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Year 6 Using and applying mathematics • Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use Jemma thinks of a number. She says, 'Add 3 to my number and then multiply the result by 5. The answer is 35'. What is Jemma's number? Sapna and Robbie have some biscuits. Altogether they have 14 biscuits. Riaz thinks of a number. He says, 'Halve my number and then add 17. The answer is 23.' What is Riaz's number? KS2 2005 Paper B level 4 Sapna has 2 more biscuits than Robbie. How many biscuits do Sapna and Robbie each have? Parveen has the same number of 20p and 50p coins. She has £7.00. How many of each coin has she? KS2 2002 Paper B level 4 Y4 optional test 2003 Paper B level 4 In a supermarket storeroom there are 7 boxes of tomato soup 5 boxes of pea soup 4 boxes of chicken soup 185 people go to the school concert. They pay £1.35 each. How much ticket money is collected? There are 24 tins in every box. How many tins of soup are there altogether? Programmes cost 15p each. Selling programmes raises £12.30. How many programmes are sold? KS2 2004 Paper B level 4 KS2 2002 Paper B level 4 Kim has some rectangular tiles. Each one is 4 centimetres by 9 centimetres. Some children do a sponsored walk. Jason is sponsored for £3.45 for each lap. He does 23 laps. How much money does he raise? 4cm Lynne wants to raise £100. She is sponsored for £6.50 for each lap. What is the least number of whole laps she must do? 9cm She makes a design with them. KS2 1997 Paper B level 4 This fence has three posts, equally spaced. height Not to scale width Calculate the width and height of her design. KS2 2000 Paper A level 4 gap 15cm gap 15cm 15cm 153cm Each post is 15 centimetres wide. The length of the fence is 153 centimetres. Calculate the length of one gap between two posts. KS2 2003 Paper B level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 1 00028-2007CDO-EN © Crown copyright 2007 • Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy represents the number of books that Alice reads each week. Which of these represents the total number of books that Alice reads in 5 weeks? How many triangles can you see in this diagram? A 5+ B 5× C ÷5 D 5÷ How can you make sure that you have counted them all? and each stand for a different number. = 34 Imagine you have 25 beads. You have to make a three-digit number on an abacus. You must use all 25 beads for each number you make. +=++ What is the value of ? Y4 optional test 2003 Paper B level 4 Each shape stands for a number. The numbers shown are the totals of the line of four numbers in the row or column. How many different three-digit numbers can you make? Write them in order. Two boys and two girls can play tennis. Ali said: ‘I will only play if Holly plays.’ Holly said: ‘I won’t play if Ben is playing.’ Ben said: ‘I won’t play if Luke or Laura plays.’ Luke said: ‘I will only play if Zoe plays.’ Zoe said: ‘I don’t mind who I play with.’ Find the remaining totals. Which two boys and which two girls play tennis? Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 2 00028-2007CDO-EN © Crown copyright 2007 • Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret results and review methods; identify and answer related questions Here are some digit cards. The graph shows how the price of a chocolate bar has changed. 30p Write all the three-digit numbers, greater than 500, that can be made using these cards. KS2 2005 Paper A level 4 20p Jason threw some darts at this board. Every dart landed on the board. Price 10p 1972 1977 1982 1987 1992 1997 2002 Year Fill in the gaps below. Between 1992 and 2002, the price of the chocolate bar increased by … p Jason scored exactly 100. How many darts did he throw? Which numbers did they land on? In 1992, the price of the chocolate bar was 6 times as much as in … The smallest increase in price was in the five years between … and … Write three more questions you cold ask about the numbers on the dartboard. This pie chart shows how the children in Class 6 best like their potatoes cooked. Write down two more statements you could make about the information shown in the graph. Y7 progress test Paper B level 4 [adapted] Class 6 count how many seeds they find under two trees. They show the data in a graph. 32 children took part in the survey. Look at the four statements below. For each statement put a tick () if it is correct. Put a cross () if it is not correct. 