The teaching of calculations will be monitored using evidence collected from: Planning scrutiny Classroom observations Scrutiny of children’s work AFL opportunities within lessons Discussions with children Evidence sheets Videos to support mathematical teaching and learning Number and value KS1 ‐ Counting in steps of one and ten KS1 ‐ Partitioning in different ways KS1 ‐ Addition and Subtraction KS1 ‐ Using resources to develop fluency and understanding KS2 ‐ Partitioning (subtraction) Multiplication https://www.ncetm.org.uk/resources/40530 KS1 ‐ Multiple Representations of Multiplication KS1‐ The commutative law for multiplication Lower KS2 ‐ Grid multiplication as an interim step Upper KS2 ‐ Moving from grid to a column Number resources/40533 KS1 ‐ Number bonds to ten KS1 ‐ Consolidation and practice (Addition and Subtraction) KS1 ‐ Reinforcing Facts KS1 ‐ Rapid recall of multiplication facts Algebra https://www.ncetm.org.uk/ resources/43649 KS1 ‐ Look at ’missing numbers’ KS2 ‐ Equations and substitution KS3 ‐ Factorising* Subtraction https://www.ncetm.org.uk/ resources/40532 Lower KS2 – Partitioning Lower KS2 ‐ Discussing Subtraction Strategies KS2 ‐ Developing Column Subtraction Upper KS2‐ Column Subtraction Fractions https://www.ncetm.org.uk/ resources/43609 KS1 ‐ Adding fractions and mixed numbers KS2 ‐ Using an array to add fractions KS2 ‐ Bar model dividing by fractions KS3 ‐ Fraction wall to add fractions* Division https://www.ncetm.org.uk/ resources/43589 KS1‐ Sharing and grouping KS 2 ‐ Place value counters for division KS 3 ‐ Group working on problems* Multiplicative reasoning https://www.ncetm.org.uk/ resources/43669 KS2 ‐ Bar model for multiplication KS3 ‐ Ratio and proportion*
Objective and Strategies Concrete Pictorial Abstract Doubling Use practical activities to show how to double a number. Draw pictures to show how to double a number. Partition a number and then double each part before recombining it back together. Counting in multiples Count in multiples supported by concrete objects in equal groups. Use a number line or pictures to continue support in counting in multiples. Count in multiples of a number aloud. Write sequences with multiples of numbers. 2, 4, 6, 8, 10 5, 10, 15, 20, 25 , 30 Repeated addition Write addition sentences to describe objects and pictures. Arrays- showing Create arrays using counters/ cubes to show multiplication sentences. Draw arrays in different rotations to find commutative multiplication sentences. Link arrays to area of rectangles. Use an array to write multiplication sentences and reinforce repeated addition.
Grid Method Show the link with arrays to first introduce the grid method. 4 rows of 10 4 rows of 3 Move on to using Base 10 to move towards a more compact method. 4 rows of 13 Move on to place value counters to show how we are finding groups of a number. We are multiplying by 4 so we need 4 rows. Fill each row with 126. Add up each column, starting with the ones making any exchanges needed. Then you have your answer. Children can represent the work they have done with place value counters in a way that they understand. They can draw the counters, using colours to show different amounts or just use circles in the different columns to show their thinking as shown below. Start with multiplying by one digit numbers and showing the clear addition alongside the grid. Moving forward, multiply by a 2 digit number showing the different rows within the grid method. Column multiplication Children can continue to be supported by place value counters at the stage of multiplication. It is important at this stage that they always multiply the ones first and note down their answer followed by the tens which they note below. Bar modelling and number lines can support learners when solving problems with multiplication alongside the formal written methods. Start with long multiplication, reminding the children about lining up their numbers clearly in columns. If it helps, children can write out what they are solving next to their answer. This to the more compact method.
Objective and Strategies Concrete Pictorial Abstract Sharing objects into groups I have 10 can you share them equally in 2 groups? Children use pictures or shapes to share quantities. Share 9 buns between three people. 9 ÷ 3 = 3 Division as grouping Divide quantities into equal groups. Use cubes, counters, objects or place value counters to aid understanding. Use a number line to show jumps in groups. The number of jumps equals the number of groups. Think of the bar as a whole. Split it into the number of groups you are dividing by and work out how many would be within each group. 28 ÷ 7 = 4 Divide 28 into 7 groups. How many are in each group? Division within arrays Link division to multiplication by creating an array and thinking about the number sentences that can be created. Eg 15 ÷ 3 = 5 5 x 3 = 15 15 ÷ 5 = 3 3 x 5 = 15 Draw an and use lines to split the array into groups to make multiplication and division sentences. Find the inverse of multiplication and division sentences by creating four linking number sentences. 7 x 4 = 28 4 x 7 = 28 28 ÷ 7 = 4 28 ÷ 4 = 7