A triangle plus a triangle makes ten, so a triangle is five. These free printable puzzles hide the same number behind the same shape and ask a child to read it back out, which is solving for an unknown before anyone has called it x.
A symbol puzzle is an equation in disguise, and that disguise is exactly what makes it useful. A child who is not yet ready for letters will happily reason that if two of the same shape make ten then one makes five — and that is precisely the move that x will later ask for. The notation is doing the intimidating, not the mathematics.
Why this sheet works
The harder puzzles chain the shapes: once the triangle is known, a triangle plus a circle making eight tells you the circle. Working out the shapes in the right order — the one you can find first, then the one it unlocks — is the reasoning the page builds, and it is the same order of operations a system of equations needs.
How this one works
One question from this sheet, worked through a step at a time.
● + ● = 28 and ◆ − ● = 5. What is ◆?
● + ● = 28 and ◆ − ● = 5. What is ◆?
28÷2=14
28÷2=14
5+14=19
Two unknown symbols and two facts. Do not start where the question points — start where there is only ONE thing you do not know, because that is the only place an answer can come from.
The first fact has the same symbol twice and nothing else, so it is that symbol doubled: half of 28 is 14.
Now the next fact has only one unknown left in it — the 14 was taken OFF it to leave 5, so put it back: 5 + 14 = 19.
