# Book 19 Reaching Competence

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Ages 10 11 Year 6 Follows Stage 6 of the New Zealand Mathematics Curriculum Created by Lucy Patston 2020 Adept Education Limited

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Book 18 Able to give the value of digits and sequence and order any whole number Able to give the number of tens or hundreds in 4 digit numbers Able to use place value to multiply by tens or hundreds Able to select from a range of strategies including a standard written form Able to multiply a 2 digit number by a single digit number using a mental method Able to multiply a 2 digit number by a single digit number using a written method Able to multiply a 3 digit number by a single digit number using a mental method Able to multiply a 3 digit number by a single digit number using a written method Able to solve multi step problems Book 19 Knows and understands square numbers up to 20 x 20 Able to use both recordings of division and Able to use multiplication facts to solve division problems Able to divide up to a 3 digit number by a single digit number Able to identify factors and multiples Able to order unit fractions Able to use improper fractions and mixed numbers Knows simple equivalent fractions Able to solve simple ratio problems using repeated replication Book 20 Overview of Books 18 20 Able to understand decimals as special fractions Able to understand decimals as an extension to the place value system Able to order decimal numbers up to three decimal places Able to round decimal numbers up to three decimal places Able to add and subtract decimal numbers up to three decimal places Able to understand percentages as special fractions Knows common percentages Able to use a calculator efficiently Uses knowledge of operations to identify number patterns 2 2020 Adept Education Limited

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Learning Intention 10 Knows and understands square numbers up to 20 x 20 You have probably heard of square numbers but you might not realise what they are Square numbers are the products of numbers that are multiplied by themselves For example 3 x 3 7 x 7 and 11 x 11 They also make a very tidy line straight through the middle of our multiplication table We notate square numbers by using a superscript 2 2 This means multiplied by itself x 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 3 4 5 6 7 8 9 10 11 12 2 2 4 6 8 10 12 14 16 18 20 22 24 3 3 6 9 12 15 18 21 24 27 30 33 36 4 4 8 12 16 20 24 28 32 36 40 44 48 Long form 5 5 10 15 20 25 30 35 40 45 50 55 60 1x1 12 1 7x7 6 6 12 18 24 30 36 42 48 54 60 66 72 2x2 22 4 8x8 7 7 14 21 28 35 42 49 56 63 70 77 84 8 8 16 24 32 40 48 56 64 72 80 88 96 9 9 18 27 36 45 54 63 72 81 90 99 108 10 10 20 30 40 50 60 70 80 90 100 110 120 Fill in the table of the different notations for the square numbers 1 to 144 Squared Product notation 3x3 Long form 9 Squared Product notation 92 42 102 5x5 11 x 11 11 11 22 33 44 55 66 77 88 99 110 121 132 36 12 12 24 36 48 60 72 84 96 108 120 132 144 144 You already know the square numbers above so let s work out what the rest are up to 20 x 20 Use your calculator to find the answers 1 13 x 13 5 17 x 17 2 14 x 14 6 18 x 18 3 15 x 15 7 19 x 19 4 16 x 16 8 20 x 20 9 We will come back to look at this page later For now simply put a circle around the answers to the following multiplications the first one has been done 1 x 3 2 x 4 3 x 5 4 x 6 5 x 7 6 x 8 7 x 9 8 x 10 9 x 11 and 10 x 12 4 2020 Adept Education Limited Sheet 19 01 4 5 1

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Learning Intention 10 Knows and understands square numbers up to 20 x 20 Using a ruler continue creating the squares Write in the square numbers and the equations x 1 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4 3x3 9 4 x 4 16 5 x 5 25 36 49 64 81 10 100 11 11 x 11 121 12 12 x 12 13 14 15 16 17 18 19 20 5 2020 Adept Education Limited Sheet 19 02 4 5 1

