Hamilton Secondary Numeracy Project Numeracy Simmering Term 1
www.hsnp.org.uk
Published by Hamilton Trust 1A Howard Street, Oxford, OX4 3AY www.hamilton-trust.org.uk [email protected] tel: 01865 253980
Development team Ruth Merttens, Jennie Kerwin Alison Fahey, Deidre Holes, Jeanette Viney, Mike O’Regan
Contents
Contents i
Introduction to HSNP ii
Table showing different levels v
Content of HSNP vi
Weekly activities 1
Optional weekly activities 42
Homework 59
Homework answers 75
HSNP © Hamilton 2012 Page i Simmering Term 1 Introduction to HSNP Structure of HSNP Numeracy - Four levels of proficiency
1. Stepping up – for those who have not achieved the level of numerical fluency expected at the end of Upper Key Stage 2. (Level 3s at entry to Y7)
2. Keeping up – for those who have just about achieved the level expected at the end of Upper Key Stage 2 but who are not secure with this. (Shaky Level 4s at entry to Y7)
3. Simmering – for those who have achieved the standard expected at the end of Upper Key Stage 2 and who are secure with it, but who need to sustain their numerical fluency. (Secure Level 4s)
4. Shining – for those who are good at number work and who need to sustain their proficiency and do a bit of exploration. (Level 5s)
Advice as to which pupils do which levels
Year 7
Some pupils will need Stepping up – the lowest level of numeracy intervention which provides teaching and practice of basic skills. This will suit pupils who enter Y7 with a level of numeracy no higher than Level 3.
Some pupils will require Keeping up – the slightly harder programme for those not far below where we would want them to be in terms of numeracy levels. This provides a little teaching and a HSNP © Hamilton 2012 Page ii Simmering Term 1 great deal of practice of basic numeracy skills. This suits pupils who are operating at high Level 3 or a low Level 4 in relation to numeracy.
HSNP © Hamilton 2012 Page ii Simmering Term 1 Some pupils will require Simmering – the standard numeracy programme. This recognises that these pupils have achieved a reasonable level of numeracy but that they need to practise it or else they will forget! These pupils are operating at Level 4.
Some pupils will need Shining – the advanced programme for pupils who are numerically fluent. This aims to broaden their understanding of number and to encourage deeper exploration of numerical concepts.
Year 8
A few pupils may still require the basic level, Stepping up.
Many pupils will have moved on to the next level, Keeping up.
Most Y8 pupils will hopefully be at the average level, Simmering.
A few pupils may be wanting advanced level work, provided in Shining.
Year 9
Some Y9 pupils may still not have progressed from the slightly lower than average level of Keeping up. Most will be requiring Simmering or Shining.
The following table provides an overview of how the different levels of programme operate. Some sets of pupils will be using the same level of materials for more than one year. This is because their skills, once acquired, are simply being kept ‘on-the-boil’, so to speak. To accommodate this, we shall be providing a second and even third set of these materials so that pupils will not be doing the same activities twice.
HSNP © Hamilton 2012 Page iii Simmering Term 1 This table shows which pupils may be using the different levels of programme in successive years. The column headings refer to the different ‘Turns’ pupils may have at the same level of programme. So, for example, some Y7 pupils may have three goes at the Simmering, since doing this programme keeps their numeracy skills honed over the three years of KS3.
HSNP © Hamilton 2012 Page iii Simmering Term 1 HSNP © Hamilton 2012 Page iv Simmering Term 1 Table showing how the different levels operate within HSNP
1st ‘Turn’ 2nd ‘Turn’ 3rd ‘Turn’ Y10/Y11
Stepping Between 15% Between 5% and 40% of and 10% of up Y7 Y8 20% - 30% of Y7 Y8 who need Y9 who Keeping up Y8 who were another go at cannot move in Stepping- this beyond this up in Y7 Around 50% of Y7 Y8 who were Y8/Y9 who Y9 who need Y10 who need in Keeping-up need to keep to keep their to keep their Simmering in Y7 their skills on skills skills Y9 who were the boil simmering simmering in Stepping- up and then in Keeping-up Y8, Y9 who Y9 who are 10% - 20% of are very good very good at Y7 at numeracy numeracy but Between 20% Y8/Y9 who Shining but need need and 40% of have topped something so something so cohort out of they don’t they don’t simmering forget it forget it
HSNP © Hamilton 2012 Page v Simmering Term 1 Content of HSNP Wk Term 1 Term 2 Term 3 1 Place Value - Fractions - Compare/ Decimals and Fractions Numbers to 1,000,000 order fractions on a line, - Round whole numbers Ordering on a line, mixed nos to improper & decimal numbers, comparing, place value fractions & reverse, using rounding to additions and equivalent fractions estimate answers to subtractions /reducing to simplest calculations form 2 Addition - Mental Addition of fractions - Addition of decimals addition of 2-digit nos Explain why we need and fractions - Written and multiples of common denominator addition with whole and 10,100, 1000; written and do some easy decimal numbers; column addition, additions with related adding fractions (smile choosing a strategy to denominators then then kiss) including suit specific numbers introduce ‘smile then mixed fractions kiss’ 3 Subtraction - Mental Subtraction of fractions Subtraction of decimals subtraction counting - Use notion of common & fractions - Written up; some counting denominator to do some subtraction with whole back and choosing a easy subtractions with and decimal numbers; mental strategy, related denominators then subtract fractions counting up for hard then rehearse ‘smile (smile then kiss) subtraction then kiss’ including mixed fractions 4 Multiplication - Times Multiplication - Tables, Multiplication - tables, multiples and multiples and factors, Rehearse all forms of factors, grid multiplying fractions written multiplications, multiplication, mental (compare ½ x ½ with 0.5 algorithm & grid strategies incl. x 0.5) Show ‘rule’ for (default) and doubling and halving dividing fractions as multiplication of inverse fractions inc mixed numbers 5 Division - Reverse of Division - Relate Division - Strategies for multiplication = fractions to division, written division of chunking, mental rehearse finding decimal numbers using strategies including fractions of amounts, preferred method (short chunking and e.g. 5/6 of 120. Divide division or chunking) strategies involving whole numbers by (Remove ‘point’ and halving (÷ 8 ≡ halving 3 fractions, e.g. 6 ÷ ½ as divide integers then times, ÷ 5 ≡ ÷ 10 and how many halves in six? adjust) doubling, etc.)
HSNP © Hamilton 2012 Page vi Simmering Term 1 HSNP © Hamilton 2012 Page vii Simmering Term 1 Optional6 Place weeks Value - Decimal Place value - Place value - Check PV 1 numbersPercentages - Find 10% comparing,Percentages ordering - Find ofPercentages decimal numbers - Find any by Orderingof amounts, on afind line, whole decimalsimple % numbers of amounts and ordering/% of amounts comparing using a on comparing,amount if told place 10% value (X integers,using 10% including and 1%, Find acalculator; line, compare relate & order additionsand ÷ by 10) and negativewhole amount numbers if told fractionspercentages using and subtractions with 10% or 1% (X by 10 or equivalence;decimals and decimal fractions tenths and hundredths 100) and fraction 2 (andRatio thousandths - Find simple for Proportion - Relate equivalencesProportion/ratio - measures)ratios in a context that proportion to fractions Relate fractions & 7 Additionmakes sense, - Mental e.g. Addition(1/4 of chn - Mental to 1 in and4 of Additionproportions, - Revise change additionrecipes or with paint decimal mixing. writtenchn). Find addition proportions with mentalsimple ratiosaddition to numbers, written decimalof amounts. numbers, strategies,fractions or including proportions 3 columnBIDMAS addition - Decide with the includingInverse operations adding - integersIndices - andUnderstand decimal decimalorder of numbersoperations in a negativeUse to check numbers and devise numberssquares, cubes etc. 8 Subtractionstring - Written Subtractionmental strategies - Mental SubtractionManipulate simple- Revise subtraction with whole and written subtraction mentalindices subtraction 4 thenMensuration decimal numbers.- SI units, withMensuration whole numbers, - Area and strategies,Shape/Mensuration counting up - Usemultiply decomposition and divide by includingvolume using finding a andRevise counting SI units, back shape as with10, 100, some 1000 chn for as differencemultiplication between and appropriate,and measures including problems appropriateconversion between Default = negativedivision strategies; numbers integers/decimalinvolving numeracy countingunits, round up to nearest perimeter numbers 9 Multiplicationwhole unit - Tables, Multiplication - Tables, Multiplication - multiples and factors, multiples and factors, rehearse all forms of harder grid grid multiplication and mental multiplications, multiplication, including written algorithm for 1- doubling using decimal numbers 7 x d X 2/3/4-d numbers partitioning; 8.35 as 7 X 835 ÷100 incl. decimals multiplication of fractions incl. mixed numbers 10 Division - Strategies for Division - Strategies for Division - Rehearse written division of written division strategies for dividing whole nos just above including chunking and decimals and fractions; tables facts (choice re- short form of written compare answers, e.g. chunking v. short division (Give a choice 0.5 ÷ 0.25 and ½ ÷ ¼ division) Have re-chunking v. short Use calculator remainders division)
Choose from the optional weeks according to your assessment of the pupils.
HSNP © Hamilton 2012 Page viii Simmering Term 1 Numeracy Simmering Term 1 Weekly Activities
HSNP © Hamilton 2012 Page 1 Simmering Term 1 Week 1 overview Place value
Objectives Understand place value in six-digit numbers Use place value to complete additions and subtractions Compare numbers to 1,000,000 Place numbers to 1,000,000 on a line
For this week you will need: 0-9 digit cards, a place value chart (see resources), dice, number lines (see resources), calculators, an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a
Link to homework page
Watch out for pupils who: are unsure what each digit represents in a six-digit number; they may need more time using place value charts or using place value cards to make numbers; do not know half and quarter of 100,000 or do not use this knowledge to help them place numbers on a line; have difficulty writing numbers where zero is used as place holder, e.g. 201,056; insert commas after the first three digits, rather than before the last three digits, working back through the number to do this, as this will not help them to be able to read the number.
HSNP © Hamilton 2012 Page 2 Simmering Term 1 Week 1 Place value Day 1 Objectives: Understand place value in six-digit numbers; Use place value to complete additions and subtractions
You will need: a place value chart (see resources), dice, calculators, an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy- tools.html#Toolkit%20index2a
Teacher input with whole class Show the place value chart. Ring one number from each line, e.g. 400,000, 70,000, 3000, 200, 60 and 7. Ask pupils to write the total on their whiteboards. Repeat. Ring numbers from only five lines on the place value chart, e.g. 500,000, 3000, 700, 20 and 4. Ask pupils to write total. Repeat, ringing two, three, four or five numbers.
Paired pupil work Pupils write a six-digit number, all digits must be different and on the dice they have. They then roll the dice. If the number is in their six-digit number, they subtract that number of 100,000s, 10,000s, 1000s, 100s, 10s or 1s, e.g., they write 234,126, roll 2, so subtract 200,000 or 20. They write the answer. They take it in turn to carry on playing like this until one person ends up with 0 to win.
Teacher input with whole class Write 234,678 on the board. Ask pupils to discuss in pairs and then write on their whiteboards what must be added to make 888,888. Check their suggestions using an IWB calculator Repeat with 760,423 and 802,431.
