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  1. 1. 2 Year R Comparing and ordering numbers Objectives • Use language such as more or less, greater or smaller, to compare two numbers • Order a given set of numbers: for example, the set of numbers 1 to 6 given in random order IEP • Participate in whole-group activities • Work as part of a small group GEP • Know that a number following another in the counting sequence is bigger Resources Language Hand puppet Bigger, smaller, less than, Counting stick and sticky numbers before, after, next, first Sets of cards with flowers, dots, shapes, etc. last, order Washing line and pegs Simple Starter: whole class counting of one Using the hand puppet, get the children to help it with some simple counting to 20 and back. Do more and this a few times, shouting, whispering, clapping, nodding, etc. Explain that the puppet is just one less learning to count and needs them to help it. The puppet is going to count very quietly to a number and stop and the children have to shout out the next number. Do this a few times and then ask them to shout out the number before the one you stopped at. Make sure that the teacher Model phrases like: 4 comes after 3, 4 is 1 more than 3, 4 is bigger than 3, 3 is smaller than 4, etc. • What number comes first, 4 or 3? • Which number is bigger? • How do you know? Support TA sits with the child with the IEP to help him / her concentrate and join in the activity. Main activity: whole class and small groups Show the children the number stick with numbers stuck on up to 20. Point to a range of numbers and get the children to say together the number that is one more than, one less than, bigger than, smaller than, comes before, etc. Then ask individual children to take off the numbers that you describe. Differentiate the questions for individual children. Ask the children to come and choose the numbers that you describe and stick them on the number line. Ask questions such as: • Which number is 1 more than 6? • Which number comes before 3? • What is the last number?
  2. 2. 3 Explain to the children that you have lots of sets of cards which are mixed up and you would like them to help you sort them out. Give each group a set of picture / symbol cards and sticky numbers, making sure they are well shuffled, and tell the children to take one card each. They should then sort themselves in order, then check, and finally choose and stick the correct number on each card. Get them to shuffle the cards and do it again. • Which number comes before this one? • Show me a number that is bigger than this one. • Which number comes last in this group? • Is this number more or less than this one? Get the groups to demonstrate to each other, encouraging them to use appropriate language. Support A small group of children, including the child with the IEP, carry out a similar exercise, but pegging the cards on the washing line. There may be support from a TA. GEP Children take cards off the line in response to questions from the TA or the teacher. If they are right they keep the card. If not, they peg it back on the line. Simplification Numbers up to 6 Challenge Recognise numbers that are 2 more or less than the one described. Plenary: whole class Get the children to help you order a set of cards and peg them on the washing line. Ask how they know a number comes before or after a certain number. Show a number line displaying 3, 6, 8, 14, and 17. Ask the children to tell you a number that is bigger / smaller than or comes before or after those numbers. Next, ask them if they can stick on a number that is bigger or smaller than the number you say. Do this several times, differentiating the questions appropriately.
  3. 3. 4 Year 1 Money Problems Objectives • Use mental strategies to solve simple problems using counting, addition, subtraction, explaining methods and reasoning orally • Work out how to pay an exact sum using smaller coins IEP • Begin to identify when an object is different and does not belong to given categories (P6) GEP • Sort a pile of coins by colour / size / name (P7) Resources Language Coins money, coin, pence, worth, Large coin cards value, pay, price, Items with prices on same as Computer Concept keyboard overlay Feely bag Interlocking cubes Felt boards with Velcro-backed money Simple Starter: whole class addition and Show children the net feely bag. Explain that some coins are going to be put in and they have to subtrac- say how many coins there are in the bag. tion problems Put 4 1p pieces and then 2 11p pieces into the bag. Count each amount, starting from 1 each time. • How many coins are in the bag? • How did you work it out? • What happens if I add 2 more 1p pieces? Write the number sentence on the board and ask the class to read it: 4p + 2p = 6p. Repeat with other calculations by adding coins to or taking coins from the bag. Show the class the 6 1p pieces and ask them to think of coins with equivalent values. E.g. Put 5p coin and 1p coin in bag next to one containing 6 1p coins. Value of coins Support Ask child to find all of the pennies from a pile of coins. Ask them to point to the coin in the pile which is not a penny. Tell them to count all of the pennies into the bag from the pile. Main activity: whole class Tell the children they are going to solve some problems involving money. Show large coin cards for coins: £2, £1, 50p, 20p, 10p, 5p, 2p and 1p. Ask different children to come out and stand in a line, holding the coins in front of the class. Ask the children questions to put the coins in order of value from smallest to largest. • Which coin is worth the most? • How much is this coin worth? • Which coin should it go next to?
