Oxford Mathematics 3

UNIT 8: TOPIC 1 Symmetry An objec t is symmetrical if one side is a mirror image of the other. Line symmetry can be horizontal, vertical or even diagonal. Guided practice 1 Tick if each item is symmetrical or not. Symmetrical Symmetrical Symmetrical Not Not Not symmetrical symmetrical symmetrical Symmetrical Symmetrical Symmetrical Not Not Not symmetrical symmetrical symmetrical OX FOR D U N I V E RSI T Y PR E S S 98

Independent practice 1 Draw 1 line of symmetr y on each shape. 2 Draw 2 lines of symmetr y on each shape. 3 a Which shape in question 2 has exac tly 3 lines of symmetr y? b Which shapes have exac tly 4 lines of symmetr y? OX FOR D U N I V E RSI T Y PR E S S 99

4 a Find and draw 4 symmetrical items. b Draw a line of symmetr y on each. 5 Circle the shapes with line symmetr y. 10 0 Are you symmetrical? OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Draw a symmetrical shape pic ture. 2 Create a symmetrical pic ture on the grid. Make sure that one side of the pic ture is a reec tion of the other side. OX FOR D U N I V E RSI T Y PR E S S 101

UNIT 8: TOPIC 2 Slides and turns There are examples of slides and turns all around us. What different meanings does the word “slide” have? Guided practice 1 Slide or turn? Slide Turn Slide Turn Slide Turn Slide Turn 102 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 Follow the rules to make repeating pat terns. a slide, then quar ter turn clock wise b half turn, then quar ter turn clock wise c half turn, then slide d quar ter turn, then half turn anticlock wise e half turn, slide, then quar ter turn anticlock wise OX FOR D U N I V E RSI T Y PR E S S 103

2 a Make your own slide and turn pat tern. b Write the rule for your pat tern. A flip is when an object is turned o ver to be a mirror image of itself. 3 Slide, turn or ip? 4 Find 2 examples of ip, slide or turn pat terns in your classroom. a Draw each pat tern. b Label the translations. 104 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Circle and label slides, turns and ips in these designs. 2 Design your own T-shir t pat terns using slides, turns and ips. OX FOR D U N I V E RSI T Y PR E S S 105

UNIT 8: TOPIC 3 Grids and maps The tree is at B3. The boy is at E1. The station is at E4. To nd what is at D2, put one nger on D and another on 2 and mo ve them along the lines until they meet. F Guided practice 6 5 4 3 2 1 1 What is at: a D1? b D6? c G2? d A 2? e D 4? f H4? 106 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 Write the let ters in the correc t squares. a E in C 4 6 b L in E2 5 c N in H4 4 d L in D3 3 e D in F4 2 f W in B5 1 g O in G3 A B C D E F G H I h E in I5 2 Write the grid references for these locations. 5 4 a the entrance: b the hotdog stand: 1 A B C D E F G c the dodgem cars: and , d the roller coaster: and , and and e the pirate swing: f the Ferris wheel: 107 OX FOR D U N I V E RSI T Y PR E S S

Bus yaW tibbaR Hospital daoR hsiF stop Cat Road Crab Court Car park B B Shopping centre ir Swimming d u pool S t s s r t e o e t p Dog Road daoR effariGeteertS raeBTiger StreetSkate park teertS taoG n School Lion Lane a L e s r o H Bus stop 3 a Which 2 roads is the skate park on? b Which 2 roads is the hospital on? 4 Follow the direc tions. Remember to consider where you are on the map a Star t at the Bird St bus stop. when turning left or right. b Walk along Bird St to Cat Rd. c Turn lef t onto Cat Rd. d Keep walking until you reach Goat St. e Turn lef t and walk to the corner of Dog Rd. f Where are you now? 5 Write your own direc tions from the swimming pool to the school. 108 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Create a map of your classroom or school. 2 Write direc tions from one place on your map to another. 3 5 Write the grid reference for: 4 a a tree. 3 b the picnic table. c the slide. 2 d the ducks. 1 A B C D E F OX FOR D U N I V E RSI T Y PR E S S 109

UNIT 9: TOPIC 1 Collecting data You can collec t data from many dif ferent sources. Which source of data might be best for nding out where your class likes to go for holidays? Guided practice 1 Match the data with the best source. favourite food favourite number of students in in your class food in your people who your class walked past who know countr y the school their times during lunch tables obser vation sur vey test results other sources, such as government depar tment ofs t atis tic s 2 What answers might you expec t if you asked your classmates about: a their favourite spor t? b their favourite colour? c what pets they have? 110 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 a Write a sur vey question to nd out about your classmates’ hobbies. b Ask 10 people your question and record their responses in the table. Number of people Responses 1 2 3 4 5 6 7 8 9 10 2 Circle the best question to ask if you want to nd out the number of brothers and sisters your classmates have. a Do you have any brothers and sisters? b How many people in your family? c How many brothers and sisters do you have? 3 Ask 5 people the question you chose and record their answers with ticks. 0 1 2 3 4 or more Number of 111 brothers and sisters OX FOR D U N I V E RSI T Y PR E S S

4 The data in this list was collec ted in a sur vey. Reorganise the data as a table using tally marks. Sur vey question: What is your favourite colour? Lis t Table blue, red, blue, green, red, red, Colour Responses green, blue, pink, red, blue, red 5 Sur vey 12 people in your class about their favourite animal. a Write the question you will ask them. b List their responses. c Show their responses in a table. 112 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 These shapes have been sor ted into 3 groups. a Explain how they are grouped. b What source do you think was used to classif y the data? 2 a Choose and record one t ype of data you could collec t in the classroom through obser vation. b Collec t and record the data in a list or table. OX FOR D U N I V E RSI T Y PR E S S 113

UNIT 9: TOPIC 2 Graphs This is a bar graph. HOW WE GOT TO SCHOOL stneduts fo rebmuN 8 The x-axis is also called the 7 horizontal axis, and the y -axis 6 5 is called the vertical axis. 4 3 2 1 0 Walk C ar Bike Bus Scooter Trans por t me thod Guided practice FAVOURITE SODA FLAVOURS IN 3P a What is the title of the graph? 1 8 7 stneduts fo rebmuN 6 5 4 3 b What does the x -axis show? 2 1 0 Lemonade Raspberr y Cola Lime c What does the y -axis show? Flavour s d How many dif ferent avours are recorded? e What is the highest number on the y -axis? f Which avour was the favourite of the least number of students? 114 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 This table shows the favourite day of the week in class 3S. Day Monday Tuesday Wednesday T hur sday F r iday S a t ur day Sunday Number || of | s tudent s a Use the data to complete the graph. FAVOURITE DAY OF THE WE EK IN 3S 12 11 10 9 8 stneduts fo rebmuN 7 6 5 4 3 2 1 0 Monday Tuesday Wednesday T hursd ay Friday S aturd ay Sunday Days of the week b Which day is the most popular? c Which day is the least popular? d What does the x -axis show? e What does the y -axis show? f What was the highest total recorded? 115 OX FOR D U N I V E RSI T Y PR E S S

2 a Sur vey 10 classmates about their favourite meal and record the data as a list. b Make a pic tograph with the data. Number of people Ho w is a pictograph different from a bar Break fast graph? Ho w are they Lunch the same? Dinner c Which meal was the most popular? d How many people preferred break fast? 3 Make a table with tally marks using the bar graph data. WHERE I WAS BORN WHERE I WAS BORN Countr y elpoep fo rebmuN 8 Number 7 of 6 5 people 4 3 2 1 0 ylatI dnalaeZ weN ailartsuA manteiV Country 116 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Sur vey 15 classmates to nd out their bir th order in their family. a Record your results in the table. Position 1s t 2nd 3rd 4th 5th 6th or more Number of s tudent s b Make a pic tograph with c Make a bar graph with the results. the results. 1s t 15 2nd 14 13 3rd 12 4th 11 5th 10 6th or more 9 8 7 6 5 4 3 2 1 0 d Give both graphs a title and labels. e Which graph do you nd easier to read? Why? OX FOR D U N I V E RSI T Y PR E S S 117

UNIT 9: TOPIC 3 Interpreting data HOURS OLEG SPE NT TRAINING THIS WE EK 8 7 • Oleg did the most training on Wednesday. 6 • He didn’t do any sruoH 5 training on Sunday. 4 • He did 2 hours of training on Monday. 3 What else does the 2 graph tell you? 1 0 Mon Tues Wed Thur s Fri Sat Sun Days of the week Guided practice 1 Use the data to answer the questions. HOW I FE EL ABOUT SCHOOL 10 a Which response was most 9 popular? 8 stneduts fo rebmuN 7 b Least popular? 6 5 c Which response did 4 6 students choose? 3 2 1 0 Fun Boring Challenging Interesting Hard Responses d Which 2 responses were chosen by the same number of students? e How many students were sur veyed? 118 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 Use the data to answer the questions. MOST POPULAR AFTERNOON SNACK IN YEAR 3 12 11 10 9 8 stneduts fo rebmuN 7 6 5 4 3 2 1 0 Milkshake Fruit Sandwich Cookie Popcorn Other Snacks a How many more students chose fruit than popcorn? b Did more students choose milkshakes or cookies? c What might “O ther” be? 2 Write 4 more statements about the data on the graph. OX FOR D U N I V E RSI T Y PR E S S 119

3 These graphs show how many goals 5 students scored in a football season. GOALS SCORE D IN SEASON GOALS SCORE D IN SEASON slaog fo rebmuN 8 7 6 5 4 3 2 1 0 David Hayley Kenadee Miller Ming Name a List 2 features the bar graph has that Ho w do you kno w which the pic tograph doesn’t. one is the bar graph? b When might you use the rst t ype of graph? c When might you use the second t ype of graph? d Write 2 fac ts from the data in the graphs. e How many more did the highest goal scorer score than the lowest? f How many goals did the students score altogether in the season? 120 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 a Choose a sur vey topic (such as favourite foods) and write a question to ask your classmates. Topic: Ques tion: b Sur vey 12 students and record their responses. c Make a graph of the results. d Write 3 statements about your data. OX FOR D U N I V E RSI T Y PR E S S 121

UNIT 9: TOPIC 4 Diagrams We use diagrams to sor t information in dif ferent ways. We could use a Venn diagram. We could use a Carroll diagram Cat Dog Brown Not brown Ho w else could they be sorted in the diagrams? Guided practice 1 a Look at the Venn diagrams. Sor t the cats and dogs from above into the correc t places. b Sor t the cats and dogs into the correc t places in the Carroll diagrams. White Cat Dog Not white 122 OX FOR D U N I V E RSI T Y PR E S S

Independent practice Look at these 2D shapes. 1 a Sor t the shapes into groups in the Venn and Carroll diagrams. Blue Not blue b Which shapes are not blue and are not 4 - sided? c Which shape is red and 4 -sided? 2 Look at how the shapes have been sor ted. Write labels on the Vennand Carroll diagrams. 3 Complete the Venn diagram using the numbers. Odd Number in number the 3 times table 30 18 23 11 15 12 13 5 21 6 27 3 OX FOR D U N I V E RSI T Y PR E S S 123

4 If you toss a coin and call “heads”, you might be right and you might be wrong. Could you get “heads” t wice in a row? We can use a tree diagram to show the chance of this happening. 2nd There are four possible toss outcomes: 1st Heads Heads/Heads toss • heads then heads Tails Tails Heads/Tails • heads then tails • tails then heads Heads Tails/Heads • tails then tails. Tails Tails/Tails There is one chance for heads and heads. That means that there is a quar ter of a chance of get ting heads t wice. a What frac tion of a chance does tails and tails have? b What frac tion of a chance does heads and tails have? Possible outcomes 5 This is Billy ’s sock game. Ina box, there are four socks – t wo are red and 2nd pick sock and t wo are blue. 1st pick sock Billy ’s mother blindfolds sock and him and says, “Take sock out one sock and then sock and another.” Can he get a sock pairof socks the same colour? a Colour and complete the tree diagram to show the possible outcomes sock and sock b Circle the correc t answer below. The chance of get ting a blue pair of socks is: less than a red pair. more than a red pair. the same as a red pair. c What frac tion of a chance is there for a pair of red socks? d Explain why there is more chance of get ting an odd pair than a bluepair. 124 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 a Complete the diagrams using the numbers below from various multiplication tables. 50 24 6 35 36 10 21 40 18 12 x2 x7 b Write another number that could go in the place where the t wocircles overlap. c What other number could go in the same space as 21? 2 Year 3 is having a special hat day. The students can choose a red, blue or yellow hat. They can decorate it with a ower, a star or a smiley face. Red hat + a Complete the tree diagram to show the dif ferent hats that the students could make. Blue hat + Yellow hat + b How many dif ferent t ypes of hats could there be? c There are 36 children in Year 3. How many hats are likely to be red and have a ower? OX FOR D U N I V E RSI T Y PR E S S 125

UNIT 10: TOPIC 1 Chance events If you have 2 ice - cream avours and 2 toppings, these are the combinations you could make: The possible combinations can also be called outcomes. Guided practice 1 a Predic t how many outcomes would be possible with 3 avours and 2 toppings. b Draw or write each of the combinations. c How many are there? 126 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 a Jawad put a red, a blue, a green and a yellow marble in a box. List the possible outcomes if he draws out 2 of them at once. b How many possible outcomes do you think there will be if he adds a purple marble? c List or draw all the possibilities. d How many are there? e How likely is it that Jawad draws out a red marble on the rst tr y? impossible less likely most likely cer tain f How likely is it that he draws out a black one? impossible less likely most likely cer tain OX FOR D U N I V E RSI T Y PR E S S 127

2 a How many dif ferent outcomes are possible on this spinner? b How likely is it to land on: i red? ii green? iii pink? iv yellow? c What is the arrow most likely to land on? When might you need to kno w ho w likely something is? d What is the arrow least likely to land on? 3 Colour the spinner so that: a it is most likely to land on green. b it is least likely to land on blue. c it is impossible to land on yellow. d it is possible to land on red. 4 How many outcomes are possible if you toss: a 1 coin? b 2 coins? c 3 coins? 5 Why do you think people use tossing coins to make decisions? 128 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Imagine a box containing 1 red and 1 blue counter. If you draw the counters out of the box one -by- one, 2 outcomes are possible: red blue or blue red a Predic t how many combinations are possible if there are 3 colours. b Draw or list the possible outcomes if a pink counter is added. 2 Write 3 likelihood statements about the gumballs in this machine. 1. 2. 3. OX FOR D U N I V E RSI T Y PR E S S 129

UNIT 10: TOPIC 2 Chance experiments Af ter 10 rolls of a dice, Penny recorded the following results. Outcome 1 2 3 4 5 6 Number || | |||| || | of times If Penny rolls again, what do you think the next number will be? Guided practice 1 Now it ’s your turn. a Predic t what your results will be if you roll a dice 10 times. Outcome 1 2 3 4 5 6 Predic ted number of times b Conduc t the experiment and record the results. Outcome 1 2 3 4 5 6 Ac tual number of times c Was your predic tion correc t? d Why or why not? 130 OX FOR D U N I V E RSI T Y PR E S S

Independent practice 1 a Roll a dice 30 times and record the results. Outcome 1 2 3 4 5 6 Number of times b If you repeat the experiment, do you think the results will be the same? Why or why not? c Roll a dice another 30 times. Outcome 1 2 3 4 5 6 Number of times d Were the results dif ferent? Why or why not? e What would you expec t if you did the experiment again? f How might the results be dif ferent if you repeated the experiment with a 10 -sided dice? OX FOR D U N I V E RSI T Y PR E S S 131

2 a What are the 2 possible outcomes if you toss a coin? b What are the 4 possible outcomes if you toss 2 coins? c How likely are you to toss 2 heads rather than the other outcomes? less likely equally likely more likely d Conduc t 20 trials and record the results. Outcome Tail/tail Tail/head Head/tail Head/head Number of times e Which outcome came up most of ten? Have you ever made a decision by tossing a coin? f Which came up least of ten? g Do you think your results are the same as other people in your class? h Compare your results with a classmate. What do they tell you about chance? 3 Circle the ac tivities in which chance plays a par t. • winning a raf e • get ting a per fec t score on a spelling test • catching a cold • going to the movies with your friends 132 OX FOR D U N I V E RSI T Y PR E S S

Extended practice 1 Put 5 dif ferent coloured counters into a container. a If you take out 1 counter, what colour do you think it will be? Why? b Conduc t the experiment 25 times, returning the counters to the box each time. Complete the table and record your results. Outcome Number of times c Make a pic tograph of the results. COUNTER EXPERIME NT OUTCOME S Number of people ruoloC d Write 2 statements about the results. 1. 2. OX FOR D U N I V E RSI T Y PR E S S 133

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 T O Examples: 14 horizontal algorithms 12 2 4 + 13 = 3 7 2 4 ver tical 10 algorithms + 1 3 8 6 3 7 4 2 0 analogue time Time shown Cricket Soccer Net- Rugby Foot- Basket- ball ball ball on a clock or watch face with Sport numbers and hands to indicate the hours and minutes. base The bottom edge of angle The space between two a 2D shape or the bottom lines or sur faces at the point face of a 3D shape. base where they meet, usually measured in degrees. capacit y The amount that a container can hold. 75 - degree angle anticlock wise Moving Example: The jug has a capacit y of 4 cups. in the opposite direction to the hands of a clock. Car tesian plane A grid system with numbered horizontal and ver tical axes that area The size of an allow for exact locations to be described and object’s sur face. found. y Example: It takes 12 tiles 10 to cover this poster. 9 8 7 6 area model A visual way of solving 5 4 multiplication problems by constructing a 3 2 rectangle with the same dimensions as the x numbers you are multiplying and breaking –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10 –1 the problem down by place value. –2 –3 10 8 6 × 10 = 6 0 –4 –5 6 × 8 = 48 –6 –7 6 so –8 –9 6 × 18 = 10 8 –10 134 OX FOR D U N I V E RSI T Y PR E S S

3 categorical variables The different groups coordinates A combination of 2 that objects or data can be sor ted into based on numbers or numbers and letters 1 common features. that show location on a grid map. A B C Example: Within the categor y of ice - cream corner The point where two edges of a avours, variables include: shape or object meet. Also known as a vertex corner cross-sec tion The sur face or shape that vanilla choc olate s trawberr y results from making a straight cut through a 3D shape. centimetre or cm A unit for measuring the length of smaller items. cube A rectangular prism where all six faces are squares of equal size. Example: Length is 8 0 cm. 3 A unit for measuring cubic centimetre or cm c ir c umfe re nc e The distance around the volume of smaller objects. Example: This cube 1 cm the outside of a circle. 1 cm is exactly 1 cm long, clock wise Moving in the 1 cm wide and 1 cm deep. 1 cm same direction as the hands of a clock. cylinder A 3D shape with two parallel circular bases and one cur ved sur face. common denominator Denominators that data Information gathered through are the same. To nd a common denominator, methods such as questioning, sur veys you need to identif y a multiple that two or more or obser vation. denominators share. decimal frac tion A way of writing a number that separates any whole numbers 1 1 1 4 2 1 Example: + + = + + from fractional par ts expressed as tenths, 2 4 8 8 8 8 hundredths, thousandths and so on. 7 = 8 1 10 compensation strategy A way of solving a problem that involves rounding a number to Example: 1.9 is the same as 1 whole make it easier to work with, and then paying 9 and 9 par ts out of 10 or 1 10 back or “compensating” the same amount. degrees Celsius A unit used to measure the Example: 24 + 99 = 24 + 100 – 1 = 123 temperature against the Celsius scale where 0°C is the freezing point and 10 0°C is the composite number A number 6 boiling point. 2 that has more than two factors, 1 that is, a number that is not denominator The bottom a prime number. number in a fraction, which shows how many pieces the 3 4 cone A 3D shape with a circular whole or group has been base that tapers to a point. dividedinto. OX FOR D U N I V E RSI T Y PR E S S 135

diame te r A straight line from one equilateral triangle A triangle with side of a circle to the other, passing three sides and angles the same size. through the centre point. equivalent frac tions Different fractions that digital time Time shown represent the same size in relation to a whole on a clock or watch face with or group. numbers only to indicate the hours and minutes. 1 2 3 4 2 4 6 8 division/dividing The process of sharing e s timate A thinking guess. a number or group into equal par ts, with or even number A number that can be divided without remainders. equally into 2. dot plot A way of representing pieces of data Example: 4 and 8 are even numbers using dots along a line labelled with variables. face The at sur face of a 3D shape. Favourite pet s face cat dog rabbit fac tor A whole number that will divide evenly double/doubles Adding two identical into another number. numbers or multiplying a number by 2. Example: The factors of 10 are 1 and 10 Example: 2+2=4 4×2=8 2 and 5 duration How long something lasts. nancial plan A plan that helps you to Example: Most movies have a duration organise or manage your money. of about 2 hours. ip To turn a shape over horizontally or edge The side of a shape or the line where ver tically. Also known as reection two faces of an object meet. horizontal flip edge vertical flip edge equal Having the same number or value. frac tion An equal par t of a whole or group. Example: One out of two par ts or 1 is shaded. 2 grams or g A unit for measuring the Example: Equal size Equal numbers mass of smaller items. equation A written mathematical problem where both sides are equal. Example: 4+5 = 6+3 = 136 10 0 0 g is 1 kg OX FOR D U N I V E RSI T Y PR E S S

graph A visual way to represent data or isosceles triangle A triangle with two information. sides and two angles of the same size. Pets in our class Pets in our class Cats elpoep fo rebmuN 8 7 6 jump strategy A way to solve number 5 Dogs 4 problems that uses place value to “jump” along 3 2 0 Cats Dogs Rabbits a number line by hundreds, tens and ones. Rabbits Type of pet Example: 16 + 22 = 38 GST or Goods and Ser vices Tax A tax, +10 +10 +1 +1 such as 10%, that applies to most goods and 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 ser vices bought in many countries. Example: Cos t + GST (10%) = Amount you pay $10 + $ 0.10 = $10.10 kilograms or kg A unit for measuring the mass of hexagon A 2D shape larger items. with six sides. horizontal Parallel with the horizon or going straight across. kilometres or km A unit for measuring long horizontal distances or lengths. line Orange Grove Tr a n ’s house Glenbrook Way improper frac tion A fraction where the S w a n P a r a d e 5 km numerator is greater than the denominator, L aw son L ane 3 ev irD alaoK such as yaW yballaW daoR allesoR 2 yaW tabmoW integer A whole number. Integers can be daoR um E positive or negative. –5 –4 –3 –2 –1 0 1 2 3 4 5 kite A four- sided shape where two pairs of adjacent sides are inverse operations Operations that are the the same length. opposite or reverse of each other. Addition and subtraction are inverse operations. legend A key that tells you what the symbols on a map mean. Example: 6 + 7 = 13 can be reversed with 13 – 7 = 6 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. invoic e A written list of goods and ser vices provided, including their cost and any GST. Priya’s Pet Store Tax Invoice line graph A t ype of Today’s temperature Item Quantity Unit price Cost C° ni erutarepmeT 35 graph that joins plotted 30 Siamese cat 1 $50 0 $50 0.0 0 25 data with a line. 20 Cat food 20 $1.50 $30.0 0 15 10 Total price of goods $53 0.0 0 5 GST (10%) $53.0 0 0 10:00 12:00 02:00 04:00 06:00 Total $583.0 0 am pm pm pm pm Time OX FOR D U N I V E RSI T Y PR E S S 137

litres or L A unit for measuring near doubles A way to add two nearly the capacit y of larger containers. identical numbers by using known doubles facts. Example: The capacit y of this bucket is 8 litres. 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. number line A line on which numbers can be placed to show their order in our number milligram or mg A unit for measuring the system or to help with calculations. mass of lighter items or to use when accuracy of measurements is impor tant. 0 10 20 30 40 50 60 70 80 90 100 number sentence A way to record calculations using numbers and mathematical 70 0 mg symbols. millilitre or mL A unit for 2L Example: 23 + 7 = 30 1L measuring the capacit y of smaller numeral A gure or symbol used to containers. represent a number. 10 0 0 mL is 1 litre Examples: 1 – one 2 – two 3 – three millimetre or mm A unit for measuring numerator The top number in a thelength of ver y small items or to use when 3 4 fraction, which shows how many accuracy of measurements is impor tant. pieces you are dealing with. obtuse angle An angle that is larger than a right angle or 9 0 degrees, but smaller than cm 1 2 3 18 0 degrees. There are 10 mm in 1 cm. mixed number A number that contains both a whole number and a fraction. right angle 3 Example: 2 4 multiple The result of multiplying a par ticular oc tagon A 2D shape whole number by another whole number. with eight sides. Example: 10, 15, 20 and 10 0 are all multiples of 5. 138 OX FOR D U N I V E RSI T Y PR E S S

