Angles: a week of ready-to-teach maths
Five days of lessons for Year 4 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out angle cards and a right-angle tester, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Cut out the angle cards once; they are reused across the week. Print a tester sheet per child.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. An angle is an amount of turn. In Year 4 children do not measure angles with a protractor; they compare them with a right angle. Smaller is acute, bigger is obtuse, two right angles make a straight angle, four make a revolution, and anything between a straight angle and a revolution is reflex.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
The right-angle tester
Children fold a paper circle in half and in half again; the folded corner is a right angle. Held in the corner of an angle, it shows at once whether the angle is smaller, equal or bigger. The interactive unit also names the sizes in degrees (a right angle is 90), which children meet properly in Year 5.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Angles are turns | See an angle as an amount of turn, make a right-angle tester, and find square corners | An angle is a turn; The right angle |
| 2 | Acute, right or obtuse | Compare angles with the tester: smaller than a right angle, a right angle, or bigger | Acute, right or obtuse |
| 3 | Straight, reflex, revolution | Meet the half turn, the full turn and the angles between them, each as right angles | Angles on a line; Angle types by degrees |
| 4 | Compare and order | Order angles by how far they open, not by how long their arms are, and estimate in right angles | Compare two angles |
| 5 | Angles around us | Name and estimate the angles of clock hands, doors and scissors | Self-check quiz; Angle types by degrees |
How the week builds
Day 1 makes the right angle the yardstick for the week. Day 2 names angles smaller and bigger than it, and Day 3 goes beyond, to the straight angle, the reflex angle and the revolution. Day 4 compares and orders angles and estimates them in right angles, and Day 5 finds them in the world. It builds on turning and directions from earlier years, and on reading the clock (AC9M4M03).
Materials for the week (one trip)
- From the classroom: scissors, coloured pencils, a large demonstration clock, and this pack printed.
- Optional: split pins and card strips for angle makers, and a door or a pair of scissors to open slowly.
- Cut out once, use all week: the angle cards. Print one tester sheet per child.
Words for the word wall
angle, turn, arm, vertex, right angle, acute, obtuse, straight angle, reflex, revolution, quarter turn, half turn, full turn, compare, estimate
Dear families
This week in maths, Year 4 learns that an angle is an amount of turn, and names angles by comparing them with a right angle: a square corner.
Try this at home
- Hunt for right angles: the corner of a book, a window, a tile. Are any corners not right angles?
- Open a door slowly. When is the angle acute, a right angle, obtuse?
- Look at a clock at 3 o’clock and 6 o’clock. What angles do the hands make?
- Turn on the spot: a quarter turn, a half turn, a full turn. How many right angles is each?
Angles I found this week
Fill one row a day. Write where you found an angle and its name.
| Day | Where I found it | Its name |
|---|---|---|
| Monday | ||
| Tuesday | ||
| Wednesday | ||
| Thursday | ||
| Friday |
Printed from the free seegongsik Angles teaching pack · seegongsik.com/au/y4/measurement/AC9M4M04/pack
Angles are turns
An angle is the amount of turn between two arms that meet at a point. The right angle, a quarter turn, is the yardstick for the whole week: children fold a right-angle tester and hunt for square corners. They also turn on the spot: a quarter turn is one right angle, a half turn two, and a full turn four.
We are learning to
- see an angle as the turn between two arms,
- make a right-angle tester and use it to check corners,
- link quarter, half and full turns to right angles.
Success criteria
- I can use my tester to find right angles, whichever way they face.
- I can say how many right angles make a quarter, half, three-quarter and full turn.
You need
The tester sheet (cut-out sheet 2), one per child, and scissors. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Turn on the spot Everyone faces the front, then makes a quarter turn to the right, another, another and another. Ask: “How many quarter turns brought you back to the front? What is a half turn?” |
| 30 min | Make a tester Show the board (see the box). Children cut out and fold a tester, do Part A, then check corners around the room. Ask: “How can you tell a corner is exactly a right angle, not just close to one?” |
| 10 min | Turns in right angles Children do Parts B and C. Ask: “How many right angles fit in a half turn? In a full turn?” |
Two half-sessions instead? Split after making the testers; start Session B with Part A.
Watch for these ideas
- Judging an angle by its arms. Long arms do not make a bigger turn.
- Thinking a right angle must sit like the letter L. Turned any way, it is still a right angle.
- Mixing up a right angle with the right-hand side.
Answers
- Part A: 1 yes, 2 no, 3 no, 4 yes, 5 yes, 6 no.
- Part B: a quarter turn is one right angle; a half turn is two right angles; a three-quarter turn is three right angles; a full turn is four right angles. Part C: answers vary, such as the corners of a book, a door frame or a tile.
Angles are turns
A. Check each corner with your tester. Is it a right angle?
B. How many right angles make each turn?
| a quarter turn | ______ right angles |
| a half turn | ______ right angles |
| a three-quarter turn | ______ right angles |
| a full turn | ______ right angles |
C. Find three right angles in the classroom. Write where they are.
Acute, right or obtuse
With the tester in the corner of an angle, children see at once how it compares with a right angle. If the second arm hides inside the tester, the angle is acute; if it lines up with the edge, it is a right angle; if it sticks out beyond, but stays short of a straight line, it is obtuse. The angles face every way and have arms of different lengths, so only the turn counts.
