This snapshot, taken on
10/08/2011
, shows web content acquired for preservation by The National Archives. External links, forms and search may not work in archived websites and contact details are likely to be out of date.

The UK Government Web Archive does not use cookies but some may be left in your browser from archived websites.

# Unit 3 learning overview

You can use this overview to inform your planning and help secure children's learning of the mathematics covered in the unit. It includes recognising odd or even numbers in a counting sequence, adding two-digit numbers, rounding two-digit and three-digit numbers, using partitioning to multiply and divide, and using lists or tables to organise solutions to problems.

Children consolidate their counting on and back in steps of two, three, four, five, six and ten. They recognise when the numbers in a counting sequence are odd or even. For example, counting in steps of four from three will generate odd numbers only, while when counting in steps of three from four the numbers alternate between odd and even. Children count in steps of two-digit numbers such as 12s from 3, using a 10 and 2 count, to generate 3, 13, 15, 25, 27, 37, 39, 49, 51… alternately whispering quietly and shouting aloud the numbers involved.

Children solve problems and puzzles involving all four operations. They identify relevant information and select the appropriate operations in order to solve word problems such as:

• 'There are 12 stamps in a sheet. Each stamp costs 28 p. I buy a quarter of the sheet. How many stamps is this?'
• 'I pour out 180 ml and then 270 ml from a one-litre bottle of squash. How much is left?'

Children use counting strategies and partitioning to add and subtract combinations of one-digit and two-digit numbers. They add two-digit numbers by partitioning one or both of the numbers. For example, they work out $58+74$ by partitioning 58 into 50 and 8 then adding 50 and 8 to 74.

Children use a similar strategy for subtraction, for example working out $94-58$ or $294-58$ by partitioning 58 and subtracting 50 then 8. They use counting-up strategies where appropriate, as in $124-68$ where they count up from 68 to 70, to 100, to 124, recording and adding the steps 2, 30 and 24. Children use a number line to note the steps and to explain how they did the calculation. Children also subtract by counting on from the smaller to the larger number in their heads when the difference is small, as in $305-297$, making notes to support calculation.

Children develop their use of the empty number line to support their calculations. They begin to record vertically addition and subtraction calculations that cannot be easily done mentally. They partition one of the numbers and add or subtract the units, tens and hundreds separately:

$76+47$
$267-149$

Children recognise the relationship between the vertical presentation and the steps on the number line. They begin to use an expanded layout that underpins the standard written method. For example, for $76+47$ and $83-48$ children use:

76 goes into 70 plus 6 whilst 47 goes into 40 plus 7. 70 plus 40 equals 110 and 6 plus 7 equals 13. 110 plus 13 equals 123 which is the final result of 76 plus 47.
83 goes into 80 plus three and 70 plus 13 whilst 48 goes into 40 plus 8. 70 minus 40 equals 30 and 13 minus 8 equals 5, thus, 30 plus 5 equals 35 which is the final result of 83 minus 47.

Children round two-digit and three-digit numbers to the nearest 10 and 100 and use this to give approximate answers to addition and subtraction calculations. For example, they recognise that the answer to $247+76$ will be just less than $250+80$ or 330, and $183-48$ is about $180-50$ or 130. They understand that finding an approximate answer is a useful strategy for checking a calculation.

Children begin to work systematically, using lists or tables to organise their solutions to problems such as: 'A farmer has cows and chickens on the farm. Altogether the animals have 24 legs. How many cows and chickens could there be on the farm?'

Using problems such as these gives the opportunity to assess children's ability to communicate their mathematics and, in particular, to show how they are looking to develop organised approaches to recording their work.

Children use their understanding of place value to support multiplication and division involving multiples of ten to answer questions such as:

• 'Three pencils cost 90 p altogether. How much does each pencil cost?'
• 'Rani picks up seven 50 g weights. How much do these weigh altogether?'
• 'Sam is making cards. Each card takes 20 minutes. He starts at 4.30 and makes four cards. What time does he finish?'

Children begin to use partitioning to multiply and divide two-digit numbers. For example, they calculate $24×4$ by partitioning 24 into 20 and 4 and working out $20×4+4×4$, and $96÷3$ by partitioning 96 into 90 and 6 and dividing each part by 3 to get the answer 32. They identify remainders in related calculations such as $95÷3$, and begin to round the remainder up or down when the context demands it. For example, if cars can each transport up to 4 people, they work out that 12 people would need 3 cars but 13 people require 4 cars.

Children solve problems such as:

• 'Use three of the digits 2, 3, 4, 5 and 6 to create multiplication calculations (e.g. $34×6$)'
• 'What products can you make? What is the largest/smallest product?'

They work in pairs or groups, with all children in the group contributing to decisions about the methods they use, whether they will use resources and how they will record their work.