Math · Unit 3

Shapes and Patterns

2D and 3D shapes, patterns, position and symmetry

Geometry starts long before angles and proofs, with recognising shapes, noticing what makes them the same, and describing where things are.

The unit covers 2D and 3D shapes and their properties, symmetry, position and direction, and pattern - which is arguably what mathematics is about in general, introduced here in its most visible form.

This unit breaks down into 21 short steps and 120 questions, starting at difficulty 1 and building to 2. Below you can see exactly what it covers, how the path is structured, and worked examples with explanations.

Steps: 21
Questions: 120
Difficulty: 1-2

What this unit covers

Patterns and Sorting
3D Shapes
Position and Direction
2D Shapes
Symmetry

Where this fits

Independent of the arithmetic units. Geometry picks it up formally much later.

Where people slip

A shape is still itself when rotated. A square balanced on a corner is a square, not a diamond, and that is a genuinely common sticking point.

How the unit is structured

Shapes and Patterns runs as 21 short steps that unlock in order. 15 are practice rounds and 6 are challenge rounds that pull together everything before them. Questions start at difficulty 1 and climb to 2 as you progress.

Step 1 · easierStep 21 · harder

Challenge rounds

Example questions

30 real questions from this unit, with the answer and the reason behind it, grouped by what they practise. There are 120 in the unit altogether.

2D Shapes

Choose all that applyLevel 1
1. Which shapes have exactly 4 sides? Pick all that apply.
- Squarecorrect
- Rectanglecorrect
- Triangle
- Circle
A square and a rectangle each have 4 sides; a triangle has 3 and a circle has none.
Fill the blankLevel 1
2. A shape with 6 straight sides is a ____.
- hexagoncorrect
- pentagon
- octagon
- square
A hexagon has 6 straight sides.
Multiple choiceLevel 1
3. How many sides does a rectangle have?
- 4correct
- 3
- 5
- 6
A rectangle has 4 sides, with opposite sides the same length.
Picture questionLevel 1
4. 🔺 What flat shape is this?
- Trianglecorrect
- Square
- Circle
- Hexagon
This shape has 3 sides and 3 corners, so it is a triangle.
Match the pairsLevel 2
5. Match each shape to how many sides it has.
Answer: Rectangle = 4 sides; Pentagon = 5 sides; Hexagon = 6 sides
A rectangle has 4 sides, a pentagon 5, and a hexagon 6.
Odd one outLevel 2
6. Which shape does NOT have straight sides?
- Circlecorrect
- Square
- Triangle
- Pentagon
A circle is round with no straight sides; the others are made of straight sides.

3D Shapes

Guess the numberLevel 1
7. A can is shaped like a cylinder. How many flat faces does it have?
Answer: 2
A cylinder has 2 flat faces, one circle at the top and one at the bottom.
Multiple choiceLevel 1
8. How many faces does a cuboid (a box shape) have?
- 6correct
- 4
- 5
- 8
A cuboid has 6 flat faces, just like a cereal box.
Choose all that applyLevel 2
9. Which of these shapes have at least one flat face? Pick all that apply.
- Cubecorrect
- Cuboidcorrect
- Cylindercorrect
- Sphere
A cube, a cuboid, and a cylinder all have flat faces; a sphere is round with none.
Fill the blankLevel 2
10. A ____ has two flat circle faces and a curved side, like a can.
- cylindercorrect
- cone
- cube
- sphere
A cylinder has two circle faces joined by a curved surface.
Match the pairsLevel 2
11. Match each 3D shape to its number of flat faces.
Answer: Cylinder = 2 flat faces; Cube = 6 faces; Cone = 1 flat face
A cylinder has 2 flat faces, a cube has 6, and a cone has 1.
Sort into groupsLevel 2
12. Sort each 3D shape into Has a point or No point.
Answer: Cone = Has a point; Sphere = No point; Pyramid = Has a point; Cylinder = No point
A cone and a pyramid come to a point, while a sphere and a cylinder do not.

