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FS Calculating • Begin to relate addition to combining two groups of objects and subtraction to ‘taking away’ There are four cups on the table. [Count 5 pennies into a purse and shut it. Put two more cups on the table. Show 2 more pennies in your hand.] How many cups altogether are on the table now? How many pennies are there altogether? There are nine biscuits on this plate. We have four easels. Take three of the biscuits to eat. There are seven children who want to paint. How many biscuits are left on the plate? How many more easels do we need? • In practical activities and discussion begin to use the vocabulary involved in adding and subtracting One, two, three, … What goes next? There are six toys in a box. I take away three of the toys. Hop three spaces on this number track. Now hop How many toys are left in the box? two more. Where are you now? Start with two. Hold it in your head. Count on to five. How many grey rabbits are there? How many white rabbits are there? I have two toys in a box. How many rabbits are there altogether? I add four more toys to the box. How many toys are there in the box now? Find all the dominoes that have a total of six spots. Count 5 small toys into this cloth bag. How many objects in the bag? Now count 2 more small toys into the bag. How many small toys in the bag now? What is the difference between the number of grey rabbits and the number of white rabbits? Show me 5 fingers on one hand. Show me 2 fingers on the other hand. How many fingers altogether? Here are five toy cars. How many more cars are needed to make a set of I have hidden two cubes in this box. There are three eight cars? cubes on the table. How many cubes are there altogether? John has four books. Lisa has one book. How many more books has John than Lisa? Y1 Calculating • Understand subtraction as ‘take away’ and find a ‘difference’ by counting up; use practical and informal written methods to support the subtraction of a one-digit number from a one- or two-digit number and a multiple of 10 from a two-digit number I'm giving each of you two number cards [from 0 to What is the difference between twelve and sixteen? 5]. KS1 1998 level 2b [oral] What is the difference between your two numbers? KS1 1999 level 1 [oral, adapted] What is left if five is subtracted from twelve? Y4 optional test Mental test level 2 15 ducks are on the pond. 11 of them go away. How many are left? What is forty-eight subtract ten? [oral question] What is thirty-two subtract five? KS1 1999 level 2c [oral question] Find the answer. 72 – 8 = KS1 1999 level 2c Write the answer. 65 – 40 = KS1 1998 level 2c [adapted] Work out the difference between 80 and 20. Show how you worked it out in the box. KS1 2000 level 2a [adapted] • Use the vocabulary related to addition and subtraction and symbols to describe and record addition and subtraction number sentences Write the total. 7+3+8+2= KS1 2004 level 2c Write the answer. 25 – 12 = KS1 2005 level 2c Buy 2 different comics and spend 16p. Tick the 2 Match each subtraction to its answer. comics. 16 – 6 8 Write an addition to show what you did. KS1 1999 level 1 [oral] 9 15 – 10 13 Look at the numbers. 19 – 11 15 7 16 8 10 Use two of these numbers to make this correct. 18 – 9 5 –=7 KS1 1999 level 2c KS1 2004 level 2c Put a number in the box to make this correct. Write a number in the box to make this correct. 3 + + 9 = 17 16 – = 10 KS1 1998 level 2b KS1 2000 level 2c Write numbers in the shapes to add to 12. + = 12 KS1 1996 level 2c Y2 Calculating • Add or subtract mentally a single-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers Write the answers. Write the total. 5 + 10 = 61 + 11 = 15 + 10 = KS1 2004 level 3 25 + 10 = KS1 2001 level 2c Write the total. 36 + 29 = Write the total. KS1 2002 level 2a 35 + 40 = KS1 1998 level 2c Write the answer 79 – 34 = Find the answer. KS1 1996 level 2a 72 – 8 = KS1 1999 level 2c Write the answer. 82 – 45 = Write the total. KS1 2004 level 3 58 + 9 = KS1 2000 level 2c Write the answer. 63 – 37 = Write the answer. KS1 2002 level 3 30 – 15 = KS1 2003 level 2b Write the number which is 11 less than 40. KS1 2004 level 2a Write the answer 25 + 10 + 9 = Work out the difference between 46 and 18. KS1 1997 level 2a KS1 2000 level 3 Tick () the two numbers which total 50. Write the answer. 