Oxford Mathematics 5

A pyramid has one One hexagonal Two hexagonal base. It usually sits on its base bases base. A prism has two bases. A prism often sits on one of the side faces and not on the base. 3 Complete this table. 3D shape Number Base shape Side face shape The objec t is of bases sit ting on: e.g. Hexagonal pyramid 1 hexagon triangles the base a Square pyramid b Triangular prism c Triangular pyramid d Rectangular prism 4 A rectangular prism would open out to make a net like this: For which 3D shapes are these the nets? a b This is the net for a This is the net for a 98 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Drawing 3D shapes is dif cult, because you have to make a 2D drawing look as though it has depth. Tr y to draw these objects on the isometric grid. The dotted lines show the “hidden” edges. It might take a few tries to make them look right. a This is a: b This is a: c This is a: d This is a: 2 If you made a cross - section of a cone in this direction, you would see a circle. What 2D shape would you see if you cut across each object in the direction of the arrow? a b c OX FOR D U N I V E RSI T Y PR E S S 99

UNIT 7: TOPIC 1 Angles are 18 0 ° Angles measured in degrees (°). There are six t ypes of angles: 90° from 1° to 8 9 ° from 91° to 179 ° 360° from 181° to 359 ° Perpendicular lines meet at a right angle. The lines on the right angle above are perpendicular to each other. Guided practice 1 Write the name of each t ype of angle. a b c d e f 2 Draw a line that is perpendicular to each green line. 3 Use a pencil and ruler to draw each angle from the dot on its base line. a an acute angle b a right angle c an obtuse angle 100 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 80 100 Angles are measured with a protractor. 90 1 The base line of the protractor needs 1 to be on the base line of the angle. You 0 have to make sure you read the correct track. This angle is on the inside track: 100 80 0 7 1 0 1 0 0 5 2 1 0 3 1 0 4 4 0 1 Make sure the 3 0 protractor is 0 4 positioned properly 0 3 0 2 6 0 1 0 2 071 Read the 01 01 track that starts at 0 081 0 Make sure the protrac tor is positioned properly. 1 Write the t ype and size of each angle. a An acute angle b An angle ° ° 80 100 80 100 1 100 100 3 0 90 1 0 90 1 0 7 1 7 1 0 0 80 1 80 2 0 7 0 0 0 7 1 0 6 1 0 1 1 0 0 0 0 5 2 5 2 1 1 0 0 3 3 4 1 1 0 0 Read the 4 0 Read the 1 4 0 4 4 1 1 0 0 3 0 3 4 0 4 0 0 0 3 3 inside track outside 0 2 0 track 2 6 0 6 0 1 1 0 0 2 2 071 01 071 01 071 01 01 081 0 081 0 c An angle d An angle ° ° 80 100 80 100 100 100 0 90 1 0 90 1 7 1 7 1 0 0 80 1 80 1 2 2 0 7 0 0 0 7 0 1 0 6 1 0 1 1 0 0 0 0 5 2 5 2 1 1 0 0 3 3 1 1 0 Read the 4 0 4 4 0 4 0 1 1 3 3 0 0 0 0 4 4 0 0 3 3 inside track 0 2 0 2 6 0 6 0 1 1 0 0 2 2 071 01 071 01 071 01 01 081 0 081 0 2 Write the t ype of angle. Circle the best estimate for the size of the angle. a acute angle b c angle angle 10 0° 10 0° 20 ° 80º 14 0 º 120 º 40 º 170 º 60º d e f angle angle angle 20 ° 80° 70 ° 60º 90º 90º 80º 10 0 º 110 º OX FOR D U N I V E RSI T Y PR E S S 101

3 Write an estimate for the size of each angle. Think about the t ype of angle. You could also think about how the size compares to a right angle. a Estimate b Estimate c Estimate ° ° ° d Estimate e Estimate ° ° f Estimate g Estimate h Estimate ° ° ° 4 Use a protractor to measure the size of each angle in question 3. a b c d e f g h 5 Use a protractor, pencil and ruler to draw the angle on each line. Star t at the dot. a 70 ° b 115° 102 OX FOR D U N I V E RSI T Y PR E S S

Extended practice This diagram shows one strategy you can use to nd the size of a reex angle. 40º 1 Without using a protractor, write the size ?º of the reex angle in this diagram. 2 Use a strategy of your choice to nd the size of these reex angles. a b ° ° c d ° ° 3 There are two angles a Estimate the size of each angle. shown here. A Angle A estimate: Angle B estimate: B b Explain how you estimated the size of each angle. c Measuring just one of the angles, write the sizes of both angles. Angle A = Angle B = d Explain how you found the size of the angle that you did not measure. OX FOR D U N I V E RSI T Y PR E S S 103

UNIT 8: TOPIC 1 Transformations Patterns can be made by transformation. This means that as you move a shape in a cer tain way, it star ts to make a pattern. When the pattern is formed, the shapes must remain congruent, which means that they are always the same shape and size. Here are some ways to begin a pattern by transforming a shape: Translation (sliding it) Reec tion (ipping it over) Rot ation (turning it) Guided practice I don’t kno w if I like this 1 What method of transformation has been used? rotation pattern! a b c 2 Complete the patterns. Remember to keep the shapes congruent. a Rotate the triangle. b Translate the triangle. c Reect the triangle. d Make a pattern of your choice. e How did you transform the pentagon? 104 OX FOR D U N I V E RSI T Y PR E S S

Independent practice Patterns can be made by transforming shapes horizontally, ver tically or diagonally Tr a n s l a t i on Reec tion ver tic al ver tic al hor izont al hor izont al diagonal diagonal 1 Describe these patterns. Pat tern De s c rip tion a b c d e f 2 Continue this pattern and describe the way it grows. OX FOR D U N I V E RSI T Y PR E S S 105

3 Look at the way these patterns grow. Complete each pattern, then describe it. a b c 4 a Design a transformation pattern using this shape. b Describe the way you made your pattern. 106 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 You can create designs in a few minutes with the help of a computer and a program such as Microsoft Word (or similar). a Open a blank document. Make sure you can see the Drawing menu bar. If you cannot see it, click on View, then Toolbars, then Drawing b Click on the Autoshapes icon and choose an interesting shape. c Draw the shape at the top of the page by clicking and dragging. d Copy the shape. e Paste the shape. f Use the arrow keys to move the shape so that its left edgejoins the right edge of the rst shape, like this: g Repeat steps d –f as many times as you like. 2 This activit y involves rotating copies of a simple shape on top of the original shape. a Open a new blank document. b Click on the Autoshapes icon and choose a double arrow. c Draw the arrow on the page by clicking and dragging. d Copy and paste the shape as you did in question 1. e Use the arrow keys to move the shape so that it is exactly over the top of the rst shape. f Select the shape to change it. (PC users: right- click and choose format Autoshape Mac users: hold control as you click and choose format Autoshape. ) g Click the size tab and look for the rotation menu. Rotate and sc ale ____________ h Change the rotation amount from 0° to 30° Rot a tion: 30º and click OK i Copy, paste and move the new shape by repeating steps e – h. j Repeat, increasing the angle of rotation by 30° each time. OX FOR D U N I V E RSI T Y PR E S S 107

