SERIES Reading and Understanding Whole Numbers

Transcription

1 F Teacher Student Book Reading and Understanding Whole Numbers Name

2 Contents Series F Reading and Understanding Whole Numbers Topic Section Looking Answers at whole (pp. ) numbers (pp. 8) read looking and at write whole numbers to place order value numbers of whole to 999 numbers create round and estimate compare numbers 7 it s holiday time! apply / / / / / / / / the new place is right! apply Section Assessment with answers (pp. 5 0) Topic Place value of whole numbers (pp. 9 6) Section Objectives (p. ) looking at whole numbers 5 place value of whole numbers 7 round expanded notation estimate 9 / / place value to digits / / place value to 6 digits place value mastermind apply Date completed / / / / / / who am I? solve / / Topic Round and estimate (pp. 7 ) round to a power of 0 estimate calculations round and estimate challenges solve shop till you drop apply / / / / / / / / / / Series Authors: Rachel Flenley Nicola Herringer Copyright

3 Looking at whole numbers read and write numbers to We read and write numbers in the order that we say them. Thousands Hundreds Tens Units six thousand seven hundred and fifteen Express the following in numerals: a four thousand three hundred and sixty two 6 b three hundred and twenty four c eight thousand nine hundred and three 8 90 d four thousand eight hundred and forty one 8 e seven hundred and three f five thousand four hundred and two Write the following in words: a 5 86 five thousand eight hundred and sixteen b 95 nine hundred and fifteen c 8 66 eight thousand four hundred and sixty six d 5 two hundred and fifty four e 7 65 f 598 seven thousand six hundred and fifteen two thousand five hundred and ninety eight Match the numerals with the words: 69 six thousand seven hundred and ninety 709 one thousand and three 8 four thousand six hundred and thirty nine 00 two thousand seven hundred and nine eight thousand three hundred and forty one F TOPIC

4 Looking at whole numbers read and write numbers to We read and write large numbers in groups of three We work from right to left and we put a gap between each group of numbers. These numbers have been grouped incorrectly. Re-group the numbers and read the new numbers out loud to a friend. Ask them to check your grouping. Are you correct? a b c d e f 5 5 Did you know? 5 Convert the following abbreviations into numerals: a 60 K The abbreviation K comes from the Greek word khilioi, and it means thousand. It is used in many job advertisements and in measurement. A salary of 70 K is , and 000 grams is kilogram. When else do we use the term kilo or K? b kilograms 000 grams c 66 K d 8 kilometres metres 6 Are the following statements true or false? a 6 K = 600 b Seventy four thousand three hundred and two = 7 0 c Six hundred and seventy four thousand and thirty nine = d 5 K = e Two hundred thousand eight hundred and two = f Fifty one thousand and sixty = True / False True / False True / False True / False True / False True / False F TOPIC

5 Looking at whole numbers order numbers to When ordering numbers, we need to pay close attention to the position and value of each digit. Which is the largest? Circle the larger number: a 8 / 8 0 b 5 9 / 5 69 c 7 05 / 7 50 d 9 80 / e 85 / 58 f 5 9 / 5 9 g 768 / h / Insert > (greater than) or < (less than) to make each statement true. a 6 8 < 6 68 b 9 5 > 9 60 c 8 95 < d 999 < 009 e 69 < 69 f 75 6 > 7 56 g 9 05 > 9 50 h 7 89 > 7 85 Arrange the following numbers in ascending order: 6 87, 68 57, 5 68, 50 05, 98 65, , 6 87, 98 65, 5 68, 50 05, Arrange the following numbers in descending order: 6 87, 08 5, 5 68, 5 0, 89 6, , 5 0, 5 68, 89 6, 6 87, 898 F TOPIC

6 Looking at whole numbers order numbers to Look at each set of numbers and list some that come in between. Write them in order. a 560 b 69 c 0 0 Answers will vary Write a number that is: Answers will vary. a More than b Close to c A little less than 78 9 d Almost double 000 e Between 6 and 8 90 f Less than half of g Now write more problems for a friend to answer: Answers will vary. 7 Here are the heights of 5 pupils. Place them on the number line. Find your height and that of two friends and add these to the number line. Sarah Huy Jack Emma Nikita 7 cm 5 cm 8 cm 67 cm cm Answers may vary. Nikita Jack Huy Emma Sarah 00 cm 50 cm 00 cm F TOPIC

