Ages 9 to 11 Follows Stage 6 of the New Zealand Mathematics Curriculum Created by Lucy Patston 2020 Adept Education Limited t a Reach Education
Table of Contents Introducing Reaching Competence 5 Overview of Books for Ages 9 to 11 7 Book 20 Learning Intention Completion Chart 8 Learning Intention 19 Able to understand decimals as special fractions 9 Learning Intention 20 Able to understand decimals as an extension to the place value system 17 Learning Intention 21 Able to order decimal numbers up to three decimal places 25 Learning Intention 22 Able to round decimal numbers up to three decimal places 33 Learning Intention 23 Able to add and subtract decimal numbers up to three decimal places 41 Learning Intention 24 Able to understand percentages as special fractions 53 Learning Intention 25 Knows common percentages 57 Learning Intention 26 Able to use a calculator efficiently 65 Learning Intention 27 Uses knowledge of operations to identify number patterns 71 Answers to Book 20 80 About the Author 87 Reach Fish for Fractions Card Pack 89 Reach Decimal Duel Card Pack 91 Reach Certificates of Competence 92 2020 Adept Education Limited t a Reach Education
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 for Ages 9 to 11 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 3 2020 Adept Education Limited t a Reach Education
Book 20 Learning Intention Completion Chart Learning Intention 19 Able to understand decimals as special fractions 20 Able to understand decimals as an extension to the place value system 21 Able to order decimal numbers up to three decimal places 22 Able to round decimal numbers up to three decimal places 23 Able to add and subtract decimal numbers up to three decimal places 24 Able to understand percentages as special fractions 25 Knows common percentages 26 Able to use a calculator efficiently 27 Uses knowledge of operations to identify number patterns 4 2020 Adept Education Limited t a Reach Education Date Sticker
practice practice practice Learning Intention 19 Able to understand decimals as special fractions Numbers occurring between 0 and 1 may be a strange concept for some children even though they have met decimals and fractions before Now is a good time to discuss the importance of the placeholder zero By convention it is not necessary after a whole number e g 1 but it is necessary before a decimal point e g 0 5 Help your child form this good habit now Activities 1 Sheet 20 01 Remembering the scale of decimals Take a moment to examine this page with your child The information here is of vital importance and the page should not be glossed over Ask the following questions to ensure there is a deep level of understanding see Answer Section a How many tenths are in one whole b How many hundredths are in one whole c How many thousandths are in one whole d What will half of 1 be as a fraction of 10 e What will half of 1 be as a fraction of 100 f What will half of 1 be as a fraction of 1 000 10 1 g Is ten hundredths 100 the same fraction of one whole as one tenth 10 h Why Or how do we know 2 Sheet 20 02 Practising the relationship between decimals and fractions 3 Sheet 20 03 Decipipes and decimats This page introduces different material ways to visualise decimals Students usually prefer one way over the other and this is good information to know 5 2020 2020 Adept Adept Education Education Limited Limited t a t a Reach Reach Education Education
Learning Intention 19 Able to understand decimals as special fractions Whole numbers have place values and so do decimals Here is our model of the place value system Remember that every column is 10 times smaller than the last including as we cross the decimal point 1 10 0 1 and 0 1 x 10 1 Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones Tenths 100 000 10 000 1 000 100 10 1 0 1 x 10 Hundredths Thousandths 0 01 0 001 10 1 If this bar represents 1 whole then one tenth of the bar 10 is the same as 0 1 of the bar We would need 10 lots of 0 1 to make 1 whole 1 1 10 1 or 0 1 2 3 4 5 A hundredth is 1 100 of 0 1 and 1 100 7 8 9 10 of 1 If this bar represents 1 whole 1 1 10 1 10 6 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 or 0 01 A thousandth is 1 10 of 0 01 1 100 of 0 1 and 1 1 000 of 1 1 1 10 1 100 1 1 000 or 0 1 or 0 01 or 0 001 We would need 10 of these to make 1 whole We would need 100 of these to make 1 whole We would need 1 000 of these to make 1 whole 6 2020 Adept Education Limited t a Reach Education Sheet 20 01
