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

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). https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study

Year 3 – Doodle Maths https://www.doodlemaths.com/custom-content/uploads/2016/12/71-Angle-Investigations.pdf

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. https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study

Year 5 – Doodle Maths https://www.doodlemaths.com/starters/yr6-geo-5-recognise-angles-where-they-meet-at-a-point-are-on-a-straight-line-or-are-vertically-opposite-and-find-missing-angles/

Expected Standard – Key Stage 2

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

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

My Year 7s...

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

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

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 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.

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.

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

Adjacent angles on a straight line

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

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: https://staffrm.io/@mrmattock/3s9XZSXZ8q but avoid the ambiguous “angles on a straight line”

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 http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI13.html http://mathonthemckenzie.blogspot.co.uk/2011/08/euclids-elements-book-1-proposition-13.html

Clarify the meaning of adjacent

Show a large number of examples and non-examples

Wrmh https://www. dropbox

WRMH

WRMH

Simple practice resources: https://www.tes.com/teaching-resource/angles-on-a-straight-line-worksheet-6317911 or https://www.tes.com/teaching-resource/angles-on-a-straight-line-11202079 And https://www.tes.com/teaching-resource/angles-on-a-straight-line-11202079

https://www.tes.com/teaching-resource/calculating-missing-angles-6370244 via Cazoom Maths More practice here: http://www.cimt.org.uk/projects/mepres/book7/bk7_5.pdf

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

Interior Angles in a Triangle

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

http://ictedusrv.cumbria.ac.uk/maths/pgdl/unit9/ANGLES.PDF

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

Read this about triangle demonstrations: http://mathonthemckenzie

https://keats. kcl. ac. uk/pluginfile https://keats.kcl.ac.uk/pluginfile.php/1647865/mod_folder/content/0/Maths/Angles%20and%20Triangles%20Problems%20%20Misconceptions_Redacted%20A%2072.pdf?forcedownload=1

https://www.geogebra.org/m/g3eWs3F8

https://www.tes.com/teaching-resource/measuring-angles-in-a-triangle-6125454

https://www.ncetm.org.uk/public/files/318889/NCETM_Mathematics_Department_Workshops_Angle_Properties_Resource_Sheet_HT2.APR.5.pdf

Demonstrations

Proof comes later... Gif by Ed Southall Other proofs: http://math-problems.math4teaching.com/proofs-of-sum-of-angles-of-triangles/

Practice – finding missing angles Worksheets: https://solvemymaths.files.wordpress.com/2016/02/triangles-worksheet.pdf https://solvemymaths.files.wordpress.com/2016/01/angles_worksheet.pdf

Homework resource: https://drive. google

White Rose: https://www. tes

CIMT

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

CIMT

Source: Higher Sum Books

MathsPad

Angle chases combine angle facts. On the left: from White rose Maths Hub Lots here: https://www.dropbox.com/s/sd0vesek3tpq9zw/Angle%20Chase.pdf?dl=0

Colin Foster

Colin Foster

(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

(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 http://donsteward.blogspot.co.uk/2015/06/angles-with-algebra.html 2e d + 30 e + 60 d + 20 f

MathsPad

https://twitter.com/MathsDunbar/

Source: CIMT

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

Colin Foster – solve with algebra or using ratio

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.

http://www.counton.org/resources/ks3framework/

three angles in a triangle b 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: https://drive.google.com/file/d/0B9L2lYGRiK2bTnl6ZjZUQkMzVXM/view?usp=sharing (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

(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: https://drive.google.com/file/d/0B9L2lYGRiK2bTGpad1AtajRfNDg/view?usp=sharing b P a R S prove that 4a + b = 180o

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: https://drive.google.com/file/d/0B9L2lYGRiK2bTGpad1AtajRfNDg/view?usp=sharing k C A

http://www.counton.org/resources/ks3framework/ Plenty of proofs only require Year 7 angle facts

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

Problem Solving These are from the Intermediate Maths Challenge. Lots more puzzles here: https://drive.google.com/file/d/0B9L2lYGRiK2bTUtnaEdfd3ZpNDA/view?usp=sharing

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

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