Angle Relationships: a week of ready-to-teach maths
Five days of lessons for Year 6 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus angle partner cards, a paper circle and crossing strips to cut out, 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 partner cards once for each pair; print the circle and strips sheet for each pair.
- 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. The big idea of the week: three rules find angles you cannot measure. Angles that sit together on a straight line make 180°. Angles all the way round a point make 360°. Where two straight lines cross, the angles opposite each other are equal. Naming the rule you used is part of every answer.
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.
Words to watch
A straight angle is 180°, half a turn; a full turn is 360°. Vertically opposite means across from each other where two lines cross, not up and down. An angle bigger than 180° is a reflex angle. The angles on the worksheets are drawn at their true size, so children can measure them with a protractor even if the page prints a little larger or smaller.
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 | On a straight line | Measure angles that sit together on a straight line, find that they make 180°, and find a missing one | Angles on a straight line |
| 2 | At a point | Measure angles all the way round a point, find that they make 360°, and cut a paper circle to check | Angles at a point |
| 3 | Vertically opposite | Cross two card strips, see that opposite angles stay equal, and explain why with the straight-line rule | Vertically opposite angles |
| 4 | Find the unknown | Choose the rule, find unknown angles in one and two steps, and use equal angles marked with the same letter | Unknown angle on a line; Unknown angle at a point |
| 5 | Give your reasons | Write the rule for each step, follow a chain of angles, and correct reasoning that used the wrong rule | Reasoning about angles |
How the week builds
Days 1 to 3 meet the three rules by measuring and then explaining; Day 4 uses them to find unknown angles; and Day 5 writes the reasons down. It builds on the Year 5 work of measuring and constructing angles with a protractor (AC9M5M04). It leads to the Year 7 angles made by parallel lines and a transversal (AC9M7M04) and the angle sum of a triangle (AC9M7M05).
Materials for the week (one trip)
- From the classroom: a protractor and a ruler each, scissors, glue, and this pack printed.
- For Days 2 and 3: a split pin (paper fastener) for each pair, and the circle and strips sheet.
- Cut out once: the angle partner cards, one set per pair.
Words for the word wall
angle, degree, protractor, straight angle, full turn, reflex angle, angles on a straight line, angles at a point, vertically opposite, unknown, rule, reason
Dear families
This week in maths, Year 6 learns three angle rules: angles on a straight line make 180°, angles round a point make 360°, and where two lines cross the opposite angles are equal. We use them to work out angles without measuring, and we explain which rule we used.
Try this at home
- Open scissors and look at the angles where the blades cross. Which angles are equal?
- Cut a pizza or a cake from the centre. Do the angles at the centre make a full turn?
- Find two roads, paths or lines on a map that cross. Name a pair of opposite angles.
- Lean a ruler on a book so it makes two angles with the table. If one is 40°, what is the other?
Angles this week
Fill one row a day. Draw or describe an angle you found, the rule it shows, and its size.
| Day | Where we saw it | The rule | The angle |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Angle Relationships teaching pack · seegongsik.com/au/y6/measurement/AC9M6M04/pack
On a straight line
A straight line makes a straight angle of 180°, half a turn, so angles that sit side by side along a straight line always add to 180°. Children measure pairs of angles on a line and find the total is 180°, give or take a degree of measuring, then use the rule to find a missing angle without measuring.
We are learning to
- measure angles on a straight line with a protractor,
- explain why angles on a straight line add to 180°,
- find a missing angle on a straight line.
Success criteria
- I can show that the angles I measured on a line add to about 180°.
- I can find the angle next to 130° on a straight line, and say the rule.
You need
The worksheet, one per child, and a protractor and a ruler each.
Lesson flow (about 50 minutes)
| 10 min | Half a turn Show the board (see the box). Children say the partner angle before you press. Ask: “The angles change every time. Why does the total stay at 180°?” |
| 25 min | Measure and add Children measure the angles in Part A, then find the missing angles in Part B without measuring. Ask: “Your two angles add to 179°. Is the rule wrong, or the measuring?” |
| 15 min | Could they? Children test each set of angles in Part C. Ask: “Could three angles on a straight line all be 60°? Could they all be 70°?” |
Two half-sessions instead? Split after Part A; start Session B with the missing angles in Part B.
Watch for these ideas
- Reading the wrong scale on the protractor, so 35° is read as 145°.
- Taking the angle away from 360° or 100° instead of 180°.
- Doubting the rule when measured angles add to 179° or 181°.
