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

Recently Viewed Presentations

• Data and Applications Security Developments and Directions Guest Lecture Dr. Kevin Hamlen Given in February 2012
• Phys.Lett.B677,(2009)239 Ecm(GeV) L(pb-1) R s(S) 2.60 1.222 2.18 0.02 0.08 3.07 2.291 2.13 0.02 0.07 3.65 6.485 2.14 0.01 0.07 In good agreement with previous results BESIII: < 2% Resonance parameter fit Heavy charmonia parameters were fitted with the data...
• Monosomy X, called . Turner syndrome, produces X0 females, who are sterile; it is the only known viable monosomy in humans . Disorders Caused by Structurally Altered Chromosomes. The syndrome . cri du chat ("cry of the cat"), results from...
• Nike, Inc. Freeport-McMoran Copper & Gold Inc. This list is taken from the . Corporate Responsibility Magazine . ... balance sheet. 8. cash-flow statement. Capital can either come from friends and relatives or from banks, credit unions and/or loan companies.
• The Internet offers many websites that contain information about the hairstyles and cosmetics used in Ancient Egypt, Rome, and Greece. In addition, sites can be found that depict styles of each century and many decades back to the 13th century....
• Channel Member Selection and Channel Design. The channel member selection is the last phase of channel design (phase 7). Selection decisions can also be made independently of channel design decisions when new channel members are added to the channel or...
• LYU0002 Wireless Cyber Campus Supervisor: Prof. Michael R. Lyu Student: Jang Kim Fung Tang Ho Man Presentation Outline Introduction Project Aim Progress of 1st Semester Problem faced & Solution Progress of 2nd Semester Future Work Conclusion Introduction (1) Traditional Campus...
• CS/COE0447 Computer Organization & Assembly Language Chapter 3*