Year 2 Teaching Sequence autumn M1 – Length (four days) Prerequisites: Estimate, measure and compare objects, choosing and using suitable uniform non-standard or standard units (see Year 1 teaching sequence M1) Recite numbers to 100 (see teaching sequence 1 and oral and mental starter bank M1) Order numbers to 100, compare two numbers, say which is more or less (see teaching sequence 1 and oral and mental starter bank M1) Say a number between any given neighbouring pairs of multiples of ten (e.g. 40 and 50) (see teaching sequence 1 and oral and mental starter bank M1) Overview of progression: Children recognise that we measure distances (lengths and heights) by repeating a unit. They also realise that the unit must be uniform. Chn are introduced to standard units – metres and centimetres. They measure objects to the nearest 10 centimetres (decimetre) and then to the nearest centimetre. They estimate the lengths of items by choosing a range. They use string to measure curved lines. They choose which pieces of measuring equipment and units (centimetres, decimetres or metres) are best for measuring different distances. Note that it can be helpful to have a purposeful context for measurement, for example measuring wood for a model in D&T, or jumps and throws in PE. Try to build in these cross-curricular links if possible. Note that it is important that children have some ‘benchmarks’ such as a decimetre, a 30cm ruler and a metre stick to help them to estimate distances, particularly until they have more experience of measuring. Watch out for children who forget that a centimetre and a metre are units and see them only as marks on a ruler. Watch out for children whose counting and ordering skills are insecure making measuring difficult. Try to ensure that the items they measure are not longer than the number they can count up to with confidence. © Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y2 Maths TS_M1 – Aut – 4days Objectives: Estimate, measure and compare lengths, choosing and using suitable standard units and suitable measuring instruments Whole class Group activities Paired/indiv practice Resources Show children some wax crayons – you need some which are of varying lengths. Choose a child, and ask him or her to hold one arm out straight. We are going to measure the length of Sam’s arm in crayons. Choose short crayons and measure Sam’s arm. Write how many crayons. Then repeat this selecting all the longer crayons. Write how many. Ask children why we got two different answers? Had Sam’s arm shrunk?! No! The first lot of crayons were shorter and so more fitted along Sam’s arm. Discuss how this means we need to use something that is ALWAYS the same length to measure with. Show children the decimetre rods. These rods are all the same length. They do not vary. Measure Sam’s arm using the rods. Record the length. Sam’s arm is 5 rods long. Discuss what happens if it is not exact – we could say that it is five and half rods. Choose a child to lie on a table in front of the class. How long is Annie? Discuss how we might measure her length. Pass round some 1cm cubes. Show chn a decimetre strip (see resources). This is a decimetre; it is ten centimetres. Pass round several strips. Decimetres or ten centimetres are useful units for measuring things. How many decimetres long is Annie? Encourage chn to Groups of 5/6 children Lay out some decimetre rods along the table. Give children a pile of pieces of string. Each child also needs a whiteboard and pen. Children have to choose one piece of string and spread it out. In turn, go round the group and ask each child to estimate how many rods will fit along their string. They each write their estimate on their whiteboard. Then allow each child in the group to measure their string using one rod, and laying it repeatedly all along the string. They must make sure that they do not overlap it or leave gaps so that they get an accurate measurement. Each child writes the length of their string – how close were their estimates? Several groups of 2 or 3 Help several groups of 2 or 3 children to measure each other in decimetres. One child lies on the floor and the others lay decimetres (cardboard strips or rods) along her length. They must make sure that the decimetre strips or rods do not overlap and also that there are not big gaps between Chn work in pairs. They put a strip of paper round their head like a crown. They tear off the strip so it will be the right length. Before they stick the ends together with sellotape, they use a decimetre rod to measure the length of their crown. They write the length of their crown in rods on the crown alongside their own name. Wax crayons of varying lengths Decimetre rods (Dienes, Cuisenaire or colour factor) Whiteboards and pens Strips of paper Scissors Sellotape Pens Chn make their own decimetre strip with their name on it. See resources for a template. The strips need to be made of card so that they are fairly robust. Children can then measure the length of their tray in decimetres. How long is the tray? How wide is it? Encourage them Centicubes or any 1cm cubes Decimetre strips (made of card). Decimetre rods (Dienes, Cuisenaire or colour factor) © Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y2 Maths TS_M1 – Aut – 4days estimate. Write some of their guesses on the board. Collect up the decimetre strips and point out that they are all exactly the same length. Lay decimetre strips along the length of Annie and work out how long she is. Discuss what happens if she is not an exact number – some children will understand the concept of a