Look at this tiled floor and this honeycomb. What do you notice about the way the shapes fit together?
Is there any empty space left between them, or do they fit snugly with nothing to spare?
Take two or three hands-up answers, not open call-outs. Listen for the word gaps and revoice it: so the shapes meet with no gaps between them.
Look at these three surfaces. First, squares. Then hexagons, like the honeycomb. Then circles.
As you look at each one, ask yourself: are there any gaps, and do any shapes overlap? That is the test for tessellation.
Squares first: point out that four square corners meet at a point and the straight edges match, so no gaps appear.
Hexagons next: same test — do they meet edge to edge? They do; this is the honeycomb.
Circles are the one to hold on. Ask before revealing the picture: will these leave gaps? Then point to the little curved spaces the picture shows between every group of circles, the ones the round edges cannot close. This is the case pupils reason from in the wrap.
Today we tile a floor together on the board using squares, laying them one at a time so each meets the next edge to edge with no gaps. First, predict: will squares fill the space with no gaps left over?
Watch as copies of the square are laid to fill the space, each one meeting the next edge to edge. Look for gaps and overlaps, and call out what you see.
Squares have straight edges, so they close up the space. Later, in your copy, you will draw a shape with three or six straight edges and see the same thing happen.
Talk this one through together — pupils take turns at the board laying squares, and the class agrees or corrects out loud. Squares fill the floor cleanly because every straight edge matches its neighbour. Keep asking gaps or no gaps? as the single test.
Between each pupil's turn, keep the watching class working: ask for a prediction before the next square goes down, take two hands-up answers, and revoice a pupil's observation before revealing. Rotate four pupils so different children get a turn at the board.
Remind them that hexagons work the same way because their edges are straight too, like the honeycomb. Pupils will draw triangle and hexagon tilings by hand in the next step.
In your maths copy, choose one shape that tessellates — a triangle, a square or a hexagon — and draw at least six copies of it fitting together with no gaps, like floor tiles.
Make each copy the same size and let the edges touch, so there is no empty space between them.
This is where triangles and hexagons get drawn by hand, which shows their true edge-to-edge tiling far better than any grid could. Walk the room glancing for edges that touch and copies that are the same size — no marking, this is whole-class copybook practice, not assessment. Nudge anyone drawing circles toward a square, triangle or hexagon: try a shape with straight edges.
Today we work through tiling challenges together on the board with squares. Each one fills a little more space than the last. First we tile a short strip. Then we fill a small square floor. Then we fill a wider floor. Last, we fill a larger floor with no gaps left anywhere.
Before each challenge, predict whether the squares will fit. Then we fill the space and check for gaps together. Because squares have straight edges, they should close up the whole space with nothing to spare.
This is the practice round — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining, and take a quick prediction before each challenge starts.
The last challenge fills the largest floor. Ask before it starts is any square going to leave a gap? so pupils reason rather than guess. Link back to the honeycomb and copybook drawings: hexagons and triangles fill space the same way because their edges are straight too.
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