PART AUTUMN first half NUMBER: PLACE VALUE ADDITION AND SUBTRACTION SECTION Putting numbers into words SECTION Multiplying and dividing by 0 and 00 SECTION Positive and negative numbers SECTION Addition SECTION Subtraction SECTION Calculating with money SECTION Addition and subtraction problems Key Stage National Strategy CROWN COPYRIGHT 00
SUGGESTED TIME NUMBER: PLACE VALUE ADDITION AND SUBTRACTION hours TEACHING OBJECTIVES Read and write whole numbers in figures and in words, and know what each digit represents. Multiply and divide any positive whole number up to 0 000 by 0 or 00 and understand the effect. Order positive and negative integers (number line, temperature). Calculate temperature rises across 0 C. Approximate first and use informal pencil and paper methods to support, record or explain addition and subtraction. Extend written methods to addition and subtraction of two integers less than 0 000. Extend written methods to addition of more than two integers less than 0 000. Develop calculator skills and use a calculator effectively, interpret the display in different contexts. Solve word problems SECTION Putting numbers into words SECTION Multiplying and dividing by 0 and 00 SECTION Positive and negative numbers SECTION Addition SECTION Subtraction SECTION Calculating with money SECTION Addition and subtraction problems Key Stage National Strategy CROWN COPYRIGHT 00 HOMEWORK Practice exercises on positive and negative numbers. Following on from Star Challenge in Section, there is further work on arithmogons in the Framework for teaching mathematics: Years, 8 and 9. Many pupils will need further practice at written addition and subtraction and solving word problems.
Key Stage National Strategy PART CHECKLIST Unit Checklist for pupils Putting numbers into words You will: read and write numbers using figures and words Multiplying and dividing by 0 and 00 You will: multiply whole numbers by 0 and 00 divide whole numbers by 0 and 00 Positive and negative numbers You will: put positive and negative numbers in order work with temperature differences Addition and subtraction You will: add numbers subtract numbers recognise when to add and when to subtract numbers Calculating with money You will: practise calculating with money work with bills Addition and subtraction problems You will: use addition and subtraction to solve word problems Key Stage National Strategy CROWN COPYRIGHT 00
SECTION : PUTTING NUMBERS INTO WORDS DIRECT TEACHING POINTS Use this section as the basis of short mental activities during the term. Use place value cards to demonstrate how can be thought of as 00 + 0 + rather than hundreds, tens and units. 0 0 0 Pay attention to the correct spelling of number names. Give pupils practice in writing large numbers in words and numerals. Exercise is a consolidation exercise. Star Challenge is a good diagnostic exercise to test pupils understanding of place value. In Star Challenge, encourage pupils to discuss their answers. They can repeat the exercise generating their own numbers, by throwing dice. KEY TO VOCABUL ARY LEAR USE AND number names (correct spelling) place value Key Stage National Strategy CROWN COPYRIGHT 00 8
Key Stage National Strategy PART SECTION Putting numbers into words Numbers and words MHThTThThH T U 0... in words two hundred and one two hundred and ten Look at the column headings. They will help you.... three hundred and six 0 five hundred and thirty... six hundred and forty... seven hundred and fifteen... nine hundred and six 8... nine hundred and sixty 9... three hundred and forty-six 0... 0... 0... 0 one thousand, two hundred and four... two thousand and five... two thousand and fifty... three thousand, one hundred and three... three thousand, one hundred and thirty 8 0 0 two thousand, five hundred 9... two thousand, five hundred and four 0... two thousand, five hundred and forty Key Stage National Strategy CROWN COPYRIGHT 00... 0 0 9 0 0 six thousand and ten...... 0...... 0 0... 9
