MEP NUMERACY SUMMER SCHOOL HOMEWORK BOOK NAME
CONTENTS NUMERACY SUMMER SCHOOL HOMEWORK... 2 RECORD OF HOMEWORK... 3 RECORD OF EXTRA WORK... 5 PLACE VALUE... 7 ADDING AND SUBTRACTING IN YOUR HEAD... 9 MULTIPLYING AND DIVIDING IN YOUR HEAD... 12 MULTIPLYING BY MULTIPLES OF 10... 13 DIVIDING BY MULTIPLES OF 10... 14 ADDITION... 16 SUBTRACTION... 17 MULTIPLICATION... 18 DIVISION... 19 PERCENTAGES AND DECIMALS... 20 FRACTIONS, DECIMALS AND PERCENTAGES... 21 USING FRACTIONS AND PERCENTAGES... 22 TIME... 23 ADDITION CROSSNUMBER PUZZLE... 29 NUMERACY WORD SEARCH... 27 MAGIC SQUARES... 28 WALLS... 29 TRIANGLES... 30 CIMT, University of Exeter
NUMERACY SUMMER SCHOOL HOMEWORK The aim of the activities in this book is to help you to improve your numeracy skills. You must not use a calculator for any of the activities. Try to find a quiet place to work and sit at a table so that you can do your best work. Do your homework early in the evening so that you are not too tired to do your work well. If you are having problems, try to find an adult who can help you. Your homework should take about thirty minutes. If it is taking a lot longer than that, leave it and tell your teacher the next day. Do not worry if you find the work difficult. Do the best you can then leave it and ask your teacher for help the next day. The pages at the front of this book are exercises which will be set by the teacher. You will be told when to do these activities. The pages at the back are extra tasks that you can do at any time if you want to. Fill in the record sheet for each piece of homework you do. Sign it and ask a parent to sign it. You can also make a comment if you want to. CIMT, University of Exeter 2
RECORD OF HOMEWORK CIMT, University of Exeter 3
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RECORD OF EXTRA WORK CIMT, University of Exeter 5
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PLACE VALUE A. Write each of the following numbers in words. 1. 2 364..... 2. 3 045........ 3. 1 999........ 4. 74 306......... 5. 84 293......... B. Write each of the following numbers in figures. 1. Three thousand two hundred and forty one.... 2. One thousand four hundred and fifteen.. 3. Eight thousand and fifty six... 4. Twenty five thousand seven hundred and ninety five.... 5. Seventeen thousand and three... C. Fill in the numbers in the boxes. 1. 6 831 = 6 000 + + 30 + 1 2. 5 172 = + 100 + + 2 3. 2 987 = + + + 4. 83 416 = 80 000 + 3 000 + + 10 + 5. 56 823 = + 6 000 + + 20 + CIMT, University of Exeter 7
D. Fill in the numbers in the boxes. 1. 6 830 = 4 830 + 2. 9 152 = + 9 112 3. 7 654 = 9 654 4. 8 930 = 1 000 5. 12 345 = 9 345 + E. Round each of the numbers in the first column. The first one has been done for you. Number To the nearest 10 To the nearest 100 To the nearest 1 000 1 5 326 5 330 5 300 5 000 2 8 764 3 6 058 4 8 475 5 14 362 F. Write these numbers in order starting with the smallest. 1. 3 642, 3 624, 6 243, 4 623, 3 426... 2. 6 032, 6 320, 6 230, 6 302, 6 203... 3. 6.28, 6.54, 8.37, 7.56, 9.00... 4. 8.325, 8.3, 8.35, 8. 53, 8.352... 5. 0, -12, -16, -3, -10... CIMT, University of Exeter 8
