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Year 3 Block D - Calculating, measuring and understanding shape Unit 2

Objectives Children's learning outcomes are emphasised	Assessment for learning
Represent the information in a puzzle or problem using numbers, images or diagrams; use these to find a solution and present it in context, where appropriate using £.p notation or units of measure I can draw a picture, make jottings or write calculations to help me answer a problem	What did you write down to help you answer this problem? Look at this problem. Two snakes are 56 cm and 83 cm long. What is the difference in their lengths? Draw a picture that will help you to solve the problem. What part of your picture shows the difference? Becky has three £1 coins and four 1p coins in her purse. Write down the amount of money she has altogether.
Add or subtract mentally combinations of one-digit and two-digit numbers I can add or subtract two 2-digit numbers I know how to find the difference between two 2-digit numbers	A 95 g orange is placed in some balance scales. There is 35 g in the other pan. How much needs to be added to the 35 g so that the scales balance? How did you work this out? The difference between the heights of two children is 37 cm. What could their heights be? Are your suggestions reasonable? Roughly how old do you think the children would be? Find the different totals you can make by adding pairs of these numbers: 47 50 8 29 Choose two calculations where you used a different strategy to find the total. Explain why you chose different strategies.
Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers I can record how I work out an addition or subtraction calculation showing each step	Find the total cost of a book costing £2.50 and a comic costing 99p. Jot down your method showing each step. Bill records these steps to work out a calculation: 263 – 40 = 223 223 – 5 = 218 What calculation did he work out?
Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 × 3, 50 ÷ 4); round remainders up or down, depending on the context I can multiply a 'teen' number by a one-digit number I can divide a two-digit number by a one-digit number	A square pool has sides 12 m long. If you walked around the edge of it, how far would you walk? What calculation did you do? How did you work it out? Altogether the four sides of a square picture frame are 60 cm long. How long is each side? What calculation did you do? How did you work it out? What two multiplication facts could you use to work out 13 × 3?
Find unit fractions of numbers and quantities (e.g. ¹/₂, ¹/₃, ¹/₄ and ¹/₆ of 12 litres) I can use division to find ¹/₂, ¹/₃, ¹/₄ ¹/₅ and ¹/₆ of a measurement	Milly has a 100 ml bottle of medicine. She takes one fifth of the medicine each day. How many days does she take the medicine for? How much medicine does she take each day? What calculation did you do to work this out? John has a 120 g bar of chocolate. He cuts it into six equal pieces. How much does each piece weigh? What fraction of the bar is this?
Draw and complete shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side I can reflect a shape in one of its sides	Draw the reflection of this shape in the mirror line. A letter d is reflected in its straight side. Its reflection is a different letter. Which one?
Read and record the vocabulary of position, direction and movement, using the four compass directions to describe movement about a grid I can follow and give instructions to make turns	If you stand facing north, then make a half turn, what direction would you be facing? Give instructions to draw the route below. Use the direction words: north, south, east and west. Give the exact length of each line.
Use a set-square to draw right angles and to identify right angles in 2-D shapes; compare angles with a right angle; recognise that a straight line is equivalent to two right angles I can identify right angles in shapes and use a set-square to check	Use a set-square and a ruler to draw a square with sides of 12 cm. How many right angles are there in this pentagon? How could you check?
Know the relationships between kilometres and metres, metres and centimetres, kilograms and grams, litres and millilitres; choose and use appropriate units to estimate, measure and record measurements I know how many cm make 1 metre and how many metres make 1 km I can decide whether a length would be measured in centimetres, metres or kilometres	A bench is 2 metres and 40 centimetres long. How many centimetres is this? Explain how you worked this out. How many 100 m runs would you need to do to run a total of 1 km? What calculation did you to work this out? Suggest an object whose length would be measured in metres. What about centimetres? And millimetres? Match the measurement to the appropriate unit: the amount of water in a cup kg the length of a road ml the weight of a dog km
Explain a process or present information, ensuring items are clearly sequenced, relevant details are included and accounts ended effectively I can give and follow instructions to make turns	Make a compass with a card arrow and a split pin. Label it north, south, east and west. Write instructions such as: Start with the arrow facing north. Turn it three right angles clockwise. Decide which direction the arrow will end up facing. Swap instructions with someone else. Compare your results. Did you agree where the arrow would end up? If not, what error did you make?