Paired pupil work
HSNP © Hamilton 2012 Page 3 Simmering Term 1 Pupils write a number between 100,000 and 1,000,000 and decide what to add or to subtract to make all the digits the same. They test out their ideas using a calculator.
HSNP © Hamilton 2012 Page 3 Simmering Term 1 Week 1 Place value Day 2 Objectives: Understand place value in six-digit numbers; Compare numbers up to 1,000,000
You will need: 0-9 digit cards
Teacher input with whole class Write 452,523 and 542,523 on the board. Which number is larger? Ask pupils to explain why the second number is larger. Ask pupils to write on their whiteboards the sign (> or <), we should write between them. Ask pupils to use the same digits to write the biggest possible number and the smallest possible six-digit number on their whiteboards. Discuss how they decided where to place each digit. Repeat with several other pairs of five-digit numbers. Ask each pupil to draw □□□,□□□ on their whiteboards. Shuffle a set of 0 to 9 digit cards. Show one to the class. Pupils choose where to write this digit in their boxes to begin to create a six-digit number. Repeat five more times. You do the same after each card is drawn. Show your number to the class. Each pupil that has a bigger number than yours scores 10 points. If it is equal, they score 5 points. If your number is bigger than anyone’s, you score 50 points! Repeat five more times. Who scored most points?
Paired pupil work Pupils work in pairs. They shuffle a pack of 0 to 9 digit cards, and turn over the top six cards one at a time. They each choose where to write them in a six-digit number □□□,□□□. The pupil with the number closest to 500,000 wins. Repeat twice more.
Teacher input with whole class Ask five pupils to each write a number between 0 and 1,000,000 on a whiteboard and stand at the front holding them up. Ask the rest of the
HSNP © Hamilton 2012 Page 4 Simmering Term 1 class to help them to stand in order from the smallest number to the largest.
HSNP © Hamilton 2012 Page 3 Simmering Term 1 Week 1 Place value Day 3 Objective: Place numbers to 1,000,000 on a line
You will need: number lines (see resources), 0-9 digit cards
Teacher input with whole class Display the 100,000 to 200,000 line with landmarks of multiples of 10,000. Draw an arrow to where 155,000 might be and ask pupils to discuss in pairs what number you have labelled. They write the answers on their whiteboards. Discuss their reasons for their estimates. Repeat with numbers such as 125,000, 171,000, 197,500 and 132,500. Display the 0 to 1,000,000 line and mark numbers such as 750,000, 275,000, 999,000 and 425,000. Ask pupils to estimate each.
Paired pupil work Pupils draw a 0 to 1,000,000 line, making it as long as possible (preferably on A3 paper). They mark on the multiples of 100,000 and share this line. They take it in turns to shuffle a pack of 0 to 9 digit cards, take the top six cards and use them to make a six-digit number. They mark this number on the line, labelling it with the number and their initials. They keep taking it in turns to label numbers on the line until one person has three numbers in a line without their opponent’s marks in between. If time, repeat.
Teacher input with whole class Draw an empty 0 to 1,000,000 line and write six numbers such as the following on the board: 478,459, 130,276, 789,234, 321,427, 499,254 and 643,290. Invite a pupil to secretly choose one of them and to mark it on the line. The rest of the class guess which number has been chosen. Repeat several times.
HSNP © Hamilton 2012 Page 5 Simmering Term 1 Week 2 overview Addition
Objectives Add any pair of two-digit numbers mentally Use strategies for adding pairs of two-digit numbers to mentally add multiples of 10, 100 and 1000 Use written column addition to efficiently add three- or four-digit numbers Choose to use a mental or written method according to the numbers involved
For this week you will need: 1-9 digit cards, addition grid (see resources), Blu tack®
Link to homework page
Watch out for pupils who: have difficulty when the addition means passing through the next multiple of 100/1000, e.g. 84 + 32, 840 + 320; give more practice counting in 10s/100s through multiples of 100/1000; struggle with the place value when adding numbers such as 640 and 520; it may help to see 500 and 600 as making 11 hundred, recording this and then seeing it as one thousand, one hundred; try to keep all the steps in their head and lose track; encourage them to use jottings, modelling how to use these if necessary.
HSNP © Hamilton 2012 Page 6 Simmering Term 1 Week 2 Addition Day 1 Objectives: Add any pair of two-digit numbers mentally You will need: none required
Teacher input with whole class Write the following additions on the board and ask pupils to discuss in pairs how they would solve each:
84 + 31, 45 + 19, 67 + 67, 47 + 68, 72 + 28
Draw out strategies such as: . partitioning and recombining (e.g. 47 + 68 = 40 + 60 + 7 + 8 = 100 + 15 = 115, or doubling 67 by doubling 60, doubling 7, then adding 120 and 14); . counting on in tens and ones (adding 31 by adding 30, then 1); . adding the nearest multiple of 10 and adjusting (e.g. 45 + 19 = 45 + 20 – 1 = 65 – 1 = 64); . spotting a pair to 100 (72 + 28). Paired pupil work Pupils work in pairs to draw a pyramid of boxes, beginning with four on the bottom row. They choose four numbers between 10 and 20 to write in the bottom row. They add neighbouring numbers and write the number in the box that overlaps the pair of numbers. They continue up the pyramid until they reach a total at the top, e.g.
113 56 57 29 27 30 13 16 11 19
How many of these pyramids can they complete in five minutes?
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Challenge pupils to produce a pyramid with 133 at the top, all other numbers should be two-digit numbers.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 2 Addition Day 2 Objective: Use strategies for adding pairs of two-digit numbers to mentally add multiples of 10, 100 and 1000 You will need: pdf of addition grid (see resources) Teacher input with whole class Write the following additions on the board and ask pupils to discuss in pairs how they would solve each: 420 + 350 760 + 490 380 + 240 2500 + 3600 1900 + 4500 4600 + 4600 48,000 + 24,000 57,000 + 25,000 37,000 + 29,000 Draw out using similar strategies to those they’ve used for adding pairs of two-digit numbers, e.g. adding 490 by adding 500 and subtracting 10; doubling 46 and multiplying by 100 to find 4600 + 4600.
Individual practice Pupils find the answers to each addition, then swap to mark each others’ work. They then come up with two pairs of multiples of 10 with a total of 720, two pairs of multiples of 100 with a total of 6800 and two pairs of multiples of 1000 with a total of 51,000. Pupils swap their ideas with a maths partner. Teacher input with whole class Display pdf of addition grid and play Three in a line. Divide the class into four teams and assign a different colour pen to each. Each team take it in turns to choose a number from the grid, and say which two numbers below the grid have this number as a total. If correct, ring the chosen number in their colour. Carry on playing until one team has three ringed numbers in a line, horizontally, vertically or diagonally. 7800 900 63,000 890 6700 80,000 4300 660 74,000 1020 6600 47,000 8700 6000 930 980 8200 810 7300 91,000
270 540 350 390 630 HSNP © Hamilton 2012 Page 8 Simmering Term 1 1900 6300 4200 3600 2400 3100 62,000 45,000 29,000 18,000
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 2 Addition Day 3 Objectives: Use written column addition to efficiently add three- or four- digit numbers; Choose to use a mental or written method according to the numbers involved You will need: IWB or cards and Blu-tack®
Teacher input with whole class Write 3784 + 2867 and discuss how we would do this. It is too hard to do mentally. Demonstrate how to add these two numbers using column addition. Discuss where students are comfortable writing their ‘carry’ digits (above or below the line).
Individual practice Write the following numbers on the board and ask pupils to choose pairs to add together using column addition: 4587, 3724, 8231, 7834, 2368, 5827 and 4529. Challenge them to see how many they can accurately work out in five minutes. They swap with a partner to mark them. Teacher input with whole class Write the following additions in individual text boxes on the IWB or on separate cards: 7346 + 2874, 7436 + 2004, 5432 + 3100, 326 + 384 + 678, 478 + 8274, 640 + 360 + 324, 4900 + 2347 Write two headings: ‘mental’ and ‘written’. Point to/hold up the first addition and ask pupils to vote on whether they would work this calculation out mentally or using written column addition. Place the calculation under the heading with most votes. Repeat for each addition.
Individual practice Ask pupils to work out each addition. They then think of four more additions for each category but write them in random order for a partner to work out. Did their partner agree with their choice of method? HSNP © Hamilton 2012 Page 9 Simmering Term 1 HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 3 overview Subtraction
Objectives Subtract pairs of two-digit numbers or ‘friendly’ three-digit numbers by counting up Subtract pairs of two-digit numbers or ‘friendly’ three-digit numbers by counting back Choose when to use each strategy Subtract pairs of three/four-digit numbers by counting up
For this week you will need: pdf of subtraction grid (see resources), 0 to 9 digit cards
Link to homework page
Watch out for pupils who: do not work out quickly and accurately complements to the next multiple of 100, e.g. think that 47 needs to be added to 63 to make 100, because they look for tens which add to 100, not 90; do not have a sufficient mental map of the number line to know whether numbers are close or far apart and so find it hard to decide when to count up and when to count back; try to keep all the steps in their head and lose track; encourage them to use jottings, modelling how to use these if necessary.
HSNP © Hamilton 2012 Page 10 Simmering Term 1 Week 3 Subtraction Day 1 Objective: Subtract pairs of two-digit numbers or ‘friendly’ three-digit numbers by counting up You will need: pdf of subtraction grid (see resources)
Teacher input with whole class Ask pupils to discuss in pairs how they would work out 84 – 67, 73 – 68, 81 – 56, 103 – 87 and 700 – 654. Take feedback and draw out counting up from the smaller number to the larger number using number bonds and place value to be efficient. Model the first one, drawing a number line jotting to show the steps: the difference between 67 and 70 is 3 and the difference between 70 and 84 is 14 so the difference between 67 and 84 is 17. 14 3
67 70 84 Paired pupil work Pupils work in pairs to work out the remaining differences.
Teacher input with whole class Display pdf of subtraction grid and play Three in a line. Divide the class into four teams and assign a colour and the numbers 18, 25, 36 and 39 to each. Each team take it in turns to spot a pair of numbers on the grid which have a difference of their given number. If correct, ring both numbers in their colour (even if another team has already ringed the number). Carry on playing until one team has three ringed numbers in a line, horizontally, vertically or diagonally (NB team 25 will find it the easiest to spot a line of 3). 300 214 35 200 250 198 45 175 85 164 46 161 71 223 53
HSNP © Hamilton 2012 Page 11 Simmering Term 1 110 81 78 282 63
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 3 Subtraction Day 2 Objectives: Subtract pairs of two-digit numbers or ‘friendly’ three-digit numbers by counting up; Subtract pairs of two-digit numbers or ‘friendly’ three-digit numbers by taking away; Choose when to use each strategy You will need: 0 to 9 digit cards
Teacher input with whole class Write 85 – 21 on the board. Ask pupils how they would do this. Draw out that some pupils would ‘take away’ or count back. 80 – 20 and 5 – 1 to give 64. Point out that taking away is easy if the numbers in each column are larger in the first number. Write the following subtractions on the board and ask pupils to discuss in pairs how they would solve them: 42 – 38; 94 – 79; 56 – 31; 42 – 27; 84 – 19; 87 – 33; 52 – 29 345 – 199; 102 – 97; 304 – 297; 356 – 201; 434 – 220; 203 – 189 Take feedback asking which subtractions pupils would work out using taking away or counting back, ring these in red, e.g. 56 – 31 as 50 – 30 and 6 – 1 (25) and 345 – 199, by counting back 200, then adding 1. Ask which they would work out using counting up, ring these in blue, e.g. 42 – 38 as 38 + 2 + 2 (4). Discuss any where there is no consensus, e.g. 52 – 29 where some pupils may count up but others may count back by subtracting 30, then adding 1. Ask pupils to work out each answer.