  4. 4. 5 • Which coin will buy you the most sweets? • Show me the smallest silver coin. • Show me all the silver coins. Support Working out how Once coins are in order, point to the coins up to 5p and ask the children to say how much they to pay are worth. Respond to questions about the value of the coins using a personal number line. Invite a child to select one coin from a pile of silver coins and one coin from a pile of bronze coins. Tell the class that in your pocket you have a mixture of coins. Hold up different pairs of coins and ask children to find the total value of the coins. • How much is this coin worth? • How much have I got altogether? Give the children some items marked with prices. Ask them to work in small groups to find the two items whose total is less than 10p. Repeat for two items whose total is less than 20p. • Which coins could I use to pay for the item? • Is there another way of making this amount? Encourage children to record money calculations in different ways by sticking coins to the board / flip chart. Go through other examples, asking children to come and stick the correct coins on the board / flip chart. Support Use a computer programme which presents familiar items in a shop with the prices 1p, 2p, 5p and 10p shown. Children must press the correct coin on the concept keyboard to match the price. Encourage children to sort all sweets and label them 1p each / all apples and label them 5p each. Plenary: whole class Put an item costing 7p in front of the class. Ask children to discuss in pairs the coins that could be used to pay for it. Take some suggestions and scribe them as number sentences on the board / flip Fewest chart. coins to pay E.g. 2p + 2p + 2p + 1p = 7p 5p + 2p = 7p When several examples have been written up ask the children to decide which one uses the smallest number of coins. Repeat with other examples. Children on GEP and IEP sit with teaching assistant support. Teaching assistant sticks value tokens on the board as teacher writes 2p, 5p, 7p, etc. Teaching assistant represents scribed number sentence on a felt board with the value tokens and encourages children to stick coins beneath to match.
  5. 5. 6 Year 2 Number properties Objectives • Recognise odd and even numbers to at least 30 • Read whole numbers to at least 100 IEP target • Listen to other children without interrupting GEP • Recognise numerals to 5 Resources Language Counting stick odd, even, digit, 1-30 number track pattern, sequence, predict, Interlocking cubes continue, after, before, Hundred square Number cards Place value cards Count in Starter: whole class two from a given Show the children a counting stick and ask them to count in twos from zero to 20 along the number counting stick and back again. Then point to random divisions on the counting stick, asking the class to say what number is being pointed to. Repeat process, counting up from 1 to 21 and back. Extend to different starting numbers. Support Ask the child with the IEP to listen to the numbers the class says and then point to the last number said on the hundred square. • Point to number 4. • What number comes halfway between 0 and 20? • How do you know this number is 12? • If we know this number is 15 what number is on the next division? • If we carried on counting, what would the next number be? Looking at pattern of odd and Main activity: whole class even numbers Show the children a number track with numbers from 1 to 30 on it. Point to various numbers and ask different children to read them. Ask children to read numbers between 1 and 5 (GEP). Tell the children they are going to look at a pattern in the numbers. Ask children to call out different numbers that appear on the number track. Point to the numbers that have been given on the number track and read them out. Shade even numbers on the track in one colour and odd numbers in a contrasting colour. When several numbers have been shaded, ask children what they notice. Ask children to come out and shade some more numbers called out. • Which number do you need to shade? (IEP) • Do you think it should be shaded in yellow or blue? Why? • What sort of numbers are the numbers shaded in yellow? • Is four coloured yellow? (GEP)
  6. 6. 7 • What colour is 1? • What other numbers are the same colour? • What do all the even numbers end in? • What is special about an even number? Make some towers out of even numbers of cubes and illustrate how an even number can be split into two equal towers. Repeat with an odd number of cubes and illustrate that, when split, the towers cannot both have the same number of cubes in. (Use the same colours to represent numbers in towers as on the number track, i.e. all even numbered towers have a yellow cube on the top.) Play a game of ‘odd or even’ with the class. Take a set of number cards 1 to 30 and explain that the children will play against the teacher. The teacher will collect odd cards; the children will collect even cards. Place the cards in a pile face down on the table. Take it in turns to pick a card. If it is the type being collected, the player keeps the card. If not, it gets taken out of play (can be put to one side). When all the cards have been selected, check to see who has the most cards. Point to unit digits between 1 and 5 and ask children to read them (GEP). Recognis- ing odd • Is this odd or even? and even • Which digit do you