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Year 4 Block D - Calculating, measuring and understanding shape Unit 2

Objectives Children's learning outcomes are emphasised	Assessment for learning
Solve one-step and two-step problems involving numbers, money or measures, including time; choose and carry out appropriate calculations, using calculator methods where appropriate I can work out how to solve problems with one or two steps I can solve problems involving measures and time I can choose what calculation to work out and I can decide whether a calculator will help me	A piece of rope 204 cm long is cut into 4 equal pieces. Which of these gives the length of each piece in centimetres? A. 204 ÷ 4, B. 204 × 4, C. 204 - 4, D. 204 + 4 How did you know whether to add, subtract, multiply or divide? What clues did you look for in the problem? What are the important things to remember when you solve a word problem? Look at this problem: Jenny can walk 103 metres in 1 minute. How far can she walk in 2 minutes? Explain what you should do to get your answer. Show me how to record any calculations you need to do to solve the problem.
Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and £.p I can add and subtract a two-digit and a three-digit number using an efficient written method	Sunil is 138 cm tall. His younger brother is 47 cm shorter. How tall is Sunil's brother? Mary drove 58 km to Andover. She then drove 238 km to Cambridge. How far did Mary drive altogether? Show me the calculations that you did to solve these problems. Is there a more efficient way to do them?
Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple I know my tables to 10 × 10	Look at these number sentences. What number goes in the box? How do you know? × 7 = 35 9 × = 72 What numbers are missing? × = 36 If 7 × 9 = 63, what is 63 ÷ 7? What other facts do you know? If I multiply a number by 8 and then divide the answer by 8, what happens?
Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders (e.g. 15 × 9, 98 ÷ 6) I can record how to multiply and divide a two-digit number by a one-digit number	One length of the swimming pool is 25 metres. Jane swims 5 lengths of the pool. How far does Jane swim altogether? Kiz swims 225 metres in the pool. How many lengths does he swim? Explain how you solved these problems. Could you have done them differently?
Draw rectangles and measure and calculate their perimeters; find the area of rectilinear shapes drawn on a square grid by counting squares I can draw a rectangle and work out its perimeter	The perimeter of a square is 28 cm. What is the length of one side? Use centimetre squared paper to draw different rectangles with a perimeter of 28 cm. Draw different rectangles with an area of 12 cm².
Know that angles are measured in degrees and that one whole turn is 360°; compare and order angles less than 180° I know that angles are measured in degrees I know that a whole turn is 360 degrees or four right angles	Tell me an angle that is bigger than one right angle and smaller than two right angles. Two of these angles are the same size. Put rings around the two angles which are the same size. Draw an angle which is bigger than a right angle.
Recognise horizontal and vertical lines; use the eight compass points to describe direction; describe and identify the position of a square on a grid of squares I can use the eight compass points I can give directions, follow directions and say how good someone else's directions are	Kelly is facing north. She turns clockwise through 3 right angles. Which direction is she facing now? Aled is facing north-west. He turns clockwise through 2 right angles. Which direction is he facing now?
Use decimal notation for tenths and hundredths and partition decimals; relate the notation to money and measurement; position one-place and two-place decimals on a number line I can write lengths like 5 metres and 62 centimetres using decimal points	Tell me what the digit 7 represents in each of these amounts: 7.35 m, 0.37 m, 2.7 cm. Which is larger: 239 cm or 2.93 m? Why? Put these in order: 0.56 m, 125 cm, 3.6 m. Which is the smallest? How do you know? Which is the largest? How do you know? What length comes next: 1.76 m, 1.86 m, 1.96 m, ...?
Choose and use standard metric units and their abbreviations when estimating, measuring and recording length, weight and capacity; know the meaning of 'kilo', 'centi' and 'milli' and, where appropriate, use decimal notation to record measurements (e.g. 1.35 m or 0.6 kg) I can estimate and measure a length using metres, centimetres or millimetres I know the relationships between metres, centimetres and millimetres	Estimate the height of the door. The width of your table. Tick () the correct box. The length of a banana is about... 2 cm 20 cm 200 cm 2000 cm What unit would you use to measure the length of the River Thames? The length of a drinking straw? Look at these cards. They have lengths in kilometres, metres, centimetres or millimetres. 1000 m, 2 km, 3 cm, ¹/₂ m, 4.5 m, 40 cm, 5 cm, 400 mm Put the cards in order from the smallest to the largest. How did you order the cards? Why did you put this measurement here? Were any of the measurements hard to order? Why? Can you tell me another way to say or write 2 km? What about 4 m? And 5 cm?
Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit I can use a measuring tape, metre stick or ruler to measure a length accurately	Explain to someone else how to measure the length of a line that is between 4 cm and 5 cm long. Measure accurately the length of the diagonal of this square. Give your answer in centimetres.
Take different roles in groups and use the language appropriate to them, including roles of leader, reporter, scribe and mentor I can play the role of ... in group work I can work as a member of a group to decide how to measure and record capacity	Discuss in your group how to find out which of these six containers holds the most water. I would like ... to be the group leader, ... to take notes and ... to draw any diagrams that you need. Tell me about the contribution you made to the group work.