Learning Intention 19 Able to understand decimals as special fractions The number line below is equal to 1 It has been divided into 10 equal parts 0 0 1 0 2 A 0 4 B 0 6 0 7 0 8 C 1 0 10 D E 3 10 4 10 F G 7 10 H 9 10 10 10 1 What do A B and C represent 2 What do D E F G and H represent 3 Which is closer to zero 0 2 or 0 9 4 Which is closer to one 0 2 or 0 5 5 Which is closer to zero 4 10 or 0 1 6 Which is closer to one 0 8 or 7 10 7 Write 0 5 as a fraction 8 Write 6 10 as a decimal The diagrams below represent one whole 9 What decimal is shaded 12 Shade 0 3 10 What fraction is shaded 8 13 Shade 10 11 What decimal is shaded 14 Shade 25 7 2020 Adept Education Limited t a Reach Education Sheet 20 02
Learning Intention 19 Able to understand decimals as special fractions Here are two more ways to think of wholes and tenths Decipipes Decimats This decipipe shows 0 8 This decimat shows 0 3 Draw and shade the following decimals using decipipes and then decimats 1 0 1 2 0 4 3 0 5 4 0 7 5 1 8 2020 Adept Education Limited t a Reach Education Sheet 20 03
apply Learning Intention 19 Able to understand decimals as special fractions Activities 1 Sheet 20 04 Matching fractions to decimals The aim of these pages is to make the connection between fractions and the common decimals and to get students to understand the importance of why equivalent fractions are equivalent 2 Sheet 20 05 Equivalent fractions and their decimals 3 Sheet 20 06 Marking number lines The aim of this activity is to make the connection between equivalent fractions and their decimals AND distance or length Being able to divide a length into common fractions decimals is a good skill for life in general 4 Play the Reach game Fish for Fractions This game helps students commit some of the more common fractions and decimals to memory It is played the same as the card game Fish Cut both the Fish for Fractions card packs up and shuffle the entire pack How to play Deal out 5 cards to each player and leave the rest of the pack upside down in the middle The first player asks for the card that will pair with one of their cards For example if Player 1 has the card 0 5 they would ask Do you have the fraction one half If they had the card 1 3 they would ask Do you have the decimal 0 333 If Player 2 has the card they hand it to Player 1 and Player 1 puts the cards together and off to one side If not Player 1 picks up the top card from the pack and it is Player 2 s turn to ask for a card The winner is the player with the most fraction decimal pairs at the end of the card pack 9 2020 2020 Adept Adept Education Education Limited Limited t a t a Reach Reach Education Education
Learning Intention 19 Able to understand decimals as special fractions Draw lines between the fraction and the correct decimal number Use your calculator to check more difficult matches 6 9 0 8 0 75 5 5 10 12 5 10 0 667 1 8 10 0 833 0 25 3 4 4 5 7 7 0 5 0 833 1 8 0 6 0 4 3 12 5 6 1 0 8 9 12 3 5 0 125 1 4 10 1 4 0 667 0 75 2 6 3 9 0 25 0 333 6 6 3 6 0 5 0 333 4 6 2 3 0 2 0 667 2 5 6 8 0 333 0 4 1 3 1 5 0 5 0 6 1 10 0 75 0 25 0 2 0 1 2 10 1 2 10 2020 Adept Education Limited t a Reach Education 4 8 6 10 Sheet 20 04
Learning Intention 19 Able to understand decimals as special fractions Why do different fractions result in the same decimal Work through the table below to help you answer this question 1 Using your answers from the previous page list the fractions that resulted in these decimal numbers 0 125 0 20 1 8 1 5 0 60 0 667 0 25 0 333 0 4 0 5 0 75 0 8 0 833 1 2 What type of fractions result in the same decimal 3 Write in one more fraction for each decimal number 4 Find four fractions that do not result in one of these decimal numbers 11 2020 Adept Education Limited t a Reach Education Sheet 20 05
Learning Intention 19 Able to understand decimals as special fractions Complete the table with one equivalent fraction and the decimal for the given fraction Next mark and label where the decimal would lie on the number line Fraction Equivalent fraction e g 1 4 2 8 1 2 3 0 1 2 4 5 0 1 3 1 8 0 1 4 1 3 0 1 5 3 4 0 1 6 1 2 0 1 7 1 5 0 1 8 2 5 0 1 Decimal 0 25 Number line 0 25 0 1 Before you start cut this portion of the page out and refer to it when you re finished to see how close your number line estimates were 0 3 7 4 8 6 1 5 2 12 2020 Adept Education Limited t a Reach Education 1 Sheet 20 06