odd number A number that cannot be p e rime te r The distance 7m divided equally into 2. around the outside of a 6m Example: 5 and 9 are odd shape or area. 5m numbers. Example: Perimeter = 3m 10 m 7 m + 5 m + 10 m + 3 m operation A mathematical process. The + 6 m = 31 m four basic operations are addition, subtraction, multiplication and division. pic tograph A way of representing data using y 6 5 pictures so that it is easy to understand. origin The point on a 4 3 Example: Favourite juices in our class 2 Car tesian plane where the x 1 2 3 4 x - axis and y - axis intersect. origin –1 –2 –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 place value The value of a digit depending distance apar t and so will never cross. on its place in a number. M H Th T Th Th H T O 2 2 7 4 8 parallel parallel not parallel 7 4 8 6 4 8 6 3 2 2 8 6 3 1 7 7 4 polygon A closed 2D shape with three or parallelogram A four- sided shape where more straight sides. each pair of opposite sides is parallel. pat tern A repeating design or sequence polygons not polygons of numbers. polyhedron (plural polyhedra) A 3D shape Example: with at faces. Shape pattern Number pattern 2, 3, 6, 8, 10, 12 pentagon A 2D shape with ve sides. polyhedra not polyhedra per cent or % A fraction out of 10 0. power of The number of times a par ticular 62 number is multiplied by itself. Example: or 10 0 3 Example: 4 is 4 to the power of 3 62 out of 10 0 or 4 × 4 × 4. prime number A number that has just two factors – 1 and itself. The rst four prime is also 62%. numbers are 2, 3, 5 and 7. OX FOR D U N I V E RSI T Y PR E S S 139

prism A 3D shape with parallel bases of the reex angle An angle that is between same shape and rectangular side faces. 18 0 and 36 0 degrees in size. remainder An amount left over after dividing one number by another. triangular rectangular hexagonal Example: 11 ÷ 5 = 2 r1 prism prism prism rhombus A 2D shape with four sides, all of probabilit y The chance or likelihood of the same length and opposite sides parallel. a par ticular event or outcome occurring. Example: There is a 1 in 8 chance this spinner will land on red. protrac tor An right angle An angle of exactly 9 0 degrees. 80 100 100 0 90 1 7 1 0 80 0 7 1 0 1 instrument used to 0 0 1 5 2 3 1 0 0 3 1 measure the size of 90º arms 3 0 0 2 1 6 0 6 1 0 0 2 angles in degrees. 071 01 01 071 081 90º 0 0 vertex pyramid A 3D shape with a 2D shape as a right-angled triangle A triangle where base and triangular faces meeting at a point. one angle is exactly 9 0 degrees. 90º rotate Turn around a point. square pyramid hexagonal pyramid rotational symmetr y A shape has rotational y 6 quadrant A quar ter of 5 symmetr y if it ts into its own outline at least 4 a circle or one of the four 3 once while being turned around a xed centre 2 quar ters on a Car tesian plane. x point. –5 –4 –3 –2 –1 1 2 3 4 –1 –2 1s t p o s i t i o n Back to the s tar t –4 × × –5   quadrant  ×   × × quadrant 2nd p osition quadrilateral Any 2D shape with four sides. round/rounding To change a number to another number that is close to it to make it easier to work with. radius The distance from the centre 229 can be of a circle to its circumference or edge. rounded down to the nearest 10 0 rounded up to OR the nearest 10 reec t To turn a shape over horizontally 230 20 0 or ver tically. Also known as ipping ver tical horizontal reection reection scale A way to represent large areas on maps by using ratios of smaller to larger measurements. Example: 1 cm = 5 m 140 OX FOR D U N I V E RSI T Y PR E S S

scalene triangle A triangle where 2 no sides are the same length and square centimetre or cm 1 cm 1 cm no angles are equal. A unit for measuring the area of smaller objects. It is exactly 1 cm long and 1 cm wide. sec tor A section of a circle bounded by two radius lines and an arc. 2 A unit square metre or m for measuring the area of larger 1m 1m spaces. It is exactly 1 m long and arc 1 m wide. radius lines sector square number The result of a number being multiplied by itself. The product can be represented as a square array. 2 semi- circle Half a circle, bounded by an arc Example: 3 × 3 or 3 =9 and a diameter line. straight angle An angle that is exactly semi-circle 18 0 degrees in size. 18 0 º arc s trategy A way to solve a problem. In diameter line mathematics, you can often use more than onestrategy to get the right answer. Example: 32 + 27 = 59 Jump strategy skip counting Counting for wards or backwards by the same number each time. 32 42 52 53 54 55 56 57 58 59 Examples: Split strategy Skip counting by ves: 5, 10, 15, 20, 25, 30 30 + 2 + 20 + 7 = 30 + 20 + 2 + 7 = 59 Skip counting by twos: 1, 3, 5, 7, 9, 11, 13 slide To move a shape to a new position subtrac tion The taking away of one without ipping or turning it. Also known as number from another number. Also known as translate subtracting, take away, difference between and minus. See also vertical subtraction Example: 5 take away 2 is 3 sphere A 3D shape that is sur vey A way of collecting data or per fectly round. information by asking questions. split strategy A way to solve number problems that involves splitting numbers up using place Strongly agree Agree value to make them easier to work with. Disagree Strongly disagree Example: 21 + 14 = 20 + 10 + 1 + 4 = 35 symmetr y A shape or pattern has symmetr y when one side is + = + + + = a mirror image of the other. OX FOR D U N I V E RSI T Y PR E S S 141

table A way to organise information that uses triangular number A number that can be columns and rows. organised into a triangular shape. The rst four are: Flavour Number of people Chocolate 12 Vanilla 7 Strawberry 8 tally marks A way of keeping t wo - dimensional or 2D A at shape that has two dimensions – width length and width. countthatusessingle lines with ever y fth line crossed to make a group. length term A number in a series or pattern. turn Rotate around a point. Example: The sixth term in this pattern is 18. 3 6 9 12 15 18 21 24 unequal Not having the same size or value. te s s e llation A pattern Example: Unequal size Unequal numbers formed by shapes that t together without any gaps. the rmome te r An instrument for value How much something is wor th. measuring temperature. Example: This coin is wor th $1. This coin is wor th 5c. three - dimensional or 3D A shape that has three dimensions – length, width width and depth. depth 3D shapes are not at. length ver tex (plural ver tices) The point where two time line A visual representation of a period edges of a shape or object meet. Also known as of time with signicant events marked in. a corner 2 9 Januar y 2 5 March 19 May 2 8 June 3 – 6 August 17 December S cho ol Mid - y e ar corner produc tion holiday s School st ar t s E as t er C amp S cho ol holiday s  nis h e s ver tical At a right angle to the horizon or translate To move a shape to a new position straight up and down. without ipping or turning it. Also known as slide vertical line horizon trapezium A 2D shape with four sides and only one set of parallel lines. 142 OX FOR D U N I V E RSI T Y PR E S S

ver tical addition A way of x-axis The horizontal reference line showing T O recording addition so that the place - 3 6 coordinates or values on a graph or map. value columns are lined up ver tically + 2 1 Favourite sports to make calculation easier. 5 7 T O elpoep fo rebmuN 16 14 ver tical subtrac tion A way of 12 10 5 7 8 recording subtraction so that the 6 4 – 2 1 2 0 place -value columns are lined up 3 6 ver tically to make calculation easier. Rugby Foot- Basket- volume How much space an object takes up. ball ball ball Example: This object has Sport a volume of 4 cubes. x-axis y-axis The ver tical reference line showing coordinates or values on a graph or map. whole All of an item or group. Example: A whole shape A whole group Favourite sports 16 y-axis elpoep fo rebmuN 14 12 10 8 6 width The shor test dimension of a shape or 4 object. Also known as breadth 2 0 Cricket Soccer Net- Rugby Foot- Basket- ball ball ball Sport OX FOR D U N I V E RSI T Y PR E S S 143

ANSWERS Extended practice e odd UNIT 1: Topic 1 1 a 379 0 = 3 0 0 0 + 70 0 + 9 0 + 0 Guided practice s d te n u n o o u th h 3 7 9 0 1 a s a d te n n o u n u h o d th s 2 4 3 1 b 8 052 = 8 0 0 0 + 50 + 2 d te n n o u h d te n n o u 8 0 5 2 h f odd 2 4 3 1 c 24 16 0 = 24 0 0 0 + 10 0 + 6 0 te n o 2 4 3 1 s d n u n o o u th h 2 4 1 6 0 n o 2 4 3 1 2 a 4 012 b 6889 c 10 24 d 19 875 d n 2 n o a u h 2 4 3 1 3 a 9 979 1171 (or 0 070) b 9499 1411 (or 0 4 0 0) b s a d te n n o u n u 21 23 25 27 29 31 33 35 37 h o d th s 8 2 7 6 b UNIT 1: Topic 2 d te n n o u h 8 2 7 6 44 46 48 50 52 54 56 58 60 Guided practice c te n o 8 2 7 6 1 Teacher note: The way students 20 24 28 32 36 40 44 48 52 choose to make pairs of items n o 8 2 7 6 3 a & b: will var y, however it should be apparent if the number is odd or d n n o u h even depending on whether or not 8 2 7 6 there is a lef t over item. a odd b even Independent practice c odd d even c 2, 4, 6, 8, 0 (in any order) 1 a four thousand, ve hundred d 1, 3, 5, 7, 9 (in any order) and six t y - eight Independent practice 4 b eight thousand and for t y -three 1 a odd c seven thousand, one hundred Odd Eve n 14 3 76 and nine 10 3 575 25 8 2 1974 13 61 3 870 Th H T O b even 8 67 50 02 4 5 6 8 9998 8 0 4 3 9999 7 1 0 9 3 a 226 5 b 3 0 57 5 a odd b even 4 c even d even Eve n t numb e r Number of people Extended practice 3 525 5 1 4 8 91 c even 1 a 8 b 24 c 36 d even 5 3 971 6 3 812 2 a 8 b 28 c 30 d even 2 16 9 3 4 16 8 8 3 a 9 b 27 c 39 d odd 4 a 11 b 27 c 37 d odd 5 a even b odd c odd d even e even f odd d even 5 8710 6 a 8720 b 870 0 c 8730 d 8690 e 8 810 f 8 610 UNIT 1: Topic 3 g 8 910 h 8 510 i 9710 j 7 710 7 23 3 8 Guided practice 1 a 7 and 17 b 8 and 18 d 5 and 25 c 10 and 20 144 OX FOR D U N I V E RSI T Y PR E S S

Independent practice Independent practice Extended practice 1 a 9 and 29 b 8 and 18 1 a 97 1 a 8 02 d 9 and 3 9 c 6 and 26 e 10 and 4 0 72 82 92 93 94 95 96 97 375 475 575 675 775 785 795 796 797 798 799 800 801 802 2 a 60 b 8, 80 c 10, 10 0 d 4, 20, 20 b 16 9 e If 8 + 8 = 16, b 923 then 8 0 + 8 0 = 16 0. f If 1 + 1 = 2, 112 122 132 142 152 162 163 164 165 166 167 168 169 then 10 0 + 10 0 = 20 0. 6 81 781 8 81 8 91 9 01 911 9 21 9 2 2 9 2 3 g If 6 + 6 = 12, then 6 0 0 + 6 0 0 = 120 0. c 29 4 2 a 178 8 b 3 519 c 75 87 h If 7 + 7 = 14, then 70 0 + 70 0 = 14 0 0. 3 8 67 Teacher to check strategies. 231 241 251 261 271 281 291 292 293 294 Teacher: Look for students 3 a 23 + 12 = 3 0 + 5 = 3 5 who choose an appropriate b 50 + 7 = 57 c 8 0 + 7 = 87 d 3 61 strategy, and can follow the steps d 80 + 9 = 89 e 6 0 + 10 = 70 sequentially to nd the correct 4 a 6 + 4 + 7 = 17 answer. b 25 + 5 + 4 = 3 4 320 330 340 350 3 6 0 3 61 c 17 + 3 + 2 + 4 = 26 d 11 + 19 + 3 + 2 = 3 5 UNIT 1: Topic 5 e 4 39 5 a 18 0 b 98 c 41 d 40 e 89 f 10 0 0 Guided practice 414 424 4 34 4 35 4 36 4 37 4 38 4 39 g 78 h 50 1 a 3, 13 b 7, 17 c 2, 12 d 4, 24 Extended practice Guided practice 1 a 12 + 8 + 7 = 27 Independent practice 1 a 96 b 16 8 c 3 87 b 23 + 7 + 12 = 42 d 74 6 e 879 f 996 1 a 2, 12 b 1, 21 c 5, 15 c 221 + 3 9 + 8 = 26 8 g 474 h 888 i 909 d 6, 26 e 3, 3 3 f 2, 8 2 2 a 54 + 39 = 93 g 3, 9 3 b 221 + 23 = 24 4 2 a 3 5 – 13 = 3 5 – 10 – 3 = 22 c 13 5 + 5 4 = 18 9 Independent practice b 4 8 – 15 = 4 8 – 10 – 5 = 3 3 d 221 + 13 5 = 3 5 6 c 52 – 21 = 52 – 20 – 1 = 31 2 8 6 3 d 67 – 3 4 = 67 – 30 – 4 = 33 UNIT 1: Topic 4 e 9 6 – 25 = 9 6 – 20 – 5 = 71 3 1 3 5 f 124 – 13 = 124 – 10 – 3 = 111 9 8 + + g 38 9 – 57 = 38 9 – 50 – 7 = 3 32 Guided practice 5 9 3 a 26 – 8 = 26 – 6 – 2 = 18 1 37 b 32 – 7 = 32 – 2 – 5 = 25 + 10 + 10 +1 4 6 3 5 8 c 35 – 9 = 35 – 5 – 4 = 26 d 21 – 6 = 21 – 1 – 5 = 15 2 2 4 2 1 e 43 – 5 = 43 – 3 – 2 = 38 8 + + 16 26 36 37 f 6 4 – 7 = 6 4 – 4 – 3 = 57 6 7 7 9 g 76 – 9 = 76 – 6 – 3 = 67 2 59 h 14 5 – 8 = 14 5 – 5 – 3 = 137 4 8 0 8 9 1 Extended practice 35 45 55 56 57 58 59 2 1 7 2 0 6 + + 1 a 2, 20 b 7, 70 c 4, 4 0 d 2, 20 0 e 1, 10 0 3 179 6 9 7 1 0 9 7 2 a 14 b 59 c 141 d 124 14 6 15 6 16 6 176 17 7 17 8 179 3 2 8 2 3 6 Teacher: Look for students who can ar ticulate how they arrived 4 5 1 6 0 3 at the answer and what mental strategies they used. + + 7 7 9 8 3 9 OX FOR D U N I V E RSI T Y PR E S S 145

2 a 14 + 17 = 31, 17 + 14 = 31, UNIT 1: Topic 6 8 6 1 7 3 31 – 14 = 17, 31 – 17 = 14 b 32 + 4 6 = 78, 4 6 + 32 = 78, Guided practice 3 6 1 6 2 0 – – 78 – 32 = 4 6, 78 – 4 6 = 32 1 23 5 0 1 1 c 15 + 3 3 = 4 8, 3 3 + 15 = 4 8, –1 –1 –1 – 10 – 10 4 8 – 15 = 3 3, 4 8 – 3 3 = 15 7 9 7 8 9 6 d 16 + 3 9 = 5 5, 3 9 + 16 = 5 5, 23 24 25 26 36 46 5 5 – 16 = 3 9, 5 5 – 3 9 = 16 4 9 3 2 0 1 2 23 – – e 97 + 70 = 167, 70 + 97 = 167, 167 – 97 = 70, 167 – 70 = 97 3 0 4 6 9 5 23 24 25 26 27 28 38 48 58 f 14 3 + 135 = 278, 135 + 14 3 = 278, 9 8 6 4 5 278 – 14 3 = 135, 278 – 135 = 14 3 3 222 5 7 4 1 4 1 – – Extended practice 4 2 3 1 222 223 233 24 3 25 3 263 1 a 3 4 + 28 is the same as 34 + 30 – 2 = 62 b 26 + 29 is the same as Extended practice Independent practice 26 + 30 – 1 = 55 1 a 526 1 a 64 c 5 3 + 4 9 is the same as 5 3 + 5 0 – 1 = 102 526 527 528 529 530 531 532 542 642 742 d 4 5 + 27 is the same as 64 65 66 67 68 78 88 98 4 5 + 3 0 – 3 = 72 b 28 5 e 5 4 + 17 is the same as b 317 5 4 + 20 – 3 = 71 285 286 287 288 298 308 318 328 428 528 628 2 a 2 × 10 = 20, 10 × 2 = 20, 20 ÷ 2 = 10, 20 ÷ 10 = 2 317 318 319 3 2 0 330 340 350 360 2 a 5214 b 26 62 c 2511 b 4 × 12 = 4 8, 12 × 4 = 4 8, 3 515 Teacher to check strategy. 4 8 ÷ 4 = 12, 4 8 ÷ 12 = 4 c 747 Teacher: Look for students c 8 × 7 = 56, 7 × 8 = 56, who choose an appropriate 56 ÷ 7 = 8, 56 ÷ 8 = 7 strategy and can follow the steps 747 74 8 75 8 76 8 778 78 8 79 8 sequentially to nd the correct d 9 × 11 = 9 9, 11 × 9 = 9 9, answer. 9 9 ÷ 11 = 9, 9 9 ÷ 9 = 11 d 473 3 a 73 b 15 32 UNIT 1: Topic 7 473 474 475 476 47 7 478 488 498 598 UNIT 1: Topic 8 Guided practice e 16 9 1 a 7 b 24 c 38 Guided practice 2 a 9 b 27 c 43 1 a 15 shared bet ween 3 is 5 b 12 shared bet ween 6 is 2 16 9 17 0 171 17 2 272 372 Independent practice c 28 shared bet ween 4 is 7 1 a 6 + 4 = 10, 4 + 6 = 10, 2 a 3 groups of 3 = 9 10 – 6 = 4, 10 – 4 = 6 b 8 groups of 2 = 16 Guided practice c 3 groups of 6 = 18 b 17 + 7 = 24, 7 + 17 = 24, 1 a 23 b 4 47 c 475 24 – 7 = 17, 24 – 17 = 7 d 732 e 223 f 504 Independent practice g 20 0 h 730 i 333 c 17 + 12 = 29, 12 + 17 = 29, 1 a 3 × 4 = 12, 4 × 3 = 12 29 – 17 = 12, 29 – 12 = 17 Independent practice b 5 × 10 = 5 0, 10 × 5 = 5 0 d 40 + 8 = 4 8, 8 + 40 = 4 8, c 5 × 6 = 30, 6 × 5 = 30 4 8 – 8 = 4 0, 4 8 – 4 0 = 8 3 7 5 3 d 4 × 10 = 4 0, 10 × 4 = 4 0 e 4 5 + 37 = 8 2, 37 + 4 5 = 8 2, 2 Note: A nswers can be in any order. 1 4 3 1 82 – 37 = 4 5, 82 – 4 5 = 37 3 2 – – a 3 × 9 = 27, 9 × 3 = 27, f 10 0 + 26 = 126, 26 + 10 0 = 126, 27 ÷ 3 = 9, 27 ÷ 9 = 3 126 – 26 = 10 0, 126 – 10 0 = 26 2 2 b 10 × 2 = 20, 2 × 10 = 20, 20 ÷ 2 = 10, 20 ÷ 10 = 2 c 8 × 5 = 4 0, 5 × 8 = 4 0, 40 ÷ 5 = 8, 40 ÷ 8 = 5 146 OX FOR D U N I V E RSI T Y PR E S S