150 + 56 = 24 15 KS1 2005 level 3 38 26 What is twenty-seven subtract nine? 19 Y3 optional test 2003 Mental test level 3 KS1 2002 level 2a • Use the symbols +, –, ×, ÷ and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence, e.g. ÷ 2 = 6, 30 – = 24, Write four different numbers to make these correct. Write the same number in each triangle to make the multiplication correct. + = 17 × = 100 + = 17 KS1 2004 level 2b [oral] KS1 2003 level 2c Write the missing number in the box. Write numbers in the boxes to make this correct. 5 × 4 = 10 × 13 + + = 23 KS1 2002 level 3 KS1 2005 level 2c Write the missing number in the box. Look at these signs. ÷2=7 + × – = KS1 2001 level 2a Use one of the signs to make this correct. 9 2 = 11 Put a number in the box to make this correct. Now use the signs to make this one correct. 100 = + 42 14 2 12 KS1 1998 level 3 KS1 1997 level 2c Y3 Calculating • Add or subtract mentally combinations of one- and two-digit numbers What is twenty-seven subtract nine? Each side of this square must add up to 80. Y5 optional test 2003 Mental test level 3 Write in the missing numbers. 30 40 Add thirty-six and seventy. KS2 2002 Mental test level 3 50 What is twenty-six more than fifty? 20 40 20 KS2 1998 Mental test level 3 KS2 1998 Paper A level 3 Subtract thirty-two from seventy. This is a number triangle with some numbers KS2 2004 Mental test level 3 missing. The numbers along each edge must add up to 90. The difference between a number and twenty-nine Put all the numbers 20, 30, 50 and 60 in the circles is ten. What could the number be? to make the totals correct. KS2 1998 Mental test level 3 10 What is the sum of twenty-three and twenty-seven? KS2 2000 Mental test level 3 40 In a large fish tank there are twenty-one red fish and KS2 1995 Paper A level 3 nine blue fish. How many fish are there altogether? Y3 optional test 1998 Mental test level 3 This table shows the increase in bus fares. Bus fares In a class there are thirty-two children. If there are old fare new fare twenty-three girls, how many boys are there? 42p 48p Y4 optional test 1998 Mental test level 3 52p 57p 60p 72p In a class of thirty-two children, fourteen walked to 75p 85p school and the rest came by bus. How many came by bus? 90p £1.05 £1.20 £1.28 Y4 optional test 1999 Mental test level 3 Sohan’s new bus fare is 72p. How much has his bus fare gone up? Millie says, ‘My bus fare has gone up by 10p’. How much is Millie’s new bus fare? KS2 2001 Paper A level 3 • Develop and use written methods to record, support or explain addition and subtraction of two- and three-digit numbers Add together 24, 67 and 45. Work out the difference between 147 and 205. KS1 2001 level 2a Write the answer in the box. Write in the missing numbers. KS1 2005 level 3 + 79 = 91 60 – = 26 Write the total. KS2 1996 Paper A level 3 256 + 172 = KS1 2001 level 3 Write the total. . 156 + 83 = Calculate 309 –198. KS1 2004 level 3 KS2 2003 Paper A level 3 Write the answer. Write the answer. 176 – 49 = 1000 – 143 = KS1 2003 level 3 KS1 2004 level 3 Write in the missing number. Write the missing number in the box. + 85 = 200 456 + = 710 120 – 51 = KS1 2003 level 3 KS2 2004 Paper A level 3 Y4 Calculating • Add or subtract mentally pairs of two-digit whole numbers, e.g. 47 + 58, 91 – 35 Add seventeen and fourteen. Jenny thought of a number. Y3 optional test 1998 Mental test level 3 She doubled it and then added four. The answer was eighty-eight. Which number did she think of? How many less than forty-one is seventeen? KS2 2002 Mental test level 4 Y4 optional test 2003 Mental test level 3 Add together thirteen, forty-seven and twenty-one. Add together twenty-three and forty-eight. Y5 optional test 2003 Mental test level 3 KS2 2005 Mental test level 3 Add together twenty-three, thirty-three and forty- What number is thirty-four more than fifty-eight? three. KS2 2003 Mental test level 3 KS2 2004 Mental test level 3 How many less than forty-one is seventeen? Add together fifty-three, fifty-five and fifty-seven. Y4 optional test 2003 Mental test level 3 KS2 2002 Mental test level 3 An apple costs eighteen pence, and an orange Add together fourteen, twenty-three and forty-one. costs nineteen pence. How much are they KS2 2001 Mental test level 3 altogether? KS2 1998 Mental test level 3 Add together thirty-eight, twenty-three and forty- four. In a bag there are eighty-one red counters and KS2 1999 Mental test level 3 thirty-seven yellow counters. How many counters are there altogether? Subtract one hundred and five from two hundred. Y5 optional test 1998 Mental test level 3 KS2 2004 Mental test level 3 Emma is 21 years old today. Her father