7 Looking at whole numbers create and compare numbers Use the following digits to make: 7 6 a The highest number 76 b The lowest odd number 67 c The lowest number 67 d The amount of money you would like to win 76 e The highest even number 76 Use the digits to make different digit numbers. Answers will vary. Use the numbers you have made in Question to make the statements true: a is greater than b is less than Answers will vary. c is close to d is about double F TOPIC 5

8 Looking at whole numbers create and compare numbers This table shows the population of 0 cities. Use the information to answer the following questions: Name Population 996 Population 00 Rainsalot Funkytown Point Lonely Dullsville Nirvana Dodgy Meadows Braggersville Letsgo Notsoniceton 88 5 Mt Hero a The population of the mystery place in 00 is less than it was in 996. It has decreased by approximately 000 people. The place is. Mt Hero b You have gone back in time to 997. You live in a city that has a population of more than but less than You live in. Funkytown c It is now 00. You have decided to move to a larger city. This city has a in the units place and a zero in the thousands place. You move to. Braggersville d In 00 you decided to go on a holiday. You only visited cities that had a population of between and Which cities did you visit? Rainsalot, Funkytown, Point Lonely, Nirvana and Notsoniceton. e Many cities showed growth between 996 and 00. List the ones that grew by more than residents. Rainsalot, Funkytown, Point Lonely, Dullsville and Dodgy Meadows. f Your family moved here in 996 and since then, the population has nearly doubled. Where did you move to? Point Lonely or Dullsville 6 F TOPIC

9 It s holiday time! apply Getting ready Your family has just won the dream trip of a lifetime! You have won an all expenses paid trip to 5 towns or cities of your choice. That s right, anywhere in the world with everything paid for. What to do Your job is to plan the trip, following these guidelines: Your dad hates big cities so one place must have a population of or less. Your mum wants to shop. Big time. Your gran has always wanted to see New York. You get to choose the other two places. Record your selections in the left column of the table below: Place Population Answers will vary. What to do next Use an atlas or the internet to help you research the population of your 5 towns or cities, then use the information to answer the following: a Order your towns from smallest population to largest: b Choose two of your destinations and write their populations in words: Answers will vary. c Find a way to divide your places into two numerical categories such as odd/even, smaller than /greater than Get a friend to see if they can work out the rule that you have applied. F TOPIC 7

10 The new place is right! apply Getting ready The aim of this game is to order as many numbers on a game board as possible. You ll play the game in a group of or. You ll need a pencil and the game show boards below. What to do Oh no! She called 9 and I have nowhere to put it, I ve got 8 in the top spot. Decide who will be the game show host and who will be the contestants. The host calls a number between the values specified at the top of the board. Start with Game. Without showing the host, the contestants choose where they will put the number on their own board. The numbers must be placed in order going up from the lowest number. Once a number is placed, it cannot be moved. The host calls another number. If the contestants can place it on their board, they do so. 5 After the host has called 8 numbers, the person with the most numbers on the board wins. They score a point and a free set of steak knives. 6 Play games. The person with the highest score after games wins. 7 You can play again and choose your own number ranges. You will need to draw your own boards. Answers will vary. Game 50 Game Game F TOPIC

11 Place value of whole numbers expanded notation When we write numbers using expanded notation, we identify and name the value of each digit. = Express the numbers in expanded notation: a b c d e f g Express the expanded notation in numerals: a = 687 b = 75 c = 8 d = 69 e = 86 f = 7 95 g = 5 h = 9 8 Answer the following questions. a Tim says 9 in expanded notation is written as Is he correct? No b Now he says that 5 87 is written as Is he correct this time? Yes c Look carefully at the number Why don t we expand it as ? Because that doesn t show the place values. d What is the point of a zero in the middle of 7 09? It has no value so why not just leave it out? It holds the place value. F TOPIC 9

12 Place value of whole numbers expanded notation Play expanded notation memory with a friend. Make a copy of this page, cut out the cards, mix them up and place them face down. Take turns turning over two cards at a time. Each time you make a match, you keep the set. The person with the most cards wins. copy thousands, 9 hundreds, ten and units thousands, hundreds, 8 tens and 9 units 0 F TOPIC

