Reasoning · Grade 2-2 Multiplication Facts

Problem

Split a rectangle into product tiles

An 8×8 grid has twelve numbers scattered in its cells - 4, 3, 9, 3, 2, 6, 3, 12, 8, 4, 4, 6. Each number sits in its own rectangular tile whose cell count equals that number. Tiles neither overlap nor leave gaps. Say how many tiles the grid splits into and check the split is possible.
Your answer
How to solve
Strategy Identify Subproblems — Each number is its own little subproblem - draw a rectangle of that many cells around it. Because exactly one number lives in each tile, the number of tiles is just the count of numbers. The crucial check is that the tile areas add up to the grid area, which tells us the cut is possible with no gaps or overlaps.
1STEP 1

One tile per number

One number per tile means 12 tiles.

number of tiles = number of numbers = 12
2STEP 2

Add up the tile areas

A tile covers its own number of cells, so the total area is the sum of the numbers.

4+3+9+3+2+6+3+12+8+4+4+6 = 64
3STEP 3

Match the total to the grid area

That sum is 64 = 8 × 8, matching the grid exactly.

8 × 8 = 64 = sum of tile areas
Answer
12 tiles (areas total 64 = 8 × 8)
There are 12 numbers, so 12 tiles makes sense. The tile areas sum to 64, which matches the 8 x 8 = 64 grid exactly - no cells left over and none double-counted - so a gap-free, overlap-free cutting is possible.
Takeaway

Count the numbers to count the tiles, then add the numbers up - if they total the grid's cells, every rectangle fits like a perfect puzzle!

  • One tile per number
  • Add up the tile areas
  • Match the total to the grid area