Answers
- Part A: a = 35°, b = 145°; c = 80°, d = 100°; e = 122°, f = 58°; each pair makes 180° (a degree either way is measuring).
- Part B: 50°, 115°, 65°, 52°.
- Part C: no (95° + 95° = 190°); yes (60° + 60° + 60° = 180°); no (110° + 60° = 170°); yes (45° + 45° + 90° = 180°).
On a straight line
A. Measure and add
Measure each angle with a protractor. Extend the arms with a ruler if you need to.
a = ______ b = ______
Total ______
c = ______ d = ______
Total ______
e = ______ f = ______
Total ______
B. Find the missing angle
Do not measure. Use the rule.
? = ______
? = ______
? = ______
? = ______
C. Could they sit on a straight line?
1. 95°, 95° yes or no, and why: ______________________________
2. 60°, 60°, 60° yes or no, and why: ______________________________
3. 110°, 60° yes or no, and why: ______________________________
4. 45°, 45°, 90° yes or no, and why: ______________________________
At a point
Angles all the way round a point fill a full turn, so they always add to 360°, twice a straight line. Children measure the angles round a point and check the total, find a missing angle by taking the others away from 360°, and cut a paper circle into pieces to see the full turn.
We are learning to
- measure the angles round a point,
- explain why angles at a point add to 360°,
- find a missing angle at a point, including one bigger than 180°.
Success criteria
- I can show that the angles round a point add to about 360°.
- I can find the angle that completes 120° and 150° at a point.
You need
The worksheet, one per child, a protractor each, and the paper circle (cut-outs) with scissors for each pair.
Lesson flow (about 50 minutes)
| 10 min | A full turn Show the board (see the box). Children add each set before you press. Ask: “Why is a full turn the same as two straight lines’ worth of angle?” |
| 25 min | Measure and find Children measure round the points in Part A, then find the missing angles in Part B without measuring. Ask: “One missing angle sits next to a 200° angle. How could you measure a reflex angle with a protractor that only goes to 180°?” |
| 15 min | Paper circle Pairs cut and measure the paper circle in Part C. Ask: “Your three pieces add to 358°. Where did the 2° go?” |
Two half-sessions instead? Split after Part A; start Session B with the missing angles in Part B.
Watch for these ideas
- Taking the angles away from 180° instead of 360°.
- Reading a reflex angle as its smaller partner, such as 160° for 200°.
- Leaving an angle out when adding round the point.
Answers
- Part A: a = 100°, b = 140°, c = 120°; d = 70°, e = 110°, f = 95°, g = 85°; each set makes 360° (a degree or two either way is measuring).
- Part B: 90°, 80°, 160°, 135°.
- Part C: the pieces vary and make about 360°; folding in half twice makes four angles of 90°.
At a point
A. Measure round the point
B. Find the missing angle
Do not measure. Use the rule.
? = ______
? = ______
? = ______
? = ______
C. A paper circle
1. Cut out the circle. Draw three lines from the centre to the edge and cut along them. Measure the angle at the centre of each piece: ______, ______, ______. Total ______.
2. Put the pieces back together round the centre. What do you notice? ______________________________
3. Fold a whole circle in half, then in half again. What angles meet at the centre? ______________________
Vertically opposite
Where two straight lines cross they make four angles. The angles opposite each other are equal, because each pair beside them sits on a straight line: a + b = 180° and b + c = 180°, so a = c. Children turn two card strips joined by a split pin and watch opposite angles stay equal, measure crossing lines, then explain the rule.
We are learning to
- identify vertically opposite angles where two lines cross,
- find all four angles from one of them,
- explain why vertically opposite angles are equal.
Success criteria
- I can find all four angles where two lines cross from one angle.
- I can explain why opposite angles are equal, using angles on a straight line.
You need
The worksheet, one per child, a protractor each, and the crossing strips (cut-outs) with a split pin for each pair.
Lesson flow (about 50 minutes)
| 10 min | Opposite and equal Show the board (see the box). Children say the opposite angle before you press. Ask: “Which angles are opposite each other? Are they the ones above and below the crossing?” |
| 25 min | Turn the strips Pairs join the strips with a split pin and turn them, then measure the crossings in Part A. Ask: “As you open the strips, one angle grows. What happens to the angle opposite it, and to the one beside it?” |
| 15 min | Why? Children find the angles in Part B and write the explanation in Part C. Ask: “If you know one angle, how many others can you find, and with which rules?” |
Two half-sessions instead? Split after Part A; start Session B with the angles to find in Part B.
