Practice 1
An angle turns through 75 one-degree steps. What is its measure in degrees?
Answer and teaching response
75 · Every counted step represents one degree.
Measure an angle by its turn, not its ray length
Use a shared vertex and a circular turn to explain degree measure, then compare angles even when their drawn rays have different lengths.
Get the student and teacher materialsPrepare the group
Learning goal: A learner can explain that degree measure counts one-degree turns and remains unchanged when rays are extended.
You will need: Pencil, paper and two paper strips joined at an endpoint. A protractor is optional for checking the labelled examples.
Start with this question
Two angles both turn through 60 one-degree steps. One drawing has much longer rays. Which angle has the greater degree measure?
Neither. Both measure 60 degrees. Extending a ray changes the drawing's length, not the turn between the directions.
- Find the common endpoint, called the vertex, and follow the direction of each ray from it. The opening between those directions defines the angle.
- Imagine rotating one ray around the vertex until it reaches the other ray. A full turn contains 360 equal one-degree steps.
- Count the steps in the opening: sixty one-degree turns make a 60-degree angle. Compare it with a 90-degree quarter turn and a 120-degree angle.
- Extend either ray without rotating it. The directions are unchanged, so the same sixty steps still connect them. Do not use ray length as the angle measure.
Run the 15-minute workshop
- 3 minutes. Show two equal openings with unequal strip lengths and ask learners to predict whether the angles match.
- 4 minutes. Align the vertices and one direction; connect the matching opening to the number of one-degree turns.
- 5 minutes. Complete the practice, explaining what changes in each example and what stays fixed.
- 3 minutes. Use the final check and have learners describe how to compare angle size without comparing ray lengths.
A useful error to discuss
A learner might say: The angle with longer sides must be the larger angle.
Place the two vertices together and align one ray from each drawing. If the other rays point in the same direction, the turns match even when the visible segments end at different places.
Practise, then check independently
Use the first three tasks for guided practice. Try the final task without help. Record a drawing or equation as well as the answer.
Practice 2
A 40-degree angle has both rays extended without rotation. What is its new measure in degrees?
Answer and teaching response
40 · The directions and the turn between them remain unchanged.
Practice 3
A full turn is 360 degrees. How many degrees are in one quarter of a full turn?
Answer and teaching response
90 · Four equal quarter turns fill one full turn.
Independent check
An angle contains 110 one-degree turns. Its rays are shortened in the drawing but keep their directions. State the angle measure and explain why.
Answer and teaching response
110 · Shortening the visible segments does not change the opening.
Transfer the idea
An angle drawing is turned upside down without changing its shape. Does its degree measure change? Explain how you could check.
Discuss a possible response
No. Rotating the whole drawing preserves the turn between its rays. Align the vertex and one ray with the original to compare the other direction.
Choose the next teaching step
Look for:
- Locates the vertex and describes a turn between directions.
- Rejects ray length or page orientation as a measure of the angle.
If the idea is not secure: Use movable strips and change only one feature at a time: first length, then opening.
If the learner is ready: Sketch two differently oriented 60-degree angles and explain a way to superimpose them.
Materials for your group
Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.