1. Developing Mathematical Thinking in Addition and Subtraction

2. Aim of presentation To encourage staff reflection on approaches to teaching addition and subtraction. To stimulate professional dialogue. To use as a CPD activity for staff individually or collegiately.

3. Relevant Experiences and Outcomes I can use practical materials and can count on and back to help me to understand addition and subtraction, recording my ideas and solutions in different ways. MNU 0-03a I can use addition, subtraction, multiplication and division when solving problems, making best use of the mental strategies and written skills I have developed. MNU 1-03a Having determined which calculations are needed, I can solve problems involving whole numbers using a range of methods, sharing my approaches and solutions with others. MNU 2-03a I can use a variety of methods to solve number problems in familiar contexts, clearly communicating my processes and solutions. MNU 3-03a

4. Progression

5. 5 5 3 3 8 5 3 8 Empty Number Lines 3+ 5 = 5 + 3 Commutative property– Early level progression: ‘understand the idea that 3+4 is the same as 4+3 (commutative)’ Commutative property– Early level progression: ‘understand the idea that 3+4 is the same as 4+3 (commutative)’

6. 28 3 3 31 28 3 31 Empty Number Lines 3+ 28 = 28 + 3 Commutative property enables you to start adding from the larger number

7. 34 Empty Number Lines – Addition Counting on – no crossing of tens boundary 34+23 +10 +1 4454 +10 +1 5556 57 34 +10 +3 4454 +10 57 34 +20 +3 5457 Jumps of 10 and 1 Use the known fact 4+3 Add 20 in one jump Increasing efficiency of approach

8. 37 Empty Number Lines – Addition Counting on – crossing of tens boundary 37+25 +10 +1 4757 +10 +1 585960 37 +10 +3 4757 +10 37 +20 5760 Jumps of 10 and 1 Add on 5 by bridging through the ten Add 20 in one jump +1 61 62 +2 +3+2 62 6062 Increasing efficiency of approach

9. 374757 34 -3 374757 -10 34 -10 37 Empty Number Lines – Subtraction Counting back – not crossing of tens boundary 57-23 4757 -10 3635 -3 -20 Jumps of 10 and 1 Using known facts 7-3=4 20 in one jump 34 -10 Increasing efficiency of approach

10. 3252 -3 -2 27 324252 -10 32 Empty Number Lines – Subtraction Counting back – crossing of tens boundary 52-25 4252 -10 3130 -3 -20 Jumps of 10 and 1 Bridge through a ten. 20 in one jump 29 -10 28 27 -2 3027 Increasing efficiency of approach

11. 47 +10 506070 +10 73 47 Empty Number Lines – Subtraction Consider subtraction as counting on 73-47 +10 5060 +1 70 57 +3 +20 Jumps of 10 and 1 Jump to multiples of 10 Add 20 in one jump +10 +1 73 +3 71724849 475070 73 +3 Increasing efficiency of approach 73-47 becoming 47+ ? = 73

12. aa+3 3 3 a 3+a 3 Empty Number Lines a + 3 = 3 + a a Moving from specific to general. Commutative property - numbers can be added in any order Moving from specific to general. Commutative property - numbers can be added in any order

13. aa+b b b a b+a b Empty Number Lines a + b = b + a a Commutative property - numbers can be added in any order

14. 3 + 4 + 7 = 4 + 3 + 7 = 4 + (3 + 7) = 4 + 10 =14 Using commutative and associative properties for addition. Development and progression FIRST Level - ‘understanding and using commutative and associative properties when calculating‘ Commutative property – swap the numbers round – change the order Associative property – it does not matter how you group the numbers ie which calculation you do first What about subtraction with 2 numbers and more than 2 numbers?

15. Next steps What information willyou share with colleagues? What might you or your staff do differently in the classroom? What else can you do as to improve learning and teaching about number What impact will this have on your practice?