10 children like chips best. 25% of the children like mashed potatoes best. 1 5 of the children like roast potatoes best. 12 children like jacket potatoes best. How many seeds did they find in week 3 altogether? In how many weeks did they find more than 40 chestnut seeds? Write down two different ways in which you could extend this survey. Write down two more questions you could ask about the information shown in the graph. KS2 2005 Paper A level 5 [adapted] KS2 2005 Paper A level 4 [adapted] Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 3 00028-2007CDO-EN © Crown copyright 2007 • Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols, e.g. the cost of c pens at 15 pence each is 15c pence In this sequence each number is double the previous number. Write in the missing numbers. 3 6 12 24 The first two numbers in this sequence are 2.1 and 2.2. The sequence then follows the rule ‘to get the next number, add the two previous numbers‘. 48 Write in the next two numbers in the sequence. KS2 2003 Paper B level 4 2.1 17 multiplied by itself gives a 3-digit answer. 2.2 4.3 6.5 KS2 2003 Paper A level 4 11 10 What is the smallest 2-digit number that can be multiplied by itself to give a 4-digit answer? 9 (7, 8) 8 7 (4, 6) C 6 5 (1, 4) 3 Here is a repeating pattern of shapes. Each shape is numbered. 1 2 3 4 5 6 7 8 9 1 (4, 3) A 2 (7, 5) B 4 KS2 2005 Paper B level 4 (1, 1) (9, 5) (6, 3) (3, 1) 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Write the co-ordinates of the next triangle in the sequence. 10 The pattern continues in the same way. Write the numbers of the next two stars in the pattern. Y4 optional test Paper B level 4 Complete this sentence. Halid makes a sequence of 5 numbers. The first number is 2. The last number is 18. His rule is to add the same amount each time. Shape number 35 will be a circle because ... KS2 2003 Paper A level 4 Write in the missing numbers. What is the value of 4x + 7 when x = 5? 2 18 Y5 optional test 1998 Paper B level 4 KS2 1999 Paper B level 5 Take three shapes like this. The rule for this sequence of numbers is ‘add 3 each time’. 1......4......7......10......13......16......… Use the three shapes to make a symmetrical shape. How many different symmetrical shapes can you make using the three shapes? The sequence continues in the same way. Mary says, ‘No matter how far you go there will never be a multiple of 3 in the sequence.’ Is she correct? Circle Yes or No. Explain how you know. How many of the shapes have only one line of symmetry? How many have two lines of symmetry? KS2 2001 Paper B level 5 Sam says: ‘In a triangle, each angle must be 90 degrees or less, because the three angles add up to 270 degrees.’ Is Sam correct? Ring YES or NO. Explain how you know. Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 4 00028-2007CDO-EN © Crown copyright 2007 • Explain reasoning and conclusions, using words, symbols or diagrams as appropriate The spinner is divided into nine equal sections. Nadia is working with whole numbers. She says, 'If you add a two-digit number to a two-digit number you cannot get a four-digit number.’ 2 Which two different numbers on the spinner are equally likely to come up? Meera says, ‘2 has a greater than even chance of coming up’. Explain why she is correct. PAVING SLABS £3.50 each 2 2 Mr Singh buys paving slabs to go around his pond. Square slabs 3 1 KS2 2000 Paper B level 4 50cm by 50cm 2 2 Is she correct? Circle Yes or No. Explain why. £1.95 each 1 4 50cm KS2 2000 Paper A level 4 100cm Pond The diagram shows a square. Rectangular slabs 100cm by 50cm He buys 4 rectangular slabs and 4 square slabs. What is the total cost of the slabs he buys? 'It would cost more to use square slabs all the way round.' Explain why he is correct. KS2 2002 Paper A level 4 How many degrees is angle a? Explain how you know. Y7 progress test 2005 Paper B [adapted] Counting and understanding number • Find the difference between a positive and a negative integer, or two negative integers, in context The temperature starts at four degrees and goes down by ten degrees. What is the temperature now? What temperature is twenty degrees lower than six degrees Celsius? KS2 2004 Mental test level 5 Y5 optional test 1998 Mental test level 4 Megan makes a sequence of numbers starting with 100. She subtracts 45 each time. The temperatures were: inside outside –1°C –8°C Write the next two numbers in the sequence. 100 55 10 KS2 1999 Paper A level 5 What is the difference between these two temperatures? A sequence starts at 500 and 80 is subtracted each time. KS2 2002 Paper B level 4 500 420 340 ... The temperature inside an aeroplane is 20 °C. The temperature outside the aeroplane is –30 °C. What is the difference between these temperatures? The sequence continues in the same way. Write the first two numbers in the sequence which are less than zero. KS2 2003 Paper B level 4 KS2 2002 Paper A level 5 The temperature in York is 4°C. Rome is 7 degrees colder than York. What is the temperature in Rome? Circle two numbers which have a difference of 2. KS2 2000 Paper A level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy –1 –0.5 0 0.5 1 1.5 KS2 2001 Paper B level 4 5 00028-2007CDO-EN © Crown copyright 2007 • Use decimal notation for tenths, hundredths and thousandths, partition, round and order decimals with up to three places, and position them on the number line Write a number in the box to make this correct. Write these numbers in order. One has been done for you. 0.627 = 0.6 + 0.02 + In the number 5.375, what does the digit 7 represent? A B C D 7 1000 7 100 7 10 Y5 optional test 2003 Paper A level 5 7 Put a ring around the smallest number. 