Watch for these ideas
- Thinking vertically means up and down, and pairing the angles above and below the crossing.
- Saying the angles beside each other are equal, when they make 180°.
- Measuring four angles that make 360° but not seeing the two equal pairs.
Answers
- Part A: a = 40°, b = 140°, c = 40°, d = 140°; e = 115°, f = 65°, g = 115°, h = 65°. Equal pairs: a and c, b and d; e and g, f and h.
- Part B: x = 110°, y = 70°, z = 110°; p = 35°, q = 35°, r = 145°.
- Part C: a + b = 180° and b + c = 180°, both because angles on a straight line make 180°, so a and c are both 180° − b and a = c. Here a = c = 55° and b = d = 125°.
Vertically opposite
A. Measure the four angles
Which angles are equal? ________________________________________________
B. Find the other three
Do not measure. Use the rules.
C. Explain why
b + c = ______ because ______________________________
So a = ______, because ______________________________
Find the unknown
To find an unknown angle, first decide which rule fits the picture: angles on a straight line, angles at a point, or vertically opposite angles. When equal angles share a letter, share out what is left equally. Children choose a rule for each picture, find unknown angles, and make a puzzle for a partner.
We are learning to
- choose the rule that fits a picture,
- find unknown angles in one and two steps,
- find equal unknown angles marked with the same letter.
Success criteria
- I can say which rule I used for each unknown angle.
- I can find x when x, x and 40° sit on a straight line.
You need
The worksheet, one per child, and a ruler and a protractor each for Part C.
Lesson flow (about 50 minutes)
| 10 min | Which rule? Show the two pictures (see the box). The class votes A, B or C before each press. Ask: “How did you know whether to take the angles from 180° or from 360°?” |
| 25 min | Find them Children name the rule and find each unknown in Part A, then share out the equal angles in Part B. Ask: “Two angles are both x and they share 140°. How much is each?” |
| 15 min | Make a puzzle Children draw a puzzle for a partner in Part C, then swap and solve. Ask: “Does your puzzle have exactly one answer? How do you know?” |
Two half-sessions instead? Split after Part A; start Session B with the equal angles in Part B.
Watch for these ideas
- Using 180° for angles at a point, or 360° for angles on a line.
- Taking the angle beside a given angle as equal to it, when the two make 180°.
- Sharing what is left between the wrong number of equal angles.
Answers
- Part A: (1) 123°, angles on a straight line make 180°; (2) 70°, angles at a point make 360°; (3) 38°, vertically opposite angles are equal; (4) 118°, angles on a straight line make 180°.
- Part B: x = 70° (140° shared by 2); y = 115° (230° shared by 2); z = 60° (360° shared by 6); k = 45° (90° shared by 2).
- Part C: puzzles vary; check that the partner’s answer and rule match the maker’s.
Find the unknown
A. Name the rule, then find the angle
Rule: __________
________________
Rule: __________
________________
Rule: __________
________________
Rule: __________
________________
B. Equal letters, equal angles
Angles with the same letter are equal. Share out what is left.
C. Make a puzzle
Draw two lines that cross, or angles on a line or round a point. Measure and label every angle but one, mark that one ?, and write the rule on the back. Swap with a partner.
Give your reasons
In geometry an answer needs a reason: the rule that makes it true. Children write the rule beside each step, follow a chain where one angle leads to the next, and correct reasoning that used the wrong rule. The class finishes the week with the self-check quiz.
We are learning to
- write the rule that explains each step,
- follow a chain of reasoning from one angle to the next,
- correct reasoning that uses the wrong rule.
Success criteria
- I can write the rule for each step of my working.
- I can explain what went wrong when the wrong rule was used.
You need
The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Name the rule Show the board (see the box). The class votes A, B or C before each press. Ask: “Why is ‘the line is 180°’ a better reason than ‘I measured it’?” |
| 25 min | Reasons and chains Children write the reasons in Part A, then follow the chain in Part B. Ask: “You found a. How does a help you find c?” |
| 15 min | Fix it Children correct the reasoning in Part C. Finish with the self-check quiz as a class game. Ask: “Which rule did Alex use each time, and which one fits the picture?” |
Two half-sessions instead? Split after Part A; start Session B with the chain in Part B.
Watch for these ideas
- Writing an answer with no reason, or a reason such as ‘it looks like it’.
- Using a rule that does not fit the picture, such as 360° on a straight line.
- Stopping a chain after the first angle instead of using it to find the next.