We are learning to
- compare an angle with a right angle using the tester,
- name acute, right and obtuse angles,
- draw an angle of each kind.
Success criteria
- I can name an angle acute, right or obtuse, whichever way it faces.
- I can draw an acute, a right and an obtuse angle.
You need
The testers from Day 1. The angle cards (cut-out sheet 1), one set per pair. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Smaller or bigger? Open a book slowly from closed. Children call out “smaller”, “right” or “bigger” as the cover passes a square corner. Ask: “Is the opening smaller than a square corner, or bigger?” |
| 30 min | Test and name Show the board (see the box). Children do Part A, holding the tester in each corner. Ask: “Angle 5 has one short arm. Does that change its name? Why not?” |
| 10 min | Draw and sort Children do Part B. Pairs then sort the angle cards into acute, right, obtuse and a pile of others for Day 3. Ask: “Which cards would not fit acute, right or obtuse? What makes them different?” |
Two half-sessions instead? Split after the first four angles of Part A; start Session B with angle 5.
Watch for these ideas
- Judging the angle by its arms: a short-armed angle can be the biggest on the page.
- Calling a right angle anything else when neither arm is flat.
- Calling every wide angle obtuse. Past a straight line it is not obtuse any more.
Answers
- Part A: 1 acute, 2 right, 3 obtuse, 4 acute, 5 obtuse, 6 right, 7 acute, 8 obtuse.
- Part B: drawings vary; check each with a tester. The obtuse angle must stay short of a straight line.
Acute, right or obtuse
A. Use your tester. Ring the name of each angle.
B. Draw one of each
Straight, reflex and revolution
Two right angles side by side make a straight angle, a half turn. Four right angles make a revolution, a full turn back to the start. An angle bigger than a straight angle but smaller than a revolution is reflex: its arms can look like an acute or obtuse angle, but the turn goes the long way round, and the arc on the drawing shows which way to read it.
We are learning to
- recognise a straight angle as two right angles and a revolution as four,
- recognise a reflex angle by its arc going the long way round,
- name all six kinds of angle.
Success criteria
- I can name straight, reflex and revolution angles.
- I can say how each one compares with a right angle.
You need
Testers, the angle cards from Day 2 and a demonstration clock. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Two right angles Show “Angles on a line” (see the box), then fit two testers side by side along a ruler. Ask: “Stand a line up on a straight line. What two angles do you see? What do they make together?” |
| 30 min | The long way round Draw an acute angle, then mark the arc on the outside: the same arms now show a reflex angle. Children do Part A, reading each arc. Ask: “Two drawings have the same arms. Why do they have different names?” |
| 10 min | Sort all six Pairs sort every angle card under six names. Show “Angle types by degrees”, then children do Parts B and C. Ask: “How many right angles in a reflex angle? More than two, fewer than four?” |
Two half-sessions instead? Split after Part A; start Session B with the card sort.
Watch for these ideas
- Thinking a straight line cannot be an angle. It is a half turn: two right angles.
- Reading the small angle when the arc marks the reflex one outside it.
- Thinking a revolution is no turn at all because you end up where you started.
Answers
- Part A: 1 straight, 2 reflex, 3 acute, 4 revolution, 5 reflex, 6 obtuse, 7 reflex, 8 straight.
- Part B: 2; 4; more than 2 and fewer than 4. Part C: any reflex angle with its arc drawn the long way round.
Straight, reflex and revolution
A. Follow the arc. Write the name of each angle.
acute · right · obtuse · straight · reflex · revolution
B. Angles in right angles
A reflex angle is more than ____ right angles and fewer than ____ right angles.
C. Draw a reflex angle. Mark its arc the long way round.
Compare and order
To compare two angles, look at how far one arm turns from the other, not at how long the arms are. A tester, or one angle traced and laid over the other, settles it. Children order angles from smallest to largest and estimate each one in right angles: about half a right angle, one and a half, three.
We are learning to
- compare two angles by their turn, not their arms,
- order a set of angles from smallest to largest,
- estimate an angle as about how many right angles.
Success criteria
- I can order angles from smallest to largest and check by tracing.
- I can estimate an angle as about how many right angles it is.
You need
Thin paper for tracing, and the testers. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Long arms, small angle Draw a narrow angle with long arms and a wide angle with short arms. Take a vote on which is bigger before checking. Ask: “How could we check which angle is bigger without guessing?” |
| 30 min | Order them Show the board (see the box). Children do Part A (pairs) and Part B (order five), tracing an angle to lay over another when unsure. Ask: “Angle B has the shortest arms. Does that put it first in the order?” |
| 10 min | Estimate Children do Part C, using the tester to count right angles. Ask: “Is this angle more or less than one right angle? More or less than two?” |
Two half-sessions instead? Split after Part A; start Session B with the five angles.