d 7 × 10 = 70, 10 × 7 = 70, 3 a 2 × 13 = 26, so 26 ÷ 2 = 13 f 19 2 70 ÷ 10 = 7, 70 ÷ 7 = 10 b 3 × 9 = 27, so 27 ÷ 3 = 9 × 40 8 32 3 a 3 4 a 3÷3=1 c 5 × 9 = 4 5, so 4 5 ÷ 5 = 9 4 16 0 b 6 b 6÷3=2 d 5 × 11 = 5 5, so 5 5 ÷ 5 = 11 c 9 c 9÷3=3 g 19 0 d 12 d 12 ÷ 3 = 4 e 10 × 12 = 120, so 120 ÷ 10 = 12 × 90 5 10 e 15 e 15 ÷ 3 = 5 4 a 30 b 90 c 10 d 3 f 18 f 18 ÷ 3 = 6 2 18 0 e 32 f 12 g 6 h $80 g 21 g 21 ÷ 3 = 7 h 24 h 24 ÷ 3 = 8 Extended practice Extended practice i 27 i 27 ÷ 3 = 9 1 a 64 b 21 c 60 d 20 1 Teacher: Look for students who j 30 j 3 0 ÷ 3 = 10 are able to successfully interpret 5 a 4 b 9 c 6 the problems and choose an d 7 e 7 f9 UNIT 1: Topic 10 appropriate strategy to solve each 6 a 5 × 4 = 20 or 4 × 5 = 20 problem. Students also need to b 9 × 2 = 18 or 2 × 9 = 18 be able to accurately apply the Guided practice c 6 × 10 = 6 0 or 10 × 6 = 6 0 strategy to nd the correct answer. 1 a 2 × 20 + 2 × 6 = 4 0 + 12 = 52 d 7 × 5 = 35 or 5 × 7 = 35 a 14 8 b 96 c 19 0 e 2 × 7 = 14 or 7 × 2 = 14 b 4 × 10 + 4 × 4 = 4 0 + 16 = 5 6 d 4 × 26 = 10 4 – 3 = 101 f 9 × 10 = 9 0 or 10 × 9 = 9 0 c 3 × 10 + 3 × 9 = 3 0 + 27 = 57 Extended practice Independent practice 1 a 15 b 30 c 35 d 50 Unit 1: Topic 11 1 a 5 × 13 = 5 × 10 + 5 × 3 = 2 a 8 b 4 c 3 d 12 5 0 + 15 = 6 5 Guided practice 3 a b 6 × 21 = 6 × 20 + 6 × 1 = 120 + 6 = 126 1 a 18 b 30 Name Number Cost per Amount Mika of items item raised Andy Serena c 4 × 32 = 4 × 30 + 4 × 2 = c 14 d 40 Sophia Hao sold 120 + 8 = 128 8 $5 $40 Independent practice d 7 × 24 = 7 × 20 + 7 × 4 = 10 $2 $20 14 0 + 28 = 16 8 1 a 28 b 38 6 $10 $60 5 $9 $ 45 e 5 × 45 = 5 × 40 + 5 × 5 = c 26 d 32 9 $4 $36 20 0 + 25 = 225 2 Look for students who link b A nd y c Serena d $80 f 8 × 33 = 8 × 30 + 8 × 3 = numbers that add to 10 or 24 0 + 24 = 26 4 e $10 0 f7 multiples of 10. Likely answers are listed below. g 3 × 58 = 3 × 50 + 3 × 8 = 15 0 + 24 = 174 a 6 + 4 + 7 + 3 = 20 UNIT 1: Topic 9 2 b 18 + 2 + 5 + 5 = 3 0 Guided practice a 10 8 c 14 + 6 + 9 + 1 = 3 0 d 23 + 7 + 6 + 14 = 5 0 1 a 3, 6, 9, 12, 15, 18 × 20 7 4 80 28 b 2, 4, 6, 8, 10, 12, 14, 16 3 Look for students who group c 10, 20, 3 0 numbers that are easy to d 5, 10, 15, 20, 25, 3 0, 3 5 b 216 multiply.Possible answers are e 3, 6, 9, 12, 15, 18, 21, 24 listed below. × 30 6 36 a 5 × 2 = 10 × 7 = 70 Independent practice 6 18 0 b 6 × 6 = 36 1 a 8 x 4 = 8 x 2 x 2 = 16 x 2 = 32 c 26 5 c 5 × 2 = 10 × 3 = 3 0 b 20 x 4 = 20 x 2 x 2 = 4 0 x 2 × 50 3 15 = 80 d 2 × 3 = 6 × 7 = 42 5 25 0 c 12 x 4 = 12 x 2 x 2 = 24 x 2 4 a 23 [23 – 9 = 14] = 48 d 18 6 b 11 [11 + 14 = 25] d 30 x 4 = 30 x 2 x 2 = 60 x 2 × 60 2 c 27 [27 ÷ 3 = 9] 6 = 120 3 18 0 d 8 [8 × 5 = 4 0] 2 a 16 ÷ 2 = 8, 8 ÷ 2 = 4, e 420 e 21 [21 + 21 = 42] so 16 ÷ 4 = 4 f 5 5 [5 5 ÷ 5 = 11] b 4 0 ÷ 2 = 20, 20 ÷ 2 = 10, × 80 4 20 so 4 0 ÷ 4 = 10 g 67 [67 – 24 = 4 3] 5 400 c 6 0 ÷ 2 = 3 0, 3 0 ÷ 2 = 15, h 12 [12 × 10 = 120] so 6 0 ÷ 4 = 15 OX FOR D U N I V E RSI T Y PR E S S 147