1. Listening to you, working for you www.bexley.gov.uk Helping your child with mathematical reasoning at home March 2015

2. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk National Curriculum The national curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, reason mathematically can solve problems

3. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Development Matters EYFS Overlap in many aspects of the ‘Good Levels of Development’ Thinking and reasoning skills are crucial to the characteristics of effective learning: creating and thinking critically to communication and language, understanding and speaking Developed alongside the mathematics.

4. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk What is reasoning in mathematics? Reason mathematically in mathematics is: following a line of enquiry, conjecturing relationships and generalisations, developing an argument, justification or proof using mathematical language.

5. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Why should you help your child to reason? Research by Nunes (2009) says that ‘ability to reason mathematically is the most important factor in a pupil’s success in mathematics…Such skills support deep and sustainable learning and enable pupils to make connections in mathematics’.

6. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Creating and thinking critically at home Model being a thinker, showing that you don’t always know, are curious and sometimes puzzled, and can think and find out Encourage divergent thinking: what else is possible Value questions, and many responses, without rushing towards answers too quickly. Support your child’s interests over time, remind them of previous approaches and encourage them to make connections between their experiences

7. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk continued Model the creative process, showing your thinking in as many possible ways forward Give reasons rather than directive ‘rules’ for any limits on your child’s activities Be a sensitive conversational partner and co-thinker Show and talk about strategies - how to do things – include problem solving, thinking and learning.

8. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Challenge your child to think and talk about their own learning process with questions such as: How did you do that? How else could you have done that? What could you do when you are stuck on that? Convince me you are correct.

9. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Reasoning in stories

10. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Toys

11. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk What do we have in common? Sort into group – no more than two to start with Tell you why they have sorted them that way (Identify characteristics of each set)

12. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Animals

13. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Family photos

14. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Food

15. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Puzzles and problems Suduku

16. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Games

17. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Walking to school How shall we travel to school today? Why? Which route do you want to take? Why? Which will be the quickest? Which will be the slowest? Which car do you like? Why not this one? How are these cars similar? How are these cars different?

18. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk In the kitchen Which is more, 1.7kg of apples or 1007g of apples? Which is more, 1.25kg of apples or 1025g of apples? Decisions, decisions: which is the best container to store a drink in? Which spoon would you eat soup with? Why? Which piece of crockery would you eat a piece of cake from? Why?

19. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Getting dressed Get three items of clothing out that are appropriate for different seasons. Which top would be best worn on a sunny day? Which top would be best worn on a winter’s day? Why? Decisions, decisions Compare using size, colour Use, material, parts and shape

20. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk What’s the time True or False? There are more hours in a day than minutes in an hour. True or false? There are more days in February than there is in March.

21. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk In the bath Explore: The taller the container, the more water it holds. Is it always true, sometimes true or never true.

22. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk What is the same? What is different? What is the same and what is different about a: Number line and a clock Number line and a thermometer

23. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Money problems How to Live Forever’ costs £5.50 plus VAT in Waterstones or £6.60 minus a 10% discount in WHS. Which shop is it the cheapest in? The smaller the coin the lesser the value?

24. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk True or False Odd + odd + odd = odd When adding 4 numbers, it doesn’t matter which order I add them up in. If I start at the number 2 and count in 4’s I will say the number 32

25. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Sometimes, always or never Multiplication always makes things bigger Can you think of any multiplication you could do that would not make your starting number bigger? What happens if you multiply by a negative number?

26. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Sometimes, always or never When you multiply a number by ten you add a zero?

27. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Times tables Explore the relationships between the different times tables for example 3 and 6, 4 and 8 Always true, sometimes true, never true? 9 x tables – digits add up to 9. Is 153 in the 9 times table?

28. www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Listening to you, working for you www.bexley.gov.uk Any questions?