half. Record her length in decimetres: Annie is 13 decimetres long. Ask children to show their decimetre strips. Discuss the fact that these are all the same length. Point out that each one is divided into ten. This is because it is ten centimetres long. Tell children to put their finger on one space on the decimetre. It is one finger wide. One centimetre is one finger wide. A centimetre is a very small unit and is useful for measuring smaller things. A centimetre is used to measure things by people all over the world. It is always the same! Draw round your foot on paper, and hold it up. How long is my foot? We could measure it in centimetres. How many centimetres long is my foot? Take children’s suggestions and write some on the board. Demonstrate measuring the length of your foot to the nearest whole centimetre using several paper decimetre strips and cutting the last one to the exact length. Draw round your outstretched hand and show children how to measure a hand span. Do you think your hand span will be more or less than 20cm? each one. Children take it in turns to be the one lying on the floor. Each child records her or his own height/length, e.g. I am 12 rods long. to talk of half a strip, if it is not an exact number, e.g. it is four and a half strips long. Thin card Scissors Template for decimetre strips (see resources) Pens Group of 6-8 children Children work in pairs to drawn around their hands, and use paper decimetre strips to measure their hand span to the nearest centimetre, recording this on the drawing. Work as a group to arrange their hand spans in order of size. Harder: Some children may be able to measure to the nearest half centimetre. Give each child a sheet of A5 paper and ask them to work in pairs to draw round their partners’ foot and then to measure the length of the foot outline to the nearest centimetre – using several decimetre strips made of paper so they can cut the last one to the right length. They needn’t take off their socks! They record the number of centimetres long. NB: Keep these sheets for teaching sequence D1. Harder: Some children may be able to measure to the nearest half centimetre. Decimetre strips made of paper (lots) Thin card Scissors A5 paper Pens © Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Y2 Maths TS_M1 – Aut – 4days Show the class a 30cm ruler. Point out and demonstrate that this is the same length as three decimetres – it is 30 centimetres long. Show that this is true by laying three decimetre rods or strips along the ruler! Show children a metre stick. This is as long as ten decimetre strips. Demonstrate that this is true by laying ten strips along the metre. How many centimetres long is the metre? Yes it is one hundred centimetres long. Now give each child a 30cm ruler. Where does 10cm come up to on this ruler? Can you see anything in the classroom that might be less than 10cm long? Draw the following table and list their suggestions in the appropriate column: Less than 10cm Between 10cm and 30cm Between 30cm and 100cm More than 100cm Choose a few to check. How long is your ruler? Can you see anything than might be longer than 10cm, but shorter than 30cm? Choose a few to measure. Can you see anything that is longer than your ruler, 30cm, but shorter than a metre? Choose a few to measure. Can you see anything longer than 100cm? Choose a few to compare against the stick. Group of 4-5 children Make a short ramp from a piece of card on a large book. We’re going to roll cars down this ramp, and measure how far they travel along the ground at the bottom of the ramp. Show this with one car, and use the decimetres to measure the distance rolled across the floor. Count in tens to get the distance in centimetres. Check if this is more than one hundred centimetres. If so, point out that we can use a metre stick. Write the total distance in centimetres on a Post-it™ and stick it to the car. Take a different car. Do you think this car will roll further or not? How far do you think it might roll? Ask a child to let it go at the top of the ramp, and another pair to measure the distance it rolls. Did this car roll further or not? Write the distance rolled on a Post-it™ and stick it to the car. Repeat with each car. Ask children to arrange cars in order according to the distances they rolled. Easier: Make the ramp less steep so that the cars roll a shorter distance. The numbers of centimetres are likely to be within the children’s range. Harder: Children's estimations may be more accurate. Children choose six things on their tables to measure using cubes, e.g. rubbers, pencils, books, pencil pots, ruler, whiteboard, zip wallet etc. If there are insufficient items to measure, add some to each table. Ensure that there are items less than 10cm and things between 10cm and 30cm and some over 30cm. Without measuring them, but using estimating to help, they work in pairs to sort them into two groups as on the table (see resources), and then use rulers or cubes to measure the length of each. They write the items and their lengths in the correct columns on the table. Easier: Children sort items into two groups, those which they think might be shorter than 15cm and those with they think might be longer than 15cm (see resources). Harder: Some children may be able to measure to the nearest half centimetre. © Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users. Metre stick 30cm rulers Piece of A4 card and book Selection of different sized cars Post-its™ Objects less than 50cm for children to measure Tables to record measurements (see resources) Y2 Maths TS_M1 – Aut – 4days