look at to decide if it is odd or even? numbers • What is this digit? (GEP) Ask children to work in groups of 4 to play the game: one pair of children against another pair. Explain to the children that they need to read the number on the card that they select and discuss with the others in their group whether it is odd or even. Remind children of the need to listen to one another (IEP). When children complete the game, they can record the odd or even numbers they have collected. GEP Children each choose a number between 1 and 5 and take it in turns to pick a card as for ‘odd or even’. If they choose a card with their digit in they keep it, if not it is out of play. The winner is the person with the most cards at the end. The teacher works with this group initially. Plenary: whole class Look at a hundred square. Ask children to come out and shade in various even numbers on a hundred square. Extend to numbers over 30. Looking • How do you know that number is even? at the • If we are only shading even numbers would you shade in 45? Why/Why not? pattern of • What do you notice about the pattern on the hundred square? odd and even numbers Ask various children to say a two-digit number. Tell the rest of the class if the number is even they put their hands on their heads, if the number is odd they put their hands on their hips. Remind the children to listen to the numbers said. • How can we recognise an odd number? • Point to numbers which end in 3 (GEP). • Give me an odd number between 20 and 25. • Which other odd number comes between 20 and 25? (IEP)
  7. 7. 8 Year 3 Fractions Objectives 1 1 1 1 1 • Recognise unit fractions such as 2 , 3 , 4 , 5 , 10 • Find unit fractions of numbers IEP target • Count reliably up to 10 objects Resources Language Number fans half, double Interlocking cubes quarter, third, fifth, Counters equal parts, fraction, divide OHTs with shapes on Felt cushion, Velcro counters Starter: whole class Doubling Each pair of children has a number fan. Ask the children questions relating to doubles and halves. and Make connections between doubling and halving and illustrate connection using cubes, e.g. halving numbers ‘Double six is twelve’. Put the two towers of six together: ‘half of twelve is six’. Break the tower in to 20 half. Children discuss the answers in their pairs and then show the answers on their number fans. • What is double 8? What is half of 16? • What is double 15? • How did you work it out? • Double a number is 24. What is the number? Support Ask children to count out 4 cubes to make a tower. Tell them to make two towers that are the same and then count how many cubes there are altogether. Introduc- tion to finding fractions Main activity: whole class of Tell the children they are going to use their knowledge of fractions of shapes to help find fractions numbers using of numbers. fractions Put a picture of a square divided into halves on the OHP . of shapes • How many parts has this shape? • What fraction of the whole is each of the parts? Explain that it is one whole divided into two equal parts. Put eight counters on the OHP Explain to the children that the square which is split in half can be . used to help find half of a number. Illustrate dividing the counters into two equal groups (one group in one half of the square and the second group in the other half of the square). • How many counters are there in half the square? Point to the counters to support the counting. 1 Write on the board 2 of 8 = 4. Ask children to read the number sentence. Repeat, finding halves of other numbers and writing the corresponding number sentences on the board. Put a square divided into thirds on the OHP.
  8. 8. 9 • What fraction of the whole is each of the parts? • How many thirds make a whole? 1 • How do you think we could use this to find 3 of 12? Ask a child to model how they might divide the counters into three equal groups using the shape to support. Put 2 counters in each section – show that you have 6 left. Put 1 more in each section and ask how many you have left. Share the remaining 3 counters between the three sections. Repeat with finding quarters of shapes. Put some fractions on the board with some numbers next to each fraction, 1 e.g. 2 12, 18, 24, 30 1 3 18, 24, 30, 21 1 4 12, 24, 16, 40 1 5 20, 35, 25, 40 Ask the children to work in pairs to find the fraction shown of each of the numbers. Model how to 1 record it, e.g. 2 of 12 = 6. Support 1 1 1 Give out cards divided into 2 , 4 , and 3 . Give out a selection of numbers and a bag of counters to complete the exercise. IEP Count even number of counters up to 10 and split each group into two equal parts, using shape split in half to support. Simplifications Find halves and quarters. 1 1 1 Extension Find 6 , 8 , 10 of given numbers. Plenary: whole class 1 Write 2 of = 5 on the board. Ask the children to read the number sentence as a class and discuss with a partner how they would find the missing number. • Half of which number makes 5? • How did you work out that the missing number is 10? • Why did you double 5 to find the missing number? Model using the shape divided in half by counting 5 counters onto one half. Ask child with IEP to count the same number of counters onto the other half. Count the total number of counters as a class. 1 Repeat process with 3 of = 10. Discuss using multiplication to find the missing number.
