At a glance. One lesson of about 60 minutes. Students name points, lines, rays and angles with correct notation, classify angles by size, and read a protractor scale by choosing the one whose 0 lies on an arm.
Calculator: no calculator. Nothing here needs one. The reading is from a scale, and the checks are small whole-number subtractions.
What students will learn
Know
- The notation for points, lines, rays, segments, parallel and perpendicular.
- An angle is named with the vertex in the middle letter and measured in degrees.
- Acute, right, obtuse, straight and reflex, and the sizes that separate them.
Understand
- An angle is an amount of turn, not the length of its arms.
- Two arms make two angles that add up to 360°.
- A protractor's two scales add up to 180°, so the reading must be checked against the type of angle.
Do
- Name an angle from a diagram and from a description.
- Classify an angle from its size.
- Read the correct protractor scale and justify the choice by estimating first.
MYP assessment criteria
Wording paraphrased. What this lesson gives you evidence for, and what to look for:
- Criterion A. Knowing and understanding: names, notation and types of angle, and the protractor routine (questions 1 to 4, 6 and 9).
- Criterion B. Investigating patterns: the opening-angle figure. Ask students to predict where the type changes and to say what stays the same as the arm turns, before and after they test it.
- Criterion C. Communicating: using ∠ABC and the symbols ∥ and ⊥ correctly, and writing why a reading is wrong in a sentence (questions 6 and 9).
- Criterion D. Applying mathematics in real-life contexts: clock-hand angles and turns, where a student must choose what to measure from and in which direction (questions 4 and 7).
The one thing to do with the figure
Ask for a prediction before each slide. “Where does acute stop? What happens at 180?” Take the numbers from the room, then let the first figure settle them.
In the second figure, press the arm-direction button and ask what changed. The angle did not: only the scale that starts at 0 on the arm did. Say that sentence aloud and write it on the board; every protractor mistake in this unit is a failure to apply it.
A possible order
| 5 min | Warm-up from the student page, in silence, then answers. |
|---|---|
| 10 min | Hook, the notation list, then the first figure with predictions. |
| 10 min | Key idea. Students sort angles from the room (door, book corner, laptop lid) into the five types, then draw ∠ABC = 47° and ∠PQR = 132° and measure a partner's, to the nearest degree. |
| 10 min | Second figure, then the worked example; students finish the faded one in pairs. |
| 5 min | Question 1, the check. If many choose B, go back to the first figure. |
| 15 min | Your turn, Levels 1 to 3, at each student's own pace. |
| 5 min | Exit ticket, question 9, on paper or on screen. |
The answers
| Warm-up | 0.4; 110; 150. |
|---|---|
| Worked example | ∠PQR, 128°, obtuse. |
| Faded example | ∠YXZ, 73°, acute; the reflex angle is 287°. |
| 1. Type of an angle | D, reflex. 215° is between 180° and 360°. B is the common slip of calling every angle above 90° obtuse. |
| 2. Reading the right scale | 145. 180 − 35 = 145, the reading on the scale that starts at 0 on arm QP. |
| 3. Obtuse angles | C, 118°. A is acute, B is right, D is reflex. |
| 4. Turns and degrees | 270. Three quarter turns of 90°, or 45 × 6. |
| 5. Comparing with a right angle | 43. 133 − 90 = 43. |
| 6. Notation | B. A is parallel, C is equal length, D is not valid notation. |
| 7. Angle between clock hands | 75. 180 − 105 = 75. |
| 8. Angle the other way round | 288. 5x = 360, so x = 72 and 4x = 288. |
| 9. The wrong-scale reading | A. B confuses reflex with obtuse; C thinks arm length matters; D is a rule with no reason. If many choose C, go back to the first figure. |
What each wrong answer tells you
| They give | What it usually means | What to do |
|---|---|---|
| B in question 1 | Calls every angle above 90° obtuse, so reflex is missing from the picture. | Draw a straight line and ask what 215° looks like once it has turned past it. |
| 35 in question 2 | Reads the scale that does not start at 0 on the arm. | Have them put a finger on the 0 of the scale they used and trace to the arm. |
| 90 in question 4 | Measures the short way round, not the clockwise turn. | Use a real clock or arm gestures and ask which way the hand moved. |
| 47 in question 5 | Subtracts from 180, not from 90. | Ask what the question names as the starting point: a right angle. |
| 90 or 105 in question 7 | Treats the hour hand as fixed on the hour, or gives the hour hand's own angle. | Ask where the hour hand is at 3:30 and let them draw it. |
| 72 or 90 in question 8 | Finds one part, or divides by 4 rather than 5. | Draw the full turn as 5 equal boxes: 1 for the small angle, 4 for the reflex. |
Questions worth asking
- Does making the arms longer make the angle bigger? No. The angle is the turn between the arms. Listen for “the arms are lines that go on for ever”.