0.27 What number is exactly halfway between one point one and one point two? 0.207 0.027 2.07 2.7 KS2 2001 Mental test level 4 KS2 2005 Mental test level 4 Here are three supermarket bills. Write the number that is exactly halfway between eight point six and eight point seven. Y5 optional test 1998 Mental test level 4 Write a number that is bigger than nought point three but smaller than nought point four. Total £74.68 Total £65.90 Total £59.05 KS3 2003 Mental test level 4 Tom rounds each bill to the nearest £10 and adds them up. What is the total amount that Tom gets? Write each of these numbers to the nearest whole number. 13.7 is nearest to ............... Mary adds up the three bills exactly. What is the total difference between her total and Tom’s total? 8 ⁄8 3 is nearest to ............... KS2 2004 Paper B level 4 3.38 is nearest to ............... Circle the number closest in value to 0.1. Y5 Optional test Paper B level 3 0.01 Round each decimal to the nearest whole number. 0.05 0.11 0.2 0.9 KS2 2002 Paper B level 5 6.01 9.51 Round two point six nine four to one decimal place. 7.75 KS3 2005 Mental test level 6 Y5 optional test 2003 Paper B level 4 [adapted] Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 6 00028-2007CDO-EN © Crown copyright 2007 • Express a larger whole number as a fraction of a smaller one e.g. recognise that 8 slices of a 8 3 5-slice pizza represents 5 or 1 5 pizzas; simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator Look at these fractions. Draw one line to join two fractions which have the same value. 1 2 4 7 5 6 Mark each fraction on the number line. The first one is done for you. 2 8 1 2 1 3 0 2 5 1 1 3 1 2 KS3 2001 level 4 1 4 4 Write a fraction that is larger than ⁄5. 1 Write a fraction that is smaller than ⁄5. KS2 1998 Paper A level 4 1 3 Write a fraction that lies between ⁄4 and ⁄8. Karen makes a fraction using two number cards. She says, 1 ‘My fraction is equivalent to ⁄2. One of the number cards is 6’ Which is larger, What could Karen’s fraction be? Give both possible answers. KS2 2002 Paper A level 5 1 2 or ? 3 5 Explain how you know. Here are some number cards. or 7 5 9 3 11 Use two of the cards to make a fraction which is 1 less than 2. KS2 2003 Paper B level 4 Complete these fractions to make each equivalent to 3 . 5 How much less than 1 is your fraction? KS2 1996 Paper B level 5 10 15 12 KS2 2001 Paper A level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 7 00028-2007CDO-EN © Crown copyright 2007 • Express one quantity as a percentage of another, e.g. express £400 as a percentage of £1000; find equivalent percentages, decimals and fractions Write these decimals as percentages. Put a ring around the fraction which is equivalent to forty per cent. 0.25 …% 1 40 0.6 …% 40 60 4 10 1 4 1 400 KS2 1999 Mental test level 4 Write these percentages as decimals. 42% … Circle the two fractions that are equivalent to 0.6. 5% … 6 10 What is seven-tenths as a percentage? 1 60 60 100 1 6 Y5 optional test 2003 Paper B level 4 KS2 2005 Mental test level 4 Put a ring around the decimal which is equal to onefifth. Write 80% as a fraction in its simplest form. What is twenty out of forty as a percentage? 0.1 0.2 0.3 0.4 0.5 KS2 2004 Mental test level 4 KS2 2003 Mental test level 5 A class is collecting money for charity. They want a total of £1000. By the end of April, they have collected £400. Some of the statements below are correct. Tick () the correct ones. What percentage of their total have they collected by the end of April? Tick ( ) if correct Y7 progress test Paper A level 4 1 2 = 0.5 9 30 = 3 10 0.75 = 3 4 1 2 is equivalent to 10% 1 5 is equivalent to 5% Y7 optional test Paper A level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 8 00028-2007CDO-EN © Crown copyright 2007 • Solve simple problems involving direct proportion by scaling quantities up or down Two letters have a total weight of 120 grams On a school trip each teacher can take no more than 20 pupils. Three teachers go on a school trip. What is the greatest number of pupils they can take with them? Complete the table to show the least number of teachers that must go with each school trip. Number of pupils One letter weighs twice as much as the other. Write the weight of the heavier letter. Number of teachers Y4 optional test 2003 Paper B level 4 100 Peanuts cost 60p for 100 grams. What is the cost of 350 grams of peanuts? 