Challenges

Problems worth getting stuck on

A small shelf of curious problems, gathered for every family here. Pick one, sit down together, and if it bites back, June can work through it with your child.

7 of 21 challenges ·

Grade 2

Count the shapes hiding inside

A line, a triangle, a rectangle -- each picture holds more than it first shows. The trick is the same every time: count the small pieces, then the big ones they make.

3 problems

Grade 5

Same height, different base

Two triangles leaning on the same line share a height, so their areas follow their bases -- once you see which segment is which.

3 problems

Grade 6

Two squares and a tilted rectangle

Two squares share a baseline, and a tilted rectangle crosses them. Find its area from just one side length -- the skill is cutting the picture into triangles of equal area.

1 problem

Grade 7

A square on the centre

A circle of radius 6 cm and a square balanced on its centre -- the only number on the page is hiding in plain sight.

1 problem

Grade 8

The circle in the gap

Four equal circles leave a gap in the middle, and the circle that fills it is smaller than it looks. The skill is drawing the square the four centres make -- Pythagoras does the rest.

1 problem

No pen, no paper

A shaded rectangle sits in the corner of a right triangle and four measurements are all you get. The trick is seeing the two famous triangles hiding in the drawing.

1 problem

Two circles, one line

An 8 cm circle and a 12 cm circle perch on the same straight line, touching each other. The gap between their footprints is not what it looks like -- the right triangle through the centres does the measuring.

1 problem

Geometry