Addition EYFS/Year 1 Everything concrete before pictorial/abstract Year 2 Year 3 Year 4 Year 5 Year 6 Combining two parts to make a whole: part part whole model (PPW) Starting at the bigger number and counting on using manipulatives. Regrouping to make 10 using tens frame. Use of number tracks and number lines (marked) Adding three single digits. Combining two parts to make a whole – 2-digit numbers PPW. Use of number tracks and number lines (marked and empty) to count on. Use of Base 10 to combine two numbers. Bar model to understand problems. Use of place value counters to combine two numbers – recording pictorially. Introduce regrouping and exchanging with Base 10 and place value counters. Bar model to understand problems. Column method – with regrouping – beginning to move away from pictorial recording. Bar to understand problems. Column method – regrouping (abstract). Use of place value counters for adding decimals. Bar model to understand problems. Column method – regrouping (abstract). Use of place value counters for adding decimals. Bar model to understand problems.
Subtraction EYFS/Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Removing (taking away) ones. Counting back. Find the difference – comparing two amounts. PPW – the whole and one part given, what is the other part? Make 10 using the tens frame (14-5 = 14-4-1). Bar model to understand problems. Counting back. Finding the difference. PPW – the whole and one part given, what is the other part? Make 10 using the tens frame (14-5 = 14-4-1). Partitioning to make 10. Use of Base 10 (concrete, then pictorial). Bar to understand problems. Recording of Base 10 pictorially alongside column method (with and without regrouping). Use of place value counters for representing 3-digit numbers. Bar model to understand problems. Column method with regrouping – beginning to move away from pictorial recording. Bar model to understand problems. Column method with regrouping (abstract). Use of place value counters for decimals – with the same amount of decimal places. Bar model to understand problems. Column method with regrouping (abstract). Use of value counters for decimals – with different amounts of decimal places. Bar model to understand problems.
Multiplication EYFS/Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Recognising and making equal groups. Doubling – making two groups. Using repeated addition. Counting in multiples. Use of concrete manipulatives – counters, cubes, Numicon and other classroom objects. Using repeated addition by drawing groups of/lots of. Using repeated addition by counting along a number line. Using repeated addition by jumping along a number line. Using arrays – shows groups of clearly – emphasises commutativity of multiplication. Using arrays. Using Base 10 (concrete and recording pictorially) for x 1-digit. Partitioning. Using column multiplication – introduced with place value counters. 2- and x Using column multiplication – abstract only but may need repeat of Y4 first. Up to 4-digit x 1- and 2-digit column multiplication (abstract). Up to 4-digit x
Division EYFS/Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Sharing concrete objects into groups. Beginning to record pictorially. Division as grouping - 12÷3 – the 12 objects into groups of 3 – answer is how many groups. Division as grouping. Using repeated subtraction on a number track or number line. Division with arrays – linking to multiplication – drawing groups as columns/rows instead of just in circles. Division with a remainder – manipulatives, times tables facts, repeated subtraction, grouping, sharing. Using Base 10 or place value counters to divide 2-digit by 1-digit. Division with a remainder (pictorially). division – concrete and pictorial – up to by 1-digit). division. Up to by including remainders. Short division. Long division with Place Value Counters. Up to 4-digit by Children should exchange into the tenths and hundredths column too.