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Learning Intention 10 Knows and understands square numbers up to 20 x 20 Knowing our square numbers to 20 x 20 can help us make quick calculations for some other equations For example we know that 13 x 13 is 169 so we can work out what 12 x 13 and 14 x 13 are just by subtracting or adding 13 13 x 13 169 One lot LESS THAN 13 x 13 12 x 13 169 13 156 One lot MORE THAN 13 x 13 14 x 13 169 13 182 TRICK OF THE TRADE It can be tricky to remember which number to add or subtract Here s how to think about it If you are using 13 x 13 to solve the equation then it will always be 13 that you add or subtract Write in your strategy for solving these equations both ways Use To find And to find e g 14 x 14 13 x 14 196 14 182 15 x 14 196 14 210 1 16 x 16 15 x 16 256 16 17 x 16 256 16 2 19 x 19 18 x 19 361 20 x 19 361 3 17 x 17 16 x 17 18 x 17 4 20 x 20 19 x 20 21 x 20 5 18 x 18 17 x 18 19 x 18 6 15 x 15 14 x 15 16 x 15 6 2020 Adept Education Limited Sheet 19 03 4 5 1

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apply Learning Intention 10 Knows and understands square numbers up to 20 x 20 Activities 1 Sheet 19 04 Square number wheel This activity provides another way your learner may like to visualise the square numbers to 20 x 20 The page also provides a space to capture the numbers that are taking longer to process into memory Writing these down and thinking about how to remember them helps to forge these connections 2 Sheet 19 05 Adept Problem Solvers 7 This activity provides a strategy for quickly calculating 2 digit multiplications that have a difference of 2 Knowing the squared facts helps students quickly determine a range of other multiplications with little effort and without a calculator 3 Sheet 19 06 Brain Busters Square number quiz 7 2020 Adept Education Limited

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Learning Intention 10 Knows and understands square numbers up to 20 x 20 Fill in the circular table Can you do it from memory 1 202 12 152 4 22 Square Numbers 52 102 100 Which square numbers could you not remember List them in the space below How will you remember these in the future 8 2020 Adept Education Limited Sheet 19 04 4 5 1

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solvers 7 Learning Intention 10 Knows and understands square numbers up to 20 x 20 Tanita is using her square numbers to 20 knowledge to figure out an easy way to do 2 digit multiplications She has found a pattern but wants to know how it works 13 x 15 14 x 16 15 x 17 14 x 14 1 15 x 15 1 16 x 16 1 195 224 255 The same simple pattern works each time Check for yourself 1 16 x 18 2 17 x 19 17 x 17 1 18 x 18 1 x 13 3 Next Tanita looks at her multiplication chart Fill in the chart Does the trick always work 13 169 4 What will the answer to 19 x 21 be 15 14 14 15 16 17 18 19 20 195 196 224 225 16 5 What is the answer to 12 x 14 17 Does this trick also work for numbers less than this Go back to Sheet 19 01 and check Do you remember circling the numbers on the 12 x 12 chart Those are the ones to look at 18 19 20 9 2020 Adept Education Limited Sheet 19 05 4 5 1

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Learning Intention 10 Knows and understands square numbers up to 20 x 20 Circle the correct answers 1 What is the square number of 16 x 16 256 289 169 16 2 What is 142 361 196 400 3 What is the square number of 9 x 9 81 121 324 17 289 18 289 17 225 15 196 14 225 14 400 800 200 182 121 144 169 19 x 19 1 20 x 20 1 19 x 21 1 196 14 7 202 is equal to 80 100 8 132 is equal to 4 324 is equal to 192 324 18 6 What is 14 x 15 14 169 5 What is 17 x 18 112 172 196 Phew Take a break 9 What is the square number of 15 x 15 227 225 228 226 10 What is 172 361 324 256 289 122 131 142 14 x 14 1 14 x 14 1 15 13 x 2 15 x 15 2 15 192 is equal to 132 192 261 461 361 265 652 526 16 162 is equal to 12 196 is equal to 192 21 x 21 1 14 What is 13 x 15 11 What is the square number of 11 x 11 121 13 What is 19 x 21 112 152 256 10 2020 Adept Education Limited Sheet 19 06 4 5 1

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Here s some other pages you ll see in this book www adepteducation co nz 2020 Adept Education Limited