is 24 years Calculate the difference between five hundred and older. How old is Emma’s father? two hundred and thirty. KS1 2005 level 3 [oral] KS2 2000 Mental test level 4 • Refine and use efficient written methods to add and subtract two- and three-digit whole numbers and £.p Calculate 584 + 79. These are the prices of sandwiches, drinks and fruit. Y5 optional test 2003 Paper A level 3 Sandwiches Drinks Fruit Calculate 137 – 65. ham £1.45 milk 55p apple 15p Y5 optional test 2003 Paper A level 3 tuna £1.70 cola 45p pear 20p salad £1.20 juice 65p melon 25p Calculate 369 + 251. KS2 2000 Paper A level 3 Shereen buys a tuna sandwich, milk and a pear. How much does she pay? Calculate 309 –198. Mike has 80p to spend on a fruit and a drink. What KS2 2003 Paper A level 3 two things can he buy for exactly 80p? KS2 2004 Paper A level 3 Calculate 438 – 296. KS2 1999 Paper A level 4 Write in the missing digits. 1 7 + 6 = 200 Calculate 808 – 512. Y4 optional test 2003 Paper A level 3 KS2 1998 Paper A level 4 Write what the two missing digits could be. A shop sells three types of sunglasses. 62 + 95 = 757 KS2 1997 Paper A level 4 What is the difference in price between the most expensive and least expensive sunglasses? KS2 2004 Paper A level 4 Y5 Calculating • Extend mental methods for whole-number calculations, e.g. to multiply a two-digit by one-digit number (e.g. 12 × 9), to multiply by 25 (e.g. 16 × 25), to subtract one near multiple of 1000 from another (e.g. 6070 – 4097) What number is two less than nine hundred and What is one thousand minus one hundred and ten? one? KS2 2004 Mental test level 3 Y4 optional test 2003 Mental test level 3 What is three thousand subtract ten? What number is one hundred and ninety-nine more Y5 optional test 1998 Mental test level 3 than four hundred and twenty-eight. Y5 optional test 2003 Mental test level 4 What is the difference between one thousand nine hundred and ninety-four and four thousand and One orange costs nineteen pence. How much will three? three oranges cost? Y5 optional test 2003 Mental test level 4 Y4 optional test 2003 Mental test level 3 What is one thousand, two hundred and ninety-nine One orange costs fifteen pence. How much would add one? five oranges cost? Y5 optional test 1999 Mental test level 4 Y4 optional test 1998 Mental test level 4 What is twenty-five multiplied by eight? An apple costs seventeen pence. How much will Y4 optional test 1998 Mental test level 4 three cost? Y4 optional test 1999 Mental test level 4 What is twelve multiplied by twenty-five? KS2 2001 Mental test level 4 A fruit pie costs fifty-five pence. What is the cost of three fruit pies? KS2 2004 Mental test level 4 4 pineapples cost £3.40. Calculate the cost of 1 pineapple. Y4 optional test 2003 Paper A level 4 What is twenty-one multiplied by nine? KS2 2000 Mental test level 4 • Use efficient written methods to add and subtract whole numbers and decimals with up to two places Calculate 1025 – 336. Write what the two missing digits could be. KS2 2001 Paper A level 4 62 + 95 = 757 KS2 1997 Paper A level 4 Calculate 1202 + 45 + 367. KS2 2005 Paper A level 4 Calculate 13.6 – 2.8 KS2 2004 Paper A level 4 Calculate 6247 – 2752. Y5 optional test 2003 Paper A level 4 A shop sells sun hats. Here is the cost of pizzas. PIZZAS Small Medium Ham £4.20 £5.50 Salami £4.40 £5.75 Mushroom £4.50 £6.00 Ryan buys some sunglasses for £4.69 and a sun Cheese £3.80 £4.95 hat. How much change does he get from £10? Tuna £4.25 £5.40 KS2 2004 Paper A level 4 Extra tomato 50p Extra cheese 60p Jill orders one small cheese pizza with extra tomato. What is the total cost? Ben buys one small pizza and one medium pizza. They cost him £10. Which two could they be? KS2 1996 Paper A level 3 Y6 Calculating • Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U What is the sum of eight point five and eight point What number is halfway between thirty and eighty? 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 Circle two numbers which add to make 0.12. and nought point six. 0.1 0.5 0.05 0.7 0.07 0.2 KS2 2005 Mental test level 4 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 In a café I buy two cups of coffee and a sandwich. KS2 1999 Paper A level 5 Altogether I pay three pounds. The first two numbers in this sequence are 2.1 and The sandwich costs one pound sixty. 2.2. The sequence then follows the rule ‘to get the What is the cost of one cup of coffee? 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. 