Key Stage National Strategy PART SECTION Putting numbers into words Which of these numbers is? All correct star 00 00 00 00 000 00 00 00 00 00 00 000 000 00 Which of these numbers is four thousand and one? Which of these numbers is four million, one thousand? Which of these numbers is four million, one thousand, one hundred? Which of these numbers is two thousand and seventy? Which of these numbers is two million and seven? Which of these numbers is two thousand and seven? Making numbers to order Make the biggest number you can using each of these digits only once. Write the number in figures and words. All correct star 8... Make the smallest number you can using each of these digits only once. Write the number in figures and words.... Make the biggest number you can using each of these digits only once. Write the number in figures and words. 0 9 8 Key Stage National Strategy CROWN COPYRIGHT 00... 0
SECTION : MULTIPLYING AND DIVIDING BY 0 AND 00 DIRECT TEACHING POINTS Use this Section as the basis of mental activities during the term. Show pupils how to generalise multiplication and division by 0 so that they will be able to cope with decimals. The change in value of the digits is the key to their understanding. You need to discuss why. 0.0 and 0. 0.. Multiplying a number by 0 moves the digits one place to the left. Multiplying a number by 00 moves the digits two places to the left. Th H T U 0 0 This shows that 0 = 0 00 0 0 This shows that 00 = 00 Dividing a number by 0 moves the digits one place to the right. Dividing a number by 00 moves the digits two places to the right. Th H T U 0 0 This shows that 0 0 = 0 0 0 00 0 This shows that 000 00 = 0 Emphasise that multiplication and division by 0 (and powers of 0) is a mental calculation. Key Stage National Strategy CROWN COPYRIGHT 00 Make sure pupils can explain 0 0 as (for example) 00. Give them opportunities to explain their calculations. Star Challenge is suitable for pairs of pupils to work on together. This question is typical of National Curriculum test questions. Star Challenge will extend pupils who can quickly recall multiplication bonds. It revises square numbers from Unit. This work should form part of regular mental work and include questions like 0 0, 80 0. KEY TO VOCABUL ARY LEAR USE AND multiplication division multiply divide squared digit million thousand hundred
Key Stage National Strategy PART SECTION Multiplying and dividing by 0 and 00 Multiplying whole numbers by 0 and 00 0 00 0... 0... 00... 00 00 8 00 8 0 0 Dividing whole numbers by 0 and 00 0 0 00 0 0 0... 00... 0 9 000... 00 00 00 8 00... 0 Multiplying and dividing by 0 and 00 0 00... 0 0 00 00... 000 0 0 8 0... 000 00 9... 0 0... 00 0... 0 0 Key Stage National Strategy CROWN COPYRIGHT 00
Key Stage National Strategy PART SECTION Multiplying and dividing by 0 and 00 and puzzles Complete these. Put digit in each box. 8 9 correct stars correct star 0 0 ( marks) ( marks) Ellen puts a three-digit whole number into her calculator. She divides the number by 0. Her answer is. What is the number that she put into her calculator? 0 0 0.. ( mark) ( marks) 0 0 0 ( marks) 0 0 0 ( marks) Amy puts a single digit whole number into her calculator. She multiplies the number by 0. (a) Put in the last digit on the calculator display. (b) What number did she multiply by 0?... ( marks) 8 Peter puts a two-digit whole number into his calculator. He multiplies the number by 0. (a) Put in the last digit on the calculator display. (b) Can you tell what the middle digit is on the display? (Yes or no)... Key Stage National Strategy CROWN COPYRIGHT 00 Peter puts the same two-digit whole number into his calculator. He multiplies the number by 00. (c) Fill in the complete calculator display. 8 ( marks)
Key Stage National Strategy PART SECTION Multiplying and dividing by 0 and 00 Multiplying in your head 8 correct stars correct star Work out in your head: 0... 0... 0... 0... 8 0... 90... IDEA IDEA 00 00 00 00 00... 000... 9 0 0... 8 00... 000... 0 0 0... 9 00... 000... 0 0... 0 00... 8 000... 80 0... 00... 00... 0 0... 000... 8 8 00... 80 0... 0 squared... 0 squared... 9 00 squared... 0 squared... 8 0 squared... 0 80 squared... Key Stage National Strategy CROWN COPYRIGHT 00