Learning overview

Children learn the meaning of kilo (one thousand), centi (one hundredth) and milli (one thousandth) to help remember the relationships between kilometres, metres, centimetres and millimetres. They multiply and divide numbers by 10 and 100 and use this to convert metres into centimetres or centimetres into millimetres, completing tables such as:

Item	Length in metres	Length in cm
Metre stick	1 m	100 cm
Height of door	2 m
Length of room	9 m

and responding to questions such as: How many metres are in 8 km? How many millimetres are in 8 cm?

Children choose and use appropriate units to measure length, realising that different units are needed for different distances. They suggest lengths that would be measured in km, m, cm and mm. They undertake practical activities to increase their accuracy in estimating lengths, choosing appropriate units and measuring instruments and reading the measurement from a scale. For example, they measure how far they can throw a beanbag, or the growth of a plant over time.

Children record lengths using decimal notation, for example recording 5 m 62 cm as 5.62 m, or 1 m 60 cm as 1.6 m. They identify the whole-number, tenths and hundredths parts of numbers presented in decimal notation and relate the whole number, tenths and hundredths parts to metres and centimetres in length.

Children use a ruler to measure and draw lines to the nearest millimetre. They get extra practice using the ITP 'Ruler'.

Ruler and lines

They measure the edges of a rectangle and then combine these measurements. They realise that by doing this they are calculating its perimeter. Given the perimeter of a rectangle they investigate what the lengths of its sides could be. They work out the perimeter of irregular shapes drawn on a centimetre square grid, e.g. using the ITP 'Area'.

Grid with coloured areas

Children continue to develop and refine written methods to multiply and divide a two-digit number by a one-digit number and efficient written methods to add and subtract two-digit and three-digit whole numbers. Children who confidently explain how an expanded method works move on to a more compact method of recording.

Children draw on their calculation strategies to solve one- and two-step word problems, including those involving money and measures. They use rounding to estimate the solution, choose an appropriate method of calculation (mental, mental with jottings, written method) and then check to see whether their answer seems sensible. They throw a beanbag three times and find the difference between their longest and shortest throws. After measuring their height, they work out how much taller they would have to grow to be the same height as their teacher. They solve problems such as:

Dad bought three tins of paint at £5.68 each. How much change does he get from £20?
A family sets off to drive 524 miles. After 267 miles, how much further do they still have to go?

Children understand that angle is a measure of turn. They follow and give directions which include turning through whole, half and quarter turns. They know that a quarter turn is equivalent to 90 degrees and a whole turn is 360 degrees or four right angles. They recognise angles that are smaller than and larger than a right angle and start to order angles. They recognise which of two angles is greater and place in order a set of angles, each less than 180 degrees.

Children give directions using the eight compass directions N, S, E, W, NE, NW, SE and SW. They look at weather forecasts to track changes in wind direction. They investigate the different routes from A to B using only the directions north-west and north-east and record their results systematically in a table.

Diamond split into four sections

Children take different roles in groups of three, taking it in turns to give directions, to follow directions and to observe, commenting on how accurately directions were given and followed. For example:

Face SE and turn clockwise 180 degrees/two right angles. Which direction are you now facing?

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities
None currently available

Intervention programmes

Springboard units

None currently available

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

Diagnostic focus	Resource
Does not apply partitioning and recombining when multiplying and confuses the value of 2 digit numbers	4 Y4 ×/÷ DfES 1153-2005 (PDF 104KB)
Interprets division as sharing but not grouping	3 Y6 ×/÷ DfES 1161-2005 (PDF 94KB)
Does not make sensible decisions about when to use calculations laid out in columns	3 Y4 /- DfES 1130-2005 (PDF 101KB)
Describes the operation of multiplying by ten as 'adding a nought'	3 Y4 ×/÷ DfES 1152-2005 (PDF 68KB)

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Primary Framework for literacy and mathematics

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