Developing Mathematical Thinking in Addition and Subtraction

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.

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

Progression

Empty Number Lines 3+ 5 = 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)’

Empty Number Lines = Commutative property enables you to start adding from the larger number

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

37 Empty Number Lines – Addition Counting on – crossing of tens boundary Jumps of 10 and 1 Add on 5 by bridging through the ten Add 20 in one jump Increasing efficiency of approach

Empty Number Lines – Subtraction Counting back – not crossing of tens boundary Jumps of 10 and 1 Using known facts 7-3=4 20 in one jump Increasing efficiency of approach

Empty Number Lines – Subtraction Counting back – crossing of tens boundary Jumps of 10 and 1 Bridge through a ten. 20 in one jump Increasing efficiency of approach

Empty Number Lines – Subtraction Consider subtraction as counting on Jumps of 10 and 1 Jump to multiples of 10 Add 20 in one jump Increasing efficiency of approach becoming 47+ ? = 73

aa 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

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

= = 4 + (3 + 7) = =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?

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?