Paired pupil work Pupils work in pairs to each shuffle a pack of digit cards, and place face down. They each take two cards to make a two-digit number. They subtract the smaller number from the larger either by taking away /counting back or by counting up. Challenge them to see how many subtractions they can work out in five minutes.
HSNP © Hamilton 2012 Page 12 Simmering Term 1 HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 3 Subtraction Day 3 Objective: Subtract pairs of three/four-digit numbers by counting up You will need: none required
Teacher input with whole class Remind pupils how they can use ‘counting up’ to work out subtractions such as 423 – 378. Draw a number line jotting to show the steps. Say that some pupils may combine the first two steps. 2 20 23
378 380 400 423 Paired pupil work Pupils work in pairs to discuss which of the following subtractions will have an answer of less than 100. They work out the answers to each. 724 – 685, 546 – 479, 845 – 668, 735 – 657, 824 – 735, 378 – 245 Teacher input with whole class Write 7000 – 6485, 6000 – 5378, 8000 – 7455 on the board and ask pupils to share how they would work them out: Draw out ‘counting up’ to the next 100 and then to the larger number. Draw a number line jotting to show this. Individual practice Pupils find how many are needed to make the next multiple of 1000 for the numbers in the table below. 3788 5831 4783 7755 8472 8472 9733 4756 7327 Teacher input with whole class Remind pupils how they can use ‘counting up’ to find a difference in order to work out subtractions such as 3023 – 2978. Draw a number line jotting to show the steps. Individual practice
HSNP © Hamilton 2012 Page 13 Simmering Term 1 Pupils work out the following: 3045 – 2968, 4002 – 3789, 6234 – 5945, 7076 – 6977, 5008 – 4824 and 8013 – 7859.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 4 overview Multiplication Objectives Know the 6 and 9 times tables Identify multiples of 2, 3, 4, 5, 6 and 9 Find factors of two-digit numbers Double and halve two-digit numbers Multiply teens numbers by single-digit numbers mentally Multiply three-digit numbers by single-digit numbers using the grid method
For this week you will need: pdf of a 12-section counting stick (see resources), packs of 0 to 12 cards (see resources), dice, Double and half dartboard at http://www.wmnet.org.uk/resources/gordon/Dart%20Board%20- %20doubles%20&%20halves.swf, Grid method at http://www.topmarks.co.uk/Flash.aspx?f=gridmethodpvcardsv3 Link to homework page Watch out for pupils who: do not know their 2, 3, 4, 5 times tables. This lack of knowledge will really slow down their work in multiplication and division so use day 1’s activities with other tables as necessary; struggle to remember all the facts from the 6 times table; encourage them to turn the multiplication round, e.g. if they don’t know three 6s, to use six 3s, and to use doubling, e.g. double four 6s to find eight 6s; struggle with the mental addition when adding the three partial products when using grid multiplication. It may help to rotate the grid so that the addition is presented vertically.
HSNP © Hamilton 2012 Page 14 Simmering Term 1 Week 4 Multiplication Day 1 Objectives: Know the 6 and 9 times tables up to the 12th multiple; Identify multiples of 2, 3, 4, 5, 6 and 9; Find factors of two-digit numbers You will need: pdf of a 12-section counting stick (see resources), packs of 0 to 12 cards (see resources) Teacher input with whole class Remind pupils of the trick for answering questions in the 9 times table: hold hands facing towards you. For three 9s, put down the 3rd finger, the number of fingers on the left is 2, the number of tens and the number on the right is 7, the number of units, giving 27. Practise using this trick. What are eleven 9s? And twelve 9s? How can you work out twelve 9s if you can’t remember it? (E.g. 90 plus 18) Paired pupil work Pupils shuffle a pack of 0 to 12 cards and place in a pile face down. They take it in turns to turn them over one at a time and multiply each number by 9. How quickly can they get through the pack of cards? Teacher input with whole class Write the multiples of 6 (0 to 72) under the counting stick. Use it to support chanting of the 6 times table: one 6 is 6, two 6s are 12, three 6s are 18… 12 6s are 72. Rub out all the numbers bar 30 and 60 repeat.
Paired pupil work Pupils shuffle a pack of 0 to 12 cards and place in a pile face down. They take it in turns to turn them over one at a time and multiply each number by 6. How quickly can they get through the pack of cards? Teacher input with whole class Write the following numbers on the board: 30, 36, 48, 54, 27, 72. Ask question such as: Which are multiples of 6? Which have 4 as a factor?
HSNP © Hamilton 2012 Page 15 Simmering Term 1 Pupils respond by writing all the appropriate numbers on their whiteboards.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 4 Multiplication Day 2 Objectives: Double and halve two-digit numbers; Multiply teens numbers by single-digit numbers mentally You will need: dice, Double and half dartboard at http://www.wmnet.org.uk/resources/gordon/Dart%20Board%20- %20doubles%20&%20halves.swf
Teacher input with whole class Choose ‘Doubles - TU’ from the left panel on Double and half dartboard. Click on the green spaces, and ask pupils to copy the dartboard and double each number as quickly as they as they can. Discuss strategies, e.g. partition numbers into 10s and 1s, doubling each part and then recombining, e.g. double 46 by doubling 40, doubling 6 and adding 80 and 12 to give 92.
Repeat, this time choosing ‘Halves – TU’. Pupils to halve each number. Remind pupils how they can use partition to multiply two-digit numbers by single-digit numbers, e.g. 43 × 6, using a jotting if they find it helpful. Discuss how they might multiply by 4 by doubling twice. Paired pupil work Pupils play the following game in pairs. They take it in turns to roll a dice twice to make two-digit number. They then choose a number between 1 and 10 to multiply by the number made from the dice. They score the units digit in the answer. E.g. roll 32, choose 4, answer 128,
HSNP © Hamilton 2012 Page 16 Simmering Term 1 so score 8 points. The winner is the person with the highest score when you ask them to stop.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 4 Multiplication Day 3 Objective: Multiply three-digit numbers by single-digit numbers using the grid method You will need: dice, Grid method at http://www.topmarks.co.uk/Flash.aspx?f=gridmethodpvcardsv3
Teacher input with whole class Choose HTU × U from the top part of the menu for Grid method. Click on the place value cards so they appear in the grid. Remind pupils how the grid method works and ask them to copy and complete the grid.
Click on each question mark and then on the place cards inside the grid to confirm the total of the partial products. Repeat several times.
Paired pupil work Pupils play the following game in pairs. They take it in turns to roll a dice three times to make a three-digit number. They then choose a number between 2 and 10 to multiply by the number made from the dice. They score the total of the digits in the answer. E.g. roll 323, choose 6, answer 1938, so score 21 points. The winner is the person with the highest score when you ask them to stop.
Teacher input with whole class
HSNP © Hamilton 2012 Page 17 Simmering Term 1 Choose HTU × U from the lower part of the menu and ask pupils to work in pairs to work out what numbers were multiplied together. Click on the question marks to confirm. Repeat.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 5 overview Division Objectives Use multiplication facts to work out divisions Use chunking to divide numbers just beyond the times tables Use halving twice to divide by 4 and by 8 Divide by 5 by dividing by 10 and doubling
For this week you will need: cards with multiples of 6 and 9 to the 12th multiple (see resources), 1 to 12 cards (see resources for week 4), Remainders after division bingo at http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_reso urces/848/remainders.swf ITP Number Dials at http://www.teachfind.com/national- strategies/mathematics-interactive-teaching-program-itp-number-dials-2
Link to homework page
Watch out for pupils who: do not know their multiplication facts and so can’t make use of them to solve divisions; try to partition numbers into 10s and 1s to divide (as they would for multiplication), rather than into a multiple of 10 of the divisor and the rest, e.g. partition 52 into 50 and 2 to divide by 4 rather than in 40 and 12; do not know halves of odd numbers of multiples of 10, e.g. 30, 50, 70 and 90 and so can only halve numbers with even digits.
HSNP © Hamilton 2012 Page 18 Simmering Term 1 Week 5 Division Day 1 Objective: Use multiplication facts to work out divisions You will need: cards with multiples of 6 and 9 to the 12th multiple (see resources), 1 to 12 cards (see resources for week 4), Remainders after division bingo at http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_reso urces/848/remainders.swf Teacher input with whole class Explain that we are doing our 6x table backwards! We are asking, ‘How many sixes in...?’. Shuffle the multiples of 6 cards and hold up one at a time. Pupils respond by holding up number cards to show how many 6s are in the multiple. Repeat for multiples of 9. Paired pupil work Pupils work in pairs to write as many division facts as they can beginning with 36, 48 and 72. (e.g. 36 ÷ 6 = 6, 36 ÷ 9 = 4, 36 ÷ 4 = 9, 36 ÷ 3 = 12…). Which pair recorded the most division facts for each number? Teacher input with whole class Write the following divisions on the board: 45 ÷ 6 32 ÷ 3 81 ÷ 9 37 ÷ 4 43 ÷ 9 54 ÷ 6 127 ÷ 10 Which divisions will leave a remainder? How do you know? Ask pupils to find the remainder in each case. Play Remainders after division bingo.
HSNP © Hamilton 2012 Page 19 Simmering Term 1 Pupils each choose 5 of the given numbers. Click ‘Play’. They work out the given division, and ring the remainder if they have it. The first person to ring all 5 of their numbers wins.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 5 Division Day 2 Objective: Use chunking to divide numbers just beyond the times tables You will need: ITP Number dials at http://www.teachfind.com/national- strategies/mathematics-interactive-teaching-program-itp-number-dials-2
Teacher input with whole class Display the ITP Number dials, choose 6 as the multiplier and click to show all the products. How could we use this dial to work out 84 ÷ 6? Draw out splitting 84 into 60 and 24. Agree that are ten 6s in 60 and four 6s in 24, so there are fourteen 6s in 84. Ask pupils to use the dial to show how many 6s are in 96. Change the multiplier to 9 and ask how many 9s are in 117. Demonstrate subtracting the multiple of ten, 10 X 9 = 90, 117 – 90 = 27, and 3 x 9 = 27. So 13 x 9 = 117. Repeat to divide 144 by 9.
