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Ages 9 10 Year 5 Follows Stage 5 6 of the New Zealand Mathematics Curriculum Created by Lucy Patston 2020 Adept Education Limited

Book 15 Able to use a range of mental strategies for addition Able to use a written algorithm for addition Able to use a range of mental strategies for subtraction Able to use a written algorithm for subtraction Able to read numbers greater than one thousand Able to explain the value of digits in numbers greater than one thousand Knows multiplication facts x6 Knows multiplication facts x8 Knows multiplication facts x7 Has knowledge of the doubling and halving strategy Book 16 Has knowledge of the distributive property of multiplication Knows multiplication facts x11 and x12 Able to use multiplication facts to solve division problems Able to find non unit fractions of shapes Able to find non unit fractions of numbers Able to add and subtract fractions with the same denominator Able to recognise improper fractions Able to understand a decimal as a fraction Book 17 Overview of Books 15 17 Able to explain the value of digits up to two decimal places Able to order decimals with up to two decimal places Able to explain zero as a place holder Able to add and subtract decimals up to two decimal places Able to use a calculator efficiently including the memory Able to use brackets and understand the order of operations Able to identify rules to solve problems and patterns Able to select an appropriate operation to solve a problem Able to solve problems involving decimals 2 2020 Adept Education Limited

Book 17 Learning Intention Completion Chart Learning Intention 19 Able to explain the value of digits up to two decimal places 20 Able to order decimals with up to two decimal places 21 Able to explain zero as a place holder 22 Able to add and subtract decimals up to two decimal places 23 Able to use a calculator efficiently including the memory 24 Able to use brackets and understand the order of operations 25 Able to identify rules to solve problems and patterns 26 Able to select an appropriate operation to solve a problem 27 Able to solve problems involving decimals 3 2020 Adept Education Limited Date Sticker

practice practice practice Learning Intention 19 Able to explain the value of digits up to two decimal places A number has two decimal places if there are two numerals after the decimal point For example 1 29 or 459 37 Students need to know decimal fractions up to 0 99 Activities 1 Sheet 17 01 Thinking about wholes and tenths Make sure your learner realises the value of the whole line as it could be 1 mistaken for a tens stick Make the connection between 1 being 10 of 10 and 0 1 1 being 10 of 1 Ensure your learner is not making the common mistake of thinking 0 2 is the same as a half 12 Remind them that 5 is half of 10 and 0 5 is half of 1 2 Sheet 17 02 Writing fractions and decimals 3 Sheet 17 03 Thinking about tenths and hundredths 4 Sheet 17 04 Brain Busters Decimal Diagrams 5 Sheet 17 05 Reading and writing decimals 6 Sheet 17 06 Thinking about hundredths and thousandths NB Thousandths is extension material for this level 7 Sheet 17 07 Thinking about the place value of numbers including decimals 8 Sheet 17 08 Rounding decimals 4 2020 2020 Adept Adept Education Education Limited Limited

Learning Intention 19 Able to explain the value of digits up to two decimal places Let s think about our decimal system as we did in Books 15 and 16 When we work backwards through our decimal or place value system each column is ten times smaller than the last including when we go beyond the decimal point Hundreds Tens Ones Units Tenths 100 10 1 0 1 10 10 10 1 If this line represents 1 whole then one tenth of the line 10 is the same as 0 1 of the line We would need 10 x 0 1 to make 1 whole again 1 1 10 or 0 1 1 2 3 4 5 6 7 8 9 10 What number do these diagrams represent 1 5 1 5 2 6 3 7 4 8 5 2020 Adept Education Limited Sheet 17 01 4 5 1

Learning Intention 19 Able to explain the value of digits up to two decimal places Write these fractions as decimals 5 e g 5 1 3 2 10 3 10 5 5 2 10 7 10 9 10 8 4 2 5 98 6 1 7 9 8 10 2 10 1 10 9 10 9 23 3 10 4 10 10 93 11 5 5 10 6 10 Write these decimals as fractions e g 8 7 12 8 7 15 4 6 19 3 5 6 1 16 8 5 20 9 4 13 2 7 17 1 2 21 4 9 14 6 9 18 7 8 22 5 3 10 Answer these word questions 23 Katherine had sixteen whole oranges and five eighths of another orange Write how many oranges she had as a fraction 24 Ollie had twenty five dollars and fifty cents Write how much money he had as a decimal 25 Daniel had three kilos of flour and another two tenths of a kilo bag Write how much he had as a fraction 26 Jay had nine metres of wood and another seven tenths of a metre Write how much wood she had as a decimal 6 2020 Adept Education Limited Sheet 17 02 4 5 1

