Efficient written methods for calculating addition, subtraction, multiplication and division by the end of year 6.

Partition into tens and units and recombine = 12 = = = Recombine = = 8, = 48

Partition into tens and units and recombine = =

Use informal pencil and paper methods to support, record or explain addition and subtraction = ? = 539

= Use informal pencil and paper methods to support, record or explain addition = =

Using a standard written method Most significant digits first Least significant digits first + Prepares for carrying

= Using a standard written method =

Using a standard written method; carrying = =

Using a standard written method; carrying = =

Counting up from the smaller to larger number (complementary addition) – 56 = = to to 80 4 to

84 – 56 = to to 80 4 to Apply partitioning skills 84 = = = = 28 - Begin to record calculations in preparation for an efficient standard method; decomposition

84 – 56 =84 – 52 = 46 – 25 = Counting up from the smaller to larger number (complementary addition)

84 – 56 =84 – 52 = 46 – 25 = Begin to record calculations in preparation for an efficient standard method; decomposition

Record calculations in preparation for an efficient standard method; decomposition 89 = = = = = = 24 No decomposition Decomposition

89 – 57 =84 – 57 = 284 – 57 = Record calculations in preparation for an efficient standard method; decomposition

Continue to develop an efficient standard method; decomposition 754 = leading to = =

754 – 286 = 5821 – 764 =4567 – 893 = Continue to develop an efficient standard method; decomposition

Develop and use an efficient standard written method; decomposition

Develop and use an efficient standard written method; decomposition 6467 – 2684 = – 4387 =324.9 – 7.25 =

Understand multiplication as repeated addition and as an array rows of 5 = 15 3 x 5 = = 15 5 rows of 3 = 15 5 x 3 = = 15 (rows are always mentioned before columns)

Modelling the number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials, but it can also assist the children to form useful mental pictures to support memory and reasoning.

Commutative property The commutative property of multiplication can be neatly illustrated using an array. For example, the array above could be read as 2 rows of 6, or as 6 columns of 2. Or the array could be physically turned around to show that 2 rows of 6 has the same number as 6 rows of 2. Regardless of the way you look at it, there remain 12 objects. Therefore, the array illustrates that 2 x 6 = 6 x 2, which is an example of the commutative property for multiplication. Being able to apply the commutative property means that the number of multiplication facts that have to be memorised is halved.

4 x 3 =6 x 3 = Understand multiplication as repeated addition and as an array. 5 x 6 =

Use informal pencil and paper methods to support, record or explain multiplication. 23 x 3 23 x 3 = (20 x 3) + (3 x 3) 609 = x Times tables Partitioning Array Grid method

12 x 9 =26 x 3 = 35 x 16 = Use informal pencil and paper methods to support, record or explain multiplication

Grid method 346 x x =

Continue to develop an efficient standard written method Short multiplication 346 x 9 leading to x 9 40 x 9 6 x 9 x x 4 5

346 x 9 Use informal pencil and paper methods to support, record or explain multiplication Grid method Short multiplication 543 x 7 Develop an efficient standard written method

Continue to develop an efficient standard written method Long multiplication 72 x x 72 x x 8

72 x 38 Continue to develop an efficient standard written method Long multiplication

Use informal pencil and paper methods to support, record or explain divisions Chunking! Division made easy! 42 ÷ 3 = ? –12– groups of 3 10 groups of Chunks 10 chunks + 4 chunks = 14

42 ÷ 321 ÷ 3 54 ÷ 6 Use informal pencil and paper methods to support, record or explain divisions

Use informal pencil and paper methods to support, record or explain division Using multiples of the divisor (CHUNKING) x x 5 2 Answer: 14 remainder ÷

72 ÷ 3 = 72 ÷ 5 =72 ÷ 4 = Use informal pencil and paper methods to support, record or explain division

Develop an efficient standard written method Short division 196 ÷ 6 ) 6 32 R (30 x 6 = 180) (2 x 6 = 12) 4 (remainder)