ADDING AND SUBTRACTING IN YOUR HEAD A Fill in the missing numbers. 1. 3 + 7 + 8 + 4 = 2. 6 + 9 + 5 + 2 = 3. 8 + 5 + 7 + 9 = 4. 4 + 14 + 6 + 9 = 5. 11 + 13 + 15 + 6 = 6. 3 + 8 + 5 + = 23 7. 6 + 9 + 4 + = 26 8. 9 + 8 + + 7 = 31 9. 12 + 16 + 9 + = 48 10. 14 + 9 + + 19 = 52 Adding 19 is the same as adding 20 then subtracting 1. e.g. 27 + 19 = 27 + 20-1 = 46 Subtracting 49 is the same as subtracting 50 then adding 1. e.g. 83-49 = 83-50 + 1 = 34 B Copy and complete the following: 1. Adding 29 is the same as.. 46 + 29 = = 2. Subtracting 69 is the same as.. 93-69 = = 3. Adding 38 is the same as 27 + 38 = = 4. Subtracting 28 is the same as.. 83-28 = = CIMT, University of Exeter 9
Adding 41 is the same as adding 40 then adding 1 e.g. 146 + 41 = 146 + 40 + 1 = 187 Subtracting 51 is the same as subtracting 50 then subtracting 1. e.g. 273-51 = 273-50 - 1 = 222 C Copy and complete the following: 1. Adding 61 is the same as.. 123 + 61 = = 2. Subtracting 31 is the same as.. 269-31 = = 3. Adding 68 is the same as 325 + 68 = = 4. Subtracting 58 is the same as.. 297-58 = = It is often easiest to add two numbers that are close together by doubling a number and then adding or subtracting something. e.g. 45 + 46 = 2 x 45 + 1 = 91 39 + 42 = 2 x 40-1 + 2 = 81 D Copy and complete the following: 1. 82 + 83 =. 2. 78 + 79 =. 3. 62 + 59 =. CIMT, University of Exeter 10
E Fill in the missing numbers. The first one has been done for you. 1. + 6 9 2. + 8 7 3. + 12 6 3 9 12 4 5 7 13 16 6 9 4. + 5 5. + 3 7 6. + 7 4 6 9 12 8 8 6 14 7. + 10 6 8. + 12 14 9. + 24 8 15 23 9 14 7 26 10. + 19 29 11. + 35 32 12. + 27 23 39 18 30 46 69 43 13. + 41 32 14. + 21 52 15. + 26 32 27 37 24 36 48 31 16. + 38 17. + 49 18. + 68 29 38 54 99 41 83 83 37 86 CIMT, University of Exeter 11
MULTIPLYING AND DIVIDING IN YOUR HEAD A Complete the following tables. 1. x 2 4 6 2. x 6 5 9 1 9 42 56 10 15 3 30 4 24 32 12 20 45 7 21 12 30 8 80 18 3. x 9 2 5 4. x 21 81 45 49 8 64 6 12 42 4 63 35 36 9 27 72 25 B. Continue these doubling and halving patterns. 1. 1 2 4 2. 3 6 12 3. 7 14 28 4. 2560 1280 640 5. 4608 2304 1152 CIMT, University of Exeter 12
MULTIPLYING BY MULTIPLES OF 10 When we multiply by 10 all of the digits in a number move one place to the left. When we multiply by 100 all of the digits in a number move two places to the left. 46 x 10 = 460 3.25 x 10 = 32.5 645 x 100 = 64 500 H T U T U. t h TTh Th H T U 4 6 3. 2 5 6 4 5 4 6 0 3 2. 5 6 4 5 0 0 Empty spaces in columns that come before the decimal point need to be filled with 0 s. Empty spaces in columns that come after the decimal point should be left empty. A. Fill in the answers to these multiplications. It might help you to write the numbers in columns like the examples. You can do this on Page 14 if you want to. 1. 45 x 10 = 2. 684 x 10 = 3. 1 562 x 10 =... 4. 6.48 x 10 = 5. 32.543 x 10 = 6. 156 x 100 = 7. 2 314 x 100 = 8. 16.35 x 100 = 9. 14. 3 x 100 = 10. 153.241 x 100 = 11. 46 x 1 000 = 12. 43.27 x 1 000 = 13. 178 x 10 000 = 14. 271 x 100 000 = Multiplying by 20 is like multiplying by 2 then multiplying by 10 e.g. 36 x 20 = 36 x 2 x 10 = 72 x 10 = 720 B. Fill in the answers to these multiplications. 1. 32 x 20 = 2. 17 x 20 = 3. 46 x 200 = 4. 15 x 30 = 5. 32 x 40 = 6. 21 x 500 = CIMT, University of Exeter 13