Learning Intention 19 Able to explain the value of digits up to two decimal places Let s expand our decimal system out by one column in both directions We now have thousands and hundredths Thousands Hundreds Tens Ones Units Tenths Hundredths 1 000 100 10 10 10 1 1 100 1 10 of 0 1 or 100 of 1 and this represents 0 1 of 1 whole or 0 1 then this represents 0 01 of 1 whole We would need 100 of these to make 1 whole again or 0 01 If we knew this whole was a 1m ruler then and 1 If this line still represents 1 whole 1 1 10 1 0 01 10 10 10 A hundredth is 0 1 5 100 1 100 or 0 01 would be ____ centimetre s or 0 05 would be ____ centimetre s What number do these diagrams represent The first one is done for you e g 4 1 32 2 5 3 6 7 2020 Adept Education Limited Sheet 17 03 4 5 1

Learning Intention 19 Able to explain the value of digits up to two decimal places What is the number represented by each diagram 1 whole 1 4 2 100mL 100mL 100mL 1 1 1 1 1 1 50c 10c 10c 10c 1L 1L 1L 1 5 100mL 10mL test tubes 1m 1m 1kg 1kg 1kg 1kg 1kg 1m 3 6 1m 100g 30cm 30 cm 100g 100g 100g 15cm 10g weights 8 2020 Adept Education Limited Sheet 17 04 4 5 1

Learning Intention 19 Able to explain the value of digits up to two decimal places We say decimals a little bit differently to how we say numbers over 1 It s actually much easier We just say each number in order separately 3 14 is said three point one four 22 75 is said twenty two point seven five 87 08 is said eighty seven point zero eight 10 50 is said ten point five zero Write how you say the following decimal numbers 1 5 29 2 27 02 3 149 65 4 926 36 5 1 001 43 6 8 82 7 59 90 8 611 06 TRICK OF THE TRADE The only time we don t read decimals as single digits is when reading money amounts e g 2 50 is read Two dollars fifty Write the following numbers in numerals 9 Two point nine nine 10 Four point eight zero 11 Seventy eight point five one 12 Nine hundred and six point one five 9 2020 Adept Education Limited Sheet 17 05 4 5 1

Note This is extension material Learning Intention 19 Able to explain the value of digits up to two decimal places If we expand our decimal system out one more column to the right we have the thousandths Thousands Hundreds 1 000 Tens 100 10 Ones Units 10 10 Tenths 1 Hundredths Thousandths 0 1 10 10 10 Too tiny to see 0 01 0 001 10 To make one whole you need 1 000 one thousandths That s quite a few 1 1 10 1 100 1 1 000 or 0 1 or 0 01 We would need 1 000 of these to make 1 whole again or 0 001 See if you can answer these questions Remember this is difficult material so check the answers regularly to make sure you re on track 1 What is 2 What is 3 What is 4 What is 5 What is 1 10 2 10 as a decimal 6 What is as a decimal 7 What is as a decimal 8 What is as a decimal 9 What is 10 What is 1 100 2 100 1 1 000 as a decimal 10 2020 Adept Education Limited 2 1 000 20 1 000 20 100 as a decimal as a decimal as a decimal 200 1 000 63 1 000 as a decimal as a decimal Sheet 17 06 4 5 1

Note Understanding and using thousandths is extension material Learning Intention 19 Able to explain the value of digits up to two decimal places Whole numbers have place values and so do decimals Here is our place value diagram again this time extended to hundred thousands and thousandths Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Tenths Hundredths Thousandths 100 000 10 000 1 000 100 10 1 0 1 0 01 0 001 Give the value of the coloured number in each question in words and numerals Number Worded e g 939 045 Five thousandths e g 939 045 Nine hundred 1 53 97 2 172 39 3 909 03 4 690 086 5 101 944 6 429 803 7 898 105 8 65 111 9 977 711 10 70 997 Numerals 0 005 900 11 2020 Adept Education Limited Sheet 17 07 4 5 1

