Reasoning · Grade 3-1 Multiplication and Division
Problem
The four sides are minus, plus, times, divide and share their corners.
Writing every side as an equation with a shared corner turns a picture puzzle into a small set of linked number sentences I can reason about.
3.OA.A.4Make A Systematic ListThe product must stay under 9, so it is 2 × 4 or 2 × 3.
A product of two different numbers that still fits in 1-8 is very restrictive, so the multiplication side is the best place to start guessing.
3.OA.C.7Guess And CheckThe multiplication side is the best place to start, because a product of two different numbers that still fits in 1 to 8 leaves very few options.
A number in that small range can be split into two different factors in only a couple of ways, and each split brings its partner with it.
Every other pairing is ruled out immediately, so the search starts from a handful of candidates instead of the whole board.
The quotient is 2 as well, giving 6 ÷ 3 or 8 ÷ 4.
Division as an unknown-factor question ('what times LM gives TL?') narrows TL and LM to just a couple of pairs.
3.OA.A.4Eliminate PossibilitiesFitting 1, 5, 7 into the minus and plus sides yields two layouts.
Once the corners are fixed, only three numbers remain, so the subtraction and addition sides are quick to satisfy by checking the few leftovers.
3.NBT.A.2Make A Systematic ListNothing else fits, so there are exactly two.
Because every branch was forced by the multiplication and division sides, there is no room for a third distinct filling.
3.OA.C.7Eliminate PossibilitiesStart with the trickiest sides (the times and divide corners), lock those numbers in, and the add and subtract sides fall into place - all with Grade 3 number facts!