UNIT 8: TOPIC 2 Symmetry There are two t ypes of symmetr y: line (mirror) symmetr y and rotational (turning) symmetr y. Some shapes have both line symmetr y and rotational symmetr y. Line symmetr y Some shapes One side is the don’t have same as the other. any lines of symmetr y. Rotational symmetr y Line symmetr y and It t s on top of it self before it get s back to the s tar ting point . Guided practice 1 Tick the shapes that have line symmetr y. A B C D E F G H I J 2 All of the following shapes have line symmetr y. a Draw at least one line of symmetr y on each shape. b Some of the shapes also have rotational symmetr y. Colour the shapes that have rotational symmetr y. A B C D E F G H I J OX FOR D U N I V E RSI T Y PR E S S 108

Independent practice Shapes can have more than one line of symmetr y. The red dotted lines show that this shape has two lines of symmetr y. 1 All these shapes have line symmetr y. Use a strategy of your choice to nd and draw in the lines of symmetr y. Some have one, some have two — and some have four! a b c d e f g h i j k l 2 All regular 2D shapes have lines of symmetr y. A triangle has three lines of symmetr y. Identif y and draw the lines of symmetr y on these regular shapes. d e f OX FOR D U N I V E RSI T Y PR E S S 109

This shape has rotational symmetr y of “order 2”. That means that the shape ts on top of itself two times as it rotates, counting the starting position as one. 1s t position Back to the s t ar t × • • • × • × × × • 2nd position 3 Find the order of rotational symmetr y for these shapes. You may wish to trace over the shapes and use cut- outs for this activit y. × • • • × × Rotational symmetr y of order Rotational symmetr y of order Rotational symmetr y Rotational symmetr y Rotational symmetr y of order of order of order Rotational symmetr y Rotational symmetr y Rotational symmetr y of order of order of order 4 True or false? Ever y symmetrical shape has rotational symmetr y of at least order 1. 110 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Some of the digits that make up our number system are symmetrical. However, this depends on the way they are drawn. 1 2 3 4 5 6 7 8 9 0 a Draw the lines of symmetr y to show any digits that are symmetrical. b One of the 10 digits that can be drawn symmetrically is not c drawn symmetrically in the list. Which one is it? Re - draw it and draw the line of symmetr y. One of the 10 digits can be drawn so that it has an innite number of lines of symmetr y. Re - draw it so that it has an innite number of lines of symmetr y. 2 a You probably know some capital letters have lines of symmetr y, such as b capital A. What is another capital letter that has one line of symmetr y? The letter S has no lines of symmetr y but it has rotational symmetr y. What is the order of symmetr y for a capital S? c What is another capital letter with rotational symmetr y? d Some capital letters have both line symmetr y and rotational symmetr y. For example, a capital H has two lines of symmetr y and has rotational symmetr y of order two. Complete the Venn diagram, showing the letters that have: • line symmetr y Let ters with Let ters Let ters with line symmetr y with both rotational symmetr y • rotational symmetr y A H S • both line symmetr y and rotational symmetr y. 3 We often see symmetr y in nature. Or do we? Look closely at this leaf. What, if any thing, makes it asymmetrical? OX FOR D U N I V E RSI T Y PR E S S 111

UNIT 8: TOPIC 3 Enlargements and reductions When you enlarge something, you make it bigger. e There are two simple ways of enlarging a 2D iz shape using a grid of squares. You can draw the s picture on bigger squares, or you can increase the length of ever y line by the same amount. e th You can reduce the size of a picture by doing Star t Grid size the opposite of the ×2 enlargement process. 4 small squares wide 4 big squares wide D Line lengths × 2 o 8 small squares wide u b le th e Guided practice 1 Enlarge these shapes by re - drawing them on the larger grids. a b c d e f 2 Enlarge these shapes by doubling the lengths of all the lines. Star t each drawing at the red dot. a b c d e f 112 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 Enlarge each picture by drawing it on the larger grid. A B 2 Draw an enlargement of each shape on the second grid. Then make an even bigger enlargement by drawing them on the third grid. A B A B 3 Reduce the size of these letters by drawing them on the smaller grid. OX FOR D U N I V E RSI T Y PR E S S 113

You can enlarge or reduce a picture by a scale fac tor. If you want a picture to be three times as big, you enlarge it by a scale factor of three. 4 Re - draw these pictures according to the scale factor shown. Star t at the red dot. a b Reduc e by a sc ale fac tor of t wo. Enlarge by a sc ale fac tor of three. c Reduc e by a sc ale fac tor of three. d Enlarge by a sc ale fac tor of t wo. 114 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 A 2 2 cm × 2 cm square has an area of 4 cm . If you enlarge a 2 cm square by a scale factor of two, what happens to the area? Experiment on a piece of spare paper before writing the answer. 2 You will need access to a computer for the next activit y. In a program such as Microsoft Word, you can enlarge a picture by clicking and dragging. You can enlarge pictures more accurately by changing the size of the picture by a percentage amount. a Open a blank Word document. b Inser t a picture. c Select the picture to format it. (PC users: right- click and choose format pic ture Mac users: hold control as you click and choose format pic ture.) d Click the size tab and look for the scale menu. e Change the scale amount from 10 0% to Sc ale ____________________________ 20 0%. (If you click the lock aspec t ratio 10 0% button, this will change the width and height by the same amount.) Lock aspec t ratio Relative to original pic ture size f Click OK and watch the picture change. 3 a If you were formatting the size of a picture in Word and you clicked “10 0%”, what would happen to the size of the picture? b How would you enlarge a picture by a scale factor of three in Word? c Inser t another picture and nd a way to reduce the picture to half its size. How did you do it? 4 If you do not lock the aspect ratio in Word, the height and width of a picture can be changed separately. This can make the pictures look strange but it can be fun to do. Tr y enlarging the width and height of a picture by different amounts. OX FOR D U N I V E RSI T Y PR E S S 115

UNIT 8: TOPIC 4 Grid references Grid A Grid B To read a coordinate point, Grid references are a way of Showing a position first go ACROSS describing position. Grid references inside a square. the river then UP can mean the area inside a square or an exact point on the grid. the mountain! The circle is at B1 on both grids. Ona grid like Grid B, there can 0 only be one object at each point. D Showing a position at an exac t point . Guided practice 1 What is the position of these shapes on the grids at the top of the page? Grid A square: Grid B square: Grid A triangle: Grid B triangle: Grid C 2 What are the positions of these shapes on Grid C? 5 a The diamond: b The star: 4 3 c The triangle: d The circle: 2 1 B C D E A 3 Draw the following on Grid C: a The letter O at A 4 b A smiley face at B3 c The letter K at B4 d An oval at D2 e The letter R at B5 f The letter U at A5 Grid D 4 Which shape has a different grid 5 reference on Grid C and Grid D? 4 3 5 Draw the letter × at the following points on Grid D: 2 1 B4 C3 D2 E1 6 Write a coordinate point that would A B C D E 116 continue the ×s in a diagonal line. OX FOR D U N I V E RSI T Y PR E S S

Independent practice Grid E 5 4 Coordinate points are often written with two numbers, 3 rather than a letter and a number. You read the number going across rst, then the number going up. 2 The numbers are in brackets, separated by a comma. The circle is at (1,0). 1 0 1 2 3 4 5 0 1 Write the grid references for: a the star b the triangle c the diamond 2 Draw the following on Grid E. a a square at (2,3) b circles at (1,4) and (3,4) c stars at (1,2), (2,2) and (3,2) 3 a Write the rst letter of your rst name on an empt y grid point. b What is the grid reference for the letter you wrote? 4 When two coordinate points have an arrow between them, it means that you join them with a straight line. Complete the following. y 8 a The coordinate points for drawing the triangle 7 6 are: (1,5) (3,5) (2,8) . 5 b The coordinate points for drawing the square 4 3 are: (4,5) 2 1 0 x 0 1 2 3 4 5 6 7 8 5 a Draw a large rectangle on the grid lines below the triangle and the square. b Write the coordinate points for drawing the rectangle. Remember to end the drawing back at the star ting point. OX FOR D U N I V E RSI T Y PR E S S 117

6 a Write the coordinate points to show y someone how to draw this letter N. 6 5 4 3 b Draw another capital letter using straight lines. Write the coordinate points to show someone how to draw the letter. 2 1 0 x 0 1 2 3 4 5 6 7 a Draw the following picture by plotting with dots and joining the coordinate points. (1,1) (4,1) (4,4) (5,4) (5,1) (8,1) (6,2) (6,6) (8,4) (8,5) (6,7) (5,7) (5,8) (7,8) (7,9) y 12 (8,9) (8,10) (7,10) (7,11) 11 10 (6,12) (3,12) (2,11) 9 (2,10) (1,10) (1,9) (2,9) 8 7 (2,8) (4,8) (4,7) (3,7) 6 5 (1,5) (1,4) (3,6) (3,2) 4 3 (1,1) STOP! b Draw a mouth: c (3,10) (3,9) (6,9) (6,10). Draw a nose: (4,10) (5,10), then draw an oval shape around the line. d Draw two eyes. What are the 2 coordinate points? 1 0 x 0 1 2 3 4 5 6 7 8 118 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Design a coordinate picture on the grid. After wards, you can give the instructions to someone so that they can draw the picture. Some things to think about: • Don’t make the picture too complicated. • Make sure the coordinate points are correct. (If you can’t follow them, nobody else will be able to!) • Use straight lines where possible. y 12 11 10 9 8 7 6 5 4 3 2 1 0 x 0 1 2 3 4 5 6 7 8 9 10 11 12 2 Write the instructions in the way that they were written on page 122. Tr y following your instructions on a grid before you give them to somebody else. OX FOR D U N I V E RSI T Y PR E S S 119

UNIT 8: TOPIC 5 Giving directions The four main compass directions are nor th, south, east and west. To remember their position on a compass rose, some people use N sayings such as “ ever at limy orms”. We need a compass W E direction to describe the position of the dog. Guided practice S 1 The dog on the compass rose is nor th - east of the cat. a Label the four empt y arrows NE b Draw a triangle at the SW point, (nor th - east), SE (south - east), SW a circle at the NW point and a (south -west) and NW (nor th -west). square at the SE point. 2 The teacher is at the centre of this classroom. Use the plan to nd the answers. 4 Sam a Who is nor th - east of the teacher? N 3 T b Who is south -west of the teacher? 2 c Use a compass direction to describe Sam’s position. 1 Lucy A B C D 3 It is not possible to describe the position of Jack ’s table using one of the eight compass directions, but we can use a grid reference. Jack is at B1. a Use a grid reference to describe the position of Tran. b Eva is at A 2. Write her name on the plan. c Choose a position to the east of Sam and write your initials in it. d What is the grid reference for the position? e Write Jo’s name in a position between Sam and Lucy. Use a compass direction to describe the position in relation to the teacher and a grid reference for the table. 120 OX FOR D U N I V E RSI T Y PR E S S

Independent practice Orange Grove Use this map of Jo’s town for the following activities. Shopping mall Tr an’s house 5 4 Sw im Jo’s 3 c entre house 2 house N Spor t s elds 1 alaoK yballaW allesoR t abmoW daoR um E Dubbo Drive A B C D E F G 1 a In which direction would Jo go to get from home to the swim centre? b What is the grid reference for Tran’s house? c Imagine you lived at the nor th end of Rosella Road. Shade in the shor test route along the roads that would take you to the southern entrance of the spor ts elds. d Amy lives on Penrith Parade. Using compass directions and street names, write instructions to get from Amy’s house to the swim centre. e True or false? Amy’s house is nor th - east of Jo’s house. f The Magic Movie Theatre is nor th of the Swim centre, on the right-hand side of Wombat Way. Draw and label it on the map. g Write the grid reference for the nor th - eastern corner of Lawson Road Primar y School. h Using compass directions and street names, write instructions to get from Tran’s house on Wombat Way to the school entrance on Wallaby Way. OX FOR D U N I V E RSI T Y PR E S S 121

Scale: 10 0 m 3 2 A legend (or key) gives information about places on a map. If a map has a scale, you can work out real - life distances. On this 2 T = Treasure map, the treasure is at (4,1) and is 50metres S = Snake Pi t from the snake pit. 1 C S T C = Campsi te 0 1 2 3 4 5 0 a Write a coordinate b How far is the campsite for the campsite. from the treasure? N P P P S S = Snake Pi t Snake s v ille C = Crocodiles P = Poisonous Plan t s N N = Nes t of Scorpions T = Treasure Scale: 1 cm = 1 k m C 3 a Use the legend to mark these on the map: Big Bug Beach has a nest of b scorpions near it. Tin Pot Cave is 6 km south - east of Snakesville. Spider Head is 4 km south of Snakesville. Cockroach Cliff is 7 km nor th of Spider Head. Shark Point is 5 km west of Snakesville. Mark its position with a dot and write “Shark Point” on the map. 4 a There is a cur ved track from Snakesville to Shark Point that misses the b poisonous plants by going to the south of them. Draw the track on the map. Estimate the distance from Snakesville to Shark Point along the track you drew. 5 a Goanna Gorge is 2 km to the nor th - east of Spider Head. Mark it on the map with b a dot and the letter G. Draw a straight road from Spider Head to Goanna Gorge. The Treasure is buried along a straight track 50 0 m south - east of Goanna Gorge. Mark it on the map with the letter T. 122 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 CAT stands for “Computer Ar tist’s Toy”. It moves according to directions given and traces a path with a pen. The CAT needs to be programmed to draw an octagon. The rst two moves are shown. CAT is programmed Step 2 to understand distance and compass directions. Step 1 a Write the steps that would complete the octagon. Step 1. Move nor th 2 cm. Step 2. Move nor th- eas t 2 cm b Follow your own directions to see if you draw an octagon. If you want your octagon to be accurate, you will need to use a protractor. Or your teacher may ask you to use a line tool in a computer program such as Microsoft Word. 2 Draw your own Treasure Island Map. Include a legend for some interesting places on the island, a scale and a direction indicator. Label the grid so that you can give grid references for the places on the map. Legend Sc ale: OX FOR D U N I V E RSI T Y PR E S S 123

UNIT 9: TOPIC 1 Collecting and representing data A common way to represent data is Graph to show our frui t on a graph. There are several t ypes favouri te snac k choco la t e of graph. The t ype of graph used ice -cream depends on what is being represented. Guided practice Ver tical or horizontal bar graph Number of birds that visited Number of birds that visited the class bird feeder the class bird feeder 28 Mon Tues Wed T hu 0 Fri 0 Mon Tues Wed T hu Fri 28 1 a Fill in the blanks on the number b By how many was Tuesday’s axis on each graph. total less than Monday’s? Dot plot Number of pieces of fruit our group brought for snack time 2 1 2 3 4 Piec es of fruit a What is the most common b How many people The graphs 3 number of pieces of fruit? were sur veyed? in questions 1 and 2 sho w numerical data. The two main t ypes of data that are collected are numerical and categorical Numerical data can be counted (or measured). Categorical data (such as where we like to go on holidays) is not numerical. Write “N” (for numerical) or “C” (for categorical) for the t ype of data that will be collected. a What is your favourite pet? b How many pets do you have? c How tall are you? e What is your favourite d What is your favourite spor t? subject? f How long do you spend reading each day? 124 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 If you asked, “How many snacks do you eat a day?”, you would be collecting numerical data. Write a sur vey question about food that would enable you to collect categorical data. 2 If you asked, “What type of music do you like?”, you would be collecting categorical data. Write a sur vey question about music that would enable you to collect numerical data. 3 Class 5T took the noon temperature for 20 days: 19°, 18 °, 19°, 20°, 19°, 20°, 20°, 20°, Temperature Tally Frequency 19°, 18 °, 20°, 19°, 20°, 19°, 18 °, 20°, 18 °, 17°, 19°, 20° a What t ype of data did they collect? Total Noon time temperature s for 20 days b Complete the frequency table for the data. c Complete the dot plot for the data about the temperatures. 17 º 18 º 19 º 20º 4 a Create a frequency table about the colour of people’s hair in your class. Hair colour in our class Frequency table showing hair colour Colour Light M e dium Dark Total Frequency b Transfer the data onto a bar graph. elpoep fo rebmuN c Decide on a suitable scale. What other t ype of graph would also be suitable for this data? 0 OX FOR D U N I V E RSI T Y PR E S S Dar k Medium L igh t 125

5 Add to the information in question 4 by creating a two -way table showing the lengths and colours of students’ hair in your class. Hair t ype Light M e dium Dark Total Shor t length Medium length Long length Total 6 This table shows the top ten premiership winning teams in the Australian Football League. a Complete the total column. b Decide on a suitable t ype of graph and scale to display the information. Use a separate piece of paper for this. Club Year s tar ted Premiership years Total C arlton Collingwood 18 97 19 0 6, 19 07, 19 0 8, 1914, 1915, 19 3 8, 19 4 5, 19 47, Essendon 19 6 8, 1970, 1972, 1979, 19 81, 19 82, 19 87, 19 9 5 18 97 19 02, 19 0 3, 1910, 1917, 1919, 1927, 1928, 1929, 19 30, 19 35, 19 36, 19 5 3, 19 5 8, 19 9 0, 2010 18 97 18 97, 19 01, 1911, 1912, 1923, 1924, 19 42, 19 4 6, 19 4 9, 19 50, 19 62, 19 6 5, 19 8 4, 19 8 5, 19 9 3, 20 0 0 Fitzroy (18 97–19 9 6) 18 9 8, 18 9 9, 19 0 4, 19 0 5, 1913, 1916, 1922, 19 4 4 Geelong 18 97 1925, 19 31, 19 37, 19 51, 19 52, 19 6 3, 20 07, 20 0 9, Haw thorn 1925 2011 Melbourne 18 97 19 61, 1971, 1976, 1978, 19 8 3, 19 8 6, 19 8 8, 19 8 9, 19 91, 20 0 8, 2013, 2014, 2015 19 0 0, 1926, 19 39, 19 4 0, 19 41, 19 4 8, 19 55, 19 5 6, 19 57, 19 59, 19 6 0, 19 6 4 Nor th Melbourne 1925 1975, 1977, 19 9 6, 19 9 9 Richmond 19 0 8 1920, 1921, 19 32, 19 3 4, 19 4 3, 19 67, 19 6 9, 1973, 1974, 19 8 0, 2017 Sydney Swans 18 97 (formerly South 19 0 9, 1918, 19 3 3, 20 0 5, 2012 Melbourne) 126 OX FOR D U N I V E RSI T Y PR E S S

Extended practice Researchers believe that 10 -year- old children have a vocabular y of 10 0 0 0 words, but it is ver y dif cult to collect reliable data about the number of words anyone knows. 1 Without doing any research, write down three words that you think are used a lot in ever yday writing. 2 Do some research to see if you are right. You need 10 0 words of a text. a Skim through and make a mental note of any words that you think are used frequently. • Write these common words down. • Do an accurate tally of the number of times the words are used. b Which three words are most commonly used? c Compare your research with that of somebody else. How does it compare? 3 There are a lot of vowels used in the 4 0 words of this joke. A monkey goes into a café and points to a pic ture of a cheese sandwich. “ That ’s s tr ange!” says one waitress to another. “A monkey is ordering a cheese sandwich.” “I know!” says the monkey. “I usually order a hot dog.” a Find out how often each vowel is used. Make an accurate tally of the number for each vowel. Vowel A E I O U Frequency b How reliable do you think this data is as an indicator of the most frequently used vowels? Why? OX FOR D U N I V E RSI T Y PR E S S 127

UNIT 9: TOPIC 2 Representing and interpreting data Two t ypes of graphs used How muc h money was in Tran's Favourite c olour s of to represent data are line piggy bank? our class graphs and circle graphs A line graph is used to show $ 25 A circle graph is a quick way to how something changes $ 20 show small amounts of data. over time, such as the $ 15 $ 10 amount of money in a $5 piggy bank. $0 1 2 3 4 We e k Guided practice 1 The line graph above shows that the amount of money Tran had in week 1 was $5. a By how much did it go up in week 2? b In which week did Tran have the most money? c Estimate the amount of money Tran had in week 4. You can only make 2 a Circle the correct statement about the circle graph above. • Yellow is more popular than red. • Blue is the least popular colour. • Out of the 24 students in the class, 10 students chose blue. b Estimate the number of students who chose green. 3 These are the amounts Tran had in weeks 5 – 8. Use the information to make a line graph. How much money was in Tran's pigg y bank? $ 25 $ 20 • Week 5: $15 $ 15 • Week 6: $20 • Week 7: $ 3 $ 10 • Week 8: $16 $5 $0 5 6 7 8 We e k 128 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 These are Eva’s spelling scores out of 20 during the term. Represent the data on a line graph. Week 1 2 3 4 5 6 7 8 9 10 Score 20 18 19 14 6 16 20 20 17 15 a Decide on a suitable scale for the ver tical axis. 20 b Write a title for the graph. c Write appropriate labels for the horizontal and ver tical axes. d Plot the data, then join up each point. 0 1 2 3 2 a In which weeks did Eva score 10 0%? b Describe the change in scores between weeks 5 and 7. c In which week do you think Eva did not do her homework? d True or false? Eva’s average score was more than 16 out of 20. e Between which weeks was the rise in scores the biggest? OX FOR D U N I V E RSI T Y PR E S S 129

3 The circle graphs show the top ve holiday destinations for Australians in 19 50 and 20 0 0. The data was collected from a sur vey of 10 0 0 people. Favourite holiday destinations – 1950 a What was the most popular destination in 1950? New South Wales Queensland b The popularit y of which place wasthe same Victoria in 1950 and 20 0 0? New Zealand Europe c About how many people preferred to travel to Europe in 20 0 0? Favourite holiday destinations – 2000 Australia Europe Asia New Zealand USA d Why do you think the number of people who chose Europe rose between 19 50 and 20 0 0? 4 This table shows the top six girls’ names in 20 0 0. Rank Name Number of sec tions in Key (colour used in circle graph circle graph) 1 Emily 2 Ellie 3 Jessica 4 Sophie 5 Chloe 6 Lucy a The blank circle graph is divided into 24 sections. Choose the number of sections to shade for each of the names T itle: in the table. b Choose a colour for each name and shade the graph. Then shade the key in the table. c Write a title for the circle graph. d Write a question that a teacher might ask Year 5 students about the information in the graph. 130 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 This information shows the number of points scored by each player (including thesubstitute) on a basketball team. Points in Points in Points in Points in Points in Total Average Game 1 Game 2 Game 3 number points Player Game 4 Game 5 of points per game Sam 17 19 19 14 16 A my 8 7 0 2 8 Tran 5 8 4 2 11 Eva 14 15 3 11 17 Lily 2 4 1 0 3 Noah 6 2 4 2 21 T itle a Divide the total for each player by the number of games to nd their average number of points per game. Write the average scores in the table. b Use the data to create a graph of your choice. Youmay use the scaffold if you wish. Examples of questions you could focus on include: • What were the highest totals for • each player? • How did Eva’s (or anyone else’s) scores change over the ve games? What did the average scores look like after three games? c Whose average score was the highest? d Who scored the most points in a single game? e Which player do you think spent most time on the sideline? Give a reason for your answer. OX FOR D U N I V E RSI T Y PR E S S 131

UNIT 10: TOPIC 1 Chance Will it be heads or tails? If you guess heads or tails, there is just as much chance that you will be right as there is that you will be wrong. In words: As a percentage: There is an even chance. There is a 50% chance. As a frac tion: As a decimal: There is a 0.5 chance. 1 There is a a chance. 2 Guided practice Using the probabilit y words certain, likely, even chance, unlikely and impossible, describe the chance of the following things happening. 1 a The voice I hear when I turn on the radio will be a woman’s. b A cow will read the news on T V tonight. c Someone will fall over at lunchtime. d Tuesday will follow Monday next week. 2 The chance words in question 1 can be put on a number line. Write the other four words on the line: certain, likely, unlikely, impossible. Draw arrows to the positions you think are appropriate. Even chanc e 0 0 .1 0.2 0.3 0.4 0.5 0.6 0 .7 0.8 0.9 1 1 3 There is of a chance that the spinner will land on red. 4 Which fraction describes the chance of the spinner landing on blue? 4 This spinner has a 9 0% chance of landing on red. What is the percentage chance of it landing on green? 5 The chance of this spinner landing on yellow is 0.1. What chance is there that it will land on: a blue? b green? c white? 132 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 Read the descriptions of the chance of these events occurring. a Conver t the chance words to a decimal to describe the chance of the event occurring. b Fill in the gaps where necessar y. A: It is impossible to run 10 0 metres in two seconds. Value 0.1 B: It is almost impossible for me to win ten million dollars. C: It is likely that I will see a movie at the weekend. D: There is a better than even chance that I will like the movie. E: It is very likely that F: There is an even chance that the next baby born will be a girl. G: There is less than an even chance that I will go swimming tomorrow. H: It is almost certain that I: It is certain that J: It is very unlikely that K It is unlikely that 2 Place the letter for each description in question 1 at an appropriate place on B this number line. 0 0 .1 0.2 0.3 0.4 0.5 0.6 0 .7 0.8 0.9 1 3 Which do you think is more accurate when describing chance situations: number values or chance words? 4 Which spinners have the following chance of landing on blue? a 75% chance A B C D 133 b 1 out of 2 chance c 1 of a chance 3 d 10 0% chance OX FOR D U N I V E RSI T Y PR E S S

5 Colour this spinner so that the following probabilities are true: • There is 0.1 chance for yellow. • There is 0 chance for white. • • 2 • There is chance for blue. 10 There is 0.4 of a chance for green. 3 There is chance for red. 10 6 Each of these spinners can land on red, but there is not the same chance for each of them. A B C D E a Order the spinners from least likely to most likely to land on red. b Write a number value for the chance of each spinner landing on red. Spinner A: Spinner B: Spinner C: Spinner D: Spinner E: 7 Imagine this situation. There are 10 0 marbles in a bag. You know they are either red or blue. You pick out 10 marbles and nd that you have 2 red ones and 8 blue ones. How many of the 10 0 marbles are likely to be: 10 0 marbles (RED and BLUE) a red? b blue? 8 Which of these does not show the chance of choosing a blue marble from this bag? Circle one. 1 4 4 0% 0.4 4 10 10 0 marbles (6 0 RED and 4 0 BLUE) 134 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 In a pack of 52 playing cards (without the joker), there are four suits (or t ypes): diamonds, spades, clubs and hear ts. Imagine the 52 cards are face - down. a Express the chance of picking up a diamond as a fraction. b Name a t ype of card that you would have half a chance of picking up. c There are four “picture” cards in each suit. Express the chance of picking up a picture card as a fraction. d If you picked up 20 cards, how many could you expect to be hear ts? 2 Chloe invented a board game. The number of squares you move depends on the colour of the spinner you land on. The more squares you move, the less chance there is of landing on that colour. This is how it works: • Land on red: Move 1 square • Land on green: Move 4 squares • Land on blue: Move 2 squares • Land on gold: Move 6 squares a Colour the spinner so that there is the greatest chance of landing on red, less chance for green, even less chance for blue and the least chance of all for gold. b Describe the chance of landing on each colour as a fraction and a decimal. Red: Blue: Green: Gold: 3 The Jellybean Company always put 20 red ones, 10 green ones, 25 white ones, 20 yellow ones, 10 purple ones, 10 pink ones and 5 black ones in each pack. a Joel loves the yellow ones. He takes one from his pack without looking. What is the chance that he will take a yellow jellybean? b Which colour is there a quar ter of a chance Evie will take out? c Lachlan’s favourites are red and green. What fraction of a chance does he have of getting one of his favourites? d Which colour jellybean has a 1- in -20 chance of being chosen by Charlie? OX FOR D U N I V E RSI T Y PR E S S 135

UNIT 10: TOPIC 2 Chance experiments There is a 1- in -2 chance of choosing correctly when a coin is tossed. That means that if you toss the coin four times the chances are that it will land twice on heads and twice on tails. However, does that mean it will happen? It ’s sure to land 1s t toss 2nd tos s 3rd toss 4th toss Guided practice 1 Imagine a coin lands on heads 10 times in a row. Circle the chance of it landing on tails next throw. 10 0% 9 0% 75% 5 0% 25% 0% 2 a Predict the result if you toss a coin 10 times. Heads: Tails: b Toss a coin 10 times. Record the results. Tos s 1s t 2nd 3rd 4th 5th 6th 7th 8 th 9 th 10 th H or T? c Compare your prediction with what actually happened. Explain the difference. 3 There is not a 1- in -2 chance of rolling a 4 on a 6 - sided dice. a Give a number value for the chance of the dice landing on 4: b If a dice lands on 4 ten times in a row, what is the chance of it landing on 4 on the eleventh throw? 4 a Predict the result if you roll a dice 12 times. One: Two: Three: Four: Five: Six: b Roll a dice 12 times. Record the results. Tos s 1s t 2nd 3rd 4th 5th 6th 7th 8 th 9 th 10 th 11th 12 th Result c Was it more dif cult to predict the results for the coin or the dice? Tr y to give an explanation. 136 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 2 3 2 For this experiment, you will need a spinner numbered from 1 to 4. 4 1 4 1 a Circle the number value that does not describe the chance of the spinner 4 landing on number 4. 3 1 4 out of 10 1 out of 4 25% 0.25 4 4 3 b If you spin the spinner four times it should land on each number once. Do you think that will happen? Give a reason for your answer. 2 It’s time to conduct the Number on experiment. Decide on the the spinner number of spins that is 1 2 3 4 necessar yto obtain accurate Tally of the results: 12? 20? 4 0? number of ( The number needs to be a times it landed multiple of 4.) Operate the spinner and tally the results in the table. Total 3 Write a few sentences about the results of the experiment. Think about things such as: • Did it turn out how I expected? • Why did it not land the same number of times on each number? • If I star ted from the beginning again, would the results be the same? • If I doubled the number of spins, would it be ver y different? • How do my results compare to someone else’s? 4 The way an experiment is set up can affect 1 3 the results. If you made a 5 - sided spinner and 2 1 numbered it like this, how would it affect the 4 chance for each number? 4 2 OX FOR D U N I V E RSI T Y PR E S S 137

5 For this experiment, you will need two coins. There are three results that can occur. Fill in the table to show the possible results. When you toss t wo coins the result can be: They both land on heads. 6 Predict the results after 4 0 tosses of the coins. Two heads: Two tails: Heads and tails: 7 Carr y out the experiment. Tally and record the results in the table. Ways the coins landed Two heads Two tails Heads and tails Tally of the number of times they landed like that Total 8 Write a few sentences commenting on the results of your experiment. 9 Each result did not have the same Result: heads and tails Result: t wo t ails chance of occurring in the last experiment. Explain why by looking Result: t wo heads at the diagram. H T H H 138 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 We can give a number value for the chance of this spinner not stopping on white. Write the number value in as many different ways as you can. 2 Circle the statement that best describes the chance of this spinner stopping on yellow. about 5% about 15% about 25% about 50% about 75% 3 Imagine the spinner in the question 2 stops on yellow 10 times in a row. Circle the chance of this spinner stopping on yellow next time. 1 3 0 1 6 6 4 Draw seven equal squares on a piece of paper or card. Write the word MINIMUM, with one letter per square. M Cut out the seven squares. Turn them over. Move them around. a What is the chance of picking up the letter M rst go? b Have the letters N and U facing up and the other papers facing down. Describe the chance of picking up a letter I rst go. c Put all the papers face - down and shuf e them around. Pick up two without looking. There might be two letter Ms. What are all the possibilities? 5 If you carried out the experiment 42 times, how many times would you expect each letter to appear? OX FOR D U N I V E RSI T Y PR E S S 139

GLOSSARY acute angle An angle that is smaller than array An arrangement of items a right angle or 9 0 degrees. into even columns and rows to make them easier to count. balance scale Equipment that balances items of equal mass; used to compare the mass of different items. Also called pan balance or right angle equal arm balance addition The joining or adding of two numbers together to nd the total. Also known as adding, plus and + = bar graph A way of representing data using sum. See also vertical addition 3 and 2 is 5 bars or columns to show the values of each variable. algorithm A process or formula Favourite sports used to solve a problem in mathematics. elpoep fo rebmuN 16 14 T O Examples: 12 horizontal algorithms 2 4 10 2 4 + 13 = 3 7 ver tical 8 algorithms + 1 3 6 3 7 4 2 0 Cricket Soccer Net- Rugby Foot- Basket- analogue time Time shown ball ball ball on a clock or watch face with Sport numbers and hands to indicate base The bottom edge of the hours and minutes. a 2D shape or the bottom angle The space between two face of a 3D shape. base lines or sur faces at the point where they meet, usually capacit y The amount measured in degrees. that a container can hold. 75 - degree angle Example: The jug has a capacit y of 4 cups. anticlock wise Moving in the opposite direction Car tesian plane A grid system with to the hands of a clock. numbered horizontal and ver tical axes that allow area The size of an for exact locations to be described and found. object’s sur face. y 10 Example: It takes 12 tiles 9 to cover this poster. 8 7 6 5 area model A visual way of solving 4 multiplication problems by constructing a 3 2 rectangle with the same dimensions as the x –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10 –1 numbers you are multiplying and breaking –2 the problem down by place value. –3 –4 10 8 6 × 10 = 6 0 –5 –6 6 × 8 = 48 –7 6 –8 so –9 –10 6 × 18 = 10 8 140 OX FOR D U N I V E RSI T Y PR E S S

categorical variables The different groups congruent shapes Shapes that remain the that objects or data can be sor ted into based same size and shape even when they have on common features. transformed. Example: Within the categor y of ice - cream avours, variables include: coordinates A combination of 3 vanilla choc olate s trawberr y numbers or numbers and letters 2 centimetre or cm A unit for measuring the that show location on a grid map. 1 A B C length of smaller items. corner The point where two edges of a shape or object meet. Also known as a vertex Example: Length is 8 0 cm. circle graph A circular graph Joshua corner Ryan Xavier Peter Finn divided into sections that look like por tions of a pie. cross-sec tion The sur face c ir c umfe re nc e The distance or shape that results from around the outside of a circle. making a straight cut through a 3D shape. clock wise Moving in the same direction as the hands of a clock. common denominator Denominators that cube A rectangular prism where all are the same. To nd a common denominator, six faces are squares of equal size. you need to identif y a multiple that two or more cubic c e ntime tre or 3 A unit for cm denominators share. measuring the volume of smaller objects. Example: This cube 1 cm is exactly 1 cm long, 1 cm 1 1 1 4 2 1 Example: + + = + + 2 4 8 8 8 8 1 cm wide and 1 cm deep. 1 cm 7 = 8 cylinder A 3D shape with two parallel circular bases and one cur ved compensation strategy A way of solving sur face. a problem that involves rounding a number to make it easier to work with, and then paying data Information gathered through methods back or “compensating” the same amount. such as questioning, sur veys or obser vation. Example: 24 + 99 = 24 + 100 – 1 = 123 decimal frac tion A way of writing a composite number A number 6 number that separates any whole numbers 2 that has more than two factors, from fractional par ts expressed as tenths, that is, a number that is not 1 a prime number. hundredths, thousandths and so on. 9 1 10 cone A 3D shape with a circular Example: 1.9 is the same as 1 whole base that tapers to a point. 9 and 9 par ts out of 10 or 1 10 OX FOR D U N I V E RSI T Y PR E S S 141

degrees Celsius A unit used to measure the equal Having the same number or value. temperature against the Celsius scale where 0°C is the freezing point and 10 0°C is the boiling point. denominator The bottom Example: Equal size Equal numbers number in a fraction, which 3 4 shows how many pieces the equation A written mathematical problem whole or group has been where both sides are equal. divided into. Example: 4+5 = 6+3 diame te r A straight line from one side of a circle to the other, passing = through the centre point. digital time Time shown equilateral triangle A triangle with on a clock or watch face with three sides and angles the same size. numbers only to indicate the hours and minutes. equivalent frac tions Different fractions that represent the same size in relation to a whole division/dividing The process of sharing or group. a number or group into equal par ts, with or without remainders. 1 2 3 4 2 4 6 8 dot plot A way of representing pieces e s timate A thinking guess. of data using dots along a line labelled with even number A number that can be divided variables. equally into 2. Favourite pet s Example: 4 and 8 are even numbers face The at sur face of a 3D shape. cat dog rabbit face double/doubles Adding two identical numbers or multiplying a number by 2. Example: 2+2=4 4×2=8 fac tor A whole number that will divide evenly into another number. duration How long something lasts. Example: The factors of 10 are 1 and 10 Example: Most movies have a duration 2 and 5 of about 2 hours. nancial plan A plan that helps you to edge The side of a shape or the line where organise or manage your money. two faces of an object meet. ip To turn a shape over horizontally or edge edge ver tically. Also known as reection horizontal flip vertical flip 142 OX FOR D U N I V E RSI T Y PR E S S

frac tion An equal par t of a whole or group. Example: 6 + 7 = 13 can be reversed with 13 – 7 = 6 Example: One out of two par ts or 1 is shaded. 2 grams or g A unit for measuring the mass of smaller items. invoic e A written list of goods and ser vices provided, including their cost and any GST. P r iy a’s Pet Store Ta x I nvoice Item Quantity Unit price Cost Sia mese cat 1 $500 $ 5 0 0.0 0 Cat food 20 $1.5 0 $ 30.0 0 10 0 0 g is 1 kg Tota l pr ice of good s $ 530.0 0 G ST (10%) $ 53.0 0 graph A visual way to represent data or Tota l $ 5 8 3.0 0 information. Pets in our class Pets in our class isosceles triangle A triangle with two Cats elpoep fo rebmuN 8 sides and two angles of the same size. 7 Dogs 6 5 4 3 2 0 Cats Dogs Rabbits jump strategy A way to solve number Rabbits Type of pet problems that uses place value to “jump” along a number line by hundreds, tens and ones. GST or Goods and Ser vices Tax A tax, such as 10%, that applies to most goods and Example: 16 + 22 = 38 ser vices bought in many countries. +10 +10 +1 +1 Example: Cos t + GST (10%) = Amount you pay 0 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 $10 + $ 0.10 = $10.10 kilograms or kg A unit hexagon A 2D shape for measuring the mass of with six sides. larger items. horizontal Parallel with the horizon or going straight across. horizontal kilometres or km A unit for line measuring long distances or lengths. Orange Grove Glenbrook Way improper frac tion A fraction where the Sw im S w numerator is greater than the denominator, a n 3 P such as a r 2 a d e 5 km L aw son L ane Dubbo Drive integer A whole number. Integers can be ev irD alaoK yaW yballaW positive or negative. daoR allesoR yaW tabmoW daoR um E –5 –4 –3 –2 –1 0 1 2 3 4 5 kite A four- sided shape where inverse operations Operations that are the two pairs of adjacent sides are opposite or reverse of each other. Addition and the same length. subtraction are inverse operations. OX FOR D U N I V E RSI T Y PR E S S 143