Learning Intention 19 Able to explain the value of digits up to two decimal places When we round whole numbers the rules are 1 0 1 2 3 and 4 round ___________ 2 5 6 7 8 and 9 round __________ Decimals are the same 3 0 0 0 1 0 2 0 3 and 0 4 round ___________ 4 0 5 0 6 0 7 0 8 and 0 9 round __________ Draw an arrow on each diagram to show whether you would round up or down A 20 30 40 9 50 40 50 34 10 5 0 6 0 7 0 8 0 9 0 5 5 10 0 11 0 3 0 4 0 110 120 9 2 5 11 0 10 20 1 0 30 2 0 2 6 13 6 12 900 910 920 930 90 100 107 915 7 7 0 8 0 9 0 13 10 0 44 0 45 0 46 0 47 0 46 0 47 0 99 0 100 0 45 5 8 8 8 70 54 B 4 0 60 48 0 14 49 0 97 0 98 0 47 5 98 3 Round these numbers to the nearest whole number 15 91 2 17 7 9 19 51 1 16 1 5 18 9 0 20 100 7 12 2020 Adept Education Limited Sheet 17 08 4 5 1

apply Learning Intention 19 Able to explain the value of digits up to two decimal places Activities 1 Sheet 17 09 Solve the story problems 2 Sheet 17 10 Adept Problem Solvers 15 This activity and the next provide students with familiar contexts in which to practise working with tenths and hundredths Weight and distance are also utilised as measurements Work through the different problems with your learner ensuring they understand the wider context especially with Problem Solvers 1 3 Sheet 17 11 Adept Problem Solvers 16 4 Sheet 17 12 Brain Busters What s the Number 5 Splash Math Go to Grade 4 Decimals In the settings select Level 2 Decimal Place Value numbers greater than 1 13 2020 2020 Adept Adept Education Education Limited Limited

Learning Intention 19 Able to explain the value of digits up to two decimal places Solve the story problems You may use your calculator Brianna is being challenged to find three items that weigh 250g in total Jack can run the 100m sprint in 13 78s So far she has a pencil that weighs 20 8g and a stone that weighs 174 5g 1 How much do her two items weigh together 2 How heavy will her third item need to be The current world record is 9 58s 5 Rachel had 100 00 to buy birthday presents for three of her friends How much time will Jack need to decrease his time by to match the world record Tony was covering 28 cushions He needed 0 85m of material for each one The first gift cost 34 50 and the second gift cost 39 90 3 How much did Rachel have left after she bought the first gift 6 How many metres of material does Tony need altogether 4 How much did she have left to buy the third gift 7 If he can only buy the material in 5m rolls how many rolls will he need to buy 14 2020 Adept Education Limited Sheet 17 09 4 5 1

solvers 15 Learning Intention 19 Able to explain the value of digits up to two decimal places Gran and Grandpa are flying home from Fiji after their cruise but they are having a bit of trouble at the airport because of the weight of their luggage See if you can help them out 1 How much weight is Gran carrying 2 How much weight is Grandpa carrying 3 How much weight over the limit is Gran When you fly on an aeroplane there are strict rules about the weight your luggage can be Excess luggage is any weight over the per person limit of 32kg and costs 5 per kilo over Gran s Handbag Allowed Actual Gran s Carry on Gran s Luggage Grandpa s Carry on Grandpa s Luggage No limit 7kg 25kg 7kg 25kg 1 kg 8 5kg 27 8kg 6 2kg 23 1kg 4 How much will Gran have to pay in excess luggage costs 5 If Gran off loads as much as she can to Grandpa s luggage how much will her excess luggage cost 6 Can you think of a way Gran could get on the plane without paying for any of her excess weight while still taking everything she has If you re struggling with this question try working out how much weight Grandpa can take on before he reaches 32kg 7kg 25kg first 15 2020 Adept Education Limited Sheet 17 10

