Constructions and Tilings
Class 7 · Mathematics
4 ideas in Class 7 Mathematics, explained in plain words, with games and quizzes to practise.
Perpendicular bisector with arcs
Part of: Building with ruler and arcs
Any spot that sits equally far from both ends of a straight piece lies on its middle cut line. Swinging matching arcs from each end finds two such spots, one on each side. Joining them cuts the piece into exact halves and meets it square at 90 degrees. The same trick draws 90 degrees anywhere and matches old rope methods from early Indian texts.
Why it matters. It lets the child split lengths exactly without trusting printed marks.
Try it in two minutes
- Tie two equal strings to two coins.
- Swing both and mark crossings.
- Join crossings, check the middle.
Try at home. Fold a paper strip in half and crease it to find the middle.
Halving and copying angles
Part of: Building with ruler and arcs
Marks set at equal steps along both arms, plus a third spot swept equally from both marks, build two triangles whose three sides match. Matching sides force matching corners, so the join from the corner splits it exactly. The same arm-sweep idea copies a corner elsewhere, and copying corners side by side draws matching slant lines that never meet.
Why it matters. It turns guessing at corners into sure two-triangle proof.
Try it in two minutes
- Recall the 360 into 8 parts trick.
- Recall halving 90 to 45.
- Link arm marks to twin triangles.
Try at home. Fold a square paper corner twice and open it to see four equal parts.
Sixty degrees and the six-sided ring
Part of: Building with ruler and arcs
A triangle with three equal sides holds three 60 degree corners. Six such 60s add to a full 360 turn, so six matching triangles meet neatly at one point with no gaps. Their outer edges form a six-sided ring with equal sides and 120 degree corners, and halving 60 gives 30 and then 15.
Why it matters. It shows how one triangle unlocks many exact corners.
Try it in two minutes
- Recall three-equal-side triangle gives 60.
- Recall 120 joins two 60s.
- Link six triangles to the ring.
Try at home. Draw six-spoke wheel corners and check that they close fully.
Tiling grids without gaps
Part of: Covering flat space
Laying shapes with no gaps and no laps is tiling. A 2-square tile needs pairs, so any board with an odd count of squares fails at once, and odd rows times odd columns always stays odd. Colouring squares like a chessboard proves harder cases: each tile covers one dark and one light square, so unequal colour counts can never tile.
Why it matters. It teaches counting proofs that settle fit without trying forever.
Try it in two minutes
- Recall 4 by 6 needs 12 tiles.
- Recall odd by odd never pairs.
- Link colour counts to proof.
Try at home. Cover a chessboard corner with dominoes and spot leftover colours.
What your child will practise
- Halving and copying angles: Mission Control Quest (Collect the Answer)
- Halving and copying angles: Ocean Quick Fire (Quick Fire)
- Perpendicular bisector with arcs: Jungle Quick Fire (Quick Fire)
- Sixty degrees and the six-sided ring: Number Quest (Match It Up)
- Tiling grids without gaps: Jungle Puzzle (Clue Puzzle)
- Quiz: Halving and copying angles (8 questions)
- Quiz: Perpendicular bisector with arcs (8 questions)
- Quiz: Sixty degrees and the six-sided ring (8 questions)
- Quiz: Tiling grids without gaps (8 questions)