SECTION : POSITIVE AND NEGATIVE NUMBERS DIRECT TEACHING POINTS Use a number line to model positive and negative whole numbers. Pupils need experience of number lines (scales) in different orientations. The calculation of differences by counting on needs to be taught, initially between two positive numbers in Unit, and now between a negative number and a positive number. Use exercises, and as consolidation. Model the process on a thermometer scale or number line. Use this as a focus for mental work. Pupils need to work with word problems as presented in this section. Teach the key vocabulary. KEY TO VOCABUL ARY LEAR USE AND integer positive negative difference order temperature thermometer Key Stage National Strategy CROWN COPYRIGHT 00
Key Stage National Strategy PART SECTION Positive and negative numbers Winter weather Put the four missing labels on the thermometer. C The temperature is C. The temperature rises by. The new temperature is........... The temperature is C. The temperature falls by. The new temperature is........... 0 C The temperature is C. The temperature rises by. The new temperature is........... C A cold night These maps show how the temperature in Belfast changed overnight. 9 pm midnight am C C C At what time was the temperature the highest?... At what time was the temperature the lowest? Between 9 pm and midnight, did the temperature rise or fall? How many degrees did the temperature fall between midnight and am?......... Key Stage National Strategy CROWN COPYRIGHT 00
Key Stage National Strategy PART SECTION Positive and negative numbers Comparing temperatures 0 Look at the map showing temperatures at midday. Midday temperatures C Shetland Isles 9 Which place has the highest temperature?... 8 Which place has the lowest temperature?... What is the difference in temperature between London and the Shetland Isles?... What is the difference in temperature between the South West and the Scottish Highlands?... South West C C Scottish Highlands C West Midlands London C 0 Look at the map showing temperatures at midnight. Which place has the highest temperature?... Midnight temperatures C Shetland Isles Key Stage National Strategy CROWN COPYRIGHT 00 Which place has the lowest temperature?... What is the difference in temperature between the West Midlands and the Scottish Highlands?... South West C C Scottish Highlands C West Midlands London C C
Key Stage National Strategy PART SECTION Positive and negative numbers Temperature differences 9 correct stars 8 correct star 0 9 Look at the map showing temperatures at midnight. Midnight temperatures c Shetland Isles 8 Which place has the highest temperature?... Which place has the lowest temperature?... Which is colder, the Scottish Highlands or the North East?... How many degrees colder is the West Midlands than the South East?... South Wales South West c c c 0 c Scottish Highlands 8 c North East West Midlands c South East 0 Look at the map showing temperatures at midday. Which place is the coldest?... Midday temperatures c Shetland Isles C 8 Which place has the highest temperature?... What is the difference in temperature between the South West and the Shetland Isles? Now look at both maps.... Look at the Scottish Highlands. (a) Did the temperature fall or rise between midnight and midday?... South Wales South West c c (b) How many degrees did the temperature fall or rise between midnight and midday?... c c Scottish Highlands c North East West Midlands c South East Key Stage National Strategy CROWN COPYRIGHT 00 8
SECTION AND : ADDITION AND SUBTRACTION DIRECT TEACHING POINTS You need to be familiar with the progression through informal and expanded methods as shown in the Framework for teaching mathematics from Reception to Year. Make a clear assessment of pupils confidence in written methods for addition and subtraction. The aim is for all pupils to understand and use appropriately an efficient written method. Some pupils will have reached this stage but others may still be using expanded methods. 8 00 80 00 0 00 0 9 9 8 9 0 00 9 (add units first) (then add tens) (then add hundreds) 8 9 8 00 80 00 0 00 0 8 00 80 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 8 8 00 80 8 8 Key Stage National Strategy CROWN COPYRIGHT 00 800 0 00 0 800 0 00 0 00 0 00 0 00 0 9
Target the practice exercises to meet pupils needs. Not every pupil will need to do all the examples. A no regrouping B regroup T U C regroup H T D regroup H T U Use errors as teaching points. 9 8 8 9 8 8 9 8 0 8 90 8 8 Work out Work out 9 x What is wrong? What is wrong? Work out Work out 9 9 x What is wrong? What is wrong? x x Discuss Star Challenge in Section with pupils. It is a useful introduction to the solution of equations. Emphasise the links between addition and subtraction. Learning one fact or knowing one result allows pupils to deduce many others. Star Challenges and 8 are typical of National Curriculum test questions. For pupils who struggle with subtraction you may want to teach an alternative method. This one requires negative number rather than decomposition. 9 8 00 0 Key Stage National Strategy CROWN COPYRIGHT 00 80 KEY TO VOCABUL ARY LEAR USE AND addition subtraction sum minus subtract difference take away
Key Stage National Strategy PART SECTION Addition Addition 8 8 9 9 9 0 8 9 8 0 Key Stage National Strategy CROWN COPYRIGHT 00 8
Key Stage National Strategy PART SECTION Addition Addition arithmogons The number in each is the sum of the two numbers in the circles on each side of it. correct stars correct star Copy and complete each arithmogon. Show all your working in your exercise book. 0 9 9 Make up some arithmogons. Key Stage National Strategy CROWN COPYRIGHT 00 8
Key Stage National Strategy PART SECTION Subtraction Subtraction I A 9 8 B 8 9 C 8 8 9 8 Key Stage National Strategy CROWN COPYRIGHT 00 D 0 8 90 8 8 8
Key Stage National Strategy PART SECTION Subtraction Subtraction 8 89 8 8 9 8 0 0 9 08 9 Key Stage National Strategy CROWN COPYRIGHT 00 8
Key Stage National Strategy PART SECTION Subtraction Add or subtract? correct stars correct star... IDEA IDEA... IDEA IDEA Add + Subtract Calculate the missing numbers: Or count on: 0... 8 0...... 9...... 9... 0 9 0 0...... 8......... 0......... 8 Find the missing digits Key Stage National Strategy CROWN COPYRIGHT 00 8 Copy the sums. Put in the missing digits. 9 All correct star 8 8 There are six possible answers to Question. 8
SECTION : CALCULATING WITH MONEY DIRECT TEACHING POINTS Use mental work to consolidate complements to 00. 0 + = 00 + = 00 + = 00 Include some examples in context of money. You go to the shop. You have a coin. You buy a book. How much change would you get if the till showed: (a) (b) (c) 0.90 0. 0. Change from =...p Change from =...p Change from =...p Teach calculator skills. Pupils need to decide when it is appropriate to use mental, written or calculator methods to complete calculations. Discuss why. + p is not.. EY VOCABUL ARY Kchange how much? how many? TO LEAR USE AND Key Stage National Strategy CROWN COPYRIGHT 00 8
Key Stage National Strategy PART SECTION Calculating with money Pounds and pence whole pounds parts of a pound 0 pounds pence Example 0.0 p 0.0 0p 0p 0.0 0p 0.0 Complete each statement: 0p 0.0 so 0p 0p 0p p 0.0 so p p p 0p p 0. so 0p 0p p Write in pence: (a) 0....p (c) 0.80...p (b) 0....p (d) 0.08...p Key Stage National Strategy CROWN COPYRIGHT 00 Write in pounds: (a) p... (c) 9p... (b) 0p... (d) 8p... 8
Key Stage National Strategy PART SECTION Calculating with money Checking your bill You are less likely to make mistakes in bills if you: write all amounts in ( 0.0 instead of 0p) stack the figures in a column stack the figures with the decimal points below each other Each of these bills is written badly. Write a new bill beside each old one. Work out the total. Red Dragon Takeaway It s a Snip New bill New bill Chow Mein. Noodles 90p Spring rolls.0. 0.90.0 Cut and Blow.0 Conditioner 9p Coffee 0p......... Total Total Pete s Pet Shop Patel s Papers New bill New bill Gerbil food. Fish pellets.8 Bird seed 8p......... Newspapers. Sweets. Magazine p......... Total Total Key Stage National Strategy CROWN COPYRIGHT 00 88