13 Place value of whole numbers place value to digits The place or position of a digit in a number helps us understand its value. Th H T U 650 is worth 000 or two thousands 6 is worth 600 or six hundreds 5 is worth 50 or five tens 0 is worth zero or no units Fill in the place value chart for each number. The first one has been done for you. Thousands Hundreds Tens Units a b 8 97 c 5 d 798 e 507 f Write the number shown on each abacus. a b c d Th H T U Th H T U Th H T U Th H T U e f g h Th H T U Th H T U Th H T U Th H T U F TOPIC

14 Place value of whole numbers place value to digits What is the value of the 5 in these numbers? a b c d e f Write the next numbers in each sequence. The first sequence has been done for you. a b c d Zero plays an important role in numbers. It tells us that the value of the column is nothing and holds the place of the other numbers. I have Without the zero I only have 655! 5 Complete the cross number puzzle. Make sure you include the zeros in the right places Across. four thousand two hundred and seven. seven thousand and ninety four 6. two thousand five hundred and sixty 8. one thousand and forty seven 0. nine thousand and forty three Down. four thousand and eighty six. seven hundred. two hundred and four. seven thousand and fifty 5. nine thousand two hundred and seven 6. two thousand one hundred and thirty 7. six thousand four hundred and three 9. sixty F TOPIC

15 Place value of whole numbers place value to 6 digits Look at the number 56 is worth or one hundred thousand is worth or two ten thousands is worth 000 or three thousands is worth 00 or four hundreds 5 is worth 50 or five tens 6 is worth 6 or six units When we write large numbers we put a space after every three numbers. This is because our brains prefer small chunks of information. We chunk from right to left: Write the number shown in each row of this place value chart. The first one has been done for you. Hundred thousands Ten thousands Thousands Hundreds Tens Units Identify the value of the digit in bold. The first one has been done for you. a b 9 5 c d e f g 0 h i True or False? a In the number 567 9, the 7 has the value of b In the number 899 7, the 8 has the value of True False c In the number 705 5, the zero holds the value of the ten thousands place. True F TOPIC

16 Place value of whole numbers place value to 6 digits Use the clues to find the mystery numbers: I have 5 digits. Every digit is an odd number and every digit in the number is different. The greatest digit is in the units place and the smallest digit is in the ten thousands place. Both the thousands digit and the tens digit are greater than the hundreds digit. So far, I could be numbers. I am the greater of these. I am 7 59 I have 6 digits. If you add one unit to me I have 7 digits. What number am I? A useful strategy is to make lines where each digit should go and fill them in as you work them out. I am I am one half of a million plus one. What number am I? I am I have 5 digits. I have a 6 in the ten thousands place and my digit in the unit place is the smallest even number. My middle digit is one more than the units digit. My thousands digit is double my units digit and my tens digit is double my thousands digit. What number am I? I am 6 8 Write a problem for a friend to solve: Answers will vary. F TOPIC

17 Place value mastermind apply Getting ready In this game, the objective is to guess a secret digit number. You play with a partner. You ll need to rule up a page with headings like this: Number Guess Number of Correct Digits Digits in the Correct Place 5 78 What to do Player writes a secret digit number on a scrap of paper. Player writes their guess in the Number Guess column. Player writes down how many correct digits there are, and how many are in the right column. Player uses that information for guess number. 5 The game continues until the secret number is revealed. 6 Swap roles. What to do next What strategies can you use to reduce the number of guesses you need to make? If you reduced the number of digits in the number to or, does it make easier to guess? Can you work out how many digit number possibilities there are? What about digit number possibilities? Talk to other pairs. What strategies did they use? Try them out if you think they will help you! F TOPIC 5

18 Who am I? solve Getting ready In this guessing game there are many clues. Your job is to not only guess the secret number, but to identify which clues are needed and which are true but don t help solve the problem. What to do Use the clues and the hundreds chart to help you identify the secret number: The number is greater than 8. The number is less than 500. The number is not a multiple of 5. The number is a multiple of 6. The number is even. Its tens digit is even and is double its units digit. The number is in the top half of the hundreds chart. What is the number? What to do next Which clues were not needed? Explain: The number is less than 500 this is not helpful because every number in the chart is less than 500. The number is even this is not helpful because we have already been told that the number is a multiple of six (so it must be even). The number is greater than 8 this is not helpful because we are told that it has an even tens digit. 6 F TOPIC