Answers
- Part A: (1) angles on a straight line make 180°; (2) angles at a point make 360°; (3) vertically opposite angles are equal; (4) angles on a straight line make 180°.
- Part B: a = 58° (vertically opposite angles are equal); b = 122° (angles on a straight line make 180°); c = 122° (vertically opposite angles are equal, opposite b).
- Part C: (1) 220°, as angles at a point make 360°; (2) 110°, as angles on a straight line make 180°; (3) 145°, as angles on a straight line make 180°.
Give your reasons
A. Write the reason
Each step is worked for you. Write the rule that makes it true.
1. a = 180° − 65° = 115° because ____________________________________
2. b = 360° − 90° − 150° = 120° because ____________________________________
3. c = 48° because ____________________________________
4. d = 180° − 48° = 132° because ____________________________________
B. Follow the chain
b = ______ because ________________________________
c = ______ because ________________________________
C. Fix the reasoning
Alex used the wrong rule each time. Write the right answer and the rule that fits.
1. Two angles at a point are 140° and ?. Alex wrote ? = 40°, because angles at a point make 180°. ____________________________
2. Two lines cross. The angle beside a 70° angle is ?. Alex wrote ? = 70°, because vertically opposite angles are equal. ____________________________
3. On a straight line, 35° and ? sit side by side. Alex wrote ? = 325°, because a full turn is 360°. ____________________________
Angle partner cards
Cut out the twenty-four cards once, one set for each pair. Each angle is drawn at its true size.
Straight-line partners (Days 1 and 4)
- Shuffle the cards and lay them face down in rows.
- Take turns to turn over two cards. Two angles that make 180° are partners: lay them side by side to make a straight line.
- Say the sum aloud to keep the pair. If they are not partners, turn them back. Most pairs wins.
Teacher note, the twelve pairs: 15° and 165°, 20° and 160°, 25° and 155°, 35° and 145°, 40° and 140°, 45° and 135°, 50° and 130°, 55° and 125°, 65° and 115°, 70° and 110°, 75° and 105°, 80° and 100°. For a harder game, collect four cards that make 360°.
Paper circles and crossing strips
Print one sheet for each pair. Cut out the two circles and the two strips.
How to use them
- Day 2: draw three lines from the centre of a circle to its edge and cut along them. Measure the three angles at the centre and add them. Fold the other circle in half, then in half again.
- Day 3: push a split pin through the marked holes to join the two strips. Turn one strip and watch the four angles where the strips cross.
Teacher note: the circle pieces should make about 360°; a degree or two either way is measuring and cutting.
What we know: Angle Relationships
Work on your own. Give the rule you used with each answer.
- Two angles sit together on a straight line. One is 74°. What is the other? ______
- Three angles meet round a point. Two are 95° and 125°. What is the third? ______
- Two lines cross and one angle is 33°. What is the angle opposite it? ______ The angle beside it? ______
- Angles x, x and 50° sit together on a straight line. What is x? ______
- Three equal angles meet round a point and fill it. How big is each? ______
- Explain why vertically opposite angles are equal. ______________________________________________
- Alex says 25° and 165° can sit together on a straight line. Right or wrong? Why? ______________________
- Find p, q and r, and give the rule for each. ______________________________
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- 106°: angles on a straight line make 180°.
- 140°: angles at a point make 360°.
- 33° (vertically opposite angles are equal) and 147° (angles on a straight line).
- 65°: the two x angles share 130°.
- 120°: 360° shared by 3.
- Each angle and the one beside it make 180°, and so does that one with the next, so the two opposite angles are equal.
- Wrong: 25° + 165° = 190°, not 180°.
- p = 70° (straight line), q = 110° (vertically opposite the 110° angle), r = 70° (vertically opposite p).
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Straight line (Q1, Q4, Q7) | takes the angle from 360° instead of 180° | finds missing angles on a line, including equal ones | tests a set of angles against 180° and explains |
| At a point (Q2, Q5) | takes the angles from 180° instead of 360° | finds missing angles at a point | works with angles bigger than 180° |
| Vertically opposite (Q3, Q6) | pairs the angles beside each other | finds all four angles where two lines cross | explains the rule using angles on a line |
| Reasoning (Q8) | gives answers without rules | names the rule for each step | writes a chain of steps, each with its rule |
Eight questions, four ideas. A child at standard answers most questions and names the rule behind each answer.
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 | Straight line | At a point | Opposite | Unknowns | Reasons |
|---|---|---|---|---|---|
The five columns are the five days: angles on a straight line, angles at a point, vertically opposite angles, finding unknowns, and giving reasons.