- Why does an angle have two sizes? The arms split the full turn in two. Name the one you mean: usually the smaller, unless it is stated to be reflex.
- How do two protractor scales help or hurt? The right scale starts at 0 on your arm. A student who can say this has understood the instrument.
- Why do some surveyors use 400 to a full turn? 400 is a round number for decimals; 360 divides more evenly. This links to factors in Unit 1.
Differentiation
A way in for anyone stuck
- Give a clear acetate protractor and pre-draw angles with one arm already along the baseline.
- Provide a card of the five angle types with a picture and a size range, kept on the desk.
- Start with the whole-number half of the first figure: a quarter, half and three-quarter turn.
Stretch
- Question 7, then: at what other times between 3:00 and 4:00 are the hands at a right angle? (At 3:00 itself, and again at about 3:33, when the minute hand has gained 180° on the hour hand at 5.5° per minute.)
- Show that when a reflex angle is r times the other angle, r + 1 equal parts make 360, and write the reflex angle as 360 × r ÷ (r + 1).
Students learning in English as an additional language
Several words are new and several are everyday words used precisely: “acute” and “obtuse” sound alike. Say each word with its picture and sound out “ver-tex”.
| Word | Plain meaning | Example |
|---|---|---|
| vertex | the point where two arms of an angle meet | In ∠ABC the vertex is B |
| ray | a straight line that starts at a point and goes on for ever one way | Ray AB starts at A and passes through B |
| acute, obtuse | less than 90°; between 90° and 180° | 30° is acute; 150° is obtuse |
| right angle | an angle of exactly 90°, a square corner | The corner of a page |
| reflex | an angle bigger than 180° and smaller than 360° | The big angle the other way round from 40° is 320° |
| protractor | a tool with scales for measuring and drawing angles | A half circle marked 0 to 180 |
Sentence starters for explaining aloud or in writing:
- The vertex of this angle is … because …
- This angle is … because it is more than … and less than …
- I read the … scale because its 0 is on arm …
Two things not to say
“The bigger the arms, the bigger the angle.” Arm length is only the length of the drawing; the angle is the turn.
“Always read the top scale.” Which scale to read depends on where the 0 is. A rule with no reason breaks the first time the angle is drawn the other way.
Questions to set
Extra practice in three tiers, including one question from earlier work for spacing. Every answer has been checked.
1Fluency
The idea on its own, with friendly numbers. Set these first.
- TypesClassify: 12°, 90°, 91°, 180°, 270°.
Acute, right, obtuse, straight, reflex. - NamingWhich letter is the vertex of ∠PQR, and what is the name of the ray from Q through R?
Q, and ray QR.
2In context
The same idea inside a situation, where the first job is deciding what to calculate.
- TurnsA fan blade turns 120° and then another 120°. What angle is left to complete a full turn?
120°: 360 − 240 = 120. - DirectionsA runner faces north and turns clockwise to face east, then keeps turning clockwise to face west. Through how many degrees has she turned in all?
270°: north to east is 90°, east to south is another 90° and south to west is another 90°.
3Challenge
Reasoning, generalising and working backwards.
- ReasoningFrom Unit 1, lesson 6: work out 360 − (2 × 90 + 45), then say what type of angle it is.
135, obtuse. - SystemsIn the system with 400 units in a full turn, what is the angle between the hands of a clock at 3:00?
100 units: a quarter of 400.
Practicalities
Works on a phone or a shared screen. Nothing a student types is saved or sent anywhere.
Both figures work with the keyboard (tab to a slider, then the arrow keys) and by touch. Under each one, “Show me the steps” gives the same states in words.
No device? Use a card protractor and two strips of paper joined with a split pin.