Mathematics Conference on Innovative Teaching Approaches

1. 2 by 2....by more!!! North Lincolnshire Mathematics Conference John Leggott College, Scunthorpe Monday 2nd September 2013 Joe Murray Association of Teachers of Mathematics

2. Objectives 2 by 2.........by more!! • How many themes can you teach or learn with a 2 by 2 grid? • How can we turn one activity into many? • ATM support • Reflection, questions, etc

3. Problem solving & investigation...... is at the heart of mathematics Outstanding teaching & learning will: • allow children to make decisions • encourage creativity and invention • promote discussion and communication • involve children seeing pattern, connections....... making & testing hypotheses, • promote reflecting, interpreting, explaining........proving, • encourage ‘what if’ ..........and ‘what if not’ questions; • be enjoyable and contain the opportunity for surprise • offer problems that are accessible …..and extendable

4. Professional supportmathematics community......new CPD package • Professional development work with teachers...branches • Professional identity part of vision for mathematics education • MT journal 6 copies per year; articles by teachers & for teachers • e-News • ATM website archive of “old” journals, sales,.... • Publications 25% discount for members • Annual Easter Conference Sheffield 2013, BCME8, Nottingham 2014 • Branch meetings • Tax concessions £65 p.a......£52 after tax effectively £1 a week!!! Primary school membership is just £65 per year

5. Chuck the Ted”use simple formulae expressed in words” (draft N.C.)little People...Big Maths • Children sit in a circle, each child with a number that all can see. • Choose a “rule”. e.g.Find someone with a number 1 more than you • Each child takes a turn to throw the toy to another child following the rule. • Make a new rule and play again.

6. Addition squares • Add pairs of outside numbers • Add the 4 numbers inside the square • Is this total equal to double the sum of the 4 outside numbers? • Investigateother 2 by 2 squares • What about 3 by3 squares, 4 by4...? • What about rectangles??

7. Multiplication squares • Multiply pairs of outside numbers • Add these 4 new numbers What is the connection between the 4 outside numbers and the square total? • Investigate other 2 by 2 squares • Extendto bigger squares...3 by 3, 4 by 4... • What happenswith rectangles?

8. MontyRich Task Maths Monty Python is a 7-square snake on a 1 to 100 grid. • Make Monty. • Monty cards.

9. MontyRich Task Maths Monty Python is a 7-square snake on a 1 to 100 grid. • Longer and shorter Monty. • Heads and tails. Find the difference between head number and tail number. Biggest?...smallest?

10. MontyRich Task Maths Monty Python is a 7-square snake on a 1 to 100 grid. • Mystery Monty. • Monty on a “tables” grid.

11. Four-ominoes • These can be made with 4 squares...joined edge to edge • Are there any more? Investigate • Symmetries, tessellations, area, perimeter...... • 3-D figures...... with 4 cubes • Pupil “robots” What about 5 squares, 6 squares, etc

12. Four-omino activities • Make 4-ominoesUse 5 squares joined edge to edge, how many different shapes can you make? • NamesFind names for all 4-ominoes? Which is a “snake” or the “submarine”? • Symmetry Which have line symmetry? Which have rotational symmetry? • TessellationWhich 4-ominoes will tessellate? Will all 12 tessellate? • Area and perimeterWhich 4-omino has the biggest area?........longest perimeter? • Joins and perimeterInvestigate the number of joins and the perimeter. • Other “ominoes”Make some shapes using just 5 squares.....or shapes using 6 squares?? • Using triangle Use isometric paper to make shapes from 5 triangles • LOGO or RoamerWrite a LOGO programme to draw a 4-omino. .......or direct a “pupil robot” • 3-D explorationUse 5 multilink cubes to make a 3-D shape. How many can you find?

13. Stay-the-Same Numbersgenerate and describe linear number sequences (draft N.C.)8 days a Week

14. Stay-the-Same NumbersEight Days a Week

15. Stay-the-Same NumbersEight Days a Week

16. Stay-the-Same NumbersEight Days a Week

17. Stay-the-Same NumbersEight Days a Week

18. Stay-the-Same NumbersEight Days a Week

19. Place value Roll a dice & enter numbers in the boxes. Each player has own table • Biggest number • Smallest add • Biggest take-away • Place your digits and add your numbers together what if you are allowed to put numbers in another person’s boxes?

20. Braille Your task is to design a new coding system for letters in the alphabet. • The code is based on a 2 by 2 grid with up to 4 dots in the cells. • Here are a few...... • How many different “Braille tiles” are there? • How many have 2 dots, 3 dots, etc....? • Are there enough for each letter of the alphabet? • Try some 3-dot, 5-dot, 6-dot........”tiles”

21. Braille 2

22. Carroll diagram • Sort shapes by properties • Sort numbers[odd, prime, multiples, etc] • Make sets of criteria cards to create a variety of problems. • Use bigger diagrams [e.g. 3 by 3]

23. Always, sometimes, never... • Multiples of 3 are odd numbers • Squares have 4 right angles. • A 4-sided shape has a line of symmetry • An even number cannot be a prime number • A multiple of 3 cannot be a multiple of 2. • You can draw a triangle with 2 right angles • A shape with 4 sides is a square.

24. Odd one out

25. Professional supportmathematics community......new CPD package • Professional development work with teachers...branches • Professional identity part of vision for mathematics education • MT journal 6 copies per year; articles by teachers & for teachers • e-News • ATM website archive of “old” journals, sales,.... • Publications 25% discount for members • Annual Easter Conference Sheffield 2013, BCME8, Nottingham 2014 • Branch meetings • Tax concessions £65 p.a......£52 after tax effectively £1 a week!!! Primary school membership is just £65 per year

26. Thank you For further information about ATM • Membership • Publications • Branches • Conferences www.atm.org.uk or contact Joe Murray at joemurray@atm.org.uk joe1013@sky.com