DIVIDING BY MULTIPLES OF 10 When we divide by 10 all of the digits in a number move one place to the right. When we divide by 100 all of the digits in a number move two places to the right. 460 10 = 46 32.5 10 = 3.25 64 500 100 = 645 H T U. t T U. t h TTh Th H T U. t h 4 6 0. 3 2. 5 6 4 5 0 0. 4 6. 0 3. 2 5 6 4 5. 0 0 0 s that come after the decimal point, at the end of the number are not needed A. Fill in the answers to these divisions. It might help you to write the numbers in columns like the examples. You can do this on Page 14 if you want to. 1. 360 10 = 2. 890 10 = 3. 2 350 10 =... 4. 35 10 = 5. 326 10 = 6. 2 600 100 = 7. 4 750 100 = 8. 32.65 10 = 9. 27. 3 100 = 10. 1963.5 100 = 11. 83 000 1 000 = 12. 123 400 1 000 = 13. 64 000 000 10 000 = 14. 66 875 10 000 = Dividing by 20 is like dividing by 10 then dividing by 2. e.g. 540 20 = 540 10 2 = 54 2 = 27 B. Fill in the answers to these divisions. 1. 480 20 = 2. 540 20 = 3. 2600 200 = 4. 750 30 = 5. 760 40 = 6. 8500 500 = CIMT, University of Exeter 14
TTh Th H T U. t h th TTh Th H T U. t h th CIMT, University of Exeter 15
ADDITION A. Fill in the answers to each of these additions. 1. 3 6 2 2. 6 4 5 3. 1 2 6 4 + 4 1 0 + 3 1 4 + 3 7 3 5 4. 4 7 6 5. 3 9 7 6. 5 9 8 2 + 2 5 8 + 4 4 6 + 2 4 0 9 7. 4 1 8 8. 3 4 7 9. 5 4 9 3 2 7 5 9 4 8 + 1 2 4 + 8 2 4 + 6 1 3 5 B. Set out these questions like the ones in Section A and then work out the answers. 1. 284 + 165 2. 496 + 129 3. 5 107 + 2 658 4. 464 + 2 929 + 76 5. 538 + 41 + 9 + 3 640 6. 9 651 + 39 + 5 + 764 CIMT, University of Exeter 16
SUBTRACTION A. Fill in the answers to each of these subtractions. 1. 6 7 8 2. 8 4 9 3. 8 7 6 9-3 2 5-3 1 4-3 7 4 5 4. 6 7 4 5. 8 1 3 6. 5 0 3 2-2 9 8-4 7 6-2 6 0 3 7. 1 0 2 7 8. 5 0 0 3 9. 9 0 7 0-8 6 9-4 8 2 4-4 1 7 5 B. Set out these questions like the ones in Section A and then work out the answers. 1. 860-145 2. 5 621-2 193 3. 4 807-986 4. 7 841-386 5. 6 005-1 448 6. 80 921-79 284 CIMT, University of Exeter 17
MULTIPLICATION A. Fill in the answers to each of these multiplications. 1. 6 3 2. 1 2 6 3. 1 3 6 7 x 3 x 5 x 2 4. 3 7 6 5. 6 4 5 6. 5 0 3 2 x 4 x 6 x 7 7. 1 0 2 7 8. 2 5 4 9. 1 3 6 2 x 8 x 24 x 35 B. Set out these questions like the ones in Section A and then work out the answers. 1. 362 x 4 2. 5 321 x 5 3. 678 x 7 4. 2 375 x 9 5. 634 x 17 6. 4 526 x 25 CIMT, University of Exeter 18
DIVISION A. Fill in the answers to each of these divisions. 1. 2. 3.. 2 6 8 4 4 8 4 8 5 6 0 5 4. 5. 6.. 3 7 3 8 6 8 2 2 8 1 8 8 8 7. 8. 9.. 7 3 9 2 0 9 2 7 5 4 15 3 8 5 5 B. Set out these questions like the ones in Section A and then work out the answers. 1. 712 4 2. 985 5 3. 3 276 7 4. 5 056 8 5. 7 488 9 6. 5 925 25 CIMT, University of Exeter 19
