2. Shapes, Patterns & Sorting
KindergartenThe world is full of shapes and patterns — from the circle of a wheel to the stripes on a shirt. This chapter teaches us to name shapes, sort things that belong together, and spot what comes next in a pattern.
Naming shapes and sorting by a rule
Four shapes to know by sight:
- Circle — perfectly round, no straight sides, no corners.
- Square — 4 straight sides, all the same length, 4 corners.
- Triangle — 3 straight sides, 3 corners.
- Rectangle — 4 straight sides, opposite sides the same length, 4 corners.
Sorting means putting things into groups because they share something — all the red ones together, or all the round ones together. A pattern is something that repeats in a predictable way, like red, blue, red, blue, … (an "AB pattern").
Why shapes and patterns matter
Shapes help us describe and build the world: a door is a rectangle, a ball is round, a slice of pizza is close to a triangle. Once you can name a shape, you can talk about anything that has that shape.
Patterns train your brain to predict what comes next — a skill used in music, in reading, and later in almost every part of math. Sorting teaches the idea of a rule: "these belong together because…" — the very first seed of the "sets" you'll meet properly many years later.
Hands-on: hunt for shapes and finish a pattern
- Walk around a room and point at objects.
- Ask: "Is it round with no corners?" — that's a circle.
- Ask: "Does it have 4 straight sides?" — a square or rectangle.
- Sort a small pile of toys or blocks into a "round" pile and a "cornered" pile.
What comes next? red, blue, red, blue, ___?
- Look at what repeats: red then blue, over and over.
- After blue, the pattern starts over at red.
Answer: red.
Test your understanding
How many corners does a triangle have?
3 corners, and 3 straight sides — that is exactly what makes it a triangle ("tri" means three).
What makes a square different from a rectangle?
A square's four sides are all the same length. A rectangle only needs its opposite sides to match — so a square is actually a special kind of rectangle where every side happens to be equal.
What comes next: circle, circle, square, circle, circle, square, ___?
Circle. This is an "AAB" pattern — two circles, then a square, repeating — so after the second square-triplet finishes, a fresh pair of circles begins.
Can the same pile of buttons be sorted two different ways?
Yes! You could sort by color first (all reds together, all blues together), then mix them up and sort the very same buttons by size instead (all big ones, all small ones). The buttons don't change — only the rule you choose to sort by changes.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1What shape has 3 sides and 3 corners?
- Count the sides: 3 sides
- Count the corners: 3 corners
- A shape with 3 sides is a triangle
Example 2Finish the pattern: red, blue, red, blue, ___
- The pattern repeats red then blue
- After blue the pattern starts again
- So red comes next
Now you try
Work each one out first, then tap to reveal the worked answer.