Your path: Standards Site Home > Primary Framework > Mathematics > Planning > Year 6 > A. Counting, partitioning and calculating > Year 6 Block A - Counting, partitioning and calculating Unit 3

Year 6 Block A - Counting, partitioning and calculating Unit 3

Objectives Children's learning outcomes are emphasised	Assessment for learning
Explain reasoning and conclusions, using words, symbols or diagrams as appropriate I can explain my reasoning and conclusions, using symbols to represent unknown numbers	The rule for this sequence of numbers is 'add 3 each time'. 1, 4, 7, 10, 13, 16 ... The sequence continues in the same way. I think that no matter how far you go there will never be a multiple of 3 in the sequence. Am I correct? Explain how you know. What is the value of 4x 7 when x 5? Explain how you know.
Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use I can solve problems involving more than one step I can explain the reason for my choice of method and say whether I think it was effective	What are important things to remember when you solve word problems? What clues do you look for in the wording of questions? What words mean you need to add, subtract, multiply or divide? Make up two different word problems for each of these calculations. Try to use a variety of words. (17 5) × 6 12.5 ÷ 5 - 0.25
Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals with up to three places, and position them on the number line I can use decimals with up to three places and order them on a number line I can partition decimals with three places	Write a number in the box to make this correct. 0.627 0.6 0.02 What number is exactly halfway between 1.1 and 1.2? Which of these numbers is closest in value to 0.1? 0.01 0.05 0.11 0.2 0.9 How can you tell? Tell me a number with two/three decimal places that rounds to 5.0 when rounded to the nearest tenth.
Calculate mentally with integers and decimals: U.t U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U I can add, subtract, multiply and divide whole numbers and decimals in my head	Make up a question involving addition that has the answer 1.35. Now try subtraction. What about multiplication? Division? How can you use factors to multiply 17 by 12? Which of these subtractions can you do without writing anything down? Why is it possible to solve this one mentally? What clues did you look for? What is the answer to the one that can be solved mentally?
Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer I can use efficient written methods to add, subtract, multiply and divide integers and decimal numbers I can calculate the answer to HTU ÷ U and U.t ÷ U to one or two decimal places	Two numbers have a difference of 1.583 One of the numbers is 4.728. What is the other? Is this the only answer? Look at these calculations. Which of them is incorrect? Why? 12.4 × 6.6 71.23 48.6 ÷ 3 16.2 Work out 32.75 - 1.837. Explain each step to me. What tips would you give to someone to help with long multiplication of HTU × TU?
Use a calculator to solve problems involving multi-step calculations I can use a calculator to solve problems with more than one step	Printing charges for a book are 3p per page and 75p for the cover. I paid 4.35 to get this book printed. Work out on your calculator how many pages there are in the book. Write down the calculations that you did. Seeds are 1.45 for a packet. I have 10 to spend on seeds. What is the greatest number of packets I can buy? Show me how you used your calculator to find the answer.
Use approximations, inverse operations and tests of divisibility to estimate and check results I can estimate and check the result of a calculation	I added three odd numbers and my answer was 50. Explain why I cannot be correct. Roughly, what answer do you expect to get? How did you arrive at that estimate? Is this calculation correct? How do you know? What inverse operation could you use to check this result? Should the answer be a multiple of 3? How could you check?
Analyse and evaluate how speakers present points effectively through use of language, gesture, models and images I can listen to someone explain their method or solution to a problem, and evaluate whether their explanation made sense	Discuss the explanation and images used by someone explaining to the class how they solved a word problem. Could the explanation have been improved? What could you use to help you explain your conclusions? Would a table, picture or diagram help?

Learning overview

Children use decimal notation in a variety of contexts, drawing on their knowledge of measures. They order a set of decimal numbers or measures, explaining their reasoning, for example explaining that 3.2 is greater than 3.12 because 2 tenths is greater than 1 tenth, or 20 hundredths is greater than 12 hundredths. They relate this to 3 kilograms 200 grams being greater than 3 kilograms 120 grams. They can give a decimal number lying between 3.51 and 3.52, for example, and say the number lying halfway between 0.864 and 0.868 or halfway between 1.72 and 1.73. They use a calculator to change 530 to 5.3 or 0.62 to 620 in one step.