solvers 16 Learning Intention 19 Able to explain the value of digits up to two decimal places Room 1 At Garuth and Suresh s school Room 2 has been removed and the boys have been busy measuring the school grounds in metres to 2 decimal places Room 3 876 43m 38 26m 29 04m 49 57m Office Library 60 81m 46 73m 104 76m 201 66m Dental Clinic Hall 120 05m School Hall Swimming Pool Sports Field 1 Which is further a Room 1 to the Library or b Room 3 to the Dental Clinic 3 Is the swimming pool closest to the Office or the Sports Field 2 Which room 1 or 3 is closer to the Office 4 What is the closest building to the Library 16 2020 Adept Education Limited Sheet 17 11 4 5 1

Learning Intention 19 Able to explain the value of digits up to two decimal places e g Using all four numbers and the decimal point create the largest 2dp number closest to 50 00 2 TRICK OF THE TRADE 1 48 72 Using all four numbers and the decimal point create the largest 2dp number closest to 80 00 dp stands for decimal place s so 2dp means two decimal places 2 2 Make a number between 22 50 and 25 50 2 3 Make a number between 64 55 and 64 60 6 4 Make the odd number closest to 39 00 0 5 Create the next number in this sequence 12 34 23 45 34 56 7 17 2020 Adept Education Limited Sheet 17 12 4 5 1

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Learning Intention 20 Able to order decimals with up to two decimal places Circle the correct answer or write the answer into the box 1 Which number is equal to 0 06 2 Circle the smallest number 6 0 6 6 Which number is larger than 97 5 97 6 3 0 6 6 10 97 0 9 65 90 6 10 219 79 219 72 219 85 11 355 54 356 53 355 68 12 774 00 770 40 770 44 What is the number between 229 1 and 229 3 230 3 229 0 29 2 Circle the largest number 229 2 Use or to complete the equations 13 790 74 799 70 800 00 14 730 20 730 22 730 28 950 20 920 50 4 9 8 9 7 15 952 50 5 14 9 1 49 16 Which number is larger than 912 89 6 41 49 41 94 7 1 2 1 200 8 814 00 814 01 9 Number the following in order from largest to smallest 32 59 900 90 17 912 90 Which number is equal to 0 70 18 913 00 7 2 912 00 72 100 0 072 0 72 Number the following in order from smallest to largest 33 56 33 25 32 88 67 24 67 69 68 95 33 64 34 07 1 33 94 66 76 1 68 00 67 04 19 2020 Adept Education Limited 66 87 Sheet 17 13 4 5 1

Learning Intention 20 Able to order decimals with up to two decimal places 1 Write the amounts in decimals and in order from least to most A 800 1000 B 2 10 L Mr Mi wants to know which are his most and least profitable items for sale C L 2 Order the items from 1 most revenue to 5 least revenue 60 100 L Table 1 Revenue earned per item NZ Decimals Order Item Description Order Vessel Vessel Vessel Least Most Revenue Gold bracelets 365 20 Blue charms 565 15 Silver rings 365 55 Red charms 426 65 Gold rings 426 90 Judy s grandfather is wanting to know where in his garden his tomatoes grow best and when Complete the table to help you answer the questions Table 2 Average weight of tomatoes grams 3 Which month produced the heaviest tomatoes 4 In Dec which row produced the heaviest tomatoes 5 In which month did Row C produce the heaviest tomatoes Row Dec Jan Feb Mar A 21 7 25 2 22 8 20 4 B 22 8 25 6 23 1 22 5 C 20 2 23 9 23 9 19 8 Total Total 6 If Judy s grandfather had to choose only one row to grow his tomatoes which row should he choose Why 20 2020 Adept Education Limited Sheet 17 17 4 5 1

Learning Intention 22 Able to add and subtract decimals up to two decimal places The written method works very well when we re adding numbers with decimals 50 2 2 01 317 0 61 TRICK OF THE TRADE Be sure to line the decimal points up and keep every number in its correct place value column Adding in zeros can be helpful TRICK OF THE TRADE Remember to start from the right and work your way back through the columns 50 20 2 01 317 00 0 61 369 82 put a zero put zeros START Line up these additions and solve the equations using the written method 1 28 7 31 2 4 6 51 3 22 19 14 7 0 87 2 18 25 5 2 55 13 43 42 5 344 33 282 61 8 693 4 508 97 3 06 3 24 62 0 25 6 405 6 37 1 6 4 9 7 91 0 72 390 21 2020 Adept Education Limited Sheet 17 23 4 5 1