  9. 9. 10 Year 4 Properties of shapes Objectives • Classify polygons using criteria such as number of sides or right angles and whether or not they are regular IEP target • Count reliably up to 5 GEP target • Use everyday language to describe features of familiar 2-D shapes, referring to properties such as number of sides or corners Resources Language Large envelope with shapes cut from card shape, polygon, property, sides, angles, Shapes drawn on pieces of paper (a range corners, straight, square, triangle, rectangle, of regular and irregular polygons) pentagon, hexagon, octagon, Two sorting circles drawn on the board regular, irregular Sheets with a number of different shapes drawn on Starter: whole class Properties of simple Slowly reveal a shape from inside a large envelope. Ask children questions to develop their shapes thinking. Discuss shapes it could or could not be. Repeat with familiar shapes / different shapes. • What shape do you think it could be? • When I reveal more of the shape do you want to change your mind? • Why? Why not? • Are there any shapes you know it could not be? Support Once the shape is revealed, hold it up and repeat its name. Hold it in different orientations and ask ‘Is it still a square?’ Count the number of sides / angles pointing to each side / angle appropriately. Main activity: whole class Explain Explain to the children that some 2-D shapes are regular and some are irregular. Explain the regular difference. and Stick all the polygons on the board. irregular polygons • What is the same about all of these shapes? • How many sides does this shape have? • What is this shape called? (triangle) Explain that all the shapes are polygons because they are closed, flat shapes with three or more straight sides. Explain that the shapes are now going to be sorted. Ask a child to choose a shape from the board and say something about the shape they have chosen. Prompt with questions if necessary. Repeat with other shapes. Support Ask children to name the simple shapes and demonstrate checking the number of sides / angles by counting / pointing to each side / angle as appropriate.
  10. 10. 11 • How many sides does the shape have? • Are all the sides the same length? • Are any of the angles right angles? Place irregular shapes in one of the sorting circles and regular shapes in the other sorting circle. Ask the children to think about how the polygons are being sorted. • What is the same about all the shapes in this circle? • How are they different from all the shapes in the other circle? • Can you predict which circle this polygon should go in? • Why do you think it should go in that circle? When all the shapes have been sorted and the criteria for sorting have been discussed, ask the children to talk to their partner about what the different shapes should be called. Prompt the children by asking appropriate questions. Write the name of the polygon inside each one. • This shape has three sides and the sides are the same length. What sort of shape is it? • What do we call a regular triangle? Give the children a description of one of the shapes and then ask them to try to guess which shape is being described. Reinforce names and properties by counting sides / angles and pointing to the Recognis- appropriate shapes. ing regular and Ask children to work in pairs to come up with a description of one of the shapes. Take suggestions. irregular Can the rest of the class guess the shape from the description given? shapes from their properties Give the children worksheets with a range of polygons on. Children then work in pairs and each child writes a description of three of the polygons. When they have each written three descriptions they can read them to their partner to see if their partner can guess which polygon is being described. IEP Sort a given set of polygons. Find all the polygons with four sides. GEP Given set of simple polygons, match names and simple properties. Simplification Give children descriptions, already written, to match to the correct polygon. Extension Give children polygons, including some of the same type, e.g. several irregular pentagons, write descriptions to distinguish between the irregular polygons given. Plenary: whole class Give the children mini white boards. Ask different children to read out their descriptions and ask the rest of the class to draw a shape that fits the description. Compare some of the shapes. Construct- • Do both these shapes meet the criteria? ing regular and • What would you call both of these polygons? irregular • What is the same about them? What is different about them? shapes from their properties
  11. 11. 12 Year 5 Developing a standard method Objectives • Use known facts and place value to multiply • Extend written methods to HTU by U IEP target • Count in steps of 3 and 4 from 0 GEP target • Work co-operatively with a partner Resources Language Place value cards times, multiple, lots of, multiplication, Multiple line partition, hundred, tens, units Multiplication grid Starter: whole class Tell the children they are going to use known multiplication facts to work out other facts. Using known Write on the board, e.g. 6 3. Ask the children to read it as a class and then ask for the answer. tables Discuss methods. Model counting in 3s, keeping count on fingers (IEP). Write a related fact on the facts to board, e.g. 6 30, and discuss the answer. Ask the children to work with the fact 6 3 and come work out up with other facts related to it. Remind children to discuss with a partner before putting their other facts hands up (GEP). • If you know 6 3 is 18, what else do you know? • 600 3 is 1800 so what is 6 300? Why? Repeat with a different starting fact. Main activity: whole class Tell the children they are going to use their knowledge of tables facts to multiply a three-digit Multiplying number by a single-digit number. a three- digit Give child multiple lines to count along (IEP). number by a single Use place value cards to put the numbers 100, 40 and 3 on the board. Tell the children that they digit using are going to multiply each of the numbers by 6. the expanded written • What is 6 lots of 100? method • What is 6 lots of 40? • What is 6 lots of 3? (IEP). Explain that they are going to use that information to work out 143 multiplied by 6. Combine the place value cards to make 143 and underneath write 6 as a vertical multiplication. i.e. 143 6 Repeat the questions above, pointing to the appropriate digits in the calculation. Write the answer to each part underneath.
