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# 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 adding and subtracting two- and three-digit numbers, partitioning these numbers in different ways, investigating remainders in division calculations, deciding whether to round up or down, and identifying pairs of fractions that make a whole.

Children partition two and three-digit numbers in different ways. For example, they continue the patterns:

• $72=70+2$
• $72=60+12$
• $72=50+22$
• $853=800+53$
• $853=700+153$
• $853=600+253$

They use partitioning to add and subtract two and three-digit numbers, using written methods. For example, they find the sum and the difference of 85 and 46 using expanded column methods:

$\begin{array}{ccc}& 85=\phantom{1}80+\phantom{1}5& \\ +& \underline{46=\phantom{1}40+\phantom{1}6}& \\ & \phantom{46=}120+11& =131\end{array}$
$\begin{array}{cccc}\phantom{-}85& =80+5& =70+15& \\ -\underline{46}& \phantom{=}\underline{40+6}& \phantom{=}\underline{40+\phantom{1}6}& \\ & & \phantom{=}30+\phantom{1}9& =39\end{array}$

Children recall multiplication and division facts for the two, three, four, five, six and ten times-tables. They use them to solve problems involving multiplication and division. They represent the information in the problem, using images or number calculations and use these to find a solution. They work methodically, making lists of the multiplication facts they may need to solve problems such as:

• 'Tables have four legs and stools have three legs. I see 25 legs. How many tables and stools do I see?'
• 'Pentagons have five sides and rectangles have four sides. I have 28 straws to use to make some of each shape. How many of each can I make?'

Children understand that a division sentence could describe a situation involving either grouping or sharing. For example, the calculation $30÷6=5$ could represent either:

• '30 children are organised into teams of 6. How many teams are there?'
• 'Or, 30 crayons are put equally into 6 pots. How many crayons are in each pot?'

Children solve a variety of division problems, some involving sharing and some involving grouping. They use the inverse operation to check answers. For example, they solve:

• 'How many teams of 4 can be made from 32 children?'
• '27 apples are arranged equally in 3 bowls. How many apples are in each bowl?'
• 'I have £2 in my money box. All the coins are the same. How many coins could there be? Describe all the possibilities.'

Children investigate remainders in division calculations. They research the question: 'What is the biggest remainder you can have when you divide a number by three? What if you divide by four or by five?'

Children work as a group on this enquiry. They decide what examples they should try and how they will work. They discuss how they can record their findings so that it is easy to identify patterns. Children use their results to explain their answer to the question.

Children decide whether to round up or down to answer word problems such as:

• 'We have 21 building block wheels. How many four-wheeled cars can we make?'
• 'Peaches come in packs of six. I want 20 peaches. How many packs do I need to buy?'
• 'How many 30 cm lengths of ribbon can I cut from a ribbon measuring 2 metres?'

Children model such problems with objects or draw a sketch to help them. They discuss their answers and give reasons why they decided to round up or down.

Children use multiplication facts and place value to multiply a two-digit multiple of ten by two, three, four, five, six and ten, calculating, for example, $70×3$ or $4×60$.

They respond to problems such as:

• 'Find 20 multiplied by 3'
• 'What is $\frac{1}{3}\text{of}60$?'
• 'Paul has saved seven 50 p coins and six 20 p coins. How much is this altogether?'

Children use partitioning to multiply two-digit numbers by one-digit numbers. For example, they work out $13×3$ by finding $10×3$ and adding $3×3$. They record their working, using informal methods:

× 10 3
3 30 9
$30+9=39$

Children find $\frac{1}{2}$, $\frac{1}{4}$, $1/10$, $\frac{1}{3}$ or $1/5$ of numbers by using known multiplication and division facts. They read and write proper fractions such as $2/3$and understand the denominator as the number of parts of the whole and the numerator as the number of parts. They count in fractions along a number line from 0 to 1, for example 'zero, one fifth, two fifths, three fifths, four fifths, one'. They use such number lines to compare simple fractions and begin to find equivalent fractions.

Children use diagrams to identify pairs of fractions that make a whole, such as $\frac{1}{4}$ and $3/4$, $1/5$ and $4/5$, $\frac{3}{10}$ and $\frac{7}{10}$.