Primary 3 Angles Study Guide

Primary 3 angles in four short steps: the size of an angle, right angles, comparing an angle with a right angle, and finding and counting angles in a figure, with something to try at each step and worked examples to finish.

Start here

What is an angle in P3 maths?

An angle is the amount of turn between two arms.

Two straight arms meet at a point. Turn one arm away from the other and the opening between them grows. In Primary 3, your child does not measure that turn yet. They compare it with a right angle, the corner of a square.

In this chapter, your child uses this to:

  • the size of an angle is the turn, not the length of its arms;
  • a right angle is a quarter turn, like the corner of a square;
  • any angle is smaller than, equal to or greater than a right angle;
  • in a figure, find each marked angle, check it, and count it once.
1

Step 1

The size of an angle

More turn, bigger angle. The size of an angle is how far one arm has turned away from the other. Longer arms, or turning the whole angle round, do not change it.

Drag the blue dot, or use the slider

Try it

Angle x has long arms and a narrow opening. Angle y has short arms and a wide opening. Which angle is bigger?

▶ Watch the lesson: Right-angle comparisonPractise 17 questions →
2

Step 2

Right angles

A right angle is a quarter turn. It is the corner of a square. Fold any piece of paper in half, then in half again, and the folded corner is a right angle too: a right-angle checker your child can make at home.

Tap to fold the paper

Here is a piece of paper with uneven edges. None of its corners is a right angle. Fold it in half.
Try it

Open the folded paper out flat. How many right angles meet at the point where the two creases cross?

▶ Watch the lesson: Right-angle comparisonPractise 17 questions →
3

Step 3

Comparing an angle with a right angle

Put a square's corner on it. Place the corner on the point where the arms meet, with one edge along one arm. Then look at the other arm: inside the corner means smaller, along the edge means equal, outside means greater.

Pick an angle, guess, then check

Smaller than a right angle
Equal to a right angle
Greater than a right angle
Try it

Mei puts the corner of a square on angle k, with one edge along one arm. The other arm lies inside the corner of the square. Angle k is

▶ Watch the lesson: Right-angle comparisonPractise 17 questions →
4

Step 4

Finding and counting angles in a figure

Check each marked angle, and count it once. Angles are not only at the outside corners of a shape. A line drawn across a figure makes new angles, and two angles can share one point.

Tap each letter to check its angle

0smaller than a right angle
0right angles
0greater than a right angle
Eight angles are marked, a to h. Tap a letter to fit the corner of a square into that angle.
Try it

Mei draws a straight line from one corner of a square to the opposite corner. She marks all the angles inside the two triangles. How many of them are smaller than a right angle?

▶ Watch the lesson: Find and count anglesPractise 9 questions →

Primary 3 angles questions, worked step by stepTry each question first. Then show a hint, or the working one line at a time.

Right-angle comparisonBasic

Look at angles p, q and r. Which angle is greater than a right angle?

pqr
Check each angle with the corner of a square. Look at the opening, not at how long the arms are.
  1. Angle p: the other arm stays inside the corner of the square, so p is smaller than a right angle.
  2. Angle q is on a slant, but its arms fit the corner exactly, so q is a right angle.
  3. Angle r has short arms, but its other arm is outside the corner, so r is greater than a right angle.
Answer: angle r
Right-angle comparisonIntermediate

The clock shows 4 o'clock. Is the angle between the hour hand and the minute hand smaller than, equal to or greater than a right angle?

123456789101112
Where would the hour hand point if the hands made a right angle? Think of a quarter turn from 12.
  1. The minute hand points to 12. The hour hand points to 4.
  2. A quarter turn from 12 reaches 3, so hands at 12 and 3 would make a right angle.
  3. The hour hand has turned past the 3, to the 4. The opening is wider than the corner of a square.
Answer: greater than a right angle
Find and count anglesIntermediate

Ravi draws a straight line across a rectangular card, from one corner to the opposite long side. He marks angles a to g.
(a) How many of the marked angles are smaller than a right angle?
(b) How many of the marked angles are greater than a right angle?

abcdefg
The corners of a rectangle are right angles. Where the line meets a corner, it cuts that right angle into two parts.
  1. Angles c, f and g are corners of the rectangle that the line does not touch. They are right angles.
  2. The line cuts the top left corner into a and b. Each part fits inside a square's corner, so a and b are smaller.
  3. At the bottom, d fits inside the corner of a square, so it is smaller. Angle e is wider than the corner, so it is greater.
  4. Smaller: a, b and d. Number of angles = 3. Greater: e only. Number of angles = 1.
Answer: (a) 3   (b) 1
Find and count anglesChallenge

Two straight lines cross at one point and make angles w, x, y and z. Angle w is a right angle. How many of the four angles are right angles?

wxyz
Angles w and x sit side by side along one straight line. A straight line is a half turn. How many right angles make a half turn?
  1. Angles w and x together make a straight line, which is a half turn. A half turn is two right angles.
  2. Angle w is one right angle, so angle x is the other. Angle x is a right angle.
  3. In the same way, x and y make a straight line, so y is a right angle. Then y and z do too, so z is a right angle.
  4. Right angles: w, x, y and z. Number of right angles = 4.
Answer: 4
5

Step 5

Check yourself

Five quick questions from the four steps. Answers are not saved; they show where to practise next.

1. Angles m and n have the same opening. The arms of angle m are twice as long. Which angle is bigger?

2. At 9 o'clock, the hour hand and the minute hand make an angle that is

3. Ali puts the corner of a square on an angle, with one edge along one arm. The other arm is outside the corner. The angle is

4. How many right angles are there inside a rectangle?

5. How many of the marked angles in this shape are smaller than a right angle?

wxyz
0/5
Answer all five to see where to practise next.
For parents

How to use this guide. Do step 2 for real: fold a scrap of paper twice with your child, then go round the house checking corners with it. A book, a door frame, a clock at 3 o'clock, a pair of open scissors. Ask "smaller, equal or greater?" before they check. Each step takes two or three minutes; the whole guide about fifteen.

The worked examples show how the same check is used in a test question. Let your child try first, then reveal the working one line at a time and ask what comes next.

More study guides

Before this: Bar GraphsNext: Perpendicular and Parallel LinesPrimary 3 Numbers up to 10 000 study guidePrimary 3 Addition and Subtraction Within 10 000 study guidePrimary 3 Money study guide
Lessons and practice

P3 Angles lessons and practice

2 lesson videos and 38 questions across two subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →