11+ Maths Study Materials

Transcription

1 11+ Maths Study Materials Keystone Tutors, 5 Blythe Mews, London, W14 0HW.

2 Keystone Tutors 5 Blythe Mews, London, W14 0HW enquiries@keystonetutors.com All rights are reserved: No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written consent of a Director of Keystone Tutors Limted. 2

3 Contents Place Value: Whole Numbers... 5 Addition and Subtraction... 8 Multiplication and Division Angles and 2D Shapes Negative Numbers Line Graphs Fractions and Percentages Decimals Area and Perimeter Metric and Imperial Measures Number Patterns Symmetry Co-ordinates and Transformations Averages Frequency Tables and Diagrams Probability D Shapes and Volume Function Machines

4 4

5 Place Value: Whole Numbers Objectives: Round whole numbers to the nearest 10 or 100. Multiply and divide whole numbers by 10 or 100. Part 1: Preliminary assessment questions: 1. (a) Round 75 to the nearest 10. (b) Round 447 to the nearest 100. (c) Round 1003 to the nearest 10. (d) Round 28 to the nearest Work out the value of the following. (a) 34 x 10 (b) 16 x 100 (c) (d)

6 Part 2: people, to the nearest 10, went on a trip to Oxford. What is the minimum and maximum number of people that could have gone to Oxford? Mark the minimum and maximum number on the number line: Fill in the table below to calculate 23 x 10 HTh TTh Th H T U t h x Fill in the below to calculate HTh TTh Th H T U t h x Fill in the below to calculate HTh TTh Th H T U t h How might you use your understanding of place value to work out 32 x 30? 6. How might you use your understanding of place value to work out 62 20? 6

7 Part 3: 1. Round 2355 to the nearest: a) 10 b) Work out the value of the following: a) 16 x 40 b) 7 x 500 c) 26 x 30 d) 12 x Work out the value of the following: a) b) c) d)

8 Addition and Subtraction Objectives: Use efficient written methods of addition and subtraction. Part 1: Preliminary assessment questions: 1. (a) (b) (c) (a) 54 8 (b) (c)

9 Part 2: 1. Calculate the following: a d b e c f Calculate the following: a d b e c f Calculate the following: a d b e c f Calculate the following: a d b e c f

10 Multiplication and Division Objectives: Use efficient written methods of short multiplication and division. Understand and use an appropriate non-calculator method for solving problems that involve multiplying any three-digit number by any two-digit number. Part 1: Preliminary assessment questions: 1. (a) 6 x 17 (b) 23 x 58 (c) 671 x (a) 78 6 (b)

11 Part 2: 1. Calculate the following: a. 8 x 15 d. 35 x 51 b. 6 x 22 e. 242 x 33 c. 14 x 29 f. 43 x Calculate the following: g j h k i l

12 Angles and 2D Shapes Objectives: Specify location by means of angle and distance. Measure and draw angles to the nearest degree, and use language associated with angles. Part 1: Preliminary assessment questions: 1. Below is a map of an island. N Lighthouse Harbour Cabin Lookout Hill (a) In what direction is the Lookout from the Cabin? (b) What is northwest of the Hill? (c) Luke is standing outside of the Cabin facing the Lighthouse. Through how many degrees clockwise must he turn to be facing the Harbour? (d) What is northeast of the Harbour and west of the Hill? 12

13 2. Measure each of the angles below and write the name given to each angle. (a) Size:. o Name:. (b) Size:. o Name:. (c) Size:. o Name:. 3. Draw a 127 o angle in the space below. 13

14 Part 2: 1. A hunter travels 1 mile south, then 1 mile east, at which point he shoots a bear. The hunter then travels 1 mile north and arrives back where he started. What colour was the bear? 2. Label the points on the compass below: 3. If I start facing north east and turn through 180 o in which direction will I now be facing? 4. Fill in the blanks below: There are o in a full turn There are o in 3 of a turn 4 There are o in 1 2 a turn There are o in 1 4 a turn 14

15 An angle is less than 90 o A angle is exactly 90 o An obtuse angle is greater than o and less than o A reflex angle is greater than o and less than o 5. Draw a 68 o angle below. 6. Draw a 132 o angle below. 15

16 7. Label the shapes below: 8. Polygons are 2D shapes with straight sides. Regular polygons have edges and angles of length. 9. Fill in the table below: Name of Polygon Number of sides

17 A triangle with three equal sides is called an triangle. A triangle with two equal sides is called an triangle. 10. Two shapes are if they are the same size and same shape. They may be reflections or rotations of each other. 11. Two shapes are if they are the same shape but not necessarily the same size. 17

18 Part 3: 1. SAS (side angle side) I. Draw the base line of 7 cm (already shown). II. III. IV. Measure a 60 o angle and mark a point. Draw a line 4 cm long through the point. Draw a third line joining the two sides. 2. ASA (Angle Side Angle) I. Draw the base line of 8 cm (already shown). II. III. Measure a 75 o angle at the left end of the base line and draw a line extending through the angle. Measure a 55 o angle at the right end of the base line and draw a line extending through the angle. 18

19 3. SSS (Side Side Side) I. Draw the base line of 6 cm (already shown). II. Open your compasses to 8 cm and with the point at the left end of the base line draw an arc. III. Open your compasses to 5 cm and draw a second arc from the other end of the base line. IV. The arcs cross at the third corner of the triangle. 19

20 Negative Numbers Objectives: Order, add and subtract negative numbers in context. Part 1: Preliminary assessment questions: 1. Put the following numbers in order, starting with the smallest The table gives the temperatures in four cities one morning in January. Answer:. city temperature in o C Cardiff 3 Khartoum 17 Moscow -7 Vancouver -2 (a) What was the difference in temperature between Cardiff and Vancouver? (b) What was the difference in temperature between Khartoum and Moscow? (c) By the afternoon, the temperature in Vancouver had risen by 4 o C. What was the temperature in Vancouver in the afternoon? (d) The following morning it was 2 o C colder in Moscow. What was the temperature the following morning in Moscow? 20

21 Part 2: 1. Molly and Polly are sisters. They both borrow some money from their mother. Molly borrows 5 and Polly borrows 10. They both spend the money. Who has the most money, Molly or Polly? 2. Holly borrows 5 from her mother then the week after borrows another 5. How much money does Holly have? 3. Can you write an equation showing Holly s borrowing? 4. Olly borrows 5 from his mother but his father than pays off (takes away) the debt that Olly owes. Can you write a number sentence showing Olly s borrowing? 5. Look at the following equations: = = = = = = - 2 What do you notice? 6. Two adjacent minus signs can be thought of as a

22 7. Look at the following equations: = = = = = = -17 Part 3: What do you notice? 8. A plus sign adjacent to a minus sign can be thought of as just a. 1. Use the number line to work out: a) how much more is 4 than - 3? b) how much less is - 17 than 12? c) what number is 8 more than - 2? d) what number is 24 less than 9?

23 Line Graphs Objectives: Construct and interpret simple line graphs. Part 1: Preliminary assessment questions: 1. Rose recorded the temperature at hourly intervals throughout the day and recorded her results on the line graph below X 28 X X 26 X temperature in o C X 18 X 16 X 14 X time (a) What was the highest temperature that Rose recorded? (b) Between what times did the temperature stay the same? Answer:. o C The temperature at 1700 was 20 o C. (c) Plot this point and complete the line graph above. 23

24 2. The graph below can be used to convert speeds from miles per hour to kilometres per hour km/h mph 70 (a) Convert 40 miles per hour into kilometres per hour. (b) Convert 48 kilometres per hour into miles per hour. Answer: km/h. Answer:. mph. 24

25 Fahrenheit ( o F) Part 2: 1. What does the graph below show? Celsius ( o C) 2. Use the graph to convert: a) 60 o C into Fahrenheit b) 100 o F into Celsius 3. What s missing from the graph? J F M A M J J A S O N D Part 3: 1. Use the graph above to answer these questions: a) What was the average temperature in April? b) Between which two months did the temperature fall the most? c) Which month was the coldest? d) Why draw a line graph rather than a bar chart? 25

26 Fractions and Percentages Objectives: Recognise approximate proportions of a whole and use simple fractions and percentages to describe these. Calculate fractional or percentage parts of quantities and measurements. Part 1: Preliminary assessment questions: 1. A box of eighteen chocolates contains milk chocolates and white chocolates. (a) One third of the chocolates are white chocolates. How many white chocolates are there in the box? Simon eats two white chocolates and six milk chocolates. (b) What percentage of the chocolates left in the box are milk chocolates? 2. Simon asks the boys in his class what their favourite subject is. Below is a pie chart showing Simon s results. There are twenty-four boys in Simon s class. Art English Science Sport (a) How many of the boys said Science? Maths (b) Approximately what percentage of the boys said English? Answer:.... Answer:... % 26

27 Part 2: 1. In a class of 15 children, 9 of the children are boys. What fraction of the children are boys? 2. The top number in a fraction is called the. 3. The bottom number is called the. 4. What fraction of each of the grids below is shaded? 5. represent the same proportion of a whole in a different way. 6. Use the grids below to identify fractions equivalent to Equivalent fractions can be found by multiplying or dividing the numerator and denominator by the same number. x = x 2 27

28 = 2 8. In a class of 15 children, 9 of the children are boys. What fraction of the children are girls? Express your answer in its simplest form. 9. In a class of 15, one third of the children walk to school. How many of the children walk to school? 10. Three fifths of the children (in our class of 15) say that maths is their favourite subject. How many of the children enjoy maths more than any other subject? 28

29 11. To find: a) one half ( 1 ) of an amount, divide by 2 b) one third ( 1 ) of an amount, divide by 3 c) one quarter ( 1 ) of an amount, divide by 4 d) one fifth ( 1 ) of an amount, divide by Fill in the missing numbers. 2 a) = 10 5 b) 6 = c) = 4 12 d) e) f) 16 = = = Find the following: a) 1 of 25 d) 4 of b) 1 of 21 e) 5 of c) 1 of 60 f) 9 of Per cent means out of Percentages are simply another way of writing fractions of Fill in the blanks below a) = % c) 100 = 25% b) = % d) 98 = 98% 29

30 16. Converting fractions to percentages it is first necessary to find an equivalent fraction out of 100. a) x 6 = 60 = % x b) x 7 20 = 100 = % x Converting percentages to fractions: remember to simplify the fraction. a) 32% = = 8 b) 80% = 100 = 30

31 tens units tenths hundredths tens units tenths hundredths 18. Converting fractions to decimals: = = Converting percentages to decimals: a) 27% = 100 = b) 4% = 4 = c) 90% = 100 = 10 = 20. In a class of 24, 25% of the children do not have any brothers or sisters. How many of the children do not have any brothers or sisters? 25% = 100 = Therefore, 25% of 24 = of Find 10% of 40. of 24 = 24 = 10% = 100 = 22. Find 35% of 80. of 40 = 40 = 10% = 100 = of 80 = 80 = 8 If 10% of 80 =, then 30% of 80 = x 8 = and 5% of 80 = 8 = therefore, 35% of 80 = + = 31

32 23. Try to remember the following: a) 1% = 100 d) 20% = 1 b) 5% = 1 e) 25% = 4 c) 10% = 1 f) 50% = 1 Part 3: 1. Find the following: a) 10% of 70 d) 75% of 60 b) 5% of 40 e) 90% of 150 c) 50% of 120 f) 45% of

33 Decimals Objectives: Order decimals to three places. Add and subtract decimals to two places. Multiply and divide decimals by an integer less than 10. Part 1: Preliminary assessment questions: 1. Put the numbers below in order, from smallest to largest Jessica buys a sandwich for 2.89 and a packet of crisps for 77p. (a) How much does she spend? Answer:... Jessica pays with a ten pound note. (b) How much change should she receive? Answer:.. 3. A pack of six chocolate bars costs (a) What is the value of one chocolate bar? Answer:.. (b) How much would eight packs of chocolate bars cost? Answer:.. Answer:.. 33

34 tens units tenths hundredths tens units tenths hundredths Part 2: 1. Mo and Farah challenge each other to a 100 m race. Mo finishes in 12.3 seconds, Farah in seconds. Who won the race? Answer: Put the numbers below in order, starting with the smallest: Answer: Mo buys an energy drink costing 1.79 and a chocolate bar costing 65p. How much does he spend? Answer:.. 4. Mo pays with a 5 note. How much change should he receive? Answer:.. 34

35 5. What is wrong with the calculations below? Farah buys six punnets of strawberries, which cost 2.35 each. How much does Farah spend? Answer:.. 7. Farah pays for five cinema tickets. What is the value of one ticket? Answer:.. Part 3: 1. Calculate the following: a) d) b) e) c) f) Calculate the following: a) 2.29 x 4 d) b) 8.34 x 5 e) c) 7 x 6.88 f)

36 Objectives: Area and Perimeter Find areas and perimeters of simple shapes. Understand and use the formula for the area of a rectangle. Part 1: Preliminary assessment questions: 1. The shape below is drawn on centimetre-squared paper. (a) What is the perimeter of the shape? (b) What is the area of the shape? Answer:.. cm Answer: cm 2 2. A rectangle has a perimeter of 24 cm. Complete the table below to show the possible dimensions of a rectangle with a perimeter of 24 cm. length in cm width in cm perimeter in cm area in cm

37 Part 2: 1. Two farmers, Thomas and Richard, are debating about what shape their friend, Harold (also a farmer), should build his chicken coop so that his prize bantams have the most space to roam around. Harold has twenty-four pieces of fencing a metre long. Thomas thinks Harold should make the chicken coop 8 metres long by 4 metres wide. Richard thinks Harold should make the chicken coop 6 metres long by 6 metres wide. Harold thinks it makes no difference. Who's right? 2. is the space inside a shape or boundary usually measured in 3. is the distance around the outside of a shape usually measured in 4. The shape below is drawn on a centimetre-squared grid. What is the area and perimeter of the shape below? 5. The shape below is drawn on a centimetre-squared grid. What is its area? Answer:.. Answer:.. 37

38 6. Calculate the area of the rectangles below. Can you see a quick way for working out the area of a rectangle? Answer:.. Answer:.. Answer:.. 7. The area of a rectangle can be found by multiplying the length by the width. Area of rectangle = x 8. What is the longest perimeter that a rectangle with an area of 16 cm 2 can have? What is the largest area that a rectangle with a perimeter of 20 cm can have? Answer:.. Answer:.. Part 3: 1. Find the perimeter of the shape below. It is necessary to calculate the length of the missing side lengths. Answer:.. 2. Find the area of the shape below. It is easiest to divide the shape into rectangles first. Answer:.. 38

39 Metric and Imperial Measures Objectives: Choose and use appropriate units and instruments, interpreting, with appropriate accuracy, numbers on a range of measuring instruments. Know the rough metric equivalents of imperial units still in daily use and convert one metric unit to another. Part 1: Preliminary assessment questions: 1. What masses do the arrows indicate on the scales below? (a) 400 g 500 g (b) Answer:... g 3 kg 4 kg 2. Put the following capacities in order, starting with the smallest l 1.5 l 400 ml 1.45 l 45 ml Answer: kg Answer: The distance from London to Oxford is 60 miles. Approximately how far is this in kilometres? Answer:... km 39

40 Part 2: 1. How tall are you? 2. Fill out the table below: Answer:.. Measures of Distance Imperial or Metric What might you use this measure to measure? Metres (m) Miles Millimetres (mm) Feet ( ) Centimetres (cm) Inches ( ) Kilometres (km) Yards 3. Fill in the blanks: 1 cm = mm 1 m = cm (= mm) 1 km = m 1 inch cm 1 foot cm 1 yard m 1 mile km (1600 m) 5 miles km 4. The distance from Windsor to the centre of London is 40 kilometres. How far is this in miles? Answer:.. 5. Fill in the blanks: kilo means centi means milli means 6. How many grams are in a kilogram? Answer:.. 7. How many millilitres are in a litre? Answer:.. 8. Fill in the table: Measures of Mass Imperial or Metric What might you use this measure to measure? Pounds (lb) Kilograms (kg) Ounces (oz) Grams (g) Stones 40

41 N.B. 1 kg = 1000 g 1 kg 2.2 lb 9. A new born baby weighs 4 kg. How much is this in pounds? Answer: Fill in the table: Measures of Capacity Imperial or Metric What might you use this measure to measure? Pints Millilitres (ml) Litres (l) Gallons Part 3: N.B. 1 l = 1000 ml 1 l = 100 cl 1 pint 570 ml 1 gallon 4.5 l 1. What height is indicated on the ruler below? Answer:.. 2. What mass is indicated on the scale below? Answer:.. 41

42 Number Patterns Objectives: Recognise and describe number patterns and relationships, including factor, multiple, square and cube. Understand the concept of a prime number. Part 1: Preliminary assessment questions: 1. Look at the list of numbers below. Write down: (a) all the multiples of 3. (b) all the factors of 100. (c) all the prime numbers. (d) all the square numbers. (e) all the cube numbers Write down the next two numbers in each of the following sequences. (a) 13, 15, 17, 19, 21 (b) 21, 17, 13, 9, 5 (c) 1, 2, 4, 8, 16 (d) 2, 5, 10, 17, 26 42

43 Part 2: 1. Which number is more useful, 23 or 24? Answer:.. 2. are numbers which divide exactly into another number. 3. What are the factors of 24? Answer:.. 4. What are the factors of 23? Answer:.. 5. Numbers with only two factors, 1 and the number itself, are called numbers. 1 is not a prime number as it has only one factor. 6. The diagram below shows the first 4 square numbers. What are the next six square numbers? Answer:.. 7. Triangle numbers: 1, 3, 6, 10, 15 What are the next three triangle numbers? 8. Cubic numbers: 1, 8, 27, 64, 125 What are the next three cubic numbers? Answer:.. Answer:.. 9. Fibonacci numbers: 1, 1, 2, 3, 5 What are the next three Fibonacci numbers? Answer:.. 43

44 Part 3: What are the next two terms in these sequences? 1) 2.2, 3.5, 4.8, 6.1, 7.4 Answer:.. 2) 1, 3, 9, 27, 81 Answer:.. 3) 950, 870, 790, 710, 630 Answer:.. 4) 4.05, 3.25, 2.45, 1.65, 0.85 Answer:.. 44

45 Symmetry Objectives: Reflect simple shapes in a mirror line. Identify orders of rotational symmetry. Part 1: Preliminary assessment questions: 1. Reflect each of the shapes in the dashed line and write down the order of rotational symmetry of each completed shape. Order:.. Order:.. 45

46 Part 2: 1. WHICH 0F THE LETTERS IN THIS SENTENCE ARE SYMMETRICAL? 2. The of an object is the number of times that the object looks the same in one complete turn. 3. Complete the tables below: Lines of symmetry Order of Rotational Symmetry I C 0 F T E L R 46

47 Lines of symmetry Order of Rotational Symmetry 47

48 shape number of sides lines of symmetry order of rotational symmetry equilateral triangle square regular pentagon regular hexagon regular heptagon 7 regulr octagon 8 regular nonagon 9 regular decagon When reflecting shapes in a mirror line, the perpendicular distance from each point to the mirror line is equal to the perpendicular distance from the mirror line to each point s reflection. 48

49 Part 3: 1. Reflect the following shapes in the mirror line. 49

50 Co-ordinates and Transformations Objectives: Use and interpret co-ordinates in the first quadrant. Understand and use the transformations rotation and translation. Reflect simple shapes in a mirror line. Part 1: Preliminary assessment questions: 1. y x (a) (i) On the grid above, plot and label the following points A(3,4), B(6,2) and C(3,2). (ii) Join points A, B and C and label the shape J. (b) On the grid above: (i) reflect shape J in the dashed line. Label the new shape K. (ii) rotate shape J 90 o anticlockwise about the point C. Label the new shape L. (iii) translate shape J 3 units right and 5 units up. Label the new shape M. 50

51 Part 2: 1. A, B and C are three corners of a square. What are the co-ordinates of the fourth corner? y A B C x Answer:.. 2. Reflect the square in the dashed mirror line. y A B D C x 3. What are the co-ordinates of the corners of the reflected square? Answer:.. 51

52 4. Rotate the triangle 90 o anticlockwise about the point F. y E F 2 1 G x 5. Translate the square 2 units left and 4 units up. y A B D C x 52

53 Part 3: 1. Rotate the triangle 180 o about the point E. y E F 2 1 G x 2. Translate the triangle 5 units right and 1 unit down. y E F 2 1 G x 53

54 Averages Objectives: Understand and use the mode and range to describe sets of data. Understand and use the median of a set of data. Understand and use the mean of a set of data. Part 1: Preliminary assessment questions: 1. Charlotte is growing sunflowers. The heights of her sunflower plants, to the nearest centimetre, are given below (a) Calculate the range of heights of the plants. (b) Calculate the median height of the plants. (c) Calculate the mean height of the plants. (d) Explain why it is not possible to use the mode for these data

55 Part 2: 1. Below are the spelling test scores of pupils in two Year 4 classes: 4A: 9, 4, 10, 5, 4, 3, 8, 9, 2, 7, 4, 7 4B: 7, 4, 8, 7, 9, 6, 8, 9, 5 Which class did better overall? The is the most common value. What was the modal score for 4A and 4B? 4A:.. 4B:.. The is the middle value once the numbers have been put in order. What was the median score for 4A and 4B? 4A:.. 4B:.. The is calculated by adding all of the values together and then dividing by the number of values. What was the mean score for 4A and 4B? 4A:.. 4B:.. As well as calculating the average, it is often useful to calculate the of the values. The range gives an indication of the spread of the values. The is the difference between the highest value and lowest value in a set of data. What was the range of scores for 4A and 4B? 4A:.. 4B:.. 55

56 Part 3: 1. Find the missing values from the following sets of data:?, 15, 17,?, 7 mean = 11, median = 12, range = 13 7,?, 12, 14,?, 6 mean = 10, mode = 12, range = 8 56

57 sparrow blue tit great tit blackbird chaffinch Frequency Tables and Diagrams Objectives: Collect discrete data and record them using a frequency table. Group data, where appropriate, in equal class intervals, represent collected data in frequency diagrams and interpret such diagrams. Part 1: Preliminary assessment questions: 1. Rachel kept a record of the birds that visited her bird table one morning. She recorded her findings in the frequency table below. bird tally frequency sparrow blue tit great tit blackbird chaffinch (a) Complete the frequency table. IIII IIII II IIII IIII II (b) Complete the bar chart below to show Rachel s results. total: 24 frequency

58 Part 2: 1. Sophie collected information about the eye colour of all of the children in her class. a) Complete Sophie s frequency table showing the information she gathered. eye colour tally frequency blue brown IIII II IIII IIII green Total: 20 b) Complete Sophie s frequency diagram showing her findings. frequency blue brown green 58

59 Part 3: 1. Josh collected information about the height of all of the children in her class. Add Josh s data to the frequency table and complete the frequency diagram. 143 cm 137 cm 134 cm 128 cm 136 cm 117 cm 142 cm 136 cm 131 cm 125 cm 150 cm 135 cm 152 cm 122 cm 129 cm 148 cm 138 cm 147 cm 140 cm 139 cm Height in cm tally frequency Total:

60 Probability Objectives: Understand and use simple vocabulary associated with probability, including fair, certain and likely. Part 1: Preliminary assessment questions: 1. Five events are represented by the letters A, B, C, D and E on the probability scale below. A B C D E (a) Which letter represents the most likely event? Answer:.. (b) Which letter represents the probability of getting a heads when a fair coin is tossed? (c) Which letter represents an unlikely but still possible event? Answer:.. (d) Which letter represents getting three or more when rolling a fair die? Answer:.. Answer:.. (e) Which letter represents the probability of the sun rising in the west tomorrow? Answer:.. 2. A bag contains three red counters, two yellow counters and five blue counters. One counter is chosen at random from the bag. (a) What is the probability of selecting a blue counter? (b) What is the probability of not selecting a yellow counter? Answer:.. Answer:.. 60

61 Part 2: 1. What is the probability of tying the two lengths of string together? Possible combinations: A-B A-C A-D B-C B-D C-D 2. Which of the following sequences is most likely to result from rolling a fair die six times? Probabilities can be placed on a scale, like the one below. 3. Mathematicians attach numerical values to probabilities: an impossible event has a probability of, a certain event a probability of. 4. The numerical probability of an event can be expressed as a fraction, a decimal or as a percentage. Numerical probabilities can be calculated as follows: P = 61

62 Part 3: 1. Imagine rolling a fair six-sided die. On the scale below, mark the probability of: A rolling a number greater than 0 B C rolling a prime number rolling a square number 62

63 3D Shapes and Volume Objectives: Make 3D models. Find volumes by counting cubes. Part 1: Preliminary assessment questions: 1. The cuboid below measures 5 centimetres by 2 centimetres by 2 centimetres. (a) What is the volume of the cuboid? Answer:... cm 3 (b) Draw a net for the cuboid on the centimetre-squared grid below. 63

64 Part 2: 1. How big is the cuboid below? In what ways could you measure it? 2. A net is a 2D pattern that can be folded to make a 3D shape. 3. The total surface area of a shape is found by adding together the area of all of the faces. What is the total surface area of the cuboid? Answer:... cm 2 64

65 4. Volume is the amount of space inside a 3D shape. What is the volume of the cuboid below? 5. Calculate the volume of each of the cuboids below. Can you see a quick way of working out the volume of a cuboid? Answer:... cm 3 6. The volume of a cuboid can be found by multiplying the length by the width by the height. Volume = x x 65

66 Part 3: 1. How big is the cube below? Length: Width: Height: Surface area: Volume: 2. Draw a net for the cube below on the grid underneath. 66

67 Cube nets Which of the nets below fold to make a cube? 67

68 Function Machines Objectives: Use simple formulae expressed in words. Part 1: Preliminary assessment questions: 1. Fill in the missing numbers in the function machine below. (a) (b) 5... x (c) (d) (a) Matthew thinks of a number, multiplies it by 3 then subtracts 5. His answer is 16. What number did he think of? (b) Mark is 2 years older Luke, who is half the age of John. If John is 12, how old is Mark? 68

69 Part 2: 1. think of a number multiply it by 2 add 6 halve it take away the number first thought of subtract 1 n 2 x n 2 x n + 6 n Part 3: 1. Fill in the missing numbers for this function machine. 2. Amy thinks of a number, doubles it then adds 4. The answer is 18. What number did Amy think of? 3. Let the number Amy thought of be n This gives 2n + 4 = 18 2n = 14 n = 7 69