Developing Mathematical Thinking in Addition and Subtraction

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

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

7. Empty Number Lines – Addition Counting on – no crossing of tens boundary 34+23 +10 +10 +10 +10 +1 +1 +1 Jumps of 10 and 1 Use the known fact 4+3 Add 20 in one jump 34 44 54 55 56 57 Increasing efficiency of approach +3 34 44 54 57 +20 +3 34 54 57

8. Empty Number Lines – Addition Counting on – crossing of tens boundary 37+25 +10 +10 +10 +10 Jumps of 10 and 1 Add on 5 by bridging through the ten Add 20 in one jump +1 +1 +1 +1 +1 62 37 47 57 58 59 60 61 Increasing efficiency of approach +3 +2 +3 +2 37 47 57 60 62 +20 37 57 60 62

9. -1 -1 -1 Empty Number Lines – Subtraction Counting back – not crossing of tens boundary -3 -3 57-23 -10 -10 -10 -10 Jumps of 10 and 1 Using known facts 7-3=4 20 in one jump 37 47 57 34 35 36 Increasing efficiency of approach 37 47 57 34 -20 37 47 57 34

10. -20 -1 -1 -1 -1 -1 Empty Number Lines – Subtraction Counting back – crossing of tens boundary -3 -3 52-25 -10 -10 -10 -10 Jumps of 10 and 1 Bridge through a ten. 20 in one jump 27 28 29 30 31 32 42 52 Increasing efficiency of approach -2 27 30 32 42 52 -2 27 32 52

11. +10 +10 +10 +10 Empty Number Lines – Subtraction Consider subtraction as counting on 73-47 Jumps of 10 and 1 Jump to multiples of 10 Add 20 in one jump +1 +1 +1 +1 +1 +1 47 48 49 50 60 70 71 72 73 Increasing efficiency of approach 57 +3 +3 +3 +3 47 50 60 70 73 +20 47 50 70 73 73-47 becoming 47+ ? = 73

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

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

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

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