legend A key that tells you what the symbols millimetre or mm A unit for measuring on a map mean. thelength of ver y small items or to use when accuracy of measurements is impor tant. P ar k Ser vice s t ation C ampground R ail w a y Road length The longest dimension of a shape or object. cm 1 2 3 There are 10 mm in 1 cm. line graph A t ype of Today’s temperature mixed number A number that contains both C° ni erutarepmeT 35 graph that joins plotted 30 a whole number and a fraction. 25 3 Example: 2 data with a line. 20 4 15 10 5 0 multiple The result of multiplying a par ticular 10:00 12:00 02:00 04:00 06:00 am pm pm pm pm whole number by another whole number. Time litres or L A unit for measuring Example: 10, 15, 20 and 10 0 are all multiples of 5. the capacit y of larger containers. near doubles A way to add two nearly Example: The capacit y of this identical numbers by using known doubles bucket is 8 litres. facts. mas s How heav y an object is. Example: 4 + 5 = 4 + 4 + 1 = 9 net A at shape that when folded up makes a 3D shape. Example: 4.5 kilograms 4.5 grams metre or m A unit for measuring the length of larger objects. milligram or mg A unit for measuring the mass of lighter items or to use when accuracy number line A line on which numbers can of measurements is impor tant. be placed to show their order in our number system or to help with calculations. 0 10 20 30 40 50 60 70 80 90 100 70 0 mg 2L number sentence A way to record 1L millilitre or mL A unit for calculations using numbers and mathematical measuring the capacit y of smaller symbols. containers. Example: 23 + 7 = 30 10 0 0 mL is 1 litre 144 OX FOR D U N I V E RSI T Y PR E S S

numeral A gure or symbol used to parallelogram A four- sided shape where represent a number. each pair of opposite sides is parallel. Examples: 1 – one 2 – two 3 – three numerator The top number in a fraction, which shows how many 3 4 pat tern A repeating design or sequence pieces you are dealing with. of numbers. obtuse angle An angle that is larger than Example: Shape pattern a right angle or 9 0 degrees, but smaller than 18 0 degrees. Number pattern 2, 4, 6, 8, 10, 12 pentagon A 2D shape with ve sides. per cent or % A fraction out of 10 0. right angle 62 Example: or 10 0 oc tagon A 2D shape 62 out of 10 0 with eight sides. odd number A number that cannot be is also 62%. divided equally into 2. Example: 5 and 9 are odd p e rime te r The distance 7m numbers. around the outside of a 6m shape or area. 5m Example: Perimeter = operation A mathematical process. The 3m four basic operations are addition, subtraction, 10 m multiplication and division. 7 m + 5 m + 10 m + 3 y 6 m + 6 m = 31 m 5 origin The point on a 4 3 pic tograph A way of representing data using 2 Car tesian plane where the x pictures so that it is easy to understand. 1 2 3 4 x - axis and y - axis intersect. –1 Example: Favourite juices in our class –2 origin –3 –4 –5 –6 outcome The result of a chance experiment. Example: The possible outcomes if you roll a dice are 1, 2, 3, 4, 5 or 6. parallel lines Straight lines that are the same distance apar t and so will never cross. place value The value of a digit depending parallel parallel not parallel on its place in a number. M H Th T Th Th H T O 2 2 7 4 8 2 2 7 4 8 6 7 7 4 8 6 3 4 8 6 3 1 OX FOR D U N I V E RSI T Y PR E S S 145

y 6 polygon A closed 2D shape with three or quadrant A quar ter of 5 4 more straight sides. a circle or one of the four 3 2 quar ters on a Car tesian x –5 –4 –3 –2 –1 1 2 3 4 –1 plane. –2 –4 –5 polygons not polygons quadrant polyhedron (plural polyhedra) A 3D shape quadrant with at faces. quadrilateral Any 2D shape with four sides. polyhedra not polyhedra radius The distance from the centre of a circle to its circumference or edge. power of The number of times a par ticular number is multiplied by itself. reec t To turn a shape over horizontally 3 or ver tically. Also known as ipping Example: 4 is 4 to the power of 3 or 4 × 4 × 4. ver tical horizontal reection reection prime number A number that has just two factors – 1 and itself. The rst four prime reex angle An angle that is between numbers are 2, 3, 5 and 7. 18 0 and 36 0 degrees in size. prism A 3D shape with parallel bases of the same shape and rectangular side faces. remainder An amount left over after dividing one number by another. Example: 11 ÷ 5 = 2 r1 triangular rectangular hexagonal rhombus A 2D shape with four sides, all of prism prism prism the same length and opposite sides parallel. probabilit y The chance or likelihood of a par ticular event or outcome occurring. Example: There is a 1 in 8 chance right angle An angle of exactly 9 0 degrees. this spinner will land on red. protrac tor An 80 100 90º 100 0 90 1 7 1 0 80 0 7 1 0 1 instrument used to 0 1 0 2 3 5 1 0 0 3 1 measure the size of 90º arms 3 0 angles in degrees. 0 2 6 0 1 0 2 071 01 071 01 081 0 vertex right-angled triangle A triangle where one angle is exactly 9 0 degrees. pyramid A 3D shape with a 2D shape as a 90º base and triangular faces meeting at a point. rotate Turn around a point. square pyramid hexagonal pyramid 146 OX FOR D U N I V E RSI T Y PR E S S

rotational symmetr y A shape has rotational skip counting Counting for wards or symmetr y if it ts into its own outline at least backwards by the same number each time. once while being turned around a xed centre point. Back to the s tar t Examples: Skip counting by ves: 5, 10, 15, 20, 25, 30 1s t p o s i t i o n Skip counting by twos: 1, 3, 5, 7, 9, 11, 13 × • • • × slide To move a shape to a new position • × × × • without ipping or turning it. Also known as translate 2nd p osition round/rounding To change a number to another number that is close to it to make it easier to work with. sphere A 3D shape that is 229 can be per fectly round. rounded up to rounded down to split strategy A way to solve number problems the nearest 10 the nearest 10 0 OR that involves splitting numbers up using place 230 20 0 value to make them easier to work with. scale A way to represent large areas on maps Example: 21 + 14 = 20 + 10 + 1 + 4 = 35 by using ratios of smaller to larger measurements. Example: 1 cm = 5 m scalene triangle A triangle where no sides are the same length and + = + + + = no angles are equal. sec tor A section of a circle bounded by two radius lines and an arc. arc 2 1 cm 1 cm square centimetre or cm radius lines sector A unit for measuring the area of smaller objects. It is exactly 1 cm long and 1 cm wide. 2 A unit square metre or m for measuring the area of larger 1m 1m spaces. It is exactly 1 m long and semi- circle Half a circle, bounded by an arc 1 m wide. and a diameter line. semi-circle square number The result of a number being multiplied by itself. The product can be arc represented as a square array. 2 Example: 3 × 3 or 3 =9 diameter line straight angle An angle that is exactly 18 0 degrees in size. 18 0 º similar shapes Shapes whose angles remain the same size even when the lengths of the sides have been changed. OX FOR D U N I V E RSI T Y PR E S S 147