Individual practice Ask pupils to work out the following: 85 ÷ 5, 56 ÷ 4, 51 ÷ 3, 78 ÷ 6, 126 ÷ 9 and 96 ÷ 6 Teacher input with whole class Write 89 ÷ 6 on the board. Sketch a line from 0 to 89 and ask pupils if there are more than ten 6s in 89. Draw a jump to show this. How much is left? How many 6s in 29? Draw a hop and show the remainder. ten 6s four 6s r5
0 60 84 89 Repeat for 113 ÷ 9. Paired pupil work Write the following divisions on the board: 49 ÷ 3, 53 ÷ 4, 83 ÷ 6, 78 ÷ 5, 121 ÷ 9, 69 ÷ 4, 53 ÷3 and 92 ÷ 6. Pupils discuss in pairs which they think will have the biggest and smallest answer, and then find the answers to each. HSNP © Hamilton 2012 Page 20 Simmering Term 1 Week 5 Division Day 3 Objectives: Use halving twice to divide by 4 and by 8; Divide by 5 by dividing by 10 and doubling You will need: none required
Teacher input with whole class Write 104 ÷ 4, 37 ÷ 4, 84 ÷ 4, 72 ÷ 4, 82 ÷ 4 and 75 ÷ 4 on the board. Remind pupils how we can divide by 4 by halving and halving again. Demonstrate this for 104: half = 52, and half 52 = 26. Ask them to discuss in pairs which of these divisions they would prefer to work out like this and why. Take feedback. Repeat for 164 ÷ 8, 128 ÷ 8, 120 ÷ 8 and 137 ÷ 8 discussing which pupils would divide by 8 by halving three times. Individual practice Write the following divisions on the board and ask pupils to choose five to work out by halving two or three times: 96 ÷ 4, 130 ÷ 4, 140 ÷ 8, 97 ÷ 4, 248 ÷ 8, 328 ÷ 4, 135 ÷ 8, 124 ÷ 4, 227 ÷ 8. Teacher input with whole class Ask half the class to divide 80 by 10, then double the answer, and the other half of the class to divide 80 by 5. What do they notice? Draw out that as dividing by 10 and doubling gives the same answer as dividing by 5, we can use this as a strategy to divide by 5. Discuss how this might be a quicker way to divide numbers like 80 by 5. Repeat with 140 ÷ 5 and 95 ÷ 5.
Individual practice Ask pupils to divide numbers by 5, by dividing by 10, and then doubling. They can use the following table to help: ÷ 10 × 2 90 240 330 85 135
HSNP © Hamilton 2012 Page 21 Simmering Term 1 Week 6 overview Decimals
Objectives Know what each digit represents in numbers with two decimal places Use place value for tenths and hundredths to complete additions and subtractions Compare and order numbers with two decimal places Place numbers with two decimal places on a line Compare and order numbers with three decimal places in the context of measures Round to the nearest whole unit
For this week you will need: a place value grid (see resources), dice, calculators, 0-9 digit cards, an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy- tools.html#Toolkit%20index2a, Number line at http://www.topmarks.co.uk/Flash.aspx?f=NumberLinev5, Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx? f=DartboardRoundingv2
Link to homework page
Watch out for pupils who: think that 3.14 is more than 3.7 because 14 is more than 7; do not see how they can use their knowledge of ordering whole two-digit numbers to order numbers with two decimal places or place them on a line.
HSNP © Hamilton 2012 Page 22 Simmering Term 1 Week 6 Decimals Day 1 Objectives: Know what each digit represents in numbers with two decimal places; Use place value for tenths and hundredths to complete additions and subtractions You will need: a place value grid (see resources), dice, calculators, an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy- tools.html#Toolkit%20index2a
Teacher input with whole class Show the place value grid. Ring one number from each line, e.g. 7, 0.2 and 0.09. Ask pupils to write the total on their whiteboards. Repeat, including numbers such as 4.05 and 0.67. Enter the number 3.57 into an IWB calculator. Ask pupils to write on their whiteboards, the number which must be subtracted to ‘zap’ the 5. Use the calculator to subtract numbers they suggest, drawing out that 0.5 must be subtracted as the digit 5 represents 5 tenths (0.5). Repeat with 7.25 and ask pupils to ‘zap’ the ‘5’. Paired pupil task Pupils write a three-digit number with two decimal places, all digits different and on the dice. They roll the dice. If the number is in their number, they subtract that number of 1s, 0.1s, or 0.01s. E.g., they write 5.26, roll 2, so subtract 0.2. They write the answer. They take it in turns to carry on playing like this until one person ends up with 0 to win. Teacher input with whole class Write the number 5.45 on the board. Ask pupils what must be added to make 5.55. Repeat with 5.35, 5.41 and 3.35. Write the number 5.75 and ask what must be subtracted to make 5.55. Repeat with 5.85, 5.67 and 6.58. Paired pupil task Pupils take it in turns to roll a dice to make a three-digit number with two decimals places. They work out what must be added to make all
HSNP © Hamilton 2012 Page 23 Simmering Term 1 the digits the same as the highest digit in the number and what must be subtracted to make all the digits the same as the lowest digit in the number. Repeat several times.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 6 Decimals Day 2 Objectives: Compare and order numbers with two decimal places; Place numbers with two decimal places on a line You will need: dice, 0-9 digit cards, Number line at http://www.topmarks.co.uk/Flash.aspx?f=NumberLinev5 Teacher input with whole class Write 3.7 and 3.14 on the board. Which number is larger? Why? Agree that it has 7 tenths whereas the 2nd number only has one tenth. Repeat with other pairs of numbers, some with two decimal places and some with one decimal place, e.g. 3.42 and 3.6 or 3.42 and 3.24. Paired pupil work Pupils work in pairs to roll a dice three times. They use the digits to write six different three-digit numbers each with two decimal places and write them in ascending order. Teacher input with whole class Use Number line, choosing ‘guess the number’, ‘0 to 1, hundredths’. Pupils write on their whiteboards what number they think the arrow is pointing to. Click ‘show numbers’, they adjust their answers if necessary, then enter some of their suggestions to check. (NB you need to enter 0.19 for example, not .19.)
Paired pupil task Pupils work in pairs to draw a 0 to 1 line, marking on the multiples of 0.1 and making it as long as possible (preferably on A3 paper). They take it in turns to shuffle a pack of 0 to 9 digit cards, take the top two cards and use them to make a number with two decimal places. They mark this number on the line, labelling it with the number and their
HSNP © Hamilton 2012 Page 24 Simmering Term 1 initials. Continue until one person has three numbers in a line without their opponent’s marks in between.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 6 Decimals Day 3 Objectives: Compare and order numbers with three decimal places in the context of measures; Round to the nearest whole unit You will need: Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx?f=DartboardRoundingv2 Teacher input with whole class Write the following weights (masses) on the board and ask pupils to discuss which is the lightest and which is the heaviest: 3.145kg, 3.415kg, 3.541kg, 3.451kg, 3.154kg and 3.514kg. Discuss how the digit before the decimal point represents the number of whole kilograms and the three digits after the decimal point represent the number of grams. Point out that in a weight (mass) such as 3.41kg, 0.41 represents 410 grams. Ask pupils to write how we would record 3 whole kilograms and 105 grams as a number of kilograms with decimal places. Individual practice Ask pupil to add 100g to each of the following weights (masses): 5.619kg, 4.015kg, 8.337kg and 6.12kg. They then add 50 grams to the same weights (masses). Teacher input with whole class Use Dartboard rounding, choosing ‘nearest kilogram’. Click on a green segment and ask pupils to round the weight (mass) to the nearest whole kilogram. If necessary, draft a line between neighbouring whole kilograms and discuss where the measurement should be placed. Repeat for each green segment.
HSNP © Hamilton 2012 Page 25 Simmering Term 1 HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 7 overview Addition of decimals
Objectives Quickly find pairs of numbers with one decimal place with a total of 10 Apply strategies used for adding pairs of whole numbers to adding numbers with one decimal place Apply strategies used for adding pairs of whole numbers to adding numbers with two decimal places Use written column addition to add numbers with one and two decimal places
For this week you will need: Bingo addition at http://www.topmarks.co.uk/Flash.aspx?f=bingoaddition, Expanded addition at http://www.topmarks.co.uk/Flash.aspx? f=AddExpandv2 Link to homework page
Watch out for pupils who: think that 3.2 needs to be added to 7.8 for example, as they look for whole numbers which add to 10, rather than pairs of whole numbers with a total of 9, and tenths with a total of 1 to make the total up to 10; have difficulty when the addition means passing through the next multiple of 1, e.g. 7.6 + 0.7, 8.4 + 1.7; give more practice counting in 0.1s through multiples of 1; try to keep all the steps in their head and lose track; encourage them to use jottings, modelling how to use these if necessary; have difficulty with place value when using column addition. HSNP © Hamilton 2012 Page 26 Simmering Term 1 Week 7 Addition of decimals Day 1 Objectives: Quickly find pairs of numbers with one decimal place with a total of 10; Apply strategies used for adding pairs of whole numbers to adding numbers with one decimal place You will need: Bingo addition at http://www.topmarks.co.uk/Flash.aspx? f=bingoaddition
Paired pupil work Challenge pupils to work in pairs to write as many pairs of numbers with one decimal place, with a total of 10 as they can in two minutes, e.g. 4.6 + 5.4, 2.8 + 7.2, etc. Teacher input with whole class Ask pupils to do following additions: 4.8 + 0.7 4.5 + 1.9 5.6 + 5.6 6.3 + 2.4 4.8 + 2.5 5.4 + 3.7 Take feedback drawing out adding 0.7 to 4.8 by adding 0.2 to make 5, and then adding 0.5. Also adding 1.9 by adding 2 and subtracting 0.1. Remind pupils that we can use some of the same strategies that we use for adding whole numbers to add these decimal numbers. Paired pupil work Challenge pupils to work in pairs to write as many pairs of numbers with a total of 5.1 as they can in two minutes. Teacher input with whole class Play Addition bingo; choose U.t + U.t. Pupils to choose five numbers to write on their whiteboards. Click ‘play’. Keep a record of the additions. Pupils work out the additions, ringing any answers they have on their whiteboards. The first to ring all five numbers wins. Go through the questions to check, ringing the answers on the screen.
HSNP © Hamilton 2012 Page 27 Simmering Term 1 HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 7 Addition of decimals Day 2 Objective: Apply strategies used for adding pairs of whole numbers to adding numbers with two decimal places You will need: none required
Paired pupil work Challenge pupils to work in pairs to write as many pairs of numbers with two decimal places, with a total of 1 as they can in two minutes. E.g. 0.48 + 0.52, or 0.63 + 0.37. Teacher input with whole class Write the following additions on the board: 0.53 + 0.24 0.34 + 0.19 0.56 + 0.21 0.65 + 0.27 0.88 + 0.29 0.75 + 0.42 Which of these additions will have answers of more than 1? Ask pupils to discuss in pairs how the strategies for adding pairs of whole two-digit numbers could be adapted to add numbers with two decimal places. Take feedback drawing out adding 0.19 by adding 0.2 and subtracting 0.01, adding 0.42 by adding 0.4, then 0.02 for example. Pupils find the answers to each. Draw a jotting to show any that pupils are unsure of, e.g. 0.88 + 0.29: +0.3 -0.01
0.88 1.17 1.18
Paired pupil work Pupils work in pairs to use the digits 2, 3, 4 and 9 to come up with as many additions of two-digit numbers with two decimal places as they can before you ask them to stop. Ask them to make sure they include at least two with answers greater than 1. Which pairs of pupils came up with more than 10 different additions?
HSNP © Hamilton 2012 Page 28 Simmering Term 1 Week 7 Addition of decimals Day 3 Objective: Use written column addition to add numbers with one and two decimal places You will need: Expanded addition at http://www.topmarks.co.uk/Flash.aspx?f=AddExpandv2
Teacher input with whole class Remind pupils how to use column addition to work out additions such as 25.8 + 15.7. Talk though the addition of 0.8 and 0.7, giving a total of 1.5, the 1 placed in the 1s column to wait to be added to the 1s. Individual practice Pupils estimate the answers to the following and then use column addition to find the exact answers: 24.7 + 13.7; 56.4 + 22.8, 67.7 + 36.5, 28.6 + 34.5. Teacher input with whole class Use Expanded addition, choosing ‘TU.th + TU.th’. Use the toggles to change the numbers so that the tenths are greater than 1 or the hundredths greater than 0.1. Click on the arrow above the hundredths, then tenths, then ones, then tens, then on ‘answer’. Click ‘again’. Ask pupils to estimate the answer, then work it out. Click to confirm.