104 Raisins cost 80p for 100 grams. Jack pays £2 for a bag of raisins. How many grams of raisins does he get? 199 KS2 2000 Paper A level 4 KS3 2002 Paper A level 3 Here is part of a number line. Write the two missing numbers in the boxes. Jenny is going to make some cordial. The finished 1 2 drink should be 3 cordial and 3 water. Jenny puts 100 ml of cordial in a glass. How much water should she put with it? KS3 2004 Paper A level 4 Four biscuits cost twenty pence altogether. How much do twelve biscuits cost? KS2 2005 Paper A level 4 KS2 2005 Mental test level 4 Here is part of a number line. Write the missing numbers in the boxes. Two rulers cost eighty pence. How much do three rulers cost? KS3 2005 Mental test level 4 Six cakes cost one pound eighty. How much do ten cakes cost? KS2 2002 Mental test level 5 Here is a recipe for pasta sauce. Y5 optional test 2003 Paper A level 4 In a country dance there are 3 boys and 2 girls in every line. Josh makes the pasta sauce using 900g of tomatoes. What weight of onions should he use? 42 boys take part in the dance. How many girls take part? Y5 optional test 2003 Paper B level 5 KS2 1996 Paper B level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 9 00028-2007CDO-EN © Crown copyright 2007 Knowing and using number facts • Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals, e.g. 0.8 × 7, 4.8 ÷ 6 What is nought point four multiplied by nine? Divide four point eight by eight. KS2 2005 Mental test level 4 [adapted] KS2 2004 Mental test level 4 [adapted] What is nought point three multiplied by four? Divide four point two by six. KS2 2004 Mental test level 5 [adapted] Y4 optional test 1998 Mental test level 4 [adapted] What is four multiplied by nought point nine? What number multiplied by eight equals four point eight? KS2 2005 Mental test level 4 [adapted] KS3 2005 Mental test level 4 [adapted] Multiply seven by nought point six. Divide four point two by seven. KS2 2003 Mental test level 4 [adapted] KS3 2004 Mental test level 4 [adapted] What is nought point eight multiplied by six? Y3 optional test 2003 Mental test level 3 [adapted] Multiply nought point seven by nine. KS2 1999 Mental test level 4 [adapted] • Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10 What is five squared? What is the next square number after thirty-six? KS3 2001 Mental test level 4 Y7 progress test 2005 Mental test level 4 Explain why 16 is a square number. What is the next number in the sequence of square numbers? One, four, nine, sixteen ... Y5 optional test 1998 Paper B level 3 KS3 2004 Mental test level 5 Here is a sorting diagram for numbers. Write a number less than 100 in each space. Find two square numbers that total 45 even not even + = 45 a square number KS2 2005 Paper A level 5 not a square number What is thirty multiplied by thirty? [oral question] KS2 2004 Paper A level 4 • Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit whole numbers Millie and Ryan play a number game. Is it under 20? Is it under 25? Is it odd? Is it a prime number? Write the three prime numbers which multiply to make 231. No Yes Yes Yes × × = 231 KS2 2001 Paper B level 5 What is the number? The three numbers missing from these boxes are all prime numbers greater than 3. Write in the missing prime numbers. KS2 1999 Paper B level 3 × × = 1001 KS2 1996 Paper C level 6 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 10 00028-2007CDO-EN © Crown copyright 2007 • Use approximations, inverse operations and tests of divisibility to estimate and check results A car park has 76 rows for parking. There are 52 car spaces in each row. Which of these is the BEST way to estimate how many cars can park altogether? A 100 × 50 = 5000 B 90 × 60 = 5400 Julie says, ‘I added three odd numbers and my answer was 50.’ Explain why Julie cannot be correct. KS2 2004 Paper A level 5 C 80 × 60 = 4800 This sequence of numbers goes up by 40 each time. D 80 × 50 = 4000 40 E 70 × 60 = 4200 This sequence continues. Will the number 2140 be in the sequence? Circle Yes or No. Explain how you know. 80 120 160 200 … KS2 2000 Paper A level 5 Estimate the value of nine point two multiplied by two point nine. KS3 2005 Mental test level 5 Circle the best estimate of the answer to 72.34 ÷ 8.91 6 7 8 9 10 11 KS3 2002 Paper A level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 11 00028-2007CDO-EN © Crown copyright 2007 Calculating • Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U What number is halfway between thirty and eighty? What is the sum of eight point five and eight point six? KS2 2004 Mental test level 4 KS2 2002 Mental test level 4 Tick () the two numbers which have a total of 10. Add three point five to four point eight. KS2 1999 Mental test level 4 Subtract one point nine from two point seven. KS2 2003 Mental test level 4 Subtract nought point seven five from six. KS3 2003 Mental test level 4 KS2 2005 Paper A level 4 Add together nought point two, nought point four and nought point six. Circle two numbers which add to make 0.12. 