19 Round and estimate round to a power of 0 Rounding makes big numbers easier to work with. We round up if the number is exactly halfway between the 0s or over the halfway mark. We round down if the number is under the halfway mark. Rounding to the nearest 0 7 is over halfway between the 0s, so it rounds up to is under halfway between the 0s, so it rounds down to is exactly halfway between the 0s, so it rounds up to Round the following numbers to the closest hundred. Find the halfway mark first. 50 a b c d F TOPIC 7

20 Round and estimate round to a power of 0 Round the following numbers to the closest hundred: Use the number in the tens place to help you decide! a 5 00 b c d e f Round the following numbers to the closest thousand: Use the number in the hundreds place to help you decide! a b c d e f To find the hidden fact, round the numbers in the clues below and insert the matching letters above the answers. The first clue has been done for you. M O S Q U I T O E S P 70 R E F E R C H I L D R E N T O A D U L T S S 68 rounded to the nearest hundred Q 0 rounded to the nearest ten thousand T rounded to the nearest thousand P 69 rounded to the nearest ten M 7 rounded to the nearest ten N 6 rounded to the nearest hundred C 8 rounded to the nearest hundred R 8 rounded to the nearest ten I rounded to the nearest ten F 6 76 rounded to the nearest thousand D 9 rounded to the nearest hundred H 99 rounded to the nearest hundred O 7 rounded to the nearest ten L 6 rounded to the nearest ten E 59 rounded to the nearest hundred A 7 68 rounded to the nearest ten thousand U 7 rounded to the nearest ten 8 F TOPIC

21 Round and estimate estimate We use estimating when we want an approximate answer to a calculation. Rounding helps us do this. We round numbers so we can work with them more easily in our heads. Look at + 5. Rounded to the nearest 0, they are 0 and = 850 Therefore + 5 is approximately 850. Complete these steps to see why estimating is handy. a Use the problem 57 8 = 9. Time how long it takes you or a friend to solve it mentally. b Now round the numbers to the nearest ten and time how long it takes to solve this problem. Answers will vary. c Which problem is faster to solve? Answers will vary. d Can you think of an occasion you would use estimation? Answers will vary. Practise estimating with these problems. You can use the middle column to jot down your rounded number sentences or just do them in your head. If you want to add some tension to the activity, race against a partner. Sentence Rounded Sentence Answer Compare your answers with those of others. Did you all get the same answers? Why or why not? F TOPIC 9

22 Round and estimate estimate Round then estimate to find the best answer to these calculations. Circle the best answer: a 7 8 = b 57 + = Which one is best? c 6 7 = d 567 = e = f 5 + = g = Use estimation to assess whether these statements might be true. Tick the ones you think are true and cross the ones you think are false. a > 000 c < 600 e > b > 70 d 57 > f > Use estimation to answer these word problems: a Sarah is saving money to go to the fair. In week she saves, in week she saves 9 and in week she saves 9. Estimate how much money she has at the end of week. 60 b The show bags that Sarah wants cost roughly 5 each. If she wants to spend half her money on show bags, how many show bags can she buy? c For lunch, Sarah wants a hot dog, hot chips and jam doughnuts (mmm healthy). She has budgeted 0 for lunch. Look at the price list below and estimate whether she can buy what she wants and stay within her budget. Yes, with.0 left over. Menu Price Pie/pastie.50 Sausage roll.00 Hot dog.80 Jam doughnuts for.00 Hot chips.00 Hamburger F TOPIC

23 Round and estimate calculations When estimating, we always need to check that our answers are reasonable = 000. Is this estimation reasonable? Are these estimations reasonable? Explain your thinking. a Nicola wants a digital camera that costs 86 and a memory stick that costs 6. She estimates she will spend approximately 000 on both. Is this estimation reasonable? No b Shakeb says 9 + is close to 0. Is this estimation sensible? c Kylie is crazy about dolphins. She has 889 pictures of them, 89 stuffed toys, and 8 figurines. She thinks she has about items altogether. Is this estimation reasonable? Yes Yes d Sean made a list of the money he had spent on lunch over the week. He then estimated that he had spent 0 over the week. Is this a reasonable estimate? Yes Mon.50 Tues 5.65 Wed.85 Thurs 6.5 Fri 7.70 In these problems, work backwards from an estimated answer to find the possible starting points. a Daniel bought chocolate bars. He estimated the bars to cost, and.50. This would make the total estimated cost The actual cost was What could each of the chocolate bars have cost? Sample answers:.0,.60,.05 b Hung bought books. He estimated their costs to be 5, 9 and 5. This would make the total estimated cost 9. The actual cost was. What could each of the books have cost? Find two possibilities. Sample answers: 6.50, 0.50, 6.00 What is the difference between the estimation and the actual cost? How could you share that cost difference between the items? F TOPIC