Show this addition using compact addition.
Individual practice HSNP © Hamilton 2012 Page 29 Simmering Term 1 Pupils estimate the answers to the following and then use expanded column addition to find the exact answers: 3.57 + 2.35; 6.28 + 4.36; 5.83 + 2.45; 14.75 + 11.52; 34.56 + 22.78, 42.64 + 27.78
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 8 overview Subtraction
Objectives Subtract pairs of four-digit whole numbers by counting up Subtract pairs of four-digit whole numbers using decomposition Subtract pairs of numbers with one or two decimals by counting up
For this week you will need: Expanded decomposition at http://www.topmarks.co.uk/Flash.aspx? f=DecompExpandv2
Link to homework page
Watch out for pupils who: make frequent place value errors when using compact decomposition, they may need to return to using expanded decomposition or use counting up on the number line to solve subtractions; use decomposition for all subtractions, even those can be easily worked out using a mental method; having made a mistake, do not notice that their answer seems unreasonably large/small, encourage them to make estimates using rounding and mental methods; are uncertain of place value in numbers with two decimal places or do not use their pairs to 100 to work out complements to the next whole number.
HSNP © Hamilton 2012 Page 30 Simmering Term 1 Week 8 Subtraction Day 1 Objective: Subtract pairs of four-digit whole numbers by counting up You will need: none required
Teacher input with whole class Ask pupils to estimate the answer to 5243 – 3678, e.g. 5200 – 3700 = 1500. Sketch an empty number line from 3678 to 5243. Suggest that pupils mark on the next multiple of 100 after 3678 and the multiple of 100 immediately before 5243. Pupils work out the size of each ‘hop’.
22 1500 43
3678 3700 5200 5243 Point out that the addition when drawing jumps like this will always be the addition of a pair of two-digit numbers, and a multiple of 100, easy numbers to add together! Agree the answer and compare with the estimate. Repeat for 3248 – 1764.
Paired pupil work Ask pupils to discuss in pairs which of the following subtractions will have the greatest and least answers, and then sketch empty number lines, choosing their own steps to work each out: 7823 – 4578, 9256 – 7288, 7025 – 5274, 8628 – 5452, 4267 – 3623, 9782 – 4972, 4827 – 3872, 4782 – 2746 Teacher input with whole class Ask pupils how they could check their answers. Draw out using addition to check. Ask them to choose three subtractions to check using column addition.
HSNP © Hamilton 2012 Page 31 Simmering Term 1 Week 8 Subtraction Day 2 Objective: Subtract pairs of four-digit whole numbers using decomposition You will need: Expanded decomposition at http://www.topmarks.co.uk/Flash.aspx?f=DecompExpandv2
Teacher input with whole class Use Expanded decomposition choosing ThHTU – ThHTU from the left column. Use the toggles to change the given numbers so that only the 1s digit of the smaller number is more than the 1s digit in the larger number. Click on the arrow to show the partitioning of each number. Discuss what exchanges might be necessary to carry out the subtraction. Click on ‘take 10’, then on the arrow beneath each column to carry out the subtractions and ‘=’ to show the answer.
Repeat, this time choosing numbers where other types and numbers of ‘carries’ are necessary, modelling the compact form of decomposition alongside. Individual practice Pupils use decomposition or counting up (according to their preference or competence with decomposition) to find 7834 – 3465, 4572 – 3825, 5248 – 3783, 8051 – 6523, 7245 – 5867, 5224 – 3771. Teacher input with whole class Write the following subtractions on the board and ask which of them pupils could solve mentally without writing anything down: 4367 – 2001, 5678 – 4999, 8723 – 2374, 5728 – 1100, 7482 – 2010
HSNP © Hamilton 2012 Page 32 Simmering Term 1 Week 8 Subtraction Day 3 Objective: Subtract pairs of numbers with one or two decimals by counting up You will need: none required
Teacher input with whole class Draw a number line jotting to remind pupils how they could find the difference between two prices £32.47 and £27.89. Say that some pupils may combine the first two steps. 11p £2 £2.47
£27.89 £28 £30 £32.47 Individual practice Ask pupils to choose pairs of prices and find the difference between them. Challenge them to see how many they can find in three minutes. £28.93 £26.49 £13.55 £84.71 £23.75 £75.48 £46.25 £57.38 £67.34
Teacher input with whole class Remind pupils how they can use ‘counting up’ to find a difference in order to work out subtractions such as 3.24 – 1.78, 5.25 – 3.7 and 7.2 – 4.78. Draw a number line jotting to show the steps, e.g. 0.3 1.25
3.7 4 5.25 Talk through addition of the steps, pointing out the 3 tenths and 2 tenths making 5 tenths when adding 1.25 and 0.3 for example. Individual practice Pupils work out the following: 4.24 – 3.83 5.2 – 4.64 7.48 – 6.75 HSNP © Hamilton 2012 Page 33 Simmering Term 1 8.24 – 6.7 6.37 – 5.6 9.2 – 5.67
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 9 overview Multiplication
Objectives Know the 7 and 8 times tables up to the 12th multiple Identify multiples of 2 to 10 Find factors of two-digit numbers Multiply two-digit numbers by two-digit numbers using the grid method Multiply three-digit numbers with two decimal places by single-digit numbers using the grid method
For this week you will need: pdf of a 12-section counting stick (see resources), packs of 0 to 12 cards (see resources), Grid method at http://www.topmarks.co.uk/Flash.aspx? f=gridmethodpvcardsv3 Link to homework page
Watch out for pupils who: do not know their 2, 3, 4, 5, 6 and 9 times tables. This lack of knowledge will really slow down their work in multiplication and division so use day 1’s activities with other tables as necessary; struggle to remember all the facts from the 7 or 8 times tables; encourage them to turn the multiplication round, e.g. if they don’t know three 8s, to use eight 3s, and to use doubling, e.g. double four 7s to find eight 7s; struggle with place value when multiplying decimals; they may find it helpful to practice counting up in steps of 0.6 or 0.06 for example.
HSNP © Hamilton 2012 Page 34 Simmering Term 1 Week 9 Multiplication Day 1 Objectives: Know the 7 and 8 times tables up to the 12th multiple; Identify multiples of 2 to 10; Find factors of two-digit numbers You will need: pdf of a 12-section counting stick (see resources), packs of 0 to 12 cards (see resources)
Teacher input with whole class Write the multiples of 7 (0 to 84) under the counting stick. Use it to support chanting of the 7 times table: one 7 is 7, two 7s are 14, etc. Point out that we know most of these facts already. 4 x 7 is the same as 7 x 4 (28). We can remember the ‘tricky’ fact (7 x 8) by ‘five, six, seven, eight, i.e. 56 = 7 x 8.
Paired pupil work Pupils shuffle a pack of 0 to 12 cards & place them in a pile face down. They take it in turns to turn them over one at a time and multiply each number by 7. How quickly can they get through the pack of cards? Teacher input with whole class Write the multiples of 8 (0 to 96) under the counting stick. Use it to support chanting of the 8 times table. Point out that we know most of these facts already, e.g. 4 x 8 is the same as 8 x 4 (32). We can remember 8 x 8 using the mnemonic: I ate and I ate and was sick-on-the-floor (8 x 8 = 64). Paired pupil work Pupils shuffle a pack of 0 to 12 cards and place in a pile face down. They take it in turns to turn them over one at a time and multiply each number by 8. How quickly can they get through the pack of cards? Teacher input with whole class Write the following numbers on the board: 28, 32, 35, 56, 48, 21 and 84. Ask questions: Which are multiples of 8? Which have 7 as a factor?
HSNP © Hamilton 2012 Page 35 Simmering Term 1 Which are multiples of 7 and 8? Which have a pair of odd factors? Pupils respond by writing appropriate numbers on their whiteboards.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 9 Multiplication Day 2 Objective: Multiply three-digit numbers with two decimal places by single- digit numbers using the grid method You will need: none required Teacher input with whole class Remind pupils how they can use the grid method to keep track of the partitioning when multiplying three-digit numbers with two decimal places by single-digit numbers, e.g. 2.64 × 3
× 2 0.6 0.04 3 6 1.8 0.12 7.92
If necessary remind pupils that the answer to 3 × 0.6 is a tenth of the answer to 3 x 6 and the answer to 3 × 0.04 is a hundredth of the answer to 3 × 4.
Paired pupil work Pupils work in pairs to use the same digits to create different multiplications of the form □.□□ × □. What was the largest answer they found? And the smallest?
Teacher input with whole class Ask half the class to work out 732 × 3 and the other half to work out 7.32 × 3. Discuss the two answers. Draw out that the answer to the second is a hundredth of the answer to the first. Ask pupils to work out 6.24 × 3, 7.53 × 6 and 5.62 × 4 by working out 624 × 3, 753 × 6 and 562 × 4, then dividing the answer by 100. Discuss how they might find the answer to 62.4 × 3, 75.2 × 3 and 56.2 × 4.
HSNP © Hamilton 2012 Page 36 Simmering Term 1 Week 9 Multiplication Day 3 Objective: Multiply two-digit numbers by two-digit numbers using the grid method You will need: Grid method at http://www.topmarks.co.uk/Flash.aspx? f=gridmethodpvcardsv3
Teacher input with whole class Write on the board: 42 × 38. Discuss how we can estimate the answer, e.g. 40 × 40 = 1600. Remind pupils how to use the grid method to keep track of the steps. × 40 2 30 1200 60 1260 8 320 16 + 336 1596 Say that the first row records the steps in finding 30 × 42 and the second row records the steps in finding 8 × 42, and then we add these two products together to find the answer to 42 × 38. Individual practice Ask pupils to practise using the grid method, using the same four digits to create a different two-digit by two-digit multiplication. Next challenge them to use the same four digits to create pairs of two- digit numbers and find the smallest possible answer (28 × 34 = 952) and the largest possible answer (82 × 43 = 3526). Teacher input with whole class Use Grid method and choose ‘TU × TU’ from the lower part of the menu. Ask pupils to work in pairs to figure out what pair of two-digit numbers have been multiplied together.
HSNP © Hamilton 2012 Page 37 Simmering Term 1 Click on the question marks to check, and on ‘press to show calculation’ at the top to confirm.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 10 overview Division
Objectives Divide whole numbers by single-digit numbers giving an answer of between 10 and 20, without a remainder Divide whole numbers by single-digit numbers giving an answer of between 10 and 20, which leave a remainder
For this week you will need: dice, division grid of numbers for each pair (see resources)
Watch out for pupils who: do not know their multiplication facts and so can’t make use of them to solve divisions; try to partition numbers into 10s and 1s to divide (as they would for multiplication), rather than into a multiple of 10 of the divisor and the rest, e.g. partition 52 into 50 and 2 to divide by 4 rather than in 40 and 12.
