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Year 6 Block D - Calculating, measuring and understanding shape Unit 3

Objectives Children's learning outcomes are emphasised	Assessment for learning
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 with several steps and decide how to carry out the calculation	What clues do you look for in the wording of questions? What words mean you need to add, subtract, multiply or divide? This fence has three posts, equally spaced. Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of one gap between two posts. Show me the calculations that you did. Did you use a written method or a calculator? Explain why.
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	A packet of crisps costs 32 pence. Josh buys three packets. How much change does he get from one pound? Explain the mental calculations that you did to solve this problem.
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 add, subtract, multiply and divide whole numbers and decimals using efficient written methods	Make up an example of an addition/subtraction involving decimals that you would do in your head. Now make up an example you would do on paper. Explain why. Show me how to find the answer to the next problem using an efficient written method. A packet contains 1.5 kilograms of guinea pig food. Remi feeds her guinea pig 30 grams of food each day. How many days does the packet of food last?
Use a calculator to solve problems involving multi-step calculations I can use a calculator to solve problems with several steps	Show me the calculator key presses you made to solve that problem. Could you do the calculation with fewer key presses? Julie is 92 cm tall. Tom is 1.34 m tall. Lisa's height is halfway between Julie's height and Tom's height. Calculate Lisa's height. Write down the calculations that you did. 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 the result of a calculation I know several ways of checking answers	How did you arrive at that estimate? What inverse operation could you use to check this result? Should the answer be a multiple of 3? How could you check? I added three distances. Each was an odd number and my answer was 120 km. Explain why I cannot be correct.
Select and use standard metric units of measure and convert between units using decimals to two places (e.g. change 2.75 litres to 2750 ml, or vice versa) I can convert one measurement to another using a related unit. I use decimals to do this	What might you measure in kilometres? In millimetres? Put a ring round the number which is the approximate weight of a thirty-centimetre plastic ruler. 2g 20g 200g 2kg 20kg Look how much water is left in the jug. Estimate how many millilitres of water are left. Explain how you arrived at your estimate.
Solve problems by measuring, estimating and calculating; measure and calculate using imperial units still in everyday use; know their approximate metric values I know that 1 pint is just over half a litre, and that 1 litre is about 1 pints I know that 1 mile is about 1.6 km, and that 1 km is about of a mile	What might you measure in pints? In stones? A map shows that the distance from Calais to Paris is 320 kilometres. 5 miles is approximately 8 kilometres. Use these facts to calculate the approximate distance in miles from Calais to Paris. Explain how you worked out your answer. Did you use a calculator or a written method? What were your reasons?
Read and interpret scales on a range of measuring instruments, recognising that the measurement made is approximate and recording results to a required degree of accuracy; compare readings on different scales, for example when using different instruments I can read scales as accurately as a problem requires I can compare readings from different scales	Here is a drawing of a model car. What is the length of the model? Give your answer in centimetres, correct to one decimal place. On this scale, the arrow () shows the weight of a pineapple. Here is a different scale. Mark with an arrow the weight of the same pineapple.
Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares I can find the perimeter and area of shapes and estimate the area of irregular shapes	How would you calculate the area of this T-shape? What about this L-shape? This H-shape? Susan says: 'When you cut a piece off a shape, you reduce its area and perimeter.' Is Susan's conjecture sometimes true, always true or never true? Explain how you know. Here is a rectangle with 13 identical shaded squares inside it. What fraction of the rectangle is shaded?
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	Listen to and then discuss how someone explained to the class how they estimated the number of leaves of clover on the playing field. Could their method have been improved? Could their explanation have been improved? Would a table or diagram have helped?

Learning overview

Children continue to work with a range of standard metric units, comparing these with imperial units still in daily use. They suggest suitable units to measure the weight of a paperclip, the amount of milk in a tanker, the dimensions of a piece of furniture or the area of a postage stamp. They suggest suitable equipment to measure with, and the degree of accuracy needed when reading scales. They are able to convert a measurement to an alternative form, describing, for example, 1 litre 200 millilitres as 1200 ml or 1.2 litres.

Children continue to solve word problems involving several steps, or involving decimals, applying their choice of mental, written or calculator method. They make sure that measurements are converted to the same unit before calculation. They record their methods efficiently, explaining how the problem was solved. For example:

A box contains 220 matches and weighs 45 grams. The empty box weighs 12 grams. Calculate the weight of one match.
Butter costs £4.50 for 1 kg. Marie buys 200 grams of butter. How much does she pay?
Cream cheese costs £3.60 for 1 kg. Robbie buys a pot of cream cheese for 90p. How many grams of cream cheese does he buy?

Children continue to investigate practical problems in the context of measures. For example, they work out how many litres of water they use in a day, and compare that with the amount of water used per person 20 years ago. They solve related problems, such as:

A glass holds 225 ml. An adult needs about 1.8 litres of water each day to stay healthy. How many glasses is that?
An adult weighs 80 kg. 60% of his total mass is water. What is the mass of this water?
A jug holds 4.2 litres of water. Approximately how many jugs full of water are needed to fill a 50 litre tank?

Children continue to explore area and perimeter of rectilinear shapes. For example, they draw different shapes (using whole and half squares) that have an area of 12 cm², then find which has the longest perimeter. They predict whether a 14 cm square piece of paper or the label around a tin of soup will have the bigger area or longer perimeter. They work out how to check and then compare the actual measurements with their prediction. They calculate the area of shapes based on rectangles: for example, the area of a path 1 metre wide around a swimming pool, given the dimensions of the pool, or the smallest area of paper needed to cover a cuboid box that is 15 cm long, 10 cm deep and 7 cm tall.

Children estimate the size of angles and use a protractor to measure acute and obtuse angles. They measure the internal angles of regular polygons and record these systematically in a table against the number of sides of the shape. They describe the patterns and relationships that they discover. They use facts that they know, such as the angle sum of a triangle (180 degrees ) and the sum of angles around a point (360 degrees ) to calculate angles in a triangle, on a straight line and around a point. For example, they work out how many degrees the hour hand rotates from 2 o'clock to 4 o'clock.

Children use different grids to visualise, draw and transform shapes, using ICT or other approaches. For example, they transform a given shape using a reflection, rotation or translation. Their partner then transforms the shape back to its original position.

Resource links to existing published material

Mathematical challenges for able Key Stages 1 and 2

Activities	PDF 1MB
Activity 59 - Four by four

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Find perimeters of simple shapes and their areas by counting squares, and begin to use the formula in words for the area of a rectangle	Springboard 6 Unit 17 (PDF 379KB)
Develop calculator skills and use a calculator effectively	Springboard 6 Unit 6 (PDF 1.4MB)

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

Diagnostic focus	Resource
Rounding inaccurately particularly when decimals are involved. Has little sense of the size of a number	2 Y4 ×/÷ DfES 1151-2005 (PDF 93KB)

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Primary Framework for literacy and mathematics

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