Ages 8 to 10 Follows Stage 5 6 of the New Zealand Mathematics Curriculum Created by Lucy Patston 2020 Adept Education Limited t a Reach Education
Contents Introducing Reaching Competence 4 Overview of Books for Ages 8 to 10 6 Book 17 Apple and Android Applications 7 Book 17 Learning Intention Completion Chart 8 Learning Intention 19 Able to explain the value of digits up to two decimal places 9 Learning Intention 20 Able to order decimals with up to two decimal places 23 Learning Intention 21 Able to explain zero as a place holder 31 Learning Intention 22 Able to add and subtract decimals up to two decimal places 36 Learning Intention 23 Able to use a calculator efficiently including the memory 46 Learning Intention 24 Able to use brackets and understand the order of operations 51 Learning Intention 25 Able to identify rules to solve problems and patterns 57 Learning Intention 26 Able to select an appropriate operation to solve a problem 67 Learning Intention 27 Able to solve problems involving decimals 73 Reach Explains Multiplying and dividing by decimal numbers 78 Answers to Book 17 80 About the Author 91 Reach What s My Number Game Cards 93 Reach Calculator Game Cards 95 Reach Certificates of Competence 96 2020 Adept Education Limited t a Reach Education
Overview of Books for Ages 8 to 10 Book 15 Addition and Subtraction 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 Multiplication Knows multiplication facts x6 Knows multiplication facts x8 Knows multiplication facts x7 Has knowledge of the doubling and halving strategy Book 16 Multiplication Has knowledge of the distributive property of multiplication Knows multiplication facts x11 and x12 Able to use multiplication facts to solve division problems Fractions 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 Decimals 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 Problem Solving 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 3 2020 Adept Education Limited t a Reach Education
Book 17 Apple and Android Applications Apple Apps Splash Maths K5 Learning Games By StudyPad Inc This app is well designed and aligned to our learning intentions so it provides a good resource for moving through the books after this Android Apps Splash Math For PC Create an account at https www splashmat h com math skills thirdgrade As we did in Books 13 and 14 we are switching to the computer to make the most of the Splash Math online programme that taps the curriculum so beautifully Take a leap of faith and make an account for your child ren You will have to pay before long but it will be worth it Reach Education does not endorse the apps recommended here We have spent time researching apps on both Apple and Android devices to find those we feel best suit our programme for the least amount of expenditure to caregivers It should be noted that Reach Education is not in any way in partnership with the owners of these applications which may be updated without our knowledge Please contact us at support reacheducation co nz if you believe a recommended app has been changed significantly from what we describe here or you can recommend apps you feel would better suit the needs of students at this stage 4 2020 Adept Education Limited t a Reach Education
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 Date 5 2020 Adept Education Limited t a Reach Education 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 child 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 child 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 6 2020 Adept Education Limited t a Reach Education
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 7 2020 Adept Education Limited t a Reach Education 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 e g 5 5 10 1 3 2 10 2 10 3 5 5 7 10 9 10 8 10 4 2 8 5 98 6 1 1 10 10 93 7 9 9 10 11 5 2 10 9 23 3 10 4 10 5 10 6 10 Write these decimals as fractions e g 8 7 12 8 7 10 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 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 8 2020 Adept Education Limited t a Reach Education 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 Too tiny to see 1 000 100 10 10 10 1 1 1 10 1 100 1 or 0 1 or 0 01 1 10 of 0 1 or 5 100 of 1 If this line still represents 1 whole and this represents 0 1 of 1 whole then this represents 0 01 of 1 whole We would need 100 of these to make 1 whole again If we knew this whole was a 1m ruler then and 1 100 0 01 10 10 10 A hundredth is 0 1 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 9 2020 Adept Education Limited t a Reach Education 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 1 1 1 1 1 1 50c 10c 10c 10c 1L 1L 1L 1 5 100mL 100mL 1mL test tubes 1m 1m 1kg 1kg 1kg 1kg 1kg 1m 3 6 1m 100g 30cm 30 cm 100g 100g 100g 15cm 1g weights 10 2020 Adept Education Limited t a Reach Education 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 11 2020 Adept Education Limited t a Reach Education 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 Too tiny to see Way too tiny to see 0 01 0 001 0 1 10 10 10 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 1 10 as a decimal 6 What is 2 as 1 000 a decimal 2 What is 2 10 as a decimal 7 What is 20 as 1 000 a decimal 3 What is 1 100 as a decimal 8 What is 20 100 4 What is 2 100 as a decimal 9 What is 200 as 1 000 a decimal 5 What is 1 as 1 000 10 What is 63 as 1 000 a