HSNP © Hamilton 2012 Page 38 Simmering Term 1 Week 10 Division Day 1 Objective: Divide whole numbers by single-digit numbers giving an answer of between 10 and 20, without a remainder You will need: none required Teacher input with whole class Write 96 ÷ 6 on the board. Sketch a line from 0 to 96 and ask pupils if there are more than ten 6s in 96. Draw a jump to show this. How much is left? How many 6s in 36? Draw a hop to show this. Agree there is no remainder. ten 6s six 6s
0 60 96 Show how to record this vertically, saying there are more than ten 6s in 96, write 10 at the top and subtract 60 from 96. There are six 6s in 36, write 6 at the top and subtract 36: 10 + 6 = 16 6 ) 96 - 60 36 - 36 0 Repeat for 112 ÷ 8. Individual practice Write the following divisions on the board: 49 ÷ 3, 53 ÷ 4, 83 ÷ 6, 78 ÷ 5, 121 ÷ 9, 69 ÷ 4, 53 ÷3 and 92 ÷ 6. Pupils choose whether to record the division using an empty number line or by vertical recording. Teacher input with whole class Discuss how pupils should check their work, draw out using multiplication. Ask them to use multiplication to check three of their divisions. HSNP © Hamilton 2012 Page 39 Simmering Term 1 HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 10 Division Day 2 Objective: Divide whole numbers by single-digit numbers including those which leave a remainder You will need: none required
Teacher input with whole class Write 95 ÷ 7 on the board. Sketch a line from 0 to 95 and ask pupils if there are more than ten 7s in 95. Draw jump to show this. How much is left? How many 7s in 25? Draw a hop and show the remainder. ten 7s three 7s r4
0 70 91 95 Show how to record this vertically: 10 + 3, r4 = 13 r4 7 ) 95 - 70 25 - 21 4 Repeat for 53 ÷ 3. Paired pupil work Write the following divisions on the board: 52 ÷ 4 55 ÷ 4 75 ÷ 6 93 ÷ 8 100 ÷ 7 93 ÷ 5 57 ÷ 3 90 ÷ 6 59 ÷ 3 91 ÷ 7 105 ÷ 8 Pupils take it in turns to choose a division and work out the answer. They start off with 10 points. They score the remainder, but if the division leaves no remainder, they lose a point. E.g. 52 ÷ 4 = 13, so they lose a point, but 55 ÷ 4 = 13 r 3, so score 3 points. The person with the highest score when you ask them to stop, wins. If they run out of divisions, they can make up their own! Teacher input with whole class
HSNP © Hamilton 2012 Page 40 Simmering Term 1 Discuss how pupils should check their work, draw out using multiplication and adding on the remainder. Pupils check three.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 10 Division Day 3 Objective: Divide whole numbers by single-digit numbers including those which leave a remainder You will need: dice, division grid of numbers for each pair (see resources) Teacher input with whole class Write 95 ÷ 4 on the board. Sketch a line from 0 to 95 and ask pupils if there are more than ten 4s in 95. More than twenty 4s? Thirty 4s? Agree that here are between twenty and thirty 4s in 95 and draw jump to show twenty 4s. How much is left? How many 4s in 15? Draw a hop and show the remainder. twenty 4s three 4s r3
0 80 92 95 Show how to record this vertically: 20 + 3, r3 = 23 r3 4 ) 95 - 80 15 - 12 3 Repeat for 73 ÷ 3. Paired pupil work Pupils take it in turns to roll a dice. They ring a number on the grid and divide by the number on the dice. If the answer is more than 10, they score 10 points, and 20 points if the answer is greater than 20. They also score the remainder. E.g. roll 4, choose 75, 75 ÷ 4 = 18 r3 score 13. Once a number has been chosen, it cannot be used again. They continue until one person scores more than 100 to win. 57 115 100 45 95 68 49 99 75 107 91 87 HSNP © Hamilton 2012 Page 41 Simmering Term 1 103 81 54 63
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Optional week 1 overview Percentages
Objectives Know that 1/100 ≡ 0.01 or one out of a hundred, and can be written as 1% Find 10% of a quantity Find the whole if given 10% of a quantity Calculate new prices after increases and decreases of 10%
For this week you will need: pdf of blank 100 square (see resources), counting stick, DVD, Finding 10% loop cards (see resources) Link to homework page
Watch out for pupils who: do not remember WHAT a percentage is, i.e. a fraction of 100; get confused when dividing amounts of money by 10, e.g. write 10% of £54 as £5.4, and read as five pounds and four pence; do not know the equivalence between tenths, hundredths and percentages and therefore between decimals and percentages, e.g. that 50% is 0.5.
HSNP © Hamilton 2012 Page 42 Simmering Term 1 Optional week 1 Percentages Day 1 Objectives: Know that 1/100 ≡ 0.01 or one out of a hundred, and can be written as 1%; Find 10% of a quantity You will need: pdf of blank 100 square (see resources), Finding 10% loop cards (see resources) Teacher input with whole class Colour in one square of a blank 100 square. Ask what fraction of the whole square is coloured. Remind pupils that we can write 1/100 as a decimal, 0.01 and as 1%, percent, meaning out of one hundred, i.e. one part of 100 is coloured. Colour in the top row and ask pupils to write on the whiteboards how much is shaded, writing this in as many different ways as they can, .e. 10/100, 0.1, 1/10 and 10%. If the area of the whole square was 400cm2, what would the area of one little square be? It would be 1/100 or 4 cm2, What would the area of one row be? What if the area were 678cm2? What is 10% of 678? Extend pupils understanding by asking other questions> What is 10% of £57? 1.4metres? Remind pupils that digits shift one place to the right when dividing by 10 and sometimes we need a zero to hold a place, e.g. in 0.14m or in pounds, £5.70. Individual practice Ask pupils to find 10% of £780, £45, 1500m, 72cm and 495g. Teacher input with whole class Shuffle the 30 loop cards and hand out. You may need to give some pupils two cards or ask some pupils to share a card so that all cards are given out. Explain that a question is on one card, and the answer on another. Pupils need to listen carefully to the question read out by another pupil to see if they have the answer on one of their cards. If they have the answer, they read it and the next question clearly. The pupil with card: ‘£2.50, What is 10% of 56cm?’ starts. Pupil with 5.6cm at top of their card says ‘5.6cm’ and then reads the rest of the card. Eventually a pupil reads ‘What is 10% of £25?’ Owner of the first card
HSNP © Hamilton 2012 Page 43 Simmering Term 1 answers ‘£2.50’ to complete the loop. Time how long it takes! Cards are used in Spring Optional wk 1, so you can see if pupils are quicker!
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Optional week 1 Percentages Day 2 Objective: Find the whole if given 10% of a quantity You will need: counting stick, Finding 10% loop cards (see resources) Teacher input with whole class Show the counting stick. Point to the first section. If this first section was 12cm long, how long would the whole stick be? So if 10% of the whole is 12cm, the whole is 10 times as much, i.e. 120cm. What if each section was 12.5cm long? 9cm long? 10.1cm long? Pupils respond by writing the answers on their whiteboards.
Paired pupil work Write the following amounts on the board: £340, £34, £3.40, 456m, 4560m, 4500g, 450g, 45g, 870cm, 87cm. Pupils take it in turns to secretly choose one amount and find 10% of it, writing the answer on their whiteboards, The other person guesses which amount they chose, if correct they win a point.
Teacher input with whole class Shuffle the loop cards used on Day 1 and give out to pupils as before. Say that this time, someone will read out the ‘answer’, and the person with the matching question will read their question, and then the ‘answer’ on their card, so that you work backwards through the loop!
Practise the first few stages. Ask a pupil to read out £2.50, and whoever has the question (what is 10% of £25) reads out the question. They then read the ‘answer’ at the top of their card, and the pupil with the matching question reads it, and so on.
Can pupils make it all the way through the loop without making any mistakes?
HSNP © Hamilton 2012 Page 44 Simmering Term 1 Optional week 1 Percentages Day 3 Objective: Calculate new prices after increases and decreases of 10% You will need: DVD
Teacher input with whole class Show a DVD and say that the price was £12 but it has been reduced by 10% in the sale. Discuss how to find the new price, agreeing that we need to find 10%, and then subtract this from the original price to find the new price. What if the original price was £13.50? Work through the stages together. Paired pupil work Pupils copy the table below and work in pairs to find the new prices: Item Old price New reduced price DVD £16 CD £7.50 Beanie £14.90 Phone sock £4.70 Teacher input with whole class Say that the café in a school is having to increase all its prices by 10%. If a sandwich costs £1.20, how can we find the new price? Record the stages involved, i.e. find 10% and then add this to the original price. Ask pupils to work in pairs to find the new price of a sandwich which originally cost £1.40. Paired pupil work Pupils copy the table below and work in pairs to find the new prices: Item Old price New increased price Panini £1.60 Jacket potato £1.50 Pizza slice 80p Cake 60p
HSNP © Hamilton 2012 Page 45 Simmering Term 1 Optional week 2 overview Ratio
Objectives Understand, recognise and use simple ratios in a context Scale up or down using simple ratios in context Make two quantities using a given simple ratio
For this week you will need: red and yellow paint, large spoon, two paint palettes, two brushes, interconnecting cubes
Link to homework page
Watch out for pupils who: think that if 1/3 of cubes are red for example, that the ratio is 1 : 3 rather than 1 : 2; think that if you add the same number to each quantity the ratio will remain the same, rather than multiplying or dividing each quantity by the same number.
HSNP © Hamilton 2012 Page 46 Simmering Term 1 Optional week 2 Ratio Day 1 Objectives: Understand, recognise and use simple ratios in a context You will need: red and yellow paint, large spoon, two paint palettes, two brushes
Teacher input with whole class Pour two spoons of red paint and one spoon of yellow paint onto one palette and one spoon of red and two spoons of yellow onto the other. Ask pupils what colour of paint will be made when the paints are mixed on each palette, how the two colours will differ and why. Draw out that the two shades of orange will be different as you have used different ratios of red to yellow paint. Mix each and use them to paint two blobs on a large sheet of paper, writing red : orange under each, and the ratios 2 : 1 and 1 : 2. Say that each palette contained three spoonfuls of paint. Ask how many spoonfuls would be needed of each colour to make a total of 6 spoonfuls of the darker orange and of the paler orange. Record the ratios 4 : 2 and 2 : 4 under the initial ratios. What if we needed to double this amount of paint? Paired pupil work Ask pupils to work in pairs to find equivalent ratios for purple paint, made in the ratio of 3 blue spoonfuls for every 1 spoon of red paint. They copy and complete the following table. Encourage them to add their own rows. Total number of spoons Spoons of blue point Spoons of red point 4 3 1 8 12 20
Teacher input with whole class Discuss the relationship between the numbers in the second and third columns, i.e. that the numbers in the second column are 3 times the number in the third column. If purple paint is made with four spoons of
HSNP © Hamilton 2012 Page 47 Simmering Term 1 paint, what fraction of the spoonfuls is red? Blue? And if 8 spoons are used using the same ratio?
