This snapshot, taken on
11/08/2011
, 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 External links, forms and search may not work in archived websites and contact details are likely to be out of date.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 1 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 creating sequences by counting on and back from any start number, exploring sequences involving negative numbers, using and discussing mental calculation strategies for special cases involving all four operations, and consolidating written methods for addition and subtraction.

Children create sequences by counting on and back from any start number in equal steps such as 19 or 25. They record sequences on number lines. They describe and explain the patterns in a sequence. For example, when subtracting 19 to generate the sequence 285, 266, 247, …, they explain that subtracting 19 is equivalent to subtracting 20 then adding 1, so the tens digit gets smaller by 2 each time and the units digit increases by 1. They use patterns to predict the next number (228) and explore what happens when the hundreds boundary is crossed.

Children explore sequences using the ITP 'Twenty cards' or the Flash program 'Counter'.

They identify the rule for a given sequence. They use this to continue the sequence or identify missing numbers, e.g. they find the missing numbers in the sequence 89, ☐, 71, 62, ☐, recognising that the rule is 'subtract 9'. They explore sequences involving negative numbers using a number line. For example, they continue the sequence 35, 31, 27, … by recognising that the rule is 'add 4'.

Children read and write large whole numbers. For example, they work in pairs using a set of cards containing six-digit and seven-digit numbers: one child takes a card and reads the number in words; their partner keys the number they hear into a calculator; they check that the calculator display and the number card match. Children recognise the value of each digit and they use this to compare and order numbers, for example, they explain which has the greater value, the 5 in 3215067 or the 5 in 856207. They compare two numbers and explain which is bigger and how they know. They solve problems such as: 'Use a single subtraction to change 207070 to 205070 on your calculator'.

Children use calculators (possibly by setting a constant function) or the ITP 'Moving digits' to explore the effect of repeatedly multiplying/dividing numbers by ten.

They compare the effect of multiplying a number by 1000 with that of multiplying the number by 10 then 10 then 10 again (and similarly for division). They use digit cards and a place value grid to practise multiplying and dividing whole numbers by 10, 100 or 1000 and answer questions such as:

• $32500÷\square =325$
• 'How many £10 notes would you need to make £12 000?'

Children rehearse multiplication facts and use these to derive division facts, to find factors of two-digit numbers and to multiply multiples of 10 and 100, e.g. $40×50$. They use and discuss mental strategies for special cases of harder types of calculations, for example to work out $274+96$, $8006-2993$, $35×11$, $35×11$, $50×900$. They use factors to work out a calculation such as $16×6$ by thinking of it as $16×2×3$. They record their methods using diagrams (such as number lines) or jottings, and explain their methods to each other. They compare alternative methods for the same calculation and discuss any merits and disadvantages. They record the method they use to solve problems such as:

• 'How many 25 p fruit bars can I buy with £5?'
• 'Find three consecutive numbers that total 171.'

Children consolidate written methods for addition and subtraction. They explain how they work out calculations, showing understanding of the place value that underpins written methods. They continue to move towards more efficient recording, from expanded methods to compact layouts.

Addition examples (carry digits are recorded below the line, using the words 'carry ten' or 'carry one hundred', not 'carry one'):

Subtraction, illustrating 'difference', is complementary addition or counting up:

$\begin{array}{ccc}& 74& \\ -& \underset{——}{27}& \\ & \phantom{2}3& \phantom{\rule{0.1em}{0ex}}\text{to make}30\\ \phantom{-}& \underset{——}{44}& \phantom{\rule{0.1em}{0ex}}\text{to make}74\\ & 47& \end{array}$
$\begin{array}{ccc}& 326& \\ -& \underset{——}{178}& \\ & \phantom{22}2& \phantom{\rule{0.1em}{0ex}}\to 180\\ \phantom{-}& \phantom{2}20& \phantom{\rule{0.1em}{0ex}}\to 200\\ & 100& \phantom{\rule{0.1em}{0ex}}\to 300\\ & \underset{——}{\phantom{2}26}& \phantom{\rule{0.1em}{0ex}}\to 326\\ & 148& \end{array}$

The decomposition method, illustrating the 'take away' model of subtraction, begins like this:

$\begin{array}{cc}& 70+4\\ -& \underset{————}{20+7}\end{array}$

Children use written methods to solve problems and puzzles such as:

• 'Choose any four numbers from the grid and add them. Find as many ways as possible of making 1000.'  275 382 81 174 206 117 414 262 483 173 239 138 331 230 325 170
• 'Place the digits 0 to 9 to make this calculation correct: ☐ ☐ ☐ ☐ - ☐ ☐ ☐ = ☐ ☐ ☐'
• 'Two numbers have a total of 1000 and a difference of 246. What are the two numbers?'