Constructions and Tilings: common misconceptions

If your child says… “Every arc must use the same opening.”

Ask together

Did our different openings move either crossing away from the fold?

What’s true

Each crossing needs matching radii, but separate crossings can use different openings.

If your child says… “We still need a crossing below.”

Ask together

Which two points already have matching distances to X and Y?

What’s true

O already supplies one point, so C supplies the only additional point needed.

If your child says… “The arm marks can be different distances from O.”

Ask together

Which triangle sides would stop matching if A moved closer to O?

What’s true

Matching arm distances and matching crossing radii give triangles with matching sides.

If your child says… “Copying the straight gap is enough.”

Ask together

Would a larger new arc still give three matching triangle sides?

What’s true

The vertex arcs must also have matching radii.

If your child says… “The copied angle can go on either side.”

Ask together

Are both copied openings above their lines and right of the crossing line?

What’s true

Equal angle sizes need the correct positions against the same crossing line.

If your child says… “Bisecting 60° gives three 20° pieces.”

Ask together

How many equal angles does one bisecting line make?

What’s true

Bisection makes two equal angles, so halving 60° gives 30°.

If your child says… “The hexagon's corners are 60° too.”

Ask together

How many triangle corners meet at one outer corner?

What’s true

Each outer corner combines two triangle corners, making 120°.

If your child says… “Fourteen squares means seven tiles will fit.”

Ask together

Where could the extra dark squares find their light partners?

What’s true

Unequal colour counts prevent tiling; equal counts alone still do not guarantee it.