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Optional week 2 Ratio Day 2 Objectives: Understand, recognise and use simple ratios in a context; Scale up or down using simple ratios in context You will need: none required
Teacher input with whole class Display the following list of ingredients for a berry smoothie: 50g blueberries 100g of raspberries 150g of strawberries one banana 150ml apple juice What is the ratio of raspberries to blueberries? What is the ratio of strawberries to blueberries? Strawberries to raspberries? Say that this recipe serves 2 people and ask pupils what they would need to do to make smoothies for 4 people. They write the new recipe on their whiteboards. What is the ratio of raspberries to blueberries now? Discuss the other ratios and agree that they are the same, and so the smoothie will taste the same. Paired pupil work Ask pupils to work together to adapt the recipe for 6 people, then 3 people, then 5 people. Teacher input with whole class Say that cook is making up diluted squash for the pupils’ café. The squash should be mixed 1 part squash to 4 parts water. Ask pupils how much water needs to be added if she uses 100ml of squash. 300ml? 150ml? Ask how much squash she must have used if she added 800ml of water, 1600ml or 2 litres of water.
HSNP © Hamilton 2012 Page 48 Simmering Term 1 Optional week 2 Ratio Day 3
Objective: Make two quantities using a given simple ratio You will need: interconnecting cubes
Teacher input with whole class Show pupils a stick of 4 red cubes and 2 blue cubes. What is the ratio of red to blue cubes? Discuss how we can write the ratio as 4 : 2 but can simplify it to 2 : 1. Remind pupils that this means that there are twice as many red cubes as blue ones, or that there are 2 red cubes for every one blue cube.
Repeat with 6 blue cubes and 2 blue cubes and then with 6 blue cubes and 4 red cubes.
Paired pupil work Pupils work in pairs or group of four to make as many different sticks of cubes as they can in 2 minutes such that the ratio of one colour to the other is 3 to 1.
Teacher input with whole class What fraction is red? And blue? (Ensure pupils see that ¼ is in one colour and ¾ in the other, not 1/3 and 2/3.)
Paired pupil work Pupils write as many pairs of numbers as they can with a ratio of 2 to 1 in one minute, then 4 to 1, then 3 to 2.
HSNP © Hamilton 2012 Page 49 Simmering Term 1 Optional week 3 overview BIDMAS
Objectives Use and understand brackets Work out calculations by calculating what is in the brackets first Decide the order of operations in a string of calculations
For this week you will need: dice, an IWB four function calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a and an IWB scientific calculator, e.g. one at http://www.ecalc.com Link to homework page
Watch out for pupils who: are slow to realise that it DOES actually affect the answer if the operations are not done in the correct order; enter calculations in order into a basic four function calculator, not realising that it does not operate in accordance with BIDMAS rules; confuse squaring numbers with multiplying by 2.
HSNP © Hamilton 2012 Page 50 Simmering Term 1 Optional week 3 BIDMAS Day 1 Objectives: Use and understand brackets; Work out calculations by calculating what is in the brackets first You will need: none required
Teacher input with whole class Write 8 + (3 × 7) on the board and ask pupils to work out the answer. Remind them that they must work out what is in the brackets first. If we put the brackets in a different place, would we get the same answer or a different one? Try and see. Agree that the answer to (8 + 3) × 7 is different. Repeat with (28 ÷ 4) + 3 and 28 ÷ (4 + 3), and then (12 + 4) – 3 and 12 + (4 – 3). Agree that in the latter case the position of the brackets does not make a difference. Paired pupil work Ask pupils to put brackets in different places to give different answers to the following calculations: 4 × 8 – 2 24 ÷ 6 – 2 8 + 16 ÷ 2 9 + 5 × 2 22 – 8 ÷ 2 40 ÷ 5 × 2 6 × 8 ÷ 4 Teacher input with whole class Take feedback.
Paired pupil work Challenge pupils to work in pairs to write two different strings with an answer of 12. They must include at least two different operations and can be as long as they like.
HSNP © Hamilton 2012 Page 51 Simmering Term 1 Optional week 3 BIDMAS Day 2 Objective: Decide the order of operations in a string of calculations You will need: an IWB four function calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a and an IWB scientific calculator, e.g. one at http://www.ecalc.com
Teacher input with whole class Write BIDMAS on the board, and remind pupils that it stands for brackets, indices (powers, such as squares, cubes etc), division and multiplication, then addition and subtraction and that we use this to remind us of the order to carry out calculations in a string such as 32 + 4 × 2 – 4. Ask pupils to use BIDMAS to work out the answer. Take feedback, drawing out working out 32 and 4 × 2 first, then adding these subtracting 4. Repeat with 3 + 4 – 2 × 42. Paired pupil work Ask pupils to work in pairs to use the numbers 6, 2, 3 and 4 in that order and any operations and one square in each to find as many different whole number answers as they can, using BIDMAS. E.g. 62 ÷ 2 + 3 × 4 = 30. Some pupils may be able to produce negative answers, e.g. 6 – 2 × 32 + 4 = -8. Encourage them to write each stage on a separate line.
Teacher input with whole class Take feedback. Enter some of the pupils’ strings into a basic four function IWB calculator and discuss how the calculator works out the calculations in order as they are entered, not using BIDMAS. Repeat, but this time using a scientific calculator, showing how the calculator waits until = or enter is pressed before working out the calculation, and so uses BIDMAS. Discuss how to use each calculator to work out 27.5 + 64.2 × 62– 9.7.
HSNP © Hamilton 2012 Page 52 Simmering Term 1 Optional week 3 BIDMAS Day 3 Objectives: Decide the order of operations in a string of calculations; Work out calculations by calculating what is in the brackets first You will need: dice Teacher input with whole class Write 7 + 3 × 10 ÷ 5 – 3 on the board and ask pupils to work in pairs to put brackets in different places to get different answers, e.g. 7 + 3 × (10 ÷ 5) – 3; 7 + 3 × 10 ÷ (5 – 3) and (7 + 3) × 10 ÷ (5 – 3). Take feedback. Paired pupil work Ask pupils to work out the following: 6 × 5 – 7 × 4 (15 – 3) ÷ 4 + 22 8 + 6 ÷ 2 – 4 = 6 (10 + 2) ÷ (7 – 4) 6 ÷ 2 – 32 × 2 22 + 7 × 3 – 20 They then take it in turns to roll a dice and each write a calculation which gives the answer on the dice. It must include at least two different operations. The first person to write one correctly wins a point. Who has the highest score when you ask them to stop?
HSNP © Hamilton 2012 Page 53 Simmering Term 1 Optional week 4 overview Converting between units
Objectives Multiply and divide by 10 to convert between centimetres and millimetres Multiply and divide by 100 to convert between metres and centimetres Multiply and divide by 1000 to convert between metres and kilometres, grams and kilograms, millilitres and litres Round measurements to the nearest whole unit
For this week you will need: Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx? f=DartboardRoundingv2
Link to homework page
Watch out for pupils who: are uncertain of the relationships between metric units; explain how ‘cent’ means 100, and ‘milli’ and ‘kilo’ mean 1000; multiply by 10 for example by adding a zero, and so think that 1.4 × 10 = 1.40.
HSNP © Hamilton 2012 Page 54 Simmering Term 1 Optional week 4 Converting between units Day 1 Objectives: Multiply and divide by 10 to convert between centimetres and millimetres; Multiply and divide by 100 to convert between metres and centimetres You will need: none required
Teacher input with whole class Remind pupils that there are ten millimetres in a centimetre. Ask them to discuss in pairs how to convert 7.5, 34 and 0.6cm to mm. Draw out multiplying by 10. Ask pupils how to convert 3mm, 72mm and 345mm to cm. Draw out dividing by 10.
Paired pupil work Draw the following grid and ask pupils to convert the measurement in the top row from millimetres to centimetres and in the bottom row from centimetres to millimetres:
36mm 7mm 435mm 450mm 2250mm 68mm 7cm 43.5cm 89cm 52.5cm 90cm 126cm
Teacher input with whole class Remind pupils that there are 100cm in one metre. Write the following distances on the board: 70cm, 67cm, 93cm and 100cm. Ask half the class to convert 70cm to metres and the other half to convert 70cm to millimetres. Swap roles and repeat with 67cm. Ask pupils to look at each others’ answers. Can they see a way to convert from millimetres to metres? Repeat for 93cm and 100cm.
HSNP © Hamilton 2012 Page 55 Simmering Term 1 Optional week 4 Converting between units Day 2 Objective: Multiply and divide by 1000 to convert between metres and kilometres, grams and kilograms, millilitres and litres You will need: none required
Teacher input with whole class Remind pupils that there are 1000 grams in a kilogram. Ask pupils to convert 2700g and 400g to kilograms, drawing out that we divide by 1000 to do so. Repeat with 1.6kg and 0.3kg, asking pupils to convert each to grams. Draw out multiplying by 1000. Repeat, this time converting between litres and millilitres, and between metres and kilometres. Paired pupil work Pupils work in pairs to copy and complete the following table. m km ml l g kg 4500 7 2500 3.8 3600 2.4 750 2.4 7258 Teacher input with whole class Draw the following grid on the board. Ask pupils to choose six measurements to write on their whiteboards. 120cm 4600g 3.5cm 0.4l 64cm 2.7km 0.8kg 1.25m 12.5cm 7.5kg 1400ml 360mm 0.36m 0.25km 5l Read the following questions in random order, making a note of which you read. Pupils ring any answers they have. The first pupil to ring all answers wins. As a class, check their answers. What is 1.2m in cm? What is 4.6kg in grams? What is 35mm in cm? What is 400ml in litres? What is 640mm in cm? What is 2700m in km? What is 800g in kg? What is 125cm in m? What is 125mm in cm? What is 7500g in kg? What is 1.4 litres in ml? What is 36cm in mm? What is 36cm in metres? What is 250m in km? HSNP © Hamilton 2012 Page 56 Simmering Term 1 What is 5000ml in litres?
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Optional week 4 Converting between units Day 3 Objective: Round measurements to the nearest whole unit You will need: Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx?f=DartboardRoundingv2
Teacher input with whole class Sketch a line from 0 to 3m and discuss where to mark 0.75m, 1.2m, 1.49m and 2.95m. Agree the nearest whole metre for each distance. Use Dartboard rounding, and choose ‘nearest metre’. Click on the green segments one by one and ask pupils to write the nearest metre on their whiteboards.
Paired pupil work Ask pupils to work in pairs to write four distances which round to 10m, two must be less than 10m and two more than 10m. Teacher input with whole class Sketch a line from 0 to 3kg and discuss where to mark 1.499kg, 1.752kg 2.125kg. Discuss which is the nearest whole kilogram for each weight (mass). Draw a vertical line from 0 to 3 litres, and discuss where to mark on 1.678l, 2.953l and 1.079l. Agree the nearest whole litre each time. Use Dartboard rounding again, this time choosing ‘nearest kilogram’. Click on the green segments one by one and ask pupils to write the nearest kilogram on their whiteboards. Paired pupil work
HSNP © Hamilton 2012 Page 57 Simmering Term 1 Ask pupils to work in pairs to write four distances which round to 10km, two must be less that 10km and two more than 10km.
HSNP © Hamilton 2012 Page 7 Simmering Term 1 HSNP © Hamilton 2012 Page 58 Simmering Term 1 Hamilton Secondary Numeracy Project
Simmering Term 1 Homework
Name ______
HSNP © Hamilton 2012 Page 59 Simmering Term 1 Week 1 Place value
Write the value of the digit 5 in each of the following numbers: 235,360 240,567 854,438 530,267 Write the names of the following cities in order of population from the least to the greatest: Belfast 276,459 Glasgow 629,501 Birmingham 970,892 Leeds 443,247 Bristol 420,556 Liverpool 469,017 Cardiff 292,150 Reading 232,662 Edinburgh 430,082 Southampton 234,224 Open Number line at http://www.oup.com.au/__data/assets/file/0019/154045/Numberline .swf. You will be given a number. Choose which range it lies in. Scroll across to find the correct range on the line, and click on it. Click on the correct range for each new ‘zoomed-in’ line, until you see the number at the bottom of the screen. Click ‘new number’ to repeat. Click ‘new number;’ again if necessary to make sure you have the chance to work with a number in each of the ranges at the top of the screen.