  12. 12. 13 143 6 Encourage children to add the parts mentally. 600 240 18 • We know 6 100, 6 40, and 6 3. How can we use that to find 6 143? Write another calculation on the board. Ask children to decide what they will multiply first. Work through the calculation together. For the units part of the calculation, illustrate how to count up in steps of a given number using the multiple lines. Practising Repeat with a third calculation. This time ask children to work through the calculation in pairs, then multiplying ask a pair to come up and talk through how they did it. a three- digit number by Write three-digit numbers on the board, and a single-digit number. Ask children to work in pairs to a single- pick a three-digit number and a single-digit number and multiply them together. digit number IEP Roll two six-sided dice to generate a calculation, e.g. 3 5. Use a number line to calculate the answer. (If a six is rolled, roll again.) Simplification Write two-digit numbers on the board to be multiplied by a single-digit number. Challenge Teacher to work with this group initially to extend them. Multiply two-digit numbers by other two-digit numbers. Plenary: whole class Write a three-digit by a single-digit calculation on the board. Work through it together as a class. Investigat- ing what • If I were to start with the units rather than the hundreds, would I get the same answer? happens if calcula- Why/Why not? tions start with the Work through the calculation, starting with the units. least significant digit rather Repeat with another calculation. Ask the children to work through the calculation in pairs, starting than the with the units, then work through it as a class. most significant • How can we check that the answer is correct? digit
  13. 13. 14 Year 6 Calculator skills Objectives • Identify and use appropriate operations (including combinations of operations) to solve word problems based on money • Develop calculator skills and use a calculator effectively IEP target • Develop calculator skills by using a calculator with large keys GEP target • Recognise the order in which numbers / calculations are put into the calculator Resources Language Calculators which display the numbers put function, key, add, subtract, multiply, divide in memory A large key calculator (IEP) OHP calculator OHP Worksheets with problems on them Starter: whole class Calculator Show 0.5 on the OHP calculator. Tell the children that a function is going to be put into the as a function calculator and they have to guess what it is. Turn the OHP off. Put in 3 =, and turn the OHP back machine on. • What function could it be? • Is there anything else it could be? • If it is multiply by 3 and we put 0.7 in. What should come out? Try several different numbers to check out ideas. Repeat with a different function or even a two-step function. Main activity: whole class Tell the children they are going to solve problems using a calculator. Look at a problem written on the board. Read the information as a class. Word Park admission problems Adults – £7.80 to be Children – £4.75 solved using calculators How much will it cost five adults and six children to get into the park? Ask children to discuss in pairs what they might put into the calculator to solve the problem. Work with the GEP group and explain how they might put an amount of money into the calculator. • How would you start solving the problem? • If you have worked out 5 lots of £7.80, what does the calculator show? • How can you save that information in the calculator before doing the next part of the calculation?
  14. 14. 15 Ask children to work in pairs to find the solution and jot down what they put into the calculator. Ask some pairs of children to give feedback, recording for others what was put into the calculator. Ask several children to check. Include children with IEP or GEP. Discuss accuracy. Model carrying out the calculation. Ask children what the display shows. • How do we say 67.5 pounds? Repeat process with another problem. A man sells chocolate bars for £1.25 each. There are 58 bars in a box. He buys the box of bars for £85. Following the transaction does he lose money or gain money? Ask the children to discuss in pairs what they need to do to find the answer to the problem. Choosing Write the calculation down for the GEP group – i.e. 85 – (£1.25 58). Discuss with them which bit calculation to put into they will do first. Encourage them to write down the answer to the first stage, then subtract the the answer from £85, rather than using the memory function. calculator Work through the problem as a class. Give the children a set of multi-step problems to solve. IEP Use a calculator with large keys. GEP Match calculations to given one-step problems, then key the calculations into the calculator. Simplification Work on one-step problems. Challenge Work on multi-step problems, some involving percentages of amounts of money. Plenary: whole class Look at some problems written on the board. Read them together as a class. Select one and show Deciding how you would approach the question. Ask children to discuss in pairs whether they would find the on the most answer mentally, using a written method or with a calculator. appro- priate Discuss possibilities and reasons for decisions. method Look at a calculator question. • What operations do we need to use? • What should we put into the calculator? • What does the answer say? • How can we write that in pounds? Ask all the children to put the calculation into their calculators to check the answer. Go over the main points, i.e. decide on the most appropriate method, need to check the display and check the answer is reasonable.