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Learning Intention 20 Able to understand decimals as an extension to the place value system A B To divide 200 by 10 we can imagine dividing twenty tens 200 between a group of 10 monsters Each would get 2 tens or 20 To divide 20 by 10 we can imagine dividing twenty ones 20 between a group of 10 monsters Each would get 2 ones or 2 Now imagine the Base 10 equipment above is ones tenths and hundredths A To divide 2 by 10 we can imagine dividing twenty tenths 2 between a group of 10 monsters Each would get 2 tenths or 0 2 B To divide 0 2 by 10 we can imagine dividing twenty hundredths 0 2 between a group of 10 monsters Each would get 2 hundredths or 0 02 TRICK OF THE TRADE Each time we divide by 10 we push our number down the place value table by one column If we divide by 100 we push our number down two places 10 Hundreds Tens Ones 2 0 0 2 0 0 2 0 0 0 2 0 0 0 2 100 14 2020 Adept Education Limited t a Reach Education Tenths Hundredths Sheet 20 11
Learning Intention 21 Able to order decimal numbers up to three decimal places 3dp Using the decimal system we can divide the space between 0 00 and 0 01 into ten parts Each part now becomes one 0 0 1 0 2 0 3 0 4 0 5 thousandth 0 6 0 0 7 0 8 1 0 2 0 09 0 07 0 08 0 05 0 06 0 03 0 04 0 01 0 02 0 1 0 9 0 0 02 0 001 0 002 0 003 0 004 0 005 0 006 0 007 0 008 0 009 0 01 Fill in the missing numbers on these number lines 1 0 0 001 0 003 0 004 0 007 0 009 0 01 0 03 0 031 0 033 0 034 0 037 0 039 0 04 0 09 0 091 2 3 0 092 0 094 0 096 0 1 0 098 4 1 55 1 552 1 555 1 558 1 559 Follow the instructions to calculate your answer You may use a calculator 5 Add the numbers with a 6 in the hundredths place 764 863 444 910 291 7 7 Add the numbers with a 0 in the tenths place 578 791 440 65 958 969 653 906 377 11 559 7 6 Add the numbers with a 2 in the tens place 456 93 824 899 591 262 205 391 535 80 304 548 8 Add the numbers with an 8 in the thousandths place 607 21 522 740 802 2 161 384 682 634 417 538 292 588 301 516 717 839 15 2020 Adept Education Limited t a Reach Education Sheet 20 13
Learning Intention 21 Able to order decimal numbers up to three decimal places 3dp Solve the story problems George s race time was 15 32 mins Andrew s race time was 14 67 mins Anna s race time was 15 67 mins Laura s race time was 14 68 mins I have 14 68 My sister has 14 64 My brother has 14 65 1 Who has the most money 7 Who was the fastest 2 Who has the least money 8 Who was the slowest John travels 5 60 km to work Bevan travels 5 20 km to work Kieran travels 5 62 km to work Kathy was baking a cake and needed 800 grams of flour Flour is sold in 790g 820g and 850g packs 3 Who travels the most km 9 Which is nearest to 800g 4 Who travels the fewest km 10 Which bag should Kathy buy James lifted 67 806 kg Tama lifted 64 598 kg Mark lifted 66 860 kg Siasi lifted 64 568 kg John lifted 64 520 kg Melita is 1 49 cm tall Claire is 1 55 cm tall Sandy is 1 51 cm tall Tracey is 1 58 cm tall 5 Who is the tallest 11 Who lifted the most weight 6 Who is the shortest 12 Who lifted the least weight 16 2020 Adept Education Limited t a Reach Education Sheet 20 17
Learning Intention 22 Able to round decimal numbers up to three decimal places When rounding decimals the same is true 0 1 2 3 and 4 round DOWN While 5 6 7 8 and 9 round UP You ll see the rules are repeated but the numbers become increasingly complex The trick is to only concentrate on the column of interest and try to ignore the rest The column of interest is always one column to the right of the rounding column exactly the same as when rounding whole numbers If we are rounding to the nearest whole number we evaluate the number in the tenths We are wanting a number with no 1 1 1 decimal places after the decimal point 1 4 3 2 1 4 rounds down 1 0 0 0 0 1 6 7 8 5 6 rounds up 2 0 0 0 0 1 2 1 3 1 4 1 5 1 6 1 7 1 8 If we are rounding to the nearest tenth we evaluate the number in the hundredths 1 4 4 3 2 1 1 rounds down 1 4 0 0 0 1 4 7 8 5 6 rounds up 1 5 0 0 0 1 42 1 43 column decimal number 1dp after the decimal point 1 1 41 1 44 1 45 1 46 1 47 1 48 1 49 If we are rounding to the nearest hundredth we evaluate the number in the thousandths We are wanting a number with two decimal numbers 1 431 1 4 3 2 1 1 4 3 8 5 1 432 1 433 1 5 1 47 1 43 1 43 2 1 9 1 6 1 4 We are wanting a number with one column 1 434 1 rounds down 6 rounds up 1 435 2dp after the decimal point 1 4 3 0 0 1 4 4 0 0 1 436 column 1 437 1 432 1 438 1 439 1 44 1 438 17 2020 Adept Education Limited t a Reach Education Sheet 20 21
