Use angle notation and a protractor

What you will learn

• Use angle notation and a protractor

Models used: number sentences, stories, tables.

Before you start

• Draw angles

The middle letter names the corner

The two rays BA and BC meet at B. How do we name the angle between them?

1. Find the meeting point of the two rays. That point is B, the vertex of the angle.

2. Read from A along a ray to B, then along the other ray to C. Write ∠ABC; the vertex B stays in the middle.

   ∠ABC

3. Reading the other way gives ∠CBA. This names the same opening because B is still the middle letter.

   ∠ABC = ∠CBA

Worked example: A new example, together

In the angle name ∠ABC, which letter names the vertex?

1. Mathematical relationships. Read each value with the heading above its column.

   Find the vertex and compare the opening, keeping the baseline fixed.

   The middle letter identifies the shared endpoint of the rays.

   Mathematical relationships

   Feature	Observation
   Shape	Inspect its properties

2. Mathematical relationships. Read each value with the heading above its column.

   The vertex is where the two rays meet.

   Mathematical relationships

   Feature	Observation
   Shape	Inspect its properties

   In the angle name ∠ABC, which letter names the vertex?

   B

3. Mathematical relationships. Read each value with the heading above its column.

   The middle letter in a three-letter angle name is the vertex.

   Mathematical relationships

   Feature	Observation
   Shape	Inspect its properties

4. Mathematical relationships. Read each value with the heading above its column.

   So ∠ABC has vertex B.

   Mathematical relationships

   Feature	Observation
   Shape	Inspect its properties

5. Mathematical relationships. Read each value with the heading above its column.

   Check the result against the question we started with.

   The two rays are BA and BC, sharing B.

   We found B. The middle letter identifies the shared endpoint of the rays.

   Mathematical relationships

   Feature	Observation
   Shape	Inspect its properties

Common mistakes to discuss

• Naming the angle by the wrong letter. The middle letter is the vertex. ∠ABC is the angle at B, between the arms BA and BC.

Check your understanding

• Use angle notation and a protractor
• recognise or measure a turn independently of ray length
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.