Framework for teaching mathematics

Year 2

Calculations

Yearly teaching programmes, shown below, are taken from the relevant section of the Framework for teaching mathematics: Reception to Year 6. The numbers, in brackets, are page references to the relevant supplement of examples in the Framework which you can download by clicking on an icon in the 'Downloads' box on the left of this page.

Understanding addition and subtraction (p.24-29)

Extend understanding of the operations of addition and subtraction.
Use and begin to read the related vocabulary.
Use the +, - and = signs to record mental additions and subtractions in a number sentence, and recognise the use of a symbol such as n or s to stand for an unknown number.
Recognise that addition can be done in any order, but not subtraction: for example, 3 + 21 = 21 + 3, but 21 - 3 3 - 21. (p.25-29)
Understand that more than two numbers can be added.
Begin to add three single-digit numbers mentally (totals up to about 20) or three two-digit numbers with the help of apparatus (totals up to 100). (p.27)
Understand that subtraction is the inverse of addition (subtraction reverses addition). (p.25,29)

Rapid recall of addition and subtraction facts (p.30-31)

Know by heart:
all addition and subtraction facts for each number to at least 10;
all pairs of numbers with a total of 20 (e.g. 13 + 7, 6 + 14);
all pairs of multiples of 10 with a total of 100 (e.g. 30 + 70). (p.31)

Mental calculation strategies (+ and -) (p.32-41)

Use knowledge that addition can be done in any order to do mental calculations more efficiently. For example:
put the larger number first and count on in tens or ones;
add three small numbers by putting the largest number first
and/or find a pair totalling 10;
partition into '5 and a bit' when adding 6, 7, 8 or 9, then recombine (e.g. 16 + 8 = 15 + 1 + 5 + 3 = 20 + 4 = 24);
partition additions into tens and units, then recombine. (p.33)
Find a small difference by counting up from the smaller to the larger number (e.g. 42 - 39). (p.33)
Identify near doubles, using doubles already known
(e.g. 8 + 9, 40 + 41). (p.33)
Add/subtract 9 or 11: add/subtract 10 and adjust by 1.
Begin to add/subtract 19 or 21: add/subtract 20 and adjust by 1. (p.35)
Use patterns of similar calculations. (p.35)
State the subtraction corresponding to a given addition, and vice versa. (p.35)
Use known number facts and place value to add/subtract mentally. (p.37,39)
Bridge through 10 or 20, then adjust. (p.41)

Understanding multiplication and division (p.46-51)

Understand the operation of multiplication as repeated addition or as describing an array, and begin to understand division as grouping (repeated subtraction) or sharing.
Use and begin to read the related vocabulary.
Use the ×, ÷ and = signs to record mental calculations in a number sentence, and recognise the use of a symbol such as n or s to stand for an unknown number. (p.47,49)
Know and use halving as the inverse of doubling. (p.47,49)

Rapid recall of multiplication and division facts (p.52-53)

Know by heart:
multiplication facts for the 2 and 10 times-tables;
doubles of all number to 10 and the corresponding halves.
Begin to know:
multiplication facts for the 5 times-table. (p.53)
Derive quickly:
division facts corresponding to the 2 and 10 times-tables;
doubles of all numbers to at least 15 (e.g. 11 + 11 or 11 × 2);
doubles of multiples of 5 to 50 (e.g. 20 × 2 or 35 × 2);
halves of multiples of 10 to 100 (e.g. half of 70). (p.53)

Mental calculation strategies (× and ÷) (p.54-57)

Use known number facts and place value to carry out mentally simple multiplications and divisions. (p.57)

Checking results of calculations (p.58-59)

Repeat addition in a different order. (p.59)
Check with an equivalent calculation. (p.59)

NOTE
Key objectives are highlighted in bold type.