Reasoning · Grade 4-1 Joining and Cutting Figures
Problem
16 cells into 4 pieces makes each 4 cells.
Counting unit squares is how the area of any grid figure is measured, and identical pieces must have identical areas, so dividing settles the piece size before any shape is drawn.
3.MD.C.6Identify SubproblemsIdentical pieces must have identical areas, so dividing the cell count by four settles the size of one piece before any shape is drawn.
The four pieces fill the figure with no gap and no overlap, so their cell counts add back to the figure's total.
Asking how many cells go in each of four equal pieces is a division, and a remainder of zero shows the split is even possible.
The marks split too: one circle and one triangle each.
Sharing 4 marks equally among 4 pieces is straightforward division, and it turns a vague requirement into a checklist for every piece drawn.
3.OA.A.3Identify SubproblemsBegin at the corner cell with fewest options.
A corner cell has hardly any neighbours, so it is the cheapest place to start: there are only a couple of directions to try, and the mark rule kills all but one of them.
3.G.A.2Draw A DiagramThat corner piece fixes the shape as an L.
Trying the other choice and watching it break is a complete argument here, because a corner cell only ever has those two choices to try.
3.G.A.2Guess And CheckTurn the same L to cut the second piece.
Once a cell has only one free neighbour left, no choosing is involved — the drawing itself tells you where the cut must go.
3.G.A.2Guess And CheckThe third piece comes out the same way.
Working outward from the cells that are already boxed in keeps the puzzle shrinking, so each new piece has fewer options than the last.
3.G.A.2Draw A DiagramThe leftover cells form the fourth L by themselves.
If the last leftover cells had not formed the right shape, the earlier choices would have been wrong — so the fourth piece is a free check on the whole cut.
3.G.A.2Draw A DiagramEach piece has one of each mark, so the cut works.
Same shape and same size allows the piece to be rotated or flipped, exactly as a paper cut-out could be picked up and laid down the other way round.
3.G.A.2Draw A DiagramStart where there is no choice — a corner square with only two neighbours decides the very first piece for you!