This offers an opportunity to assess children's ability to reason. Look for children being able to justify their methods and give examples and counter-examples. It also offers an opportunity to assess understanding of decimals: look for children being able to order numbers that have a mixture of one, two and three decimal places.

Children use place value and partitioning to calculate mentally, for example 3.85 + square = 5, 1.2 × 9, 4.5 ÷ 3. They work out 85 - 29 = 56 to generate linked facts such as 29 + 56 = 85, 8.5 - 2.9 = 5.6, 0.85 - 0.29 = 0.56. They calculate 23 × 7 and 2.3 × 7 and explain the relationship; similarly with 95 ÷ 5 and 9.5 ÷ 5. They use facts like these to solve mental word problems, such as:

A bill of £9.50 is shared equally between 5 people. How much does each person pay?

Children use a calculator to investigate general statements such as 'dividing a number by 0.5 makes it twice as big' or 'finding 25% of an amount is the same as dividing by 4'.

This offers an opportunity to assess children's understanding of operations and the relationships between them. Look for children recognising that division is the inverse of multiplication.

Children apply efficient written methods to add, subtract, multiply and divide integers and decimal numbers in a variety of problem-solving contexts. For example, they work out the cost of carpeting different rectangular bedrooms with carpet at £12.97 per square metre. They calculate the answers to HTU÷U and U.t÷U to one or two decimal places, for example cutting up a total length of 17.3 m of curtain material into five equal lengths, checking their calculation using inverses.

This offers an opportunity to assess children's written methods. Look for children being able to multiply and divide decimal numbers by a single digit.

Children solve multi-step problems involving money, measures and time, choosing and using appropriate and efficient methods at each stage, including a calculator. They convert between units of measure where appropriate and give answers in a suitable unit and to a suitable degree of accuracy, including questions where division needs to be rounded up or down and where quotients can be given exactly using decimals or fractions. For example, they solve problems such as:

I buy 3 large pizzas costing £10.95 each and 2 small pizzas costing £7.69 each. How much do I spend altogether?

A session at a weekly gym club lasts for 1 hour and 15 minutes. To move up to an advanced group, children have to attend sessions for 675 minutes. For how many weeks will children have to attend before they can progress to the advanced group?

A carpenter needs to cut a plank of wood that is 3.73 m long into five equal pieces. What is the length of each piece in centimetres?

Every day a machine makes 100 000 paper clips which go into boxes. A full box has 120 paper clips. How many full boxes can be made from 100 000 paper clips? Each paper clip is made from 9.2 centimetres of wire. What is the greatest number of paper clips that can be made from 10 metres of wire?

A DJ has storage boxes for her CDs. The boxes are in two sizes. Small boxes hold 15 CDs. Large boxes hold 28 CDs. The DJ has 411 CDs. How could the DJ pack her CDs?

This offers an opportunity to assess children's ability to solve numerical problems. Look for children checking their answers by applying inverse operations or using approximations.

Children use rounding to find an approximate answer as a check. They also check answers to calculations using their knowledge of tests of divisibility.

Resource links to existing published material

Mathematical challenges for able Key Stages 1 and 2

Activities	PDF 1MB
Activity 79 - Spendthrift

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Choose and use the appropriate operations of addition and subtraction to solve problems, explain methods and show working	Springboard 6 Unit 12 (PDF 379KB)

Supporting children with gaps in their mathematical understanding (Wave 3)

Diagnostic focus	Resource
Has difficulty in choosing suitable methods that cross boundaries: addition	4a Y6 /- DfES 1135-2005 (PDF 94KB)
Has difficulty in choosing suitable methods that cross boundaries: subtraction	4b Y6 /- DfES 1136-2005 (PDF 103KB)

Click here for information on different file formats and their usage.

Disclaimer notice

The Department for Children, Schools and Families wishes to make clear that the Department and its agents accept no responsibility for the actual content of any materials suggested as information sources in this document, whether these are in the form of printed publications or on a website. In these materials icons, logos, software products and websites are used for contextual and practical reasons. Their use should not be interpreted as an endorsement of particular companies or their products. The websites referred to in these materials existed at the time of going to print. Tutors should check all website references carefully to see if they have changed and substitute other references where appropriate.

Skip to main navigation Skip to content navigation Skip to page content