PERCENTAGES AND DECIMALS 0% 50% 100% 0.0 0.5 1.0 A. Mark the positions of the following decimals and percentages on the number line: 1. 0.6 2. 40% 3. 90% 4. 0.2 5. 0.8 6. 70% 7. 0.3 8. 10% 9. 0.7 10. 605 11. 20% 12. 0.1 13. 80% 14. 0.4 15. 30% 16. 0.9 17. 25% 18. 0.36 19. 63% 20. 0.75 21. 42% 22. 0.08 23. 5% 24. 0.66 B. Complete the table of equivalent decimals and percentages. Decimal 0.2 0.3 0.46 0.35 0.99 0.04 0.31 1.0 Percentage 59% 74% 19% 37% 63% 70% 21% 6% CIMT, University of Exeter 20
FRACTIONS, DECIMALS AND PERCENTAGES A. Complete these families of fractions decimals and percentages. 50% 30% 1 2 0.5 0.25 2 90% 33 1 3 % 1 10 0.2 3 4 70% 0.6 4 5 B. Complete the table showing the fraction, decimal and percentage that is shaded in each shape. Shape A B C D E F G H I Fraction Decimal Percentage A B C D E 5 F G H I J CIMT, University of Exeter 21
USING FRACTIONS AND PERCENTAGES The items below are in a sale at a super store. Teddy Bear Coffee Maker Table Lamp Clock Radio 12 25 8 20 25% off Reduced by 1 3 of original price 5 4 10% off Bicycle Keyboard Camcorder 120 250 180 1 20% off Reduced by 30% 3 original price Television Briefcase Radio 400 39.50 28 40% discount Half price 75% of original price Work out the reduction for each item and complete the table below. Item Teddy Bear Original Price Reduction Sale Price Item Keyboard Original Price Reduction Sale Price CIMT, University of Exeter 22
Coffee Maker Table Lamp Clock Radio Bicycle Camcorder Television Briefcase Radio TIME A. Draw the hands in the correct positions on each clock face to represent the times given. 1. 3. 10 11 12 1 2 10 11 12 1 2 9 3 9 3 8 7 6 8.35 4 5 8 7 6 4 5 12.40 TWENTY PAST SIX CIMT, University of Exeter 23
2. 10 9 11 12 1 2 3 8 7 6 10.40 4 5 4. 10 9 8.05 11 12 1 2 3 8 7 6 4 5 TWENTY FIVE TO TEN CIMT, University of Exeter 24
B. Underneath each clock, write the time shown on the clock face in words and in figures 1. 10 11 12 1 2 2. 10 11 12 1 2 9 3 9 3 8 7 6 4 5 8 7 6 4 5.. 3. 10 9 11 12 1 2 3 4. 10 9 11 12 1 2 3 8 7 6 4 5 8 7 6 4 5.. CIMT, University of Exeter 26
C. Compete the table for am and pm and 24-hour clock times. am / pm 9.30am 4.20pm 8.10am 7.15pm 24-hour clock 0615 1145 2130 1440 B. Write down the amount of time between: 1. 8.30am and 9.15am 2. 11.30am and 1.35pm.. 3. 10.17am and 5.49pm 4. 0615 and 1100.. 5. 1430 and 1700 6. 1617 and 2003.. D. This a time table for three trains travelling from Sheffield to London Sheffield Nottingham Leicester London 0855 1000 1030 1215 1100 1200 1227 1408 1300 13.55 1420 1550 1. At what time does the 0855 from Sheffield arrive in London?. 2. How long does this journey take?... 3. How long does the 1100 train fron Sheffield take to travel from Nottingham to Leicester?... 4. I am in Nottingham at 1215. How long must I wait for a train to London?... CIMT, University of Exeter 27
EXTRA ACTIVITIES CIMT, University of Exeter 28