196 ÷ 6 Develop an efficient standard written method Short division 256 ÷ 7

Continue to develop an efficient standard written method Short division (thousands) 2196 ÷ 6 ) (300 x 6 = 1800) (60 x 6 = 360) 36 (6 x 6= 36)

Continue to develop an efficient standard written method Short division (Bus Stop Method!) 2196 ÷ 6 ) into 2 doesn’t go – carry the 2 over. 6 into 21 goes 3 remainder 3 – carry the 3 over. 6 into 39 goes 6 remainder 3 – carry the 3 over. 6 into 36 goes 6 exactly divided by 6 = 366!

2196 ÷ 6 Continue to develop an efficient standard written method Short division (thousands) 4321 ÷ ÷ 6

Know what each digit represents and partition three-digit numbers into a multiple of 100, a multiple of 10, and ones. Understand multiplication as repeated addition and as an array. Partition into tens and units and recombine. Add three two-digit numbers using apparatus or informal methods. Add or subtract a near multiple of 10 to a two-digit number, by adding or subtracting the nearest multiple of 10, and adjusting. Choose appropriate number operations and calculation methods to solve word problems.

Know what each digit represents and partition three-digit numbers into a multiple of 100, a multiple of 10, and ones What is partitioning?

What is an array? Understand multiplication as repeated addition and as an array. 3 x 5 = =

Add three two-digit numbers using apparatus or informal methods. What does it mean by informal method? = = = 8, = 48

Partition into tens and units and recombine. Why is partitioning so useful? = = 8, = = It’s one of those informal methods!

Add or subtract a near multiple of 10 to a two-digit number, by adding or subtracting the nearest multiple of 10, and adjusting. What does it mean by adjusting = ? = – 1 = 73 Round up 39 to = = 74 Partitioning Recombine A clearly written answer

Choose appropriate number operations and calculation methods to solve word problems. Use informal pencil and paper methods to support, record or explain addition and subtraction. To add/subtract by counting on or back in repeated steps of 1, 10, 100. Use informal pencil and paper methods to support, record or explain multiplication. Use informal pencil and paper methods to support, record or explain divisions.

To add/subtract by counting on or back in repeated steps of 1, 10, 100. What is counting on and back on a number line?

Use informal pencil and paper methods to support, record or explain addition and subtraction. What does it mean by informal method? = ? = 539

Use informal pencil and paper methods to support, record or explain addition and subtraction. What does it mean by informal method? £ £3.60 = ? Demonstrate the need to re-partition the numbers as: £ £3.60 = £ p subtract £3 + 60p = £4 - £3 and 120p – 60p = £1 and 60p = £1.60

Use informal pencil and paper methods to support, record or explain multiplication. What another informal method? 23 x 3 23 x 3 = (20 x 3) + (3 x 3) 609 = x Times tables Partitioning

Use informal pencil and paper methods to support, record or explain divisions. Division made easy! 42 ÷ 3 = ? –12– groups of 3 10 groups of Chunks 4 chunks + 10 chunks = 14

Choose appropriate number operations and calculation methods to solve word problems. Understand and use the principle of the associative law. Extend written methods to short division of HTU by U

Establish 5 x 16 is the same as 10 x 8 etc. Understand and use the principle of the associative law. What is associative law and do the majority of children care? GRID! 5 x 10 = 50 5 x 6 = 30 = 80

Extend written methods to short division of HTU by U Chunking! 183 ÷ 5 = ? 183 – 150 (30 x 5) = – 30 (6 x 5) = 3 Answer 36 r 3

Choose appropriate number operations and calculation methods to solve word problems. Use informal pencil and paper methods to support, record or explain addition and subtraction. To add/subtract by counting on or back in repeated steps of 1, 10, 100. Use informal pencil and paper methods to support, record or explain multiplication. Use informal pencil and paper methods to support, record or explain divisions.