2.1 2.2 4.3 6.5 Josh buys three packets. How much change does KS2 2003 Paper A level 4 he get from one pound? 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 • 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- 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 Write in the missing digit. number. 7 × 9 = 333 KS2 1996 Paper A level 4 2.46 8.61 7.38 Write in the missing digit. 11.07 1.23 5 × 8 = 456 4.92 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. Calculate 123 ÷ 5. The trays are packed in boxes. Each box contains 180 eggs. Calculate 16.5 ÷ 3. How many trays are in each box? KS2 1999 Paper A level 4 Calculate 27.6 ÷ 8. Some children go camping. Shenaz buys a pack of 24 cans of cola for £6.00 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? There are 70 children. Each tent takes up to 6 children. What is the least number of tents they will need? KS2 1998 Paper A level 4 What is the cost of each can? KS2 1998 Paper A level 5 Y6 progression to Y7 Calculating • Understand how the commutative, associative and distributive laws, and the relationships between operations, including inverse operations, can be used to calculate more efficiently; use the order of operations, including brackets Write the correct sign >, < or = in each of the Leila knows that following. 65 × 3 = 195 (10 + 5) – 9 (10 + 9) – 5 Explain how she can use this information to find the 3 × (4 + 5) (3 × 4) + 5 answer to this multiplication: 165 × 3 (10 × 4) ÷ 2 10 × (4 ÷ 2) KS2 2000 Paper A level 5 KS2 2005 Paper A level 4 Kim knows that Calculate 900 ÷ (45 × 4). 137 × 28 = 3836 KS2 2004 Paper A level 5 Explain how she can use this information to work Put a tick () in the correct box for each calculation. out this multiplication. Use a calculator. 138 × 28 less than equal to more than KS2 1997 Paper A level 5 1000 1000 1000 8.9 × 9.9 × 11.9 Liam thinks of a number. He multiplies the number by 5 and then subtracts 60 from the result. (786 – 387) ÷ 0.41 His answer equals the number he started with. 95.4 + (91 × 9.95) What was the number Liam started with? 12.5 × (21.1 + 58.9) KS2 2004 Paper A level 5 KS2 2000 Paper B level 5 • Consolidate and extend mental methods of calculation to include decimals, fractions and percentages What is fifteen multiplied by eleven? What is one point three multiplied by four? KS2 2003 Mental test level 4 KS2 2004 Mental test level 5 What is eighteen multiplied by nine? Multiply eight point seven by two. KS3 2005 Mental test level 5 KS3 2004 Mental test level 5 Multiply thirty-nine by seven. Divide thirty-one point five by ten. KS2 2005 Mental test level 5 Y5 optional test 2003 Mental test level 5 What is twenty-five multiplied by two hundred? What is seven point five divided by one hundred? KS2 2002 Mental test level 5 KS2 2004 Mental test level 5 A rectangle measures eleven centimetres by twenty Ten times a number is eighty-six. What is the centimetres. What is its area? number? KS2 2004 Mental test level 5 KS2 2002 Mental test level 5 Calculate ten minus four point three five. What is nought point two six divided by ten? KS2 2001 Mental test level 5 KS2 2001 Mental test level 5 Subtract nought point seven five from six. A tile is nought point two metres long. KS3 2003 Mental test level 4 One hundred tiles are placed end to end in a row. How long is the row? What is one and a half added to four and a half? Y5 optional test 1998 Mental test level 5 KS2 2000 Mental test level 3 What is half of six point three? What is one-half added to three-quarters? KS3 2001 Mental test level 5 KS2 2003 Mental test level 4 What is three point nine divided by two? What is two thirds of sixty-six? KS3 2003 Mental test level 6 KS2 2004 Mental test level 5 What is fifty per cent of twenty pounds? KS3 2003 Mental test level 4 What is three-quarters of five hundred? KS2 2003 Mental test level 5 What is two percent of three hundred? KS2 2000 Mental test level 5 Three-quarters of a number is 48. What is the number? What is ninety-nine per cent of two hundred? KS2 2003 Mental test level 5 KS2 2002 Mental test level 5 What is three-fifths of forty pounds? What is twenty per cent of sixty pounds? KS3 2003 Mental test level 5 KS3 2005 Mental test level 5 Tariq won one hundred pounds in a maths Increase one pound fifty by fifty per cent. competition. He gave two-fifths of his prize money KS3 2004 Mental test level 5 to charity. How much of his prize money, in pounds, did he have left? KS3 2004 Mental test level 5

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