ADDITION CROSSNUMBER PUZZLE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 ACROSS DOWN 1. 39 plus 57 2. 26 more than 35 2. Add 283 to 475 3. 420 added to 296 6. The sum of 19 and 68 4. 44 + 9 8. Increase 98 by 32 5. 454 added to 352 9. The total of 86, 218 and 235 6. 42 added to 43 12. 42 added to 24 7. Increase 59 by 14 13. Twenty eight plus thirty seven 10. 351 + 167 + 428 16. 29 more than 57 11. Seven more than nineteen. 17. 56 increased by 25 14. 28 plus 24 19. Twenty three plus 7-down 15. the total of 76 and 23 21. 14 increased by 69 16. Add together 47 and 36 22. This number is the same backwards 17. 18 more than 12-across 23. 3-across plus 18-down 18. 60 added to 15-down 25. The sum of 286, 367 and 325 20. 16 plus 17 plus 36 28. Four hundred and ninety-six plus one 21. 632 + 246 hundred and ninety. 22. See 30-across 30. The sum of the digits of 22-down 24. 2-down reversed 32. 547 + 316 26. 108 + 216 + 463 34. 39 plus 54 27. The same as 16-across 36. 19 more than 3-across 29. 23 + 23 + 23 38. Increase 33-down by 132 31. Increase 377 by 97 40. 352 + 409 + 186 33. See 38-Across 41. The sum of the digits of 3-across 35. The units digit is 7 42. 590 more than 35-down. 37. The sum of 32, 64 and 19 39. The sum of the digits of 736 426 CIMT, University of Exeter 29
NUMERACY WORD SEARCH y 14 E A N O I T C A R T B U S B F 13 K N I E Q U I V A L E N T R D 12 A O N S C L R O T C A F A E F 11 T I C G U A H I J H N C R K L 10 M T R N O M P Q A O T O T A L 9 D A E E R I S L I I U T X V U 8 N C A S Y C V T O N X Z X C B 7 A I S T A E I N D O U B L E E 6 S L E I D D I F F E R E N C E 5 U P G M D I V I S I O N H J F 4 O I I A P P R O X I M A T E K 3 H T L T E C U D E R M Z O Q S 2 T L N E P E G A T N E C R E P 1 R U T V Y S Q E S A E R C E D 0 U M I L L I O N D E R D N U H 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 x Write down the co-ordinates of the first and last letter of each word. Remember to write the x co-ordinate first. Word Start Finish Word Start Finish ADDITION (, ) (, ) HUNDRED (, ) (, ) APPROXIMATE (, ) (, ) INCREASE (, ) (, ) DECIMAL (, ) (, ) MILLION (, ) (, ) DECREASE (, ) (, ) MULTIPLICATION (, ) (, ) DIFFERENCE (, ) (, ) PERCENTAGE (, ) (, ) DIVISION (, ) (, ) REDUCE (, ) (, ) DOUBLE (, ) (, ) ROUND (, ) (, ) EQUIVALENT (, ) (, ) SUBTRACTION (, ) (, ) ESTIMATE (, ) (, ) SUM (, ) (, ) FACTOR (, ) (, ) TAKE (, ) (, ) FRACTION (, ) (, ) THOUSAND (, ) (, ) HALVE (, ) (, ) TOTAL (, ) (, ) CIMT, University of Exeter 27
MAGIC SQUARES In magic squares, the sum of every row, every column and every diagonal is the same. 6 3 16 7 5 11 9 2 6 11 4 6 11 3 5 18 4 14 4 6 12 10 9 9 CIMT, University of Exeter 28
WALLS In these walls, each number is the difference between the two numbers above it. 7 3 5 8 2 4 6 1 4 2 5 9 13 CIMT, University of Exeter 29
TRIANGLES The number in each square is the sum of the numbers in the circles on both sides of it. 10 12 25 28 8 6 28 829 75 98 648 239 CIMT, University of Exeter 30