Angles In Depth Resources, problems and approaches Teaching Year 7 angles for the
first time? What to think about...
Topic progression
Primary curriculum Assessment Misconceptions Resources Stretch and challenge
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). 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 Year 5 Doodle Maths
Key Stage 2 Assessment 2016 Key Stage 2 Sample Assessment
My Year 7s... Starting over...? Assessment Narrative
Vocabulary and Notation Instruction and Practice Assessment Distributed Practice
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
Adjacent angles on a straight line The unexpected misconception
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 but avoid the ambiguous angles on a straight line
Show a large number of examples and nonexamples Assessing Reasoning Skills Interior Angles
in a Triangle Demonstration s
Proof comes later... Practice finding missing angles algebra and triangle angles
(1) (2)
(3) 9k 3n
2f f 3f
5n n
(6) (5) (4)
11k 10k
8d 22e 5p 4p
23e 7d algebra and triangle angles
(7) (8)
(9) c 4a
b 7a
4b 2c (12) (11)
(10) 3e d + 40
3f + 20 2e d + 30
d + 20 e + 60 f
2f + 10 My students found this really hard Proofs
three angles in a triangle c
b a
(1) if a + b = 90o + c, prove that c = 45o (2) if a + b = c, prove that c = 90o (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 = b + 90o
isosceles triangle proofs (i) Q
Q (2) (1)
establish that triangle PQR is right-angled b
S R
b P prove that b = 2a
a S a
R P
(4) Q (3)
Q b a P
b a S
prove that 4a + b = 180o R
P S prove that
b = 180o 3a R GCSE questions suitable for Year 7s
Problem Solving How many lessons can we spend
looking at angles in triangles? Resources... MathsPad Don Steward
Malakiss Solve My Maths CIMT Dr Frost (including proofs) Corbett Maths
White Rose Maths Hub Resourceaholic.com