Key Stage National Strategy PART SECTION Calculating with money 9 Find the mistakes The total of each of these two bills is wrong. Write each bill correctly. Find the total. correct star Tommy s Toys Big Chance game. colouring book 80p pack of crayons.90 Total.9 Benny s Books Racer s Annual.9 Modeller s Monthly.0 Puzzle book p Total.8 There are two mistakes in the entries. Correct the mistakes. Find the total. Bobby s Bakers Key Stage National Strategy CROWN COPYRIGHT 00 loaves at 80p.0 cakes at 0p each.08 packets of crisps at p.0 swiss roll 0. Total 89
Key Stage National Strategy PART SECTION Calculating with money 0 Meet the @ symbol correct stars 0 correct star pens @ p means pens at p each pkts nails @ p means packets of nails at p per packet Find the cost of: pencils @ 0p.. loaves @ 0p.. pkts nails @ p.. tins beans @ p.. cakes @ 0p.. roses @.. Complete each of these bills: Bodger s DIY Ltd. shelves @. 8 brackets @ p packs wood screws @.0 Wood glue @ 8p Total 0.8 8 Gossips Newspaper Shop copies Daily Waffle @ p copies Evening Chat @ p magazine @ 8p comics @ p Delivery charge p Key Stage National Strategy CROWN COPYRIGHT 00 Total 90
SECTION : ADDITION AND SUBTRACTION PROBLEMS DIRECT TEACHING POINTS Teach pupils to: read a word problem extract relevant information decide which calculation is necessary do the calculation interpret the answer in the context of the problem. Model the process with some examples. Exercise and Star Challenge provide practice examples. Key Stage National Strategy CROWN COPYRIGHT 00 9
Key Stage National Strategy PART SECTION Addition and subtraction problems Do you add or subtract? Example Mary had. She bought a dress for. How much did she have left? 8 She had 8 left. For each problem: read the question write down an addition or subtraction calculation work out the answer to the calculation write down the answer to the problem Dave had. He spent. How much did he have left? Calculation In Y, there are 8 girls and 8 boys. How many students are there in Y? Calculation Answer Answer Number in Y8 : Number of Y8 present: 89 How many Y8 students are absent? Calculation Stella had in her bank. She won 0. How much does she have now? Calculation Key Stage National Strategy CROWN COPYRIGHT 00 Answer Answer 9
Key Stage National Strategy PART SECTION Addition and subtraction problems More difficult word problems For each problem: read the question write down an addition or subtraction calculation work out the answer to the calculation write down the answer to the problem ( mark) ( mark) 0 marks stars 9 marks stars marks star Key Stage National Strategy CROWN COPYRIGHT 00 8 Dave had. He spent 0 on a CD player. How much did he have left? Sue had in the bank. She puts another into her bank account. How much does she now have in the bank? Carl has in the bank. He takes out 0. How much has he left in the bank? Mary needs to go on a ski trip. She has earned. How much more does she need? In Year 9 there are boys and 8 girls. (a) How many students are there in Year 9? (b) On the last day of term, there were 9 Year 9 students in school. How many were absent? Ella was born in 99. How old will she be in 00? Eddy won 8. He gave to his mother. How much did he have left? Ben went shopping for furniture for his new flat. He bought a bed for. He bought table and chairs for 8. He bought a lamp for 9. (a) How much did he spend altogether? (b) He started with 00. How much did he have left? 9
Key Stage National Strategy PART ANSWERS Unit Answers Section Putting numbers into words Numbers and words 0 two hundred and one 0 two hundred and ten 0 three hundred and six 0 five hundred and thirty 0 six hundred and forty seven hundred and fifteen 90 nine hundred and six 8 90 nine hundred and sixty 9 three hundred and forty-six 0 seven hundred and twenty-five 0 four hundred and three 0 six hundred and seventy 0 one thousand, two hundred and four 00 two thousand and five 00 two thousand and fifty 0 three thousand, one hundred and three 0 three thousand, one hundred and thirty 8 0 0 two thousand, five hundred 9 0 two thousand, five hundred and four 0 0 two thousand, five hundred and forty 00 six thousand and ten 009 four thousand and nine 00 three thousand, one hundred 0 seven thousand and twenty three Key Stage National Strategy CROWN COPYRIGHT 00 two hundred and forty five thousand, three hundred and forty six 00 two million, four hundred and thirty two thousand and thirty 9