24 Round and estimate calculations When we use a calculator, it is tempting to rely on it and to stop thinking. Estimating helps us develop an idea of what the possible answer should be. If we make an error with the calculator, we then know to try again. Estimate the answer to these problems. Get a friend to sign off on your estimations, then use a calculator to solve the problems. Estimate Calculation a 5 5 b c 8 6 d 9 e Signed f 0 80 g 98 9 Breathe in... breathe out... breathe in... breathe out... How many breaths do you take in a day? Not exactly, an estimation will do. You ll need a clock with a second hand. You may also want to use a calculator. Ask a partner to help you keep track of how many breaths you take in a minute, then multiply as necessary. a Use this table to help you organise your calculations. Time Frame per minute Number of Breaths b Can you take it further? How many breaths could you take in a week? How many minutes in an hour? How many hours in a day? per hour per day c What about in a year? Answers will vary. F TOPIC

25 Round and estimate challenges solve Getting ready Solve these problems using your head, a calculator, a pen and paper. You may work with a friend. What to do a You have won 5 87 in a competition. The organisers have no coins and have to round off the amount so they can give you your winnings in notes. Would you rather they rounded to the nearest 0, 00 or 000? Why? How much money would you get in each case? Closest 0 = 5 90 Closest 00 = Closest 000 = You would rather it was rounded to the closest 00. b A number is rounded to the nearest thousand to make List at least 5 numbers it could be. Numbers in the range to c A number is rounded to the nearest hundred to make List at least 5 numbers it could be. Numbers in the range 5 50 to 5 9. d What two whole numbers can be multiplied to make 6 000? How many pairs of numbers can you come up with? Answers will vary. F TOPIC

26 Shop till you drop apply Getting ready You and a friend will take turns going on 60 second shopping sprees. You ll need a copy of this page, a timer or a clock with a second hand, the items below and your best estimation skills. You may also want to use a calculator for checking. copy What to do Cut out the items below. Decide who will be the first shopper and who will be the timer. The timer states a spending limit between the values of 0 and 50. The shopper then has 60 seconds to estimate what they can buy while staying under the limit. The shopper takes the items they want. It is okay to put things back. (If 60 seconds is too hard, make the time limit minutes.) 5 After the time is up, all transactions stop. Add up the purchases, using a calculator if desired. 6 If the shopper has stayed under the limit, they get a point. If they go over the limit, they get nothing. 7 Swap roles. At the end of that round, the person who was closest to their shopping limit gets a bonus point. What to do next Make up some more items for the shopping spree. Or challenge another team to a race F TOPIC

27 Looking at whole numbers Name Write in words: a 5 57 b Write in numerals: a forty seven thousand three hundred and nineteen b five hundred and eighty six thousand four hundred and ninety two Match the numerals with the words: 58 thirty two thousand six hundred and forty four 6 seven thousand four hundred and twenty one 7 fourteen thousand five hundred and thirty eight Write these numbers in ascending order: 56 8, 7 905, 57 0, Circle the smaller number: a / b 690 / 609 c 5 9 / What is the smallest number you can make using the digits 5,, 8, 9,? 7 What is the largest number you can make using the digits 8, 0,,, 7, 5? 8 Would you rather inherit 567 or one hundred and four thousand, nine hundred and ninety nine dollars? Why? Skills Not yet Kind of Got it Writes numbers to Matches numerals to words to Compares and orders numbers to Series F Topic Assessment 5

28 Looking at whole numbers Name Write in words: a 5 57 Forty five thousand, five hundred and seventy two b Nine hundred and seven thousand, four hundred and sixty three Write in numerals: a forty seven thousand three hundred and nineteen 7 9 b five hundred and eighty six thousand four hundred and ninety two Match the numerals with the words: 58 thirty two thousand six hundred and forty four 6 seven thousand four hundred and twenty one 7 fourteen thousand five hundred and thirty eight Write these numbers in ascending order: 56 8, 7 905, 57 0, , 56 8, 57 0, Circle the smaller number: a / b 690 / 609 c 5 9 / What is the smallest number you can make using the digits 5,, 8, 9,? What is the largest number you can make using the digits 8, 0,,, 7, 5? Would you rather inherit 567 or one hundred and four thousand, nine hundred and ninety nine dollars? Why? 567, because it is more money. Skills Not yet Kind of Got it Writes numbers to Matches numerals to words to Compares and orders numbers to Series F Topic Assessment