0.1 KS2 2005 Mental test level 4 0.5 0.05 0.7 0.07 0.2 KS2 2000 Paper A level 4 What is four multiplied by three point five? Circle the two numbers which add up to 1. KS2 2000 Mental test level 4 0.1 0.65 0.99 0.45 0.35 KS2 1999 Paper A level 5 In a café I buy two cups of coffee and a sandwich. Altogether I pay three pounds. The sandwich costs one pound sixty. What is the cost of one cup of coffee? The first two numbers in this sequence are 2.1 and 2.2. The sequence then follows the rule ‘to get the next number, add the two previous numbers‘. Y7 progress test 2003 Mental test level 3 Write in the next two numbers in the sequence. A packet of crisps costs thirty-two pence. Josh buys three packets. How much change does he get from one pound? 2.1 2.2 4.3 6.5 KS2 2003 Paper A level 4 KS2 2005 Mental test level 4 A magazine costs one pound forty pence. I buy two of them and pay with a five pound note. How much change should I get? KS3 2003 Mental test level 4 Two rulers cost eighty pence. How much do three rulers cost? KS3 2005 Mental test level 4 A bag of four oranges costs thirty seven pence. How much do twelve oranges cost? KS2 2000 Mental test level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 12 00028-2007CDO-EN © Crown copyright 2007 • 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 Calculate 2307 × 8. Calculate 15.05 – 14.84. KS2 2003 Paper A level 4 KS2 2002 Paper A level 5 Write in the missing digits. Calculate 8.6 – 3.75. 4 4 + 38 = 851 KS2 2000 paper A level 5 KS2 2004 Paper A level 4 In the chart any three numbers in a line, across or down, have a total of 18.45. Write the missing number. Write in the missing digit. 7 × 9 = 333 KS2 1996 Paper A level 4 2.46 Write in the missing digit. 11.07 5 × 8 = 456 4.92 8.61 7.38 1.23 3.69 9.84 KS2 1995 Paper A level 4 KS2 1997 Paper A level 4 Write in the missing number. ÷ 5 = 22 Calculate 31.6 × 7. KS2 1995 Paper A level 4 KS2 2004 Paper A level 5 Eggs are put in trays of 12. The trays are packed in boxes. Each box contains 180 eggs. How many trays are in each box? Calculate 123 ÷ 5. KS2 1999 Paper A level 4 Calculate 27.6 ÷ 8. Some children go camping. It costs £2.20 for each child to camp each night. They go for 6 nights. How much will each child have to pay for the 6 nights? Shenaz buys a pack of 24 cans of cola for £6.00. Calculate 16.5 ÷ 3. There are 70 children. Each tent takes up to 6 children. What is the least number of tents they will need? What is the cost of each can? KS2 1998 Paper A level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy KS2 1998 Paper A level 5 13 00028-2007CDO-EN © Crown copyright 2007 • Relate fractions to multiplication and division, e.g. 6 ÷ 2 = 2 of 6 = 6 × 2; express a quotient 2 as a fraction or decimal, e.g. 67 ÷ 5 = 13.4 or 13 5; find fractions and percentages of whole5 number quantities, e.g. 8 of 96, 65% of £260 1 1 Calculate 60% of 765. One third of a number is twelve. What is the number? KS2 2000 Paper B level 4 KS2 1997 Mental test level 4 In a sale, there is fifty per cent off all prices. A chair costs forty-five pounds in the sale. How much was it before the sale? What is three-quarters of two hundred? KS2 2000 Mental test level 4 KS2 1999 Mental test level 4 What is three-fifths of forty pounds? KS3 2003 Mental test level 5 John had £5. He gave 25% of it to charity. How much did he give? Joe has some pocket money. He spends threequarters of it. He has fifty pence left. How much pocket money did he have? Y4 optional test Paper B level 4 Sophie poured some water out of a litre jug. Look how much is left in the jug. Estimate how many millilitres of water are left. Y5 optional test 2003 Mental test level 4 Calculate 4 of 840. 3 KS2 2000 Paper A level 4 Fill in the missing numbers. 1 1 of 20 = of … 2 4 3 1 of 100 = of … 4 2 Y5 optional test 2003 Paper A level 4 1 2 of 60 = of … 3 3 KS3 2003 Paper 1 level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 14 00028-2007CDO-EN © Crown copyright 2007 • Use a calculator to solve problems involving multi-step calculations Three pupils answered different questions. This is what each pupil’s calculator showed: Emma saves £3.50 each week. How much has she saved after 16 weeks? Y5 optional test Paper B level 4 Asim’s question was about money. Complete the sentence: Sima thinks of a number. She divides it by 12. Her answer is 26. What is the number Sima thinks of? 3.5 means £3 and ……pence. KS2 1998 Paper B level 5 Ben’s question was about time. Complete the sentence: Nicola has £50. She buys 3 flowerpots at £12.75 each and a spade at £9.65. How much money does she have left? 3.5 means 3 hours and …… minutes. Charlie’s question was about length. Complete the sentence: 3.5 means 3 metres and …… centimetres. Seeds are £1.45 for a packet. Steffan has £10 to spend on seeds. What is the greatest number of packets he can buy? Y7 progress test Paper B level 4 KS2 1999 Paper B level 5 Here is a picture of three people. Mrs Jones prints books. Jon pays £4.35 for his book, including the cover. How many pages are in his book? KS2 1996 Paper B level 5 Lisa’s height is half-way between Julie’s height and Tom’s height. Calculate Lisa’s height. KS2 1998 Paper B level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 15 00028-2007CDO-EN © Crown copyright 2007 Understanding shape • Describe, identify and visualise parallel and perpendicular edges or faces; use these properties to classify 2-D shapes and 3-D solids These two shaded triangles are each inside a regular hexagon. Under each hexagon, put a ring around the correct name of the shaded triangle. Imagine a triangular prism. How many faces does it have? KS2 1999 Mental test level 4 Imagine a cube. How many vertices does it have? KS2 2000 Mental test level 4 Here are five shapes on a square grid. equilateral equilateral isosceles isosceles scalene scalene A B KS2 2001 Paper B level 4 C Here are six triangles. One of them is an equilateral triangle. Put a tick () in the equilateral triangle. D E Write in the missing letters. Shape has two pairs of parallel sides. Shape is a pentagon. Shape has reflective symmetry. Write one property which makes equilateral triangles different from all other triangles. KS2 1999 Paper B level 4 KS2 1998 Paper A level 4 Here is a shape on a square grid. These diagrams show the diagonals of three quadrilaterals. Write the names of the quadrilaterals in the boxes. A D C B For each sentence, put a tick () if it is true. Put a cross () if it is not true. Angle C is an obtuse angle. Angle D is an acute angle. Line AD is parallel to line BC. Line AB is perpendicular to line AD. KS2 2000 Paper B level 5 KS2 2003 Paper A level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 16 00028-2007CDO-EN © Crown copyright 2007 • Make and draw shapes with increasing accuracy and apply knowledge of their properties Draw two straight lines from point A to divide the shaded shape into a square and two triangles. Here is the net of a cube with no top. The shaded square shows the bottom of the cube. Draw an extra square to make the net of a cube which does have a top. A KS2 2003 Paper B level 4 KS2 2003 Paper B level 4 Here are five shapes on a square grid. A cube has shaded triangles on three of its faces. B A C E Here is the net of the cube. Draw in the two missing shaded triangles. D Which two shapes fit together to make a square? KS2 2001 Paper B level 4 Here are some shaded shapes on a grid. A B C KS2 2002 Paper B level 5 On the grid below, use a ruler to draw a pentagon that has three right angles. D E F Which three shapes have reflective symmetry? KS2 2000 Paper A level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy KS2 1998 Paper B level 5 17 00028-2007CDO-EN © Crown copyright 2007 • Visualise and draw on grids of different types where a shape will be after reflection, after translations, or after rotation through 90° or 180° about its centre or one of its vertices Kyle has drawn triangle ABC on this grid. Here is a shaded shape on a grid. The shape is rotated 90° clockwise about point A. Draw the shape in its new position on the grid. You may use tracing paper. A KS2 2000 Paper B level 4 The rectangle is rotated 90° clockwise about point A. Draw the rectangle in its new position. You may use tracing paper. Holly has started to draw an identical triangle DEF. What will be the coordinates of point F? Y5 optional test 2003 Paper B level 4 Draw the reflection of this shape. A Y5 optional test 1998 Paper B level 4 This pattern is made by turning a shape clockwise through 90° each time. Draw the two missing triangles on the last shape. Y3 optional test 2003 Paper B level 4 KS2 2005 Paper B level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 18 00028-2007CDO-EN © Crown copyright 2007 • Use coordinates in the first quadrant to draw, locate and complete shapes that meet given properties The diagram shows two identical squares. Here is a graph. y B (6,3) (4,2) A 0 x A is the point (10,10). What are the coordinates of B and C? The dots on the line are equally spaced. What are the coordinates of the point A? KS2 2005 Paper B level 4 Megan says, ‘The point B has coordinates (11,5).’ Use the graph to explain why she cannot be correct. KS2 1997 Paper B level 4 Here is a pentagon drawn on a coordinate grid. The pentagon is symmetrical. y B (7,10) A C (4,9) A, B and C are three corners of a rectangle. What are the coordinates of the fourth corner? E (2,0) (12,0) D 0 x Y4 optional test 2003 Paper B level 4 What are the coordinates of point C? KS2 2003 Paper A level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 19 00028-2007CDO-EN © Crown copyright 2007 • Estimate angles, and use a protractor to measure and draw them, on their own and in shapes; calculate angles in a triangle or around a point Look at the triangle. Angle x is fifty-five degrees. Calculate the size of angle y. x x y KS2 2001 Mental test level 5 Measure angle x accurately. Use a protractor (angle measurer). Two of the angles in a triangle are sixty degrees and seventy degrees. What is the size of the third angle? KS2 2004 Paper B level 5 KS3 2005 Mental test level 5 Complete the drawing below to show an angle of 157°. Label the angle 157°. A pupil measured the angles in a triangle. She said: ‘The angles are 30°, 60° and 100°.’ Could she be correct? Tick () Yes or No. Explain your answer. ______________ KS3 2004 Paper A level 5 KS3 2000 Paper A level 5 What is the angle between the hands of a clock at four o ’clock? Look at these angles. KS2 2003 Mental test level 5 This diagram is not drawn accurately. Calculate the size of angle m angle P angle Q angle R angle S angle T One of the angles measures 30°. Write its letter. KS3 2000 Paper A level 5 70º Look at the angle. m Put a ring around the number which is the approximate size of the angle. 60° 90° 110° 135° 70º KS3 2004 Paper A level 5 240° KS2 2000 Mental test level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 20 00028-2007CDO-EN © Crown copyright 2007 Measuring • 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 How many millilitres are there in three-quarters of a litre? Look at the diagram. It shows how to change metres into centimetres and millimetres. Y4 optional test 2003 Mental test level 4 ×100 Change sixty millimetres to centimetres. number of metres ×10 number of centimetres number of millimetres KS3 2001 Mental test level 4 ×1000 A table is two hundred centimetres long. How many metres is that? Change 5 metres into centimetres. Change 9 centimetres into millimetres. KS3 1999 Mental test level 4 Change 8000 millimetres into metres. This table shows the weight of some fruits and vegetables. Complete the table. potatoes grams kilograms 3500 3.5 A bottle holds 1 litre of lemonade. Rachel fills 5 glasses with lemonade. 3 She puts 150 in each glass. 2 millilitres 4 How much is left in the bottle? 1 lemonade 5 6 KS2 2003 0Paper kg A level 4 1.2 apples grapes Y7 progress test 2003 level 4 Put a ring round the number which is the approximate weight of a thirty-centimetre plastic ruler. 250 ginger 0.03 2g Primary National Strategy 200 g 2 kg 20 kg KS2 2001 Mental test level 5 KS2 2002 Paper A level 4 [adapted] Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 20 g 21 00028-2007CDO-EN © Crown copyright 2007 • 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 Here are a pencil sharpener, a key and a rubber. The diagrams in this question are not drawn accurately. The diagram shows Jo’s key. Actual size Use the scale to find the length of Jo’s key. 0 This time you cannot see all of Jo’s key. 1 2 3 4 5 6 7 8 9 cm What is the length of all three things together? Give your answer in millimetres. What is the length of the key? Give your answer in millimetres. KS2 2002 Paper A level 4 One end is at 2.8cm on the scale. Where is the other end on the scale? This scale shows the weight of Fred’s cat. Y7 progress test 2005 level 4 All the water in these two containers is to be poured into the empty container below. 5kg 4kg 500 ml 500 ml What is the weight of Fred’s cat? 400 ml 400 ml This scale shows the weight of Fred’s dog. 300 ml 300 ml 200 ml 200 ml 100 ml 100 ml 6kg 5kg Draw where the water level will be in the container. How much more does Fred’s dog weigh than his cat? 1 litre KS2 2004 Paper B level 4 On this scale, the arrow (↑) shows the weight of a pineapple. 1/2 litre 0 1 2 Y4 optional test Paper B level 4 kg The diagram shows the volume of water in two measuring jugs. Here is a different scale. 500 Mark with an arrow (↑) the weight of the same pineapple. 400 300 0 1 2 3 4 1000 200 kg 500 0 100 ml Jug A 0 KS2 2001 Paper B level 4 ml Jug B Which jug contains more water? Tick () A or B. How much more does it contain? 2003 Y7 progress test Paper B level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 22 00028-2007CDO-EN © Crown copyright 2007 • Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by counting squares Calculate the perimeter of a rectangle which is eleven metres long and four metres wide. Millie has some star-shaped tiles. Each edge of a tile is 5 centimetres long. KS2 2003 Mental test level4 5 cm Not actual size 2 The area of a rectangle is 16 cm . One of the sides is 2 cm long. What is the perimeter of the rectangle? She puts two tiles together to make this shape. Y4 optional test 1999 Paper B level 4 Here are some shapes drawn on a grid. Work out the perimeter of Millie’s shape. KS2 2004 Paper A level 4 Lauren has three small equilateral triangles and one large equilateral triangle. The small triangles have sides of 7 centimetres. Lauren makes this shape. 