All About Angles - London Maths... the web site of ATM & MA ...

All About Angles - London Maths... the web site of ATM & MA ...

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

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