the same as asking what number times 6 makes 36, because sharing a total into equal groups is the reverse of building that total by multiplying.
That number is 6, because six lengths of 6 cm joined end to end make exactly 36 cm with nothing left over.
Six lengths of 6 cm is 6 counted six times, and adding the same 6 cm over and over gives one fixed total of 36 cm.
Find the total, then divide by what one triangle needs. Just like 9 × 4 and 6 × 6 — different factors can share the same product.