Learning Intention 23 Able to use a calculator efficiently including the memory M Press MRC to see what s in the memory and again to clear the memory MRC M Some calculators have an MR button and an MC button instead of one MRC button MR MC M M 0 M 7 8 9 X C 4 5 6 AC 1 2 3 00 0 1 What do you think the MC stands for 2 What do you think the MR stands for Press M to add the number on the screen to the memory Press M to subtract the number on the screen from the memory Follow the button presses predict what will be in the memory each time and then press MRC or MR to find out if you were right CLEAR YOUR CALCULATOR MEMORY FIRST e g 10 M 2 10 M 3 M 12 MRC 15 15 CLEAR YOUR CALCULATOR MEMORY FIRST 3 9 M 6 M 5 M MRC CLEAR YOUR CALCULATOR MEMORY FIRST 4 35 M 5 M 30 M MRC CLEAR YOUR CALCULATOR MEMORY FIRST 5 50 M 5 M 10 M 22 2020 Adept Education Limited MRC Sheet 17 31 4 5 1

Learning Intention 24 Able to use brackets and understand the order of operations What is the answer to the following equation 4 3x5 There are TWO different answers you may have calculated Did you decide to do it this way or this way 4 3x5 7x5 35 4 3x5 4 15 19 The correct answer is 19 This is because we work out the multiplication part of the equation first and then carry out the addition part Mathematics has to be very precise and for this reason there exists an order of operations B E Brackets Exponents 2 Brackets come first Exponents come second D Division M A S Multiplication Addition Subtraction x These two come next We order them left to right These two come last We order them left to right Use the order of operations to find the answers to these equations 1 5 x 8 10 4 10 3 x 6 7 20 5 x 4 2 3 1 30 5 10 2 x 7 8 6 8 2 3 4 7 3 6 30 x 3 6 9 20 8 x 2 23 2020 Adept Education Limited Sheet 17 33 4 5 1

solvers 20 Learning Intention 24 Able to use brackets and understand the order of operations Josh and Ken are busy with their extracurricular activities They both have the same schedules and so their parents are carpooling and sharing the load between them Here is their weekly arrangement Day Activity Parent Monday Soccer practice Josh s Dad Tuesday Drama Ken s Mum Thursday Soccer practice Ken s Dad Friday Swimming Josh s Mum Answer the questions by writing out the equation using brackets 1 How far does Josh s Dad travel each week 2 How far does Ken s Mum travel each week 3 How far does Ken s Dad travel each week 4 How far does Josh s Mum travel each week Wednesday The parents pick up the other child from their house take the boys to their activity and then return the other child to their house before returning home Ken s House Drama 3km Josh s House Soccer 11km Swimming 24 2020 Adept Education Limited Sheet 17 36 4 5 1

Learning Intention 25 Able to identify rules to solve problems and patterns Positive Follow the number patterns through into the negative numbers Don t forget to include zero if needed 10 9 8 5 4 increasing 7 6 Another way you might like to think of numbers is in a ladder or vertical form 3 2 1 0 1 8 6 4 2 0 2 30 25 20 15 10 3 400 300 200 100 0 4 5 4 3 2 1 5 9 6 3 0 3 6 10 7 4 1 2 1 Write out these patterns as described 3 4 5 6 decreasing 2 7 10 ____ 2 ____ ____ ____ ____ ____ 8 9 Start with 30 then subtract 11 from each new number ____ ____ ____ ____ ____ ____ 9 10 Start with 4 then multiply each new number by 3 ____ ____ ____ ____ ____ ____ 7 8 Start with 10 then subtract 8 from each new number 10 Start with 0 then subtract 7 from each new number ____ ____ ____ ____ ____ ____ Negative 11 Start with 7 For each number add 1 and then multiply by 2 ____ ____ ____ ____ ____ ____ 25 2020 Adept Education Limited Sheet 17 40 4 5 1

