Clock Arithmetic These calculations are done using the clock on the right. For example, = = = = 4. 3 × 2 = 5. 2 × (3 + 4) = 6. 2× × 3 = 7.–2 = 8.1 – 5 = 9.1 – ( ) = 10.3 × (4 × 4 – 1) = 5 Finished? How many calculations can you find that give an answer of 2? Try to use addition, subtraction, multiplication and division.

Clock Arithmetic = = = 4. 3 × 2 = 5. 2 × (3 + 4) = 6. 2× × 3 = 7.–2 = 8.1 – 5 = 9.1 – ( ) = 10.3 × (4 × 4 – 1) = These calculations are done using the clock on the right. For example, = 1.

Why? What topic is this activity exploring? What could it lead into? Is it accessible? Structured? Open?

Introductions Twyford CE High School Mixed comprehensive Selective on church (etc.) attendance 1350 pupils 2011 Results 85% A*-C (GCSE incl Ma & En) 87% A*-C (GCSE Ma) 46% A*-A (GCSE Ma) 92% A*-C (A Level Ma) Year 12: 100 Ma + 28 Fm 57 statements 210 on SEN register (14%) Robert Massey 2009-present: Head of Maths 2003-present: Maths teacher at Twyford High School : PGCE at Oxford : Maths and Computer Science at Cambridge

Today Year 7 Maths workshops project Year 7 Maths workshops project – Motivation – Planning – Delivery Use of data to select and group Use of data to select and group Designing activities Designing activities Evaluating success Evaluating success

“I have come that you might have life and have it to the full”

XKCD.com Enthusiastic….….successful Exam factory? Mathematicians? Curriculum fit for all?

Planning 180 students Year Year 7 Capacity: workshops Staffing Length Content Outcomes

Group theory Group theory Factors, primes, sequences Factors, primes, sequences Trigonometry Trigonometry Coding, Cryptography, Murder Coding, Cryptography, Murder Loci, Functions and Graphs Loci, Functions and Graphs

How many ways can you wear a T Shirt?

Washing instructions Wash separately. 4 ways the T Shirts can be worn What do you do to get from one way to another?

Describing actions to change In your group, decide how you would describe the single action needed to change the T Shirt from the first way to the second.

Describing actions to change In your group, decide how you would describe the single action needed to change the T Shirt from the first way to the second.

Describing actions to change In your group, decide how you would describe the single action needed to change the T Shirt from the first way to the second. Turn back to front Turn inside out Leave it alone Turn back to front AND inside out

Turn back to front

Turn inside out Leave it alone Turn back to front AND inside out T BF T IO T L Shorthand

One action.... Followed by another...

? ? T BF T T IO

One action.... Followed by another... LT BF T IO T L T BF T IO T First action Second action T IO

One action.... Followed by another... LT BF T IO T L T BF T IO T First action Second action L = Leave as it is T = Turn inside out AND back to front T IO = Turn inside out T BF = Turn back to front Complete this table to show the single action that could replace a first action followed by a second.

One action.... Followed by another... LT BF T IO T L LT BF T IO T T BF LTT IO TLT BF T TT IO T BF L First action Second action L = Leave as it is T = Turn inside out AND back to front T IO = Turn inside out T BF = Turn back to front Complete this table to show the single action that could replace a first action followed by a second.

180 students Capacity: 60-70

53 primary schools KS2 dataTest resultsTeacher assessed CAT TestsCognitive Abilities Test VERbal reasoning QUANTative reasoning Non- VERbal reasoning Internal assessment Reliable? 6 different teachers Teacher assessment Parent assessment Missing data

Ethnicity Gender Tutor groups Special Needs Free School Meals Behaviour

Gender mix ‘Ability mix’ Group size

How would you approach the topic of trigonometry if you had two hours to teach it?

Acceleration stage Climbing stage Take-off

How far above the houses will the aircraft pass? What information do you need to answer this question? How will you answer it?

Can the airport designers use what Mathematicians know about triangles to help design their runway?

width height hypotenuse angle Right Angled Triangle

35° width height hypotenuse

Red Counters: Height ÷ Hypotenuse Blue Counters: Width ÷ Hypotenuse

35° 10 cm 7 cm height width Height ÷ Width = 0.7 ? ÷ 10 = 0.7 ? = 7

Thoughts from today What is the benefit of a workshop over a “normal” lesson? What is the benefit of a workshop over a “normal” lesson? What are important considerations when designing a workshop? What are important considerations when designing a workshop? What barriers might you face? What barriers might you face? What could you take from the workshop model to adopt in classroom lessons? What could you take from the workshop model to adopt in classroom lessons? How would the presentation style need to differ (workshop vs classroom)? How would the presentation style need to differ (workshop vs classroom)?

Workshops this year Your roles: Facilitating discussion Facilitating discussion Posing questions Posing questions Providing resources at appropriate times Providing resources at appropriate times Maintaining order Maintaining order Your role is not: To do the work and thinking for the students – ask questions instead! To do the work and thinking for the students – ask questions instead!