Watch for these ideas
- Choosing the angle with the longer arms.
- Measuring the gap between the arm ends, which also grows when the arms grow.
- Estimating a reflex angle from the inside instead of following its arc.
Answers
- Part A: pair 1: B is bigger; pair 2: A is bigger. Part B: C, A, E, B, D.
- Part C: 1 half a right angle; 2 one and a half right angles; 3 three right angles; 4 two right angles.
Compare and order
A. Which angle is bigger, A or B?
B. Order these angles from smallest to largest
C. About how many right angles is each angle?
Angles around us
Angles are everywhere: between the hands of a clock, in an opening door, in a pair of scissors. Children name the smaller angle between the clock hands at each o’clock, then the bigger angle on the other side, and name the angles in everyday things. At 4 o’clock the hands make an obtuse angle; the other way round the clock it is reflex.
We are learning to
- name the angle between the hands of a clock,
- see that the two angles at a point fill a full turn,
- name and estimate angles in everyday things.
Success criteria
- I can name the angle the clock hands make at an o’clock time.
- I can explain why the angle on the other side is reflex.
You need
A demonstration clock, a classroom door and a pair of scissors. The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Clock angles Set the clock to 3:00, 6:00, 1:00 and 4:00; children name each angle with a tester held to the clock. Ask: “At 4 o’clock, is the angle bigger or smaller than a right angle? Than a straight angle?” |
| 30 min | Both sides Children do Part A, naming the smaller angle and then the bigger one on the other side, then Part B. Ask: “Together the two angles make a full turn. How many right angles is that?” |
| 10 min | Class game Run the self-check quiz as a class game, then show “Angle types by degrees” one last time. Ask: “A door half open: about how many right angles is it?” |
Two half-sessions instead? Split after Part A; start Session B with the everyday angles.
Watch for these ideas
- Reading the reflex side when asked for the smaller angle, or the other way round.
- Thinking the hands at 6 o’clock make no angle. They make a straight angle.
- Forgetting that the two angles at the centre always fill a full turn.
Answers
- Part A: 1:00 acute, other side reflex; 3:00 right, other side reflex; 4:00 obtuse, other side reflex; 6:00 straight, other side straight; 9:00 right, other side reflex; 10:00 acute, other side reflex.
- Part B: a door opened just a little, acute; the corner of a window, right; scissors opened very wide, obtuse; a book lying open flat on a table, straight; a wheel turning once all the way round, revolution.
Angles around us
A. Name the smaller angle between the hands, then the bigger angle on the other side
| Clock | Smaller angle | Other side |
|---|---|---|
1:00 | ||
3:00 | ||
4:00 | ||
6:00 | ||
9:00 | ||
10:00 |
B. What kind of angle is it?
Angle cards
Cut out the six name headers and the twelve angle cards, one set per pair. Sort the cards under acute, right and obtuse on Day 2, then under all six names on Day 3. Follow the arc on each card.
Headers
Angle cards
Teacher note: A acute, B straight, C obtuse, D right, E reflex, F revolution, G acute, H obtuse, I right, J reflex, K straight, L revolution.
The tester sheet
One sheet per child. Cut out the circle, fold it in half, then in half again: the folded corner is a right angle. Cut out the two arms and join them at the dots with a split pin to make an angle maker.
Teacher note: label the tester “right angle” on the folded corner. Smaller than the corner is acute; bigger, up to a straight line, is obtuse.
What we know: Angles
- Name angle Q1: __________
- Name angle Q2: __________
- Name angle Q3 (follow the arc): __________
- A straight angle is ____ right angles. A revolution is ____ right angles.
- Which is bigger, Q5 A or Q5 B? ____ How do you know? ______________________
- At 3 o’clock the hands make a __________ angle. At 6 o’clock they make a __________ angle.
- Order these from smallest to largest: ____ ____ ____ABC
- Draw an obtuse angle and a reflex angle.obtusereflex
Answers and marking guide
Answers
- acute.
- obtuse.
- reflex.
- 2; 4.
- B: it turns further, even though its arms are shorter.
- right; straight.
- B, A, C.
- Check with a tester: the obtuse angle is between a right angle and a straight line; the reflex arc goes past a straight line.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Naming angles (Q1, Q2, Q3, Q8) | names only angles with a flat arm, or mixes acute and obtuse | names all six kinds, turned any way, and draws obtuse and reflex angles | explains each name by comparing with a right angle |
| Right angles (Q4, Q6) | knows the right angle only as a square corner | knows a straight angle is two right angles and a revolution is four | relates clock and everyday angles to right angles |
| Comparing (Q5, Q7) | compares by arm length | compares and orders angles by their turn | checks by tracing or with a tester without being asked |
Eight questions, three ideas. A child at standard names any angle by comparing it with a right angle, and compares angles by their turn rather than their arms.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Right angles | Acute and obtuse | Straight, reflex, revolution | Compares angles | Angles around us |
|---|---|---|---|---|---|
The five columns are the five days: right angles, acute and obtuse, the big angles, comparing, and angles around us.