Learning Intention 26 Able to select an appropriate operation to solve a problem Find the values of the shapes in each set They are all positive whole numbers 1 53 18 18 36 18 2 x 20 36 x 16 45 x 49 x 30 17 x 18 x 120 3 14 5 16 6 7 22 33 32 15 16 19 38 20 4 15 17 37 8 16 17 12 22 14 10 16 32 20 10 17 10 26 2020 Adept Education Limited 24 22 18 Sheet 17 47 4 5 1

Sheet 17 14 continued Sheet 17 15 continued R S T U V W X Y Z AA BB CC DD EE FF GG HH II JJ 3 4 2 10 2 10 5 10 2 10 0 9 2 10 0 5 1 10 2 10 1 10 5 10 0 9 6 6 1 8 6 4 6 3 0 5 1 6 0 0 5 8 1 4 1 2 3 3 9 8 2 4 7 4 3 0 9 5 8 1 Sheet 17 15 A B C D E F G H I J K L M N O P Q 0 1 0 5 1 10 1 100 0 1 1 5 100 1 10 0 9 1 100 0 1 1 5 100 2 3 5 7 2 9 8 0 5 1 0 0 4 7 2 9 8 2 4 6 7 1 3 5 6 27 2020 2020 Adept Adept Education Education Limited Limited 6 0 3 5 6 1 5 2 7 8 1 8 5 Sheet 17 17 1 2 Sheet 17 16 ACROSS The number 0 1 less than 23 57 is 23 47 The number 0 05 less than 100 is 0 95 The number 30 less than 66 18 is 36 18 The number 0 5 less than 60 05 is 60 The number 0 1 more than 81 4 is 81 5 DOWN The larger of 298 05 and 258 90 is 298 05 The number 1 more than 472 98 is 473 98 The number after 64 is 65 The number 0 5 more than 630 71 is 631 21 6 7 3 4 5 6 Vessel B Vessel C Vessel A 1 Blue charms 2 Red charms 3 Gold rings 4 Silver rings 5 Gold bracelets Jan B Feb B because overall this row produces the heaviest tomatoes Sheet 17 18 1 Delivery B Delivery A 4 84 6 27 4 23 15 34kg x commission Delivery B 6 62 5 95 12 57kg Delivery C 2 83 2 40 1 91 5 96 13 10kg Delivery D 3 93 3 82 10 83 18 58kg

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About the Author Lucy Patston BA BSc Hons PhD Lucy has 20 years of teaching experience and a strong academic background She has expertise in neuroscience psychology and human development and gained her doctorate for research investigating how childhood learning affects brain functioning in adulthood Lucy is a mum to three very energetic children all of whom have recently entered the school system As a parent and a teacher she understands how important it is for students to grasp key mathematical concepts and for parents to be actively engaged in this process where possible Lucy was raised in New Zealand during a time when the school curriculum was taught very differently to today and provides the Reaching Competence Programme direct to parents also In the Programme Lucy spends an equal amount of time helping parents understand the curriculum as she does students She believes that if parents can communicate effectively with their children about the concepts they are currently learning in the classroom then children will not only feel supported in their learning but will be open to realising how important maths is in our everyday lives When parents and teachers are using the same terminology and strategies to help their learners with numeracy our kids are winning 29 2020 Adept Education Limited

Explore the mathematics curriculum with your child at your own pace with this guided interactive programme This booklet includes learning intentions 19 through to 27 of 27 for this level Includes information about the curriculum for parents and caregivers learning intention checklist and sticker chart suggested Apple and Android applications worksheets activities board games certificates and other print and cut resources The learning intentions covered in this book are Able to explain the value of digits up to two decimal places Able to order decimals with up to two decimal places Able to add and subtract decimals up to two decimal places Able to explain zero as a place holder Able to use a calculator efficiently including the memory Able to use brackets and understand the order of operations Able to identify rules to solve problems and patterns Able to select an appropriate operation to solve a problem Able to solve problems involving decimals Online and printed versions available at www adepteducation co nz adepteducation 2020 Adept Education Limited