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 using multiplication and related division facts, multiplying and dividing mentally, refining written methods for multiplication, extending understanding of fractions, expressing small numbers as fractions of larger numbers, finding fractions of quantities, and solving word problems involving fractions.

Children recall multiplication facts to $10\times 10$ and the related division facts. They use these to multiply and divide multiples of 10 and 100, such as $30\times 7$, $4200÷6$. They use patterns to extend the facts that they know and they look at the relationships between the number of zeros that form the final digits

They use this new knowledge to extend the mental methods that they use for multiplication and division. They appreciate that multiplication can be done in any order and make sensible choices about how to multiply three numbers such as $4\times 7\times 5$. They multiply two-digit by one-digit numbers mentally by using partitioning, calculating $26\times 7$ by working out $20\times 7$ and $6\times 7$ then putting the answers together to get 182. They use factors where appropriate to help them to multiply numbers efficiently, for example calculating $35\times 6$ by working out $35\times 2\times 3$.

Children understand that $6÷3$ gives a different answer from $3÷6$. They divide two-digit by one-digit numbers mentally also by using partitioning, finding $51÷3$ by splitting 51 into 30 and 21, dividing each part by 3 and then putting the answers back together to get 17. They use factors where appropriate; for example, they work out $90÷6$ by dividing 90 by 3 and then dividing the answer by 2. Children explore patterns in linked division calculations; for example, they use a calculator to find the answers to the calculations $4000÷32$, $2000÷16$ and $1000÷8$. They explain the patterns they notice, and suggest other linked calculations that will have the same answer as each other.

Children use mental methods (with jottings where appropriate) to solve problems involving multiplication and division, such as:

• 'Is 81 a multiple of 3? How do you know?'
• 'Find a number that has exactly six factors'
• 'Find a number that is a common multiple of six and eight.'

Children develop and refine written methods for multiplication. They move from expanded layouts (such as the grid method) towards a compact layout for $\text{HTU}\times \text{U}$ and $\text{TU}\times \text{TU}$ calculations. They suggest what they expect the approximate answer to be before starting a calculation and use this to check that their answer sounds sensible. For example, $56\times 27$ is approximately $60\times 30=1800$.

Children collaborate in a group to solve problems and puzzles such as: 'Use the digits 2, 3, 5 and 7 and the × symbol once each to create a multiplication calculation, for example $572\times 3$ or $35\times 72$. How many different products can you make? What is the largest product? What is the smallest product?'

Children record their working systematically. They use reasoning to explain how they know that they found every possible solution.

Children use practical equipment and diagrams to extend their understanding of fractions. They recognise equivalence between fractions. For example, they fold a strip of 20 squares into quarters and colour $\frac{3}{4}$ of the strip to establish that $\frac{3}{4}$ is the same as 15 out of 20 or $\frac{15}{20}$. They find other fractions that are equivalent to $\frac{3}{4}$, recording their results and identifying patterns and relationships in the set of equivalent fractions. They use these patterns to predict other fractions that are equivalent to $\frac{3}{4}$ and test their predictions. (The ITP 'Fractions' can also be used to establish equivalent fractions.)

Children express a smaller number as a fraction of a larger one. For example, they compare a base-ten 'ten' stick to a 'hundred' flat, appreciate that it would take 10 'tens' to make 1 'hundred' so 10 is $\frac{10}{100}$ of 100. They compare a strip containing 3 squares with a strip containing 15 squares to establish that 3 is $\frac{1}{5}$ of 15. They use their knowledge of the relationships between measures to answer questions such as:

• 'What fraction of £1 is 50 p, 75 p, 30 p, …?'
• 'What fraction of 1 kg is 500 g, 400 g, …?'
• 'What fraction of a day is 1 hour, 12 hours, 8 hours, …?'

Children find fractions of amounts using division and multiplication. For example, to find $\frac{3}{10}$ of 20 they first find $\frac{1}{10}$ by dividing 20 by 10, then multiply the answer by 3 to find $\frac{3}{10}$. They use diagrams to confirm their calculations.

They record their working efficiently using symbols, for example:

Children solve word problems that involve fractions, choosing to use a calculator where the calculations involved merit its use. They solve problems such as:

• 'I pour $\frac{2}{5}$ of a litre of juice into a jug. How many millilitres is this?'
• 'I have cycled $\frac{7}{10}$ of a distance of 50 km. How far do I still have to go?'
• 'I have saved £194.40. I plan to spend $\frac{5}{12}$ of this on a bicycle. How much will I have left?'

Children check that each answer sounds reasonable in its original context.