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Learning Intention 12 Able to use multiplication facts to solve division problems If I have 8 jellybeans and I want to share them equally into 2 piles there will be 4 in each pile 8 2 4 If I have 2 friends and I want to give them both 4 jellybeans I will need 8 jellybeans altogether 2x4 8 8 2 4 because 2 x 4 8 They are inverse operations of each other Write the inverse operations for each of the following 1 70 10 because 10 x 70 2 24 4 because 4x 24 3 48 8 because 8x 48 4 72 6 because 6x 72 5 35 5 because 5x 35 6 60 6 because 6x 60 7 21 7 because 7x 21 8 63 9 because 9x 63 12 2020 Adept Education Limited Sheet 19 09 4 5 1

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BAK E R Y solvers 8 Learning Intention 12 Able to use multiplication facts to solve division problems Two schools have ordered food from Greg s parent s bakery Each food item comes in cartons of different sizes Greg s mum has asked Greg to put the orders together but the schools have placed their orders differently Blue School has ordered the number of items they need while Green School has ordered the number of cartons they need Help Greg fill in the table on the opposite page showing how many they ll need to make of each food item and how many cartons they ll need to fill the orders Table 1 How many items go in a standard carton Pizza Gingerbread Scone Donut Pastry Muffin 5 20 15 16 12 10 40 pizzas 300 gingerbread men 90 scones 224 donuts 144 pastries 240 muffins WORK SPACE Blue School Order 5 cartons of pizzas 18 cartons of gingerbread men 8 cartons of scones 12 cartons of donuts 6 cartons of pastries 13 cartons of muffins WORK SPACE Green School Order 13 2020 Adept Education Limited Sheet 19 14 4 5 1

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Learning Intention 13 Able to divide up to a 3 digit number by a single digit number Here is another way to work out divisions with larger numbers This time we can use a known multiplication fact that is LARGER than our dividend and then compensate using subtraction to find the answer 58 jellybeans to share They realise they could share 60 jellybeans by taking 30 each But they have 2 less than 60 so they will have 1 less than 30 each Amavi and Suresh have They would get 29 jellybeans each 60 2 2 58 2 x 3 6 so 2 x 30 60 2 58 is 2 less than 60 so we get 1 less each 30 each 1 each 29 each Use this strategy to solve these division equations Use the thought bubbles to give you a clue as to which multiplication fact to use 1 160 8 8 152 8 x 2 16 8 x 20 160 20 each 8 3 1 each 6 114 6 x 2 12 6 x 20 120 2 3 147 3 x 5 15 3 x 50 150 4 9 261 9 x 3 27 9 x 30 270 14 2020 Adept Education Limited Sheet 19 19 4 5 1

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solvers 10 Learning Intention 13 Able to divide up to a 3 digit number by a single digit number Mr Mi s new jewellery range is proving to be very popular and he is still trying to set the price just right The new items have been selling so well he has been forgetting to track his sales properly He has recorded the number of items sold and he knows how much he has received for them but he has forgotten the price he sold his necklaces for over the past 3 months Sapphire necklace Emerald necklace Diamond necklace 1 Help Mr Mi remember how he priced the necklaces May 2019 Sales Number Sold June 2019 July 2019 S E D S E D S E D 600 800 900 525 810 840 660 870 980 4 4 2 3 2 4 6 3 2 Sold for 2 Mr Mi intends to run a 50 off sale for the same 3 months next year He has predicted the Number Sold for each item over this time Help him use his previous prices to determine how much his Sales would be if he was able to sell his predicted numbers May 2020 June 2020 July 2020 S E D S E D S E D 10 10 5 10 4 6 5 4 3 Sales Number Sold 15 2020 Adept Education Limited Sheet 19 21 4 5 1

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Learning Intention 14 Able to identify factors and multiples We ve been doing so much division let s talk about multiplication for a bit We have two new words to learn Factors and Multiples Factors are the numbers we can multiply together to get a number 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Multiples are what we get after multiplying a The Factors of 10 are 1 1 x 10 10 2 2 x 5 10 5 5 x 2 10 10 10 x 1 10 number by another number The Multiples of 10 are 10 1 x 10 10 20 2 x 10 20 30 3 x 10 30 40 4 x 10 40 and so on and so on Some numbers have many factors Let s look at the number 24 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 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 1 What are the multiples of 24 to 100 2 What are the multiples of 6 to 60 3 What are the factors of 6 4 What are the factors of 20 Write down all the FACTORS for each number 5 48 6 18 7 96 16 2020 Adept Education Limited Sheet 19 22 4 5 1

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Learning Intention 14 Able to identify factors and multiples 2 and 9 are factors of 18 2 x 9 18 3 and 6 are factors of 18 3 x 6 18 What are two more factors of 18 18 is a multiple of 2 and 9 18 is a multiple of 3 and 6 What are ALL the factors of 18 Finding Factor Pairs 1 2 3 6 9 18 are factors of 18 1 18 6 3 4 5 7 8 2 9 7 2 57 are NOT factors of 18 3 6 8 2 25 4 4 5 9 2 5 3 6 They cannot be multiplied by another number to get 18 What are the multiples of 4 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 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 1x4 2x4 3x4 4x4 5x4 6 x 4 and so on ANY number x4 will be a multiple of 4 That means 0 is also a multiple of 4 and so are some negative numbers Is 15 a multiple of 3 Yes 3 x 5 15 Is 16 a multiple of 3 No There is no whole number that multiplies by 3 to give 16 1 Is 23 a multiple of 5 5 What is the closest multiple of 3 to 20 2 Is 35 a multiple of 5 6 What is the closest multiple of 7 to 40 3 Is 78 a multiple of 8 7 What is the closest multiple of 9 to 82 4 Is 42 a multiple of 8 8 What is the closest multiple of 6 to 45 9 What is the closest multiple of 5 to 45 17 2020 Adept Education Limited Sheet 19 23 4 5 1

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Learning Intention 14 Able to identify factors and multiples Sometimes when we re dividing our dividend is not always a multiple Captain Scurvy Beard and Captain Scallywag are dividing their loot equally between them They have 45 10 notes 87 1 coins Captain Scurvy Beard Captain Scallywag divides the coins like this divides the notes like this 2 x 40 is 80 Then there will be 7 coins left over We can both have 3 more but there will be 1 left over Arrrrrrgh We ll have to give this to One Eyed Billy 2 x 20 is 40 Then there will be 5 notes left over We can both have 2 more but there will be 1 left over Arrrrrrgh We ll have to give this to One Eyed Billy 45 2 22 r 1 87 2 43 r 1 22 r 1 2 45 43 r 1 2 87 Captain Shorty Pants also helped to gather the loot and he wants his fair share 1 How many 10 notes will each pirate get now 2 How many 10 notes will One Eyed Billy get 3 How many 1 coins will each pirate get now WORK SPACE 4 How many 1 coins will One Eyed Billy get 18 2020 Adept Education Limited Sheet 19 24 4 5 1

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solvers 11 Learning Intention 14 Able to identify factors and multiples The Patston Pirates are in search of treasure and want to search these two islands thoroughly They also want to know how long it will take them They have drawn a grid over their maps of the islands and marked an x on the squares they ll search They estimate each square will take them three hours to search How many hours will each island take to search 1 ______ hours to search x x x x x x x x x x x x x x x x x x x x x Hint Can you use your times tables to work out the number of squares x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x WORK SPACE x Hint What do you need to multiply the number of squares by to get the number of hours x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 2 ______ hours to search 19 2020 Adept Education Limited Sheet 19 28 4 5 1

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Learning Intention 16 Able to use improper fractions and mixed numbers Flash is sharing out 11 pizzas between him and four friends How many pizzas do they get each 11 5 2 r 1 If the remaining pizza is shared equally between them 1 they will each get 5 of the last pizza 1 The Lego men will get 2 5 pizzas each Opere has 13 biscuits to share between 3 people Anastasia has 19 apples to share between 6 people 1 How many whole biscuits do they get each 5 How many whole apples do they get each 2 How many biscuits are remaining 6 How many apples are remaining 3 What fraction of the remaining biscuits does each person get 7 What fraction of the remaining apples does each person get 4 How many biscuits does each person get 8 How many apples does each person get 20 2020 Adept Education Limited Sheet 19 34 4 5 1