Patterns and Sorting

Match the pairsLevel 1
13. Match each animal to its size.
Answer: Ant = Small; Dog = Medium; Elephant = Large
We can sort things by size: an ant is small, a dog medium, and an elephant large.
Multiple choiceLevel 1
14. What comes next? red, blue, red, blue, ___
- redcorrect
- blue
- green
- yellow
The pattern repeats red then blue, so red comes next.
Build the sentenceLevel 2
15. Build a true sentence about this number pattern.
Answer: This pattern goes up by five each time
A pattern like 5, 10, 15 goes up by five each time.
Fact or fibLevel 2
16. In the pattern 2, 4, 6, 8, the numbers go up by 2 each time.
Answer: True
Each number is 2 more than the one before, so it grows by 2.
Fill the blankLevel 2
17. In the pattern 10, 20, 30, 40, each number goes up by ____.
- 10correct
- 20
- 5
- 1
Each step adds 10 to reach the next number.
Odd one outLevel 2
18. Which number does NOT belong in the pattern 2, 4, 6, 8, 10?
- 7correct
- 12
- 14
- 16
The pattern is even numbers, so 12, 14, and 16 fit, but 7 is odd.

Position and Direction

Build the sentenceLevel 1
19. Build a true sentence about where the cat is.
Answer: The cat is under the table
Under means below something, so the cat is under the table.
Fact or fibLevel 1
20. If you spin all the way around back to the start, you make a full turn.
Answer: True
Turning all the way around to face the same way is a full turn.
Fill the blankLevel 1
21. A ball sitting in a box is ____ the box.
- insidecorrect
- outside
- above
- below
If the ball is held by the box, it is inside the box.
Multiple choiceLevel 1
22. Which word is the opposite of left?
- rightcorrect
- up
- down
- front
Left and right are opposite directions.
Sort into groupsLevel 1
23. Sort each word into Position or Shape.
Answer: under = Position; circle = Shape; beside = Position; square = Shape
Under and beside tell us position, while circle and square are shapes.
Choose all that applyLevel 2
24. Which of these are amounts of turn? Pick all that apply.
- quarter turncorrect
- half turncorrect
- triangle
- square
A quarter turn and a half turn are amounts of turn; triangle and square are shapes.

Symmetry

Fact or fibLevel 1
25. A butterfly's two wings match like a mirror.
Answer: True
A butterfly has symmetry, so its left and right wings match.
Odd one outLevel 1
26. Which letter does NOT have a line of symmetry?
- Fcorrect
- A
- H
- T
The letters A, H, and T can be folded to match, but F cannot.
Build the sentenceLevel 2
27. Build a true sentence about symmetry.
Answer: Both halves of a symmetrical shape look the same
Both halves of a symmetrical shape look the same.
Fill the blankLevel 2
28. A shape with a line of symmetry has two ____ halves.
- matchingcorrect
- different
- round
- big
A line of symmetry makes two halves that match.
Match the pairsLevel 2
29. Match each shape to its number of lines of symmetry.
Answer: Square = 4 lines; Rectangle = 2 lines; Triangle = 3 lines
A square has 4 lines, a rectangle 2, and a triangle with equal sides has 3.
Multiple choiceLevel 2
30. Which shape has the most lines of symmetry?
- Circlecorrect
- Square
- Triangle
- Rectangle
A circle has many lines of symmetry, more than a square, triangle, or rectangle.

Where these questions come from. Each unit starts as a plan of the concepts it should cover and the difficulty it should span. Questions are written against that plan with AI assistance, then checked by a validator that rejects anything without a single defensible answer, an explanation, or plausible wrong options. How we write questions sets out the whole process, and corrections are fixed in the bank and reach the site and the app the same day.

How you practise

This unit mixes 14 different question formats, so you are recalling and applying rather than recognising the same layout every time.

Build the sentence
Choose all that apply
Fact or fib
Fill the blank
Guess the number
Match the pairs
Multiple choice
Odd one out
Picture question
Put in order
Sort into groups
Spell it
True or false
Type the answer

Practise Shapes and Patterns

120 questions across 21 steps. Start with step one and crawl at your own pace.

Play this unit

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