7 cm Write the letters of the two shapes that are equal in area. Y4 optional test 2003 Paper B level 4 Here is a 1cm square grid. Some of the grid is shaded. Not actual size Calculate the perimeter of the shape. KS2 2001 Paper B level 4 Liam has two rectangular tiles like this. 11cm What is the area that is shaded? 5cm KS2 2005 Paper B level 4 He makes this L shape. Here is a map of an island. Church What is the perimeter of Liam’s L shape? Cave KS2 2000 Paper A level 5 Wood What is the area of this shape? 4cm Lighthouse Not to scale Estimate the area of the Wood. 10cm KS2 1995 Paper B level 4 7cm 10cm KS2 2002 Paper B level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 23 00028-2007CDO-EN © Crown copyright 2007 Handling data • Describe and predict outcomes from data using the language of chance or likelihood Shade this spinner so that there is a 50% chance that the arrow will land on shaded. Here are two spinners, A and B. Each one is a regular hexagon. 1 2 3 2 1 1 1 3 2 A Y7 progress test Paper A level 4 Here is a spinner which is a regular octagon. Write 1, 2 or 3 in each section of the spinner so that 1 and 2 are equally likely to come up and 3 is the least likely to come up. B For each statement, put a tick () if it is true. Put a cross () if it is not true. Scoring ‘1’ is more likely on A than on B. Scoring ‘2’ is more likely on A than on B. Scoring ‘3’ is as equally likely on A as on B. Zara spins both spinners. The score on A is added to the score on B. She says, ’The sum of the scores on both spinners is certain to be less than 7’ . Is she correct? Circle Yes or No. Explain how you know. KS2 2001 Paper A level 4 KS2 2005 Paper B level 4 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 24 00028-2007CDO-EN © Crown copyright 2007 • Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw conclusions and identify further questions to ask Table and pie chart of favourite boy bands Table and pie chart of favourite sport of Year 6 girls, produced in Microsoft Excel http://www.standards.dfes.gov.uk/primary/teachingr esources/mathematics/nns_itps/data_handling/ Table and conversion graph for euros to pounds, produced in Microsoft Excel Table, dual bar chart and stacked bar chart showing favourite colours of two Year 6 classes, produced in MicrosoftExcel Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 25 00028-2007CDO-EN © Crown copyright 2007 • Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs; interpret pie charts A school has a quiz each year. There are two teams. Here are their results. North The pie chart shows information about children who go to a nursery school. South 300 250 two years old four years old 200 Points three years old 150 100 50 0 1999 2000 2001 Year 2002 Altogether, 80 children go to the nursery school. How many of the 80 children are two years old? 2003 How many of the 80 children are four years old? In which year did North beat South by 100 points? Y7 progress test Paper A level 4 In which year did South beat North by the greatest amount? This graph shows the cost of phone calls in the daytime and in the evening. KS2 2004 Paper B level 4 60p Some children do a sponsored walk. The graph shows their results. da 50p e ytim 40p Cost of call 30p 20p evening 10p 0p 0 2 4 6 8 10 12 Length of call in minutes How much does it cost to make a 9 minute call in the daytime? How much more does it cost to make a 6 minute call in the daytime than in the evening? KS2 2002 Paper A level 4 How many children walked 21 laps or more? Y5 optional test 2003 Paper A level 4 • Describe and interpret results and solutions to problems using the mode, range, median and mean These are the marks from a spelling test. Jay Karen Dominic Tariq Lara Oliver Gemma Rob runs 100 metres ten times. These are his times in seconds. 16 13 18 13 12 14 19 13.4 13.5 13.0 14.0 13.9 14.4 13.7 13.8 13.3 14.0 What is his mean (average) time? KS2 1995 level 5 Write a different number in each of these boxes so that the mean of the three numbers is 9. What is the median number of marks? Y5 optional test Paper B level 4 Write a number in each of these boxes so that the mode of the five numbers is 11. KS2 1997 Paper A level 5 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 26 00028-2007CDO-EN © Crown copyright 2007 Helping children to achieve age-related expectations: securing Level 4 by the end of Key Stage 2 Primary National Strategy 27 00028-2007CDO-EN © Crown copyright 2007