Toward June
Sign in

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.

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 3

Six ways to sit in a row

Rebuild the missing number, seat three friends in every possible order, and spot the one story that is not really four fours. For a child learning to list every case and read past the numbers.

3 problems

Every edge counts

A wizard's stars hide edges in their valleys, and a blank inside a sum turns addition around. For a child practicing careful counting and working backwards.

2 problems

Digit riddles

The answer is a number you have to build, not compute -- count the tens, count the digits, then figure out where the 2 belongs.

3 problems

Marbles that change hands

Emma gives some marbles away and the lead shifts -- or does it? Count what the gift does to both sides.

3 problems

Grade 4

Twice his age

A brother is 8 today and the writer will be twice his age in 12 years. The arithmetic is easy; the skill is knowing which year the "twice" belongs to.

1 problem

Add it without adding

Three sums that look like work and are not -- pair the ends, balance the scale, or let the subtractions fold together.

3 problems

Grade 5

Three problems that reward a second look

A fraction sum that folds up neatly, two fractions a hair apart, and one equation to work backwards -- three chances to look for structure before reaching for arithmetic.

3 problems

The decimal point takes a walk

Shift the decimal point and a number changes by a surprising amount -- the trick is counting the nines hiding in the difference.

3 problems

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

The leftovers tell the story

Three division riddles where the remainder is the whole puzzle -- what is left over tells you what you started with.

3 problems

Six people, six days

Five people earn five thousand in five days, so six people in six days earn... six thousand, right?

1 problem

A thirtieth in three parts

Break 1/30 into three unit fractions, all with different denominators. There is more than one way -- checking a friend's answer is half the fun.

1 problem

The convenient sum

Nine improper fractions, one neat trick -- every term hides a whole one, and what is left folds up on itself.

1 problem

Grade 6

Percent up, percent down

Grow a number by 60% and it does not take 60% to bring it home -- the way back is a different rate. For a child learning to ask: a percent of what?

3 problems

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

Two numbers, two clues

Each puzzle gives two facts about hidden numbers and asks one back. The trick is the same every time: turn the clues into shares, solve the picture, then undo the twist.

3 problems

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