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Maths · Ages 10–11 · 50 minutes

Angles in a triangle

Pupils show that the angles in a triangle add up to 180°, use this and angles on a straight line to find missing angles, and give a reason for each step.

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Success criteria

  • I can explain why the angles in a triangle total 180 degrees
  • I can find a missing angle in a triangle
  • I can give a reason for each answer

Key vocabulary

  • angle
  • degree
  • triangle
  • straight line
  • interior angle
  • isosceles
  • equilateral
  • right angle
  • sum

You will need

  • paper triangles (one per pupil, all different)
  • scissors
  • protractors
  • rulers
  • mini whiteboards

Curriculum links

  • Year 6· England
  • Grade 5· United States
  • Primary 6· Nigeria
  • Class 6· India

Practice sheets

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The lesson at a glance

50 minutes in all. Timings are a guide: follow your class.

  1. Step 1: Starter

    Quick recall: "How many degrees in a right angle?
    7 minutes

  2. Step 2: Teach

    Every pupil has a different paper triangle.
    13 minutes

  3. Step 3: Guided practice

    On whiteboards, pupils write the answer and the reason: angles 90° and 35°; angles 110° and 25°; an equilateral triangle; an isosceles triangle with one angle of 100° (where can the 100° go?); a strai
    10 minutes

  4. Step 4: Independent practice

    Use the practice buttons above.
    15 minutes

  5. Step 5: Plenary

    "Can a triangle have two right angles?
    5 minutes

  6. Step 6: Assessment for learning

    Look for pupils who: subtract from 180° accurately, especially with three-digit numbers; give a reason, not just an answer; use the properties of isosceles and equilateral triangles.

  7. Step 7: Differentiation

    Pupils who need support should use the torn-corners model again for a second triangle and keep a "180 − ?" strip for mental subtraction.

  8. Step 8: Common misconceptions

    Thinking bigger triangles have bigger angle sums.

  9. Step 9: Home link

    Ask your child to cut out any triangle from scrap paper, tear off the corners and show you how they make a straight line.

1.Starter

7 minutes

Quick recall: "How many degrees in a right angle? On a straight line? In a full turn?" (90°, 180°, 360°.)

Then mental subtraction from 180 on whiteboards: 180 − 70, 180 − 125, 180 − 95 − 40. These calculations are what the whole lesson relies on, so make them quick.

2.Teach

13 minutes

Every pupil has a different paper triangle. "Mark each corner with a dot. Now tear off the three corners." (Tearing works better than cutting, because the torn edge shows which part is the corner.)

"Put the three corners together so the points meet and the edges touch." Pupils find they make a straight line. "Everyone had a different triangle, and everyone got a straight line. What do we know about angles on a straight line?" (180°.) "So the three angles in any triangle add up to 180°."

Model a missing-angle question. A triangle has angles 65° and 40°. "65 + 40 = 105. 180 − 105 = 75. The missing angle is 75°, because angles in a triangle add up to 180°."

Step by step

  1. Add the angles you knowWrite the total.
  2. Subtract from the total180° for a triangle or a straight line, 360° for angles around a point.
  3. Give the reason"angles in a triangle add up to 180°".
  4. Check the sizeDoes it look about right in the diagram?

Then special triangles. "An equilateral triangle has three equal angles: 180 ÷ 3 = 60° each. An isosceles triangle has two equal angles. If the odd angle is 40°, the other two share 140°, so each is 70°."

The rest of the plan

Guided and independent practice, the plenary, assessment for learning, differentiation, common misconceptions and the home link are free with a Crayonbird account.

  1. Guided practice10 minutes
  2. Independent practice15 minutes
  3. Plenary5 minutes
  4. Assessment for learning
  5. Differentiation
  6. Common misconceptions
  7. Home link
See the whole plan, free

Learning Wiki

Angles

An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.

Area

Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².

Coordinates

Coordinates are a pair of numbers that give an exact position on a grid, like (3, 5). The first number is how far across (x) and the second is how far up (y).

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