29 Place value of whole numbers Name Write the following numbers in expanded notation: a 8 b 58 c 5 09 Express the expanded notation in numerals: a b c d In the number 78 0, which digit: a is in the ten thousands place? b is in the tens place? c will change if one thousand is subtracted? In which place is the zero in the following numbers? a 078 b 5 70 c True or false? a In the number 90 8, the 9 has the value of nine hundred. b In the number 65 59, the 6 is worth six hundred thousand. c In the number 890, the 8 has a higher value than the 9. Skills Not yet Kind of Got it Expresses numbers in expanded notation to States the place value of any digit in numbers to Identifies the value of digits in large numbers Series F Topic Assessment 7

30 Place value of whole numbers Name Write the following numbers in expanded notation: a b c Express the expanded notation in numerals: a b c d In the number 78 0, which digit: a is in the ten thousands place? 8 b is in the tens place? c will change if one thousand is subtracted? In which place is the zero in the following numbers? a 078 hundreds b 5 70 units c 709 ten thousands 5 True or false? a In the number 90 8, the 9 has the value of nine hundred. False b In the number 65 59, the 6 is worth six hundred thousand. False c In the number 890, the 8 has a higher value than the 9. True Skills Not yet Kind of Got it Expresses numbers in expanded notation to States the place value of any digit in numbers to Identifies the value of digits in large numbers 8 Series F Topic Assessment

31 Round and estimate Name Round these numbers to the nearest 0: a 67 b 9 Round these numbers to the nearest 00: a 6 56 b Round these numbers to the nearest 000: a 99 b Join the numbers in the left column with an estimate in the right: 59 0 roughly roughly twenty five thousand 899 roughly six hundred thousand 8 9 roughly thirty thousand 5 Are these reasonable estimates? Circle your choice. a Shayla estimates 78 + is roughly 600. b Buying a drink for.50 and a sandwich for will cost you roughly 0. c Rounded to the nearest 000, there are 000 people in a stadium. The actual number could be 679. Yes / No Yes / No Yes / No 6 Circle the best estimate: a = b 0 + = 0 8 c = Skills Not yet Kind of Got it Rounds to the nearest 0, 00, 000 Makes reasonable estimates to answer real life problems Uses rounding to make reasonable estimates Series F Topic Assessment 9

32 Round and estimate Name Round these numbers to the nearest 0: a b 9 90 Round these numbers to the nearest 00: a b Round these numbers to the nearest 000: a b Join the numbers in the left column with an estimate in the right: 59 0 roughly roughly twenty five thousand 899 roughly six hundred thousand 8 9 roughly thirty thousand 5 Are these reasonable estimates? Circle your choice. a Shayla estimates 78 + is roughly 600. b Buying a drink for.50 and a sandwich for will cost you roughly 0. c Rounded to the nearest 000, there are 000 people in a stadium. The actual number could be 679. Yes / No Yes / No Yes / No 6 Circle the best estimate: a = b 0 + = 0 8 c = Skills Not yet Kind of Got it Rounds to the nearest 0, 00, 000 Makes reasonable estimates to answer real life problems Uses rounding to make reasonable estimates 0 Series F Topic Assessment

33 Series F 006 Primary Framework Core Objectives Topic Looking at whole numbers Topic Place value of whole numbers Topic Round and estimate Counting and understanding number Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers Using and applying mathematics Solve one- and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use Counting and understanding number Count from any given number in whole number and decimal steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers Using and applying mathematics Solve one- and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate calculation strategies, including calculator use Represent a problem by identifying and recording the calculations needed to solve it; find possible solutions and confirm them in the context of the problem Counting and understanding number Explain what each digit represents in whole numbers and decimals with up to two places, and partition, round and order these numbers Knowing and using number facts Use knowledge of place value and addition and subtraction of two digit numbers to derive sums an differences, doubles and halves of decimals, e.g. 6.5+/-.7, halve 5.6, double 0. Use knowledge of rounding, place value, number facts and inverse operations to estimate and check calculations Calculating Use a calculator to solve problems, including those involving decimals or fractions, e.g. to find of 50 g; interpret the display correctly in the context of measurement Series F Objectives