Key Stage National Strategy PART ANSWERS Unit Answers Section Multiplying and dividing by 0 and 00 Multiplying whole numbers by 0 and 00 0 800 0 00 8 00 00 0 Dividing whole numbers by 0 and 00 0 0 8 0 90 00 Multiplying and dividing by 0 and 00 0 0 000 0 8 0 0 9 00 0 00 Section Positive and negative numbers Winter weather C C C Key Stage National Strategy CROWN COPYRIGHT 00 C 0 C C C C C C 9
Key Stage National Strategy PART ANSWERS Unit Answers Positive and negative numbers continued A cold night 9 pm am fall Comparing temperatures South West London Scottish Highlands West Midlands 8 Section Addition Addition 9 8 98 89 9 888 9 8 9 9 9 0 80 80 Section Subtraction Subtraction A B 9 C 8 D 9 8 Subtraction 0 8 0 8 8 9 8 8 89 Key Stage National Strategy CROWN COPYRIGHT 00 9
Key Stage National Strategy PART ANSWERS Unit Answers Section Calculating with money Pounds and pence 0.0 (a) p (b) p (c) 80p (d) 8p 0.08 (a) 0. (b) 0.0 (c) 0.09 (d) 0.8 0. Checking your bill. 0.90.0..0 0.9 0.0...8 0.8... 0..0 Section Addition and subtraction problems Do you add or subtract? Calculation: 8 Calculation: 8 8 Calculation: 89 8 Answer: Dave had 8 left. Answer: There are students in Year. Answer: 8 students are absent. Calculation: 0 Answer: Stella had. Key Stage National Strategy CROWN COPYRIGHT 00 9
Key Stage National Strategy PART ANSWERS Unit Answers Star Challenge answers Which of these numbers is? 00 00 00 000 000 00 00 00 00 Making numbers to order 8 eight thousand, six hundred and forty three 9 fourteen thousand, five hundred and seventy nine 8 0 eighty six thousand, five hundred and twenty 8 9 correct stars and puzzles - correct star 0 0 00 0 0 0 0 00 0 0 0 (a) 0 (b) All correct star All correct star 00 00 8 (a) 0 (b) no (c) 800 98 Multiplying in your head 8 correct stars - correct star 0 0 8 000 000 8 9 0 0 0 00 00 0 80 8 8 00 00 8 0 0 9 0 0 00 0 0 0 0 0 800 90 0 0 0 000 00 00 80 0 00 00 00 0 0 00 00 000 80 0 800 00 00 0 squared 00 00 800 0 squared 00 000 000 0 squared 900 000 000 8 0 squared 900 000 000 9 00 squared 0 000 000 000 0 80 squared 00 Key Stage National Strategy CROWN COPYRIGHT 00
Key Stage National Strategy PART ANSWERS Unit Answers Star Challenge answers Temperature differences South East West Midlands continued North East 9 correct stars -8 correct star Scottish Highlands South Wales 8 (a) fall (b) Addition arithmogons correct stars correct star 0 8 0 8 9 9 9 9 Key Stage National Strategy CROWN COPYRIGHT 00 Add or subtract? - correct stars - correct star 8 0 9 9 0 0 9 8 9 0 0 9 99
Key Stage National Strategy PART ANSWERS Unit Answers 8 9 Star Challenge answers Find the missing digits 8 9 Find the mistakes..9 0.80.0.90 0..9.00 continued There are six possible answers: All correct star 8 8 8 8 8 8 8 8 8 8 8 8 - correct star Mistake : cakes at 0p each cost.80, not.08 Mistake : packets of crisps cost 0., not.0. The correct bill is:.0.80 0. 0..9 0 Meet the @ symbol 0p.0.00 8p.0 - correct stars 0- correct star 9.80..0 0.8 8.9 8.90. 0.8 0.0 0..8 Key Stage National Strategy CROWN COPYRIGHT 00 00
Key Stage National Strategy PART ANSWERS Unit Answers More difficult word problems Star Challenge answers continued Calculation: 0 Answer: Dave had left 0 marks stars -9 marks stars - marks star Calculation: 0 Answer: Sue now has 0 in the bank Calculation: 0 Answer: Carl has left in the bank Calculation: 9 Answer: Mary needs another 9 (a) Calculation: 8 Answer: There are students in Y9 (b) Calculation: 9 Answer: There were students absent Key Stage National Strategy CROWN COPYRIGHT 00 8 Calculation: 00 99 Answer: Ella will be in 00 Calculation: 8 0 Answer: Eddy had 0 left (a) Calculation: 8 9 Answer: Ben spent altogether (b) Calculation: 00 Answer: Ben had left 0
8 9 0 8 squared 9 squared 8 0 squared 900 n 89