A compilation this week:

- Mathematical Hooks
- Task Booklet
- Transition Booklets
- Area of a Trapezium
- Research papers – one slide summaries

From Julia Smith (**@TessMaths**), have a look at this wonderful collection of **Mathematical Hooks**.

In **Mathematical Miscellany #68** I included From Complete Maths (**@LaSalleEd**) this **brilliant 128-page Task Booklet** from Jonathan Hall (**@StudyMaths**). The tasks which aim to promote mathematical thinking and behaviour in the classroom have been designed to be used with an appropriate model or manipulative. (See also **NCETM’s Using Mathematical Representations at KS3.**)

Note the playlist, **Tasks** on the Complete Maths YouTube CPD channel where Jonathan Hall is sharing his thoughts on some of these tasks. He recently shared this on Negative Combinations:

From **Sparx Maths**, have a look at their Transition Booklets, one for Year 6 to 7 and one for GCSE to A Level; these booklets are free whether you have Sparx Maths or not. The Year 6 to 7 booklet with over 130 questions is based on the Year 6 DFE/NCETM ‘ready to progress’ guidance from June 2020. The GCSE to A Level booklet uses over 120 questions taken from 11 key topics on Sparx Maths. Answers can be obtained by completing a form with your school details.

In my post on **Proof** I included some Geometrical proofs. We could treat this diagram as a goal free problem; what is the diagram showing you? This idea came from Colin Foster’s article –**Trapezium Artist**: Some thoughts on the formula for the area of a trapezium where he discusses a Year 8 lesson on area. Colin Foster states “The formula for the trapezium stood out as being the only one that wasn’t immediately ‘see-able’. With thought, those for the triangle, rectangle, parallelogram and kite could all be seen to be correct at a glance. That got us thinking about different ways of proving the formula. We were seeking something not only believable but striking enough as an image to stick in our minds. All our methods involved converting to simpler shapes”

“I have ended up quite keen on Method 6”

For an animation to illustrate this, see **Trapezoid Area (2) from Tim Brzezinski**.

…and in case you are wondering about **Trapezid Area (1)**…

George Stone (**@DrStoneMaths**) is producing **one slide summarie**s of interesting educational research papers.

For research summaries – see also the reading pages Research – **Mathematics Learning & Teaching** including easy to digest research on Mathematics education from **Cambridge Mathematics** (see their **Espresso page**), and **Research – Learning & Teaching** which includes **Research in 100 Words **from Chris Moyse and **summaries of educational research from Tom Sherrington**.