1. Animation: http://www. learnalberta. ca/content/mejhm/index. html

2. Angles In Depth
Resources, problems
and approaches

3. Teaching Year 7 angles for the first time? What to think about...
Topic progression
Primary curriculum
Assessment
Misconceptions
Resources
Stretch and challenge

4. What do they do in primary school?
Year 2
Rotation in terms of right angles for
quarter, half and three-quarter turns
Year 3
Angles as a description of turn. Use accurate language (acute and obtuse).
Year 4
Order angles by size. Classify shapes (including types of triangle and types of quadrilateral).

5. Year 3 – Doodle Maths

6. Year 5
Draw, measure, estimate and compare angles in degrees. Identify right angles, angles at a point and angles on a straight line.
Year 6
Find missing angles in triangles and quadrilaterals (eg parallelograms). Find missing angles at a point or on a straight line (including vertically opposite angles). Relationships may be expressed algebraically.

7. Year 5 – Doodle Maths

8. Expected Standard – Key Stage 2

9. May 2016 Key Stage 2 assessment: https://www. gov

10. Key Stage 2 Sample Assessment
From sample KS2 assessment
Key Stage 2 Sample Assessment

11. My Year 7s...

12. LOADS of practice needed for measuring
LOADS of practice needed for measuring. Don’t just do questions like this. Do plenty of reflex angles.

14. Full marks awarded for measuring (2 degrees allowed) but shows a lack of understanding of angle facts

15. Starting over...? Assessment ⇢ Narrative ⇢ Vocabulary and Notation ⇢
Instruction and Practice ⇢ Assessment ⇢
Distributed Practice

16. Notation, drawing, measuring, estimating
Straight lines, around a point, vertically opposite
Angles in triangles and quadrilaterals
Quadrilateral properties
Angles in parallel lines
Angles in polygons and tessellation
Bearings
Leading to – circle theorems, trigonometry
Linked to – similarity, congruence, constructions
How many schools include angles in parallel lines in Year 7?
National Strategies stops before parallel lines in Year 7. White Rose Maths Hub stops after angles in parallel lines.

17. Don’t skip the notation!
theta?
(Source: National Strategies Year 7)
Most primary resources and assessment uses lower case letters for angles. Year 7 is time to formalise mathematical language. If you’re going to use theta, explain what it is.

18. Source: Middle School Math with Pizzazz! Book D (slightly edited by Jo). Worth spending the time on new notation, as well as practising measuring.

19. Adjacent angles on a straight line

20. The unexpected misconception
Students believe that the angle on the left is 150 degrees because these angles are on a straight line.

21. Say “angles that form a straight line”
or “adjacent angles on a straight line”
or “angles at a point on one side of a straight line”
Blog post relevant to this:
but avoid the ambiguous
“angles on a straight line”

22. What did Euclid say?
Proposition 13 in Book 1: “If a straight line set up on a straight line make angles, it will make either two right angles or angles equal to two right angles.” Ancient Greece, 300 BC

23. Clarify the meaning of adjacent

24. Show a large number of examples and non-examples

25. Wrmh https://www. dropbox

26. WRMH

27. WRMH

28. Simple practice resources:or
And

29. https://www.tes.com/teaching-resource/calculating-missing-angles-6370244 via Cazoom Maths
More practice here:

30. Assessing Reasoning Skills
Can be done without knowing vertically opposite angles. Multiple angles on diagram properly checks understanding

31. Interior Angles in a Triangle

32. A range of starting points/demonstrations exist. Pros ands cons?

34. https://giphy.com/gifs/triangle-aq3znqZ7eO8xO

35. Read this about triangle demonstrations: http://mathonthemckenzie

36. https://keats. kcl. ac. uk/pluginfile

41. Demonstrations

43. Proof comes later... Gif by Ed Southall
Other proofs:

44. Practice – finding missing angles
Worksheets:

46. Homework resource: https://drive. google

47. White Rose: https://www. tes

48. CIMT

49. http://donsteward. blogspot. co. uk/2014/01/isosceles-triangle-angles

51. CIMT

53. Source: Higher Sum Books

54. MathsPad

55. Angle chases combine angle facts.
On the left: from White rose Maths Hub
Lots here:

56. Colin Foster

57. Colin Foster

58. (1) (2) (3) 9k 3n 2f 10k 11k 3f f 5n n (5) (6) (4) 8d 22e 5p 4p 7d 23e
algebra and triangle angles 5n 3n n
(1)
(2)
(3) 9k 2f
10k
11k 3f f
23e
22e
(4)
(5)
(6) 8d 7d
Don Steward 5p 4p

59. (7) (8) (9) c 4a b 7a 4b 2c (11) (12) (10) 3e d + 40 3f + 20 2f + 10
algebra and triangle angles
(7)
(8) 4b b
(9) 7a 4a c 2c
(10)
(11)
(12) 3e
d + 40
3f + 20
2f + 10
Don Steward 2e
d + 30
e + 60
d + 20 f

60. MathsPad

61. https://twitter.com/MathsDunbar/

62. Source: CIMT

63. My students found this really hard
Miss Brookes Maths
More structure needed for algebra questions
They know angle facts and they know solving equations. Scaffolding needed.
My students found this really hard

64. Colin Foster – solve with algebra or using ratio

65. Proofs http://www.counton.org/resources/ks3framework/
It’s easy to extend high attainers without moving onto a new topic (eg angles in parallel lines). Angles in triangles offers loads of in-topic stretch.

67. three angles in a triangleb c
three angles in a triangle
(1)
if a + b = 90o + c, prove that c = 45o
(2)
if a + b = c, prove that c = 90o
Proofs from Don Steward:
(3)
if c is the average (mean) of a and b prove that c = 60o
(4)
if a + b = 180o – a prove that the triangle is isosceles
(5)
if a + b = c – b prove that c = ½ b + 90o

68. (1) (2) (4) (3) isosceles triangle proofs (i) Q b S Q R b P a S R a P
establish that triangle PQR is right-angled Q P R a b S
prove that b = 2a
(1) a b S Q R P
(4) P Q R S b a
prove that
b = 180o – 3a
(3) Q
More isosceles proofs from Don here: b P a R S
prove that
4a + b = 180o

69. triangle ABC is isosceles with AB = BC
prove that angle BDA = 3k
what angle does ‘k’ need to be for triangle ADB to be isosceles?
prove that ADC is also isosceles for this particular value of ‘k’
[the ‘golden triangle’] D k
Don Steward isosceles proofs: k C A

70.
Plenty of proofs only require Year 7 angle facts

71. GCSE questions suitable for Year 7s
Questions from Churchill Practice Papers

72. Problem Solving
These are from the Intermediate Maths Challenge. Lots more puzzles here:

73. How many lessons can we spend looking at angles in triangles?
At least 6, with all classes. There’s plenty of stretch. And keep returning to the topic eg when studying angles in parallel lines

74. Resources... MathsPad Don Steward Malakiss Solve My Maths CIMT
Dr Frost (including proofs)
Corbett Maths
White Rose Maths Hub
Resourceaholic.com