Learning Intention 23 Able to add and subtract decimal numbers up to three decimal places We can add decimal numbers using the same strategies that we use with whole numbers Here s an example 37 7 37 3 4 44 3 7 0 7 3 7 0 3 0 4 4 4 Find the next tidy tens number Find the next whole number 3 37 38 0 3 4 39 40 41 42 43 44 3 7 3 8 3 9 0 4 4 0 4 1 4 2 4 3 4 4 Draw the number line and then solve each whole decimal equivalent problem 1a 29 8 29 1 7 37 1b 2 9 0 8 29 2a 58 5 2 9 2b 5 8 0 5 58 5 8 3a 62 12 3b 6 2 1 2 4a 265 7 4b 26 5 0 7 5a 5b 9 8 0 9 98 9 18 2020 Adept Education Limited t a Reach Education Sheet 20 25
Learning Intention 26 Able to use a calculator efficiently Using calculators see who can get to the correct answer the fastest Hint 1 Remember to use your BODMAS rules Hint 2 It s faster to use the memory function of your calculator Here s a quick reminder of both Who won 1 945 59 x 6 140 1 159 2 86 x 845 x 41 964 2 980 434 3 0 21 0 54 x 869 5 94 062 4 9 90 985 394 x 2 1 970 887 5 900 0 7659 x 4 600 54 967 5 245 3855 6 3 78 x 4 60 873 47 784 x 2 60 468 432 19 2020 Adept Education Limited t a Reach Education Sheet 20 46
Learning Intention 23 Able to add and subtract decimal numbers up to three decimal places With as few button pushes as possible transform the display on your calculator from the first number to the second number 38 076 38 176 1 1 695 02 1 695 00 1 08 0 98 0 59 0 50 393 84 392 24 5 1 33 1 53 2 6 130 38 130 39 3 7 5 70 5 80 4 8 20 2020 Adept Education Limited t a Reach Education Sheet 20 31
solvers 18 Learning Intention 23 Able to add and subtract decimal numbers up to three decimal places The healthy weight of the Reach Zoo s female tigers is 180kg The zookeeper has been carefully monitoring the weight of 2 sick tigers for several weeks She has been asked to present her data to the veterinarian by using a line graph Help the zookeeper plot the graph and answer the questions Use the instructions on the opposite page to help design the graph Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Tiger 1 154 8 152 9 157 3 166 5 164 1 172 2 Tiger 2 169 5 165 2 161 0 159 8 153 8 150 2 y axis Label Legend x axis Label 21 2020 Adept Education Limited t a Reach Education Sheet 20 32 4 5 1
solvers Instructions Learning Intention 23 Able to add and subtract decimal numbers up to three decimal places 18 1 Label Weight on the y axis vertical and Time or Weeks on the x axis horizontal 2 Use the weights to be plotted from the data in the table to decide on a sensible range of weight to have on the y axis The two parallel lines indicate that you graph does not start at 0kg 3 Write your weight labels on the y axis there should be 8 labels and every 5kgs would be about right 4 Number the weeks on your x axis 5 Carefully plot the data from Tiger 1 on the graph Use dots to mark the data points Then connect the dots using a straight line 6 Do the same for the Tiger 2 data Use x s to mark the data points Then connect the x s with a dashed line 7 In some space at the top draw a legend It should show dots and lines labelled as Tiger 1 and x s and dashes labelled as Tiger 2 1 How much weight has Tiger 1 gained since Week 1 2 How much weight has Tiger 2 lost since Week 1 3 In Week 1 which tiger weighed the most 4 In Week 6 what was the difference in weight between the tigers 5 In which week did the tigers have the least difference in weight 6 In which week did the tigers have the most difference in weight 7 What does the graph show Should the vet be concerned for either of the tigers 22 2020 Adept Education Limited t a Reach Education Sheet 20 33 4 5 1
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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 worksheets activities board games certificates and other print and cut resources The learning intentions covered in this book are 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 Online and printed versions available at www reacheducation co nz ISBN 978 0 9951178 6 0 2020 Adept Education Limited t a Reach Education