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Learning Intention 16 Able to use improper fractions and mixed numbers Improper fractions are difficult to understand so we convert them into whole numbers and a fraction These are called mixed fractions or mixed numbers IMPROPER FRACTIONS MIXED FRACTIONS We like to change improper fractions into mixed fractions MIXED FRACTIONS have a whole number AND a proper fraction 7 4 3 1 4 because then they make more sense to us MIXED together Solve the equations and then write the answer as an improper fraction and a mixed fraction 1 22 3 7r1 23 3 2 31 6 5r1 31 6 3 4 7 13 5 19 4 6 39 7 51 7 7 27 8 74 9 8 49 10 4r3 19 4 4 34 9 For Questions 1 4 circle the remainders and the numerators of the mixed fraction What do you notice about the remainders and the numerators in each equation 10 For Questions 5 8 circle the divisors and the denominators of the mixed fraction What do you notice about the divisors and the denominators in each equation 21 2020 Adept Education Limited Sheet 19 35 4 5 1

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Learning Intention 17 Knows simple equivalent fractions Making a double number line is a good way to visualise and work out some problems Emiel the carpenter is constructing a fence for his neighbour He knows it takes him 6 days to build a fence that is 32 metres long Days of work 0 112 3 6 0 8 16 32 Fence length m The neighbours fence will be 8m long How many days will it take Emiel to build To build a fence half the length 16m will take Emiel half the days 3 The neighbours fence will be half as long again 8m so half of 3 days will be 112 days Use the double number lines to answer the questions It takes 10 hours for Pete to walk 6 kilometres through the bush How long does it take him to walk 1 kilometre 1 0 9hr 0 6km At school camp it takes 36 potatoes to feed 12 students dinner How many potatoes are needed for 9 students 2 0 12 st 0 36 po The pet shop uses 4 kilos of food to feed 16 animals per week How many kilos do they use when there are 14 animals 3 0 4 kg 0 16 an The 2 metre paddling pool takes 1 000 litres of water How many litres does the 5m pool take 0 2m 4 0 1 000L 22 2020 Adept Education Limited Sheet 19 39 4 5 1

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Learning Intention 18 Able to solve simple ratio problems using repeated replication A ratio says how much of one thing there is compared to another thing For example if a litter of 5 puppies has 2 boys and 3 girls The ratio of boys to girls is 2 3 We use the symbol to separate the values and we use the word to when speaking aloud The ratio of blue squares to pink squares is 2 3 When we talk about fractions however we are talking about the amount of one part The fraction of 2 blue squares is 5 compared to the whole The fraction of 3 pink squares is 5 1 What is the ratio of oranges to strawberries 9 What is the ratio of green lollies to red lollies 2 What is the ratio of strawberries to oranges 10 What is the ratio of red lollies to green lollies 3 What fraction of the fruit are oranges 11 What fraction of the lollies are green 4 What fraction of the fruit are strawberries 12 What fraction of the lollies are red 5 What is the ratio of elephants to zebras 13 What is the ratio of blue birds to orange birds 6 What is the ratio of zebras to elephants 14 What is the ratio of orange birds to blue birds 7 What fraction of the animals are elephants 15 What fraction of the birds are blue 8 What fraction of the animals are zebras 16 What fraction of the birds are orange 23 2020 Adept Education Limited Sheet 19 46 4 5 1

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Sheet 19 08 1 6 96 16 6 16 96 2 24 72 3 24 3 72 3 29 145 5 29 5 145 4 130 1 300 10 130 10 1 300 5 43 215 5 43 5 215 6 12 108 9 12 9 108 Sheet 19 11 1 2 3 4 5 6 7 8 9 10 Sheet 19 12 1 2 Sheet 19 09 1 2 3 4 5 6 7 8 7 6 6 12 7 10 3 7 3 4 5 Sheet 19 10 1 2 3 4 5 6 9 9 12 55 5 11 5 x 11 55 28 7 4 7 x 4 28 50 2 25 2 x 25 50 5 3 4 9 3 5 5 10 12 7 6 85 5 50 5 10 35 5 7 10 7 17 57 3 30 3 10 27 3 9 10 9 19 96 8 80 8 10 16 8 2 10 2 12 64 4 40 4 10 24 4 6 10 6 16 117 9 90 9 10 27 9 3 10 3 13 98 7 70 7 10 28 7 4 10 4 14 Sheet 19 15 Food Item Blue School Green School Number Number of Number Number of of Items Cartons of Items Cartons 2 2 2 3 Pizza 40 8 25 5 Gingerbread 300 15 360 18 Scones 90 6 120 8 Donuts 224 14 192 12 Pastries 144 12 72 6 Muffins 240 24 130 13 TOTALS 1 038 79 899 62 1 2 3 4 5 40 25 65 pizzas 90 120 210 scones 224 192 436 donuts 240 130 370 muffins 79 62 141 cartons Sheet 19 16 1 2 3 4 90 3 6 3 30 2 32 80 4 4 4 20 1 21 60 2 6 6 30 3 33 60 3 9 3 20 3 23 Sheet 19 17 1 2 3 4 30 3 12 3 10 4 14 80 4 16 4 20 4 24 50 5 15 5 10 3 13 30 3 27 3 10 9 19 Sheet 19 18 Sheet 19 13 1 2 3 4 5 6 7 8 9 10 4 x 278 1 112 1 332 4 333 tickets 20 x 15 300 apples 400 20 20 boxes 1 560 312 5 days 312 x 6 1 872 per day 24 x 8 192 pieces 512 8 64 rolls 12 943 15 24 2020 Adept Education Limited 1 2 3 4 120 6 6 6 20 1 21 160 4 8 4 40 2 42 300 5 10 5 60 2 62 150 3 6 3 50 2 52

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Equivalent Fraction Chart 1 1 1 2 1 2 1 4 1 4 1 8 1 8 1 4 1 8 1 8 1 8 1 3 1 8 1 6 1 1 1 12 12 12 1 1 9 9 1 1 1 1 1 18 18 18 18 18 1 6 1 12 1 9 1 18 1 6 1 5 1 1 10 10 1 1 1 15 15 15 1 1 1 1 20 20 20 20 1 1 10 10 1 1 1 15 15 15 1 1 1 1 20 20 20 20 1 1 10 10 1 1 1 15 15 15 1 1 1 1 20 20 20 20 1 14 1 14 1 7 1 14 1 14 1 6 1 1 1 12 12 12 1 1 9 9 1 1 1 1 1 18 18 18 18 18 1 5 1 7 1 12 1 9 1 18 1 14 1 6 1 1 1 1 12 12 12 12 1 1 1 9 9 9 1 1 1 1 1 1 18 18 18 18 18 18 1 5 1 5 1 1 1 1 10 10 10 10 1 1 1 1 1 1 15 15 15 15 15 15 1 1 1 1 1 1 1 1 20 20 20 20 20 20 20 20 1 7 1 14 1 8 1 3 1 5 1 14 1 8 1 3 1 6 1 7 1 4 1 7 1 14 1 14 2020 Adept Education Limited 1 7 1 14 1 14 1 7 1 14 1 14 1 14

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2020 Adept Education Limited START 48 15 20 60 One dice numbered 1 6 Two counters You will need 24 35 36 25 80 27 50 30 56 100 200 90 16 45 120 64 81 18 12 24 90 12 FINISH Designed by Lucy Patston 48 Both players begin at the START Take it in turns to roll the dice You can only move one tulip at a time to any that are directly surrounding the tulip you are currently on and only to a tulip that is divisible by your dice number e g from the START if you roll a 3 you can move to either 15 or 60 because you can divide both these numbers by 3 If you roll a 1 miss a turn If you roll a 2 take another turn The first one to the FINISH wins Instructions

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Certificate of This award gives credit to for achieving Learning Intentions 10 to 14 Division for Book 19 of the Reaching Competence Mathematics Programme Signed Date Certificate of This award gives credit to for achieving Learning Intentions 15 to 18 Fractions and Ratios for Book 19 of the Reaching Competence Mathematics Programme Signed Date 2020 Adept Education Limited