decimal a decimal 12 2020 Adept Education Limited t a Reach Education 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 100 000 10 000 1 000 100 10 1 0 1 Hundredths Thousandths 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 13 2020 Adept Education Limited t a Reach Education 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 14 2020 Adept Education Limited t a Reach Education 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 Reach 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 child ensuring they understand the wider context especially with Problem Solvers 1 3 Sheet 17 11 Reach Problem Solvers 16 4 Sheet 17 12 Brain Busters What s the Number 5 Splash Maths K5 and Splash Math for PC Go to Grade 4 Decimals In the settings select Level 2 Decimal Place Value numbers greater than 1 15 2020 Adept Education Limited t a Reach Education
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 16 2020 Adept Education Limited t a Reach Education 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 17 2020 Adept Education Limited t a Reach Education 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 18 2020 Adept Education Limited t a Reach Education 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 19 2020 Adept Education Limited t a Reach Education 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 17 913 00 Which number is equal to 0 70 18 912 90 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 21 2020 Adept Education Limited t a Reach Education 66 87 Sheet 17 13 4 5 1
solvers 17 Learning Intention 20 Able to order decimals with up to two decimal places Solve the equations below and then use the code key to find the correct numbers to enter into the A JJ spaces on the next page The first one is done for you Then calculate the answer to the clue and write it into the crossword puzzle CODE KEY A 10 100 B 5 10 0 1 2 3 4 5 6 7 8 9 0 1 0 5 0 9 1 as a decimal is 0 1 as a decimal is C One tenth as a fraction is D What fraction of 1 is 1c M 90 100 N 10 1000 O Z What is half written as a decimal AA 0 5 0 52 Q If I had 5 what BB 1c is F 10 10 16 14 K L CC R 200 grams of a kilo is what fraction 8 6 S 10 10 16 41 I 10cm is what fraction of 1m J 575 38 through 100m fraction of 100 would that be G 5cm is what fraction of 1m 575 37 83 41 83 49 L 100 30 100 40 of the way is the decimal for 100mL P 0 1 0 9 E 1 10 H Y 20m is T 0 66 U 0 77 V 660 1000 7 10 0 05 W If I cut my pizza into 10 slices and I eat 8 of these what fraction is left of a dollar 260 0 DD 4cm is 250 0 of 20cm EE 0 19 0 20 FF 80 47 81 47 GG 0 1 as a fraction is HH Complete the sequence 2 100 II 3 100 0 1 4 100 6 100 0 01 JJ Complete the sequence X 0 3 0 6 22 2020 Adept Education Limited t a Reach Education 0 7 0 8 1 0 1 1 Sheet 17 15 4 5 1
solvers 17 Learning Intention 20 Able to order decimals with up to two decimal places ACROSS CLUES 1 1 3 The number 0 1 less than A 2 B C D 4 2 K 2 S T U 7 V The number 0 5 less than DD 7 L The number 30 less than R 6 5 The number 0 05 less than J 4 6 EE FF Write the answers to Questions A to JJ from the previous page onto the grey letters in the DOWN and ACROSS clues Then solve the clue and write the answer into the crossword Good luck GG The number 0 1 more than HH II JJ DOWN CLUES 1 3 The larger of E F G H I E I G F H P Q The number 1 more than M 5 O Email us your completed and correct crossword to support reacheducation co nz along with your address to receive a prize The number after W 6 N X The number 0 5 more than Y Z AA BB CC 23 2020 Adept Education Limited t a Reach Education Sheet 17 16 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 24 2020 Adept Education Limited t a Reach Education Sheet 17 23 4 5 1
solvers 18 Learning Intention 22 Able to add and subtract decimals up to two decimal places Reach School is having their Athletics Day Groups of 6 students are competing as teams and as individuals The A Team have completed the Jumping Event Use the written method to add the scores for centimetres jumped for each team member Ava Aiden Aroha Andy Anna Amanda Jump 1 83 1 88 5 92 0 84 9 90 6 86 1 Jump 2 85 2 92 8 94 7 86 3 89 3 88 7 Jump 3 88 9 99 2 95 5 87 5 95 0 91 0 Total 1 Score 2 3 4 5 Overall Score 6 Place 7 Who did the longest single jump 8 Write in the place order for the 6 member of the A Team 9 What was the difference in centimetres between 1st and 6th place 10 What was the A Team s overall score Use your calculator to add the 6 students Total Scores 11 On the facing page fill in the missing data for the B Team 17 Who came 3rd in the B Team 18 Who was the individual winner across both teams 19 Which was the winning team 25 2020 Adept Education Limited t a Reach Education Sheet 17 28 4 5 1
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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 lovely 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 Lucy was raised in New Zealand during a time when the school curriculum was taught very differently to today so she understands how confusing it can be when children come home performing maths in the strangest ways In the Reaching Competency 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 27 2020 Adept Education Limited t a Reach Education
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 reacheducation co nz ISBN 978 0 9951200 9 9 2020 Adept Education Limited t a Reach Education