Learning overview

Children consolidate their calculation strategies in all four operations through solving one- and two-step problems involving measures. They represent the information in a problem using diagrams or calculations. They explain their method and record their working clearly, showing the steps involved. They use their understanding of operations and their inverses to check answers.

Children develop greater understanding of the term difference through problems such as:

Amy weighs 35 kg and Carl weighs 52 kg. What is the difference in their weights?
Two snakes are 56 cm and 83 cm long. What is the difference in their lengths?

Children understand that finding the difference between two measurements is the same as asking 'How much bigger is one than the other?' They recognise that one way to find this is to count up from the smaller to the larger amount. They record their working using informal methods such as number lines.

A line with distances of 56cm, 60cm, 80cm and 83cm marked on it. Number lines are used between each marked distance to show the distances between them of 4cm, 20cm and 3cm.

Children add or subtract multiples of 10 or 100 and near-multiples to solve word problems such as:

Malik uses 40 ml of paint from a tube that contains 95 ml. How much is left?
Rosie buys a comic for £1.50 and a book for £2.99. How much does this cost altogether?

Children use practical and informal written methods to solve problems involving multiplication and division, such as:

I walk around the edge of a square pool with sides of 12 m. How far do I walk?

I record two TV programs lasting 45 minutes each on a 2-hour video tape. How much time is left on the tape?

Altogether the four sides of a square picture frame are 60 cm long. How long is each side?

Kim uses ¹/₅ of a 500 g bag of flour. How much flour is this?

They recognise that finding fractions of amounts involves division and find one fifth of a quantity, for example, by dividing it by 5.

Children understand £.p notation, writing £1.29 as 129p and vice versa. They appreciate that £1.05 is 1 pound and 5 pence. They solve problems involving money, such as using a table of prices from a leisure centre to work out how much it would cost for their family to go swimming. They create their own word stories involving money and solve puzzles such as:

Two packets of sweets together cost 90p. One costs double the other. How much does the more expensive packet cost?

In my purse I have £1 coins, 10p coins and 1p coins. Find all the possible amounts I can make by choosing three of these coins.

Children know the relationship between standard units of length, mass and capacity. They know, for example, that 1 km is 1000 m and that 1 m is 100 cm. They use the relationship 1 m = 100 cm to work out that 2 m = 200 cm and 3 m = 300 cm. They recognise that the number of centimetres is the number of metres multiplied by 100. Children suggest suitable units and measuring equipment to estimate or measure length, mass or capacity. For example, they suggest lengths that would be measured in centimetres, metres or kilometres. They use a ruler to measure or draw lines accurately to the nearest half-centimetre; for example, they use a ruler and set-square to draw a square with sides of 12 cm and then discuss how long the lines are altogether.

Children understand that shapes can be reflected by considering, for example, the reflections of objects in water or by using the reflection tool in an ICT program. They predict where the image of a shape will be when it is reflected in a mirror line along one of its sides and check by placing a mirror on the line of symmetry or by using ICT.

Children understand that angle is a measure of turn. They follow and give directions, for example in PE, including instructions to turn right or left through quarter and half turns. They appreciate that two quarter turns are equivalent to a half turn. They recognise that when you turn through a half turn you end up facing the opposite direction. They learn that a quarter turn is equal to a turn of 90 degrees when, for example, programming a floor robot to follow a marked route. Through looking at the route, they appreciate that a quarter turn is also equivalent to a right angle. Children use compass points to explore, for example, how many right angles are needed to turn clockwise from east to west.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 923KB
Activity 26 - Rows of coins

Intervention programmes

Objectives for Springboard intervention unit	Springboard unit
Know by heart doubles of numbers to 10; doubles of multiples of ten up to 50 Identify near doubles using doubles already known Halve even numbers from 20 to 2 Measure and compare lengths using a standard measure	Springboard 3 Unit 4 session 2 (PDF 181KB)
Find a small difference by counting on from the smaller to the larger number Measure and compare lengths using standard units	Springboard 3 Unit 6 session 1 (PDF 149KB)

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

Diagnostic focus	Resource
Has insecure understanding of the structure of the number system, resulting in addition and subtraction errors and difficulty with estimating - spotlight 4	1 Y4/- DfES 1128-2005 (PDF 101KB)

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Primary Framework for literacy and mathematics

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