HSNP © Hamilton 2012 Page 60 Simmering Term 1 Week 2 Addition
Write as many pairs of numbers with a total of 100 as you can in one minute!
Play Speedy grid challenge at http://resources.oswego.org/games/SpeedGrid/Addition/urikaadd3res .html. Try to answer 15 questions in three minutes! You will be given a number and asked to find a pair of numbers on the grid with this total. Write down how many questions you managed to complete.
Roll a dice four times and write the digits in this addition □□00 + □□00. Find the total. What is the biggest answer you could get using these digits? And the smallest? Repeat four more times. Now repeat with □□,000 + □□,000.
Use the digits 2 to 9 to make pairs of four-digit numbers. Find a pair with the greatest possible total, the least possible total and a total as close to 8000 as you can.
HSNP © Hamilton 2012 Page 61 Simmering Term 1 Week 3 Subtraction
Play Ghostblasters 3 at http://www.oswego.org/ocsd- web/games/Ghostblasters3/ghostsub3.html. Either play against another person, or just click begin to start. Play until one score is 10 points.
Roll three dice (or roll one three times) to generate a three-digit number. Subtract this number from the next multiple of 100. Roll 4, 6, 6, work out 500 – 466. How many can you do in two minutes?
Write digits in the subtraction 5□□ – 4□□ to give an answer of less than 100. Make four different subtractions. Repeat for 5□□□ – 4□□□.
HSNP © Hamilton 2012 Page 62 Simmering Term 1 Week 4 Multiplication
Play Are you a Math Magician? at http://www.oswego.org/ocsd- web/games/mathmagician/mathsmulti.html. Choose multiplication facts for the 6 times table and then for the 9 times table. Can you answer 20 questions in one minute? Write down the time for each set of multiplication facts.
Find six multiplications of the form □□ × □ with answers between 250 and 350, e.g. 43 × 6.
Which of the following multiplications do you think will have the biggest answer? And the smallest answer? Work out the answers to each to check your prediction.
356 × 6 729 × 4 562 × 3 275 × 9 473 × 6
HSNP © Hamilton 2012 Page 63 Simmering Term 1 Week 5 Division
Play Hit the button at http://www.wmnet.org.uk/resources/gordon/Hit %20the%20button%20v9.swf. Choose ‘division facts’ and ‘÷6’. You’ll be asked division facts for the 6 times table. Click on as many answers as you can in one minute. Write down your score. Repeat for ‘÷9’.
Use ‘chunking’ to work out the following divisions: 53 ÷ 3, 123÷ 8, 92 ÷ 5, 73 ÷ 4, 84 ÷ 6, 126 ÷ 9 and 103 ÷ 6
Write two other divisions with an answer between 10 and 20.
Use halving to solve the following problems: . A pack of 4 pens cost £1.56. How much does each pen cost? . A cyclist is cycling 288 miles for charity. If she takes four days and cycles the same distance each day, how far does she need to cycle each day? . A pack of 8 desserts costs £4.48, how much does one dessert cost? . 248 pupils are split into eight equal classes. How many are in each class? Use dividing by 10 and doubling to divide each of the following numbers by 5: 70, 170, 95, 230 and 145.
HSNP © Hamilton 2012 Page 64 Simmering Term 1 Week 6 Decimals
Help Builder Ted to order bricks at http://www.bbc.co.uk/education/mathsfile/shockwave/games/ladder game.html. Choose level 1.
Work out what needs to be added to each of the following numbers to make all the digits 9: 9.59, 9.92, 9.45, 4.59, 4.92, 3.46
Sketch a line from 0 to 1 and place the numbers on it. 0.45, 0.79, 0.15, 0.28, 0.63, 0.92
Round each of the capacities to the nearest litre: 3.678l 1.294l 2.712l 8.492l
HSNP © Hamilton 2012 Page 65 Simmering Term 1 Week 7 Addition of decimals
6 7 3 2 . . . . 7 6 3 1 Use the above numbers to make an addition with an answer . of exactly 10 . more than 10 . less than 10
Play Decimal addition at http://www.sheppardsoftware.com/mathgames/decimals/matchingDe cimalsAdd.htm. Match the additions to their answers, and level up each time! What level did you reach and how many correct matches did you make?
Estimate the answers to the following addition, then use column addition to find the exact answers:
4.56 + 2.72 25.6 + 17.5 4.56 + 3.28 78.6 + 23.7
HSNP © Hamilton 2012 Page 66 Simmering Term 1 Week 8 Subtraction
Write a pair of four-digit numbers and find the difference between the two. You can only use each digit once in each subtraction. Try to get an answer as close to 1600 as possible.
Write digits in the subtraction 6.□□ – 3.□□ to give an answer of less than 3. Make three different subtractions. Repeat for 6.□ – 3.□□ and 6.□□ – 3.□.
Three of these subtractions are wrong! Which do you think they are and why? Find the correct answers. Use addition to check your answers to make sure you aren’t wrong too! 7246 – 2378 = 5132 8542 – 6327 = 2215 4236 – 2152 = 2084 6278 – 3489 = 3211 8432 – 5071 = 3061 7252 – 2431 = 4821
HSNP © Hamilton 2012 Page 67 Simmering Term 1 Week 9 Multiplication
Play Ghostblasters at http://www.oswego.org/ocsd- web/games/Ghostblasters1/gbcd.html. Choose multiples of 7. Click on any ghost with a multiple of 7. How long did it take you to spot 100 multiples? Write down the time. Repeat for multiples of 8.
Use grid multiplication to find the area of these rectangles: 24cm 54cm 35cm 18cm
76cm
14cm
HSNP © Hamilton 2012 Page 68 Simmering Term 1 Multiply each of these numbers by a number between 1 and 10. Try to get an answer as close to 20 as you can. Which answer was closest?
4.54 3.26 7.24 5.78
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Week 10 Division
Play Are you a Math Magician? at http://www.oswego.org/ocsd- web/games/mathmagician/mathsmulti.html. Choose division facts for the 7 times table and then for the 8 times table. Can you answer 20 questions in one minute? Write down the time for each set of division facts.
Use 1-9 digit cards or take the 10s, Js, Qs, Ks and Jokers out from a set of playing cards and shuffle the remaining cards. Take two and use them to make a two-digit number, using the cards in either order. An Ace counts as 1. Divide the number by a single-digit number of your choice. If the answer is more than 10, you score the remainder. If the answer is less than 10, you score nothing. For example, you could use the cards 3 and 5 to make 35 or 53, and divide by 4. If you divide 35 by 4 you score nothing because the answer is less than 10. If you divide 53 by 4, the answer is 13 r 1, so you score 1. Repeat, and add your remainder to your previous score. Keep going. Can you reach a score of 30 in fewer than 10 goes?
HSNP © Hamilton 2012 Page 69 Simmering Term 1 Optional week 1 Percentages Play Number invaders at http://www.mathplayground.com/balloon_invaders_percent.html. Choose 10%. Use the arrow keys to move from side to side and the space bar to pop the balloons with the correct answers on. You’ll need to be quick! Write down your score. Play again. Did you improve your score?
Sarah has being selling unwanted items on an online auction site and has worked out 10% of each item sold as she’s going to give 10% to her favourite charity. But she’s spilt coffee over the prices she got for each item! Help her by working out the prices.
Item Sold for 10% Scarf 65p Jumper 72p Hand held game £3.60 School trousers 32p DVD box set £2.80
Tom says that if a price goes up by 10%, and then goes down by 10% it will be the same price as it was at the beginning. His mate Jimmy says he is talking rubbish. What do you think? Make up an example to show who is right. HSNP © Hamilton 2012 Page 70 Simmering Term 1 Optional week 2 Ratio
Green paint is made by mixing blue paint and yellow paint. A limey shade can be made using a ratio of yellow to blue, 2 : 1. Fill in the missing amounts in the following table to make sure each batch of paint is the same colour.
Yellow paint Blue paint
100ml
75ml
400ml
150ml
Draw five different size rectangles so that the ratio of the longer side to the shorter side is 3 : 1.
This list of ingredients makes enough tomato soup for four people. Scale it up so that it will be enough for 6 people.
1 onion, peeled and finely chopped 1 clove of garlic, peeled and finely chopped 2 carrots, peeled and coarsely grated a handful of fresh basil, leaves picked, stalks finely chopped 1 tablespoon of olive oil 6 tablespoons double cream 1kg super-ripe tomatoes 1 litre vegetable stock sea salt and freshly ground black pepper to taste
HSNP © Hamilton 2012 Page 71 Simmering Term 1 Optional week 3 BIDMAS
Mark the following pupil’s work. Write the correct answers by the side and ring where you think the person might have gone wrong.
1. 4 + 22 × 6 - 2 = 94
2. 5 + (2 × 3) – 7 = 4
3. 9 + 7 – 12 ÷ 2 = 2
4. 3 × 4 + 10 ÷ 2 - 7= 10
5. (4 + 2)2 × (12 – 2) = 360
6. 16 – 8 ÷ 22 + 6 = 8
7. 30 – 42 + 8 × 2 = 30
8. (70 + 2) ÷ (2 × 3)2 = 2
9. -10 + 4 = 6 Use the numbers 2, 3, 4 and 6 and any operations and brackets to see if you can10. create -5 –calculations 3 = 2 with every answer from 1 to 15. You don’t have to use all four numbers in each calculation, but must use at least three and you cannot use any number more than once in one calculation. You can use 2 as a power to square a number. Make sure your calculations follow the BIDMAS rules and add brackets where necessary.
HSNP © Hamilton 2012 Page 72 Simmering Term 1 Optional week 4 Converting between units
Copy and complete the following tables:
mm cm m m km 36 600 750 8.3 4.25 7259
Find four tins/packets of food that weigh between 100g and 2kg. For each write their weight (mass) in grams and then in kilograms. Round each to the nearest whole kilogram.
Find four bottles which contain between 100ml and 2 litres of liquid. Write the amount in millilitres, and then in litres. Round each to the nearest whole litre.
HSNP © Hamilton 2012 Page 73 Simmering Term 1 HSNP © Hamilton 2012 Page 74 Simmering Term 1 Hamilton Secondary Numeracy Project
Numeracy Simmering Term 1 Homework answers
HSNP © Hamilton 2012 Page 75 Simmering Term 1 Week 1 Place value
Write the value of the digit 5 in each of the following numbers: 235,360 240,567 854,438 530,267 5000 500 50,000 500,000
Write the names of the following cities in order of population from the least to the greatest: Belfast 276,459 Glasgow 629,501 Birmingham 970,892 Leeds 443,247 Bristol 420,556 Liverpool 469,017 Cardiff 292,150 Reading 232,662 Edinburgh 430,082 Southampton 234,224 Reading, Southampton, Belfast, Cardiff, Bristol, Edinburgh, Leeds, Liverpool, Glasgow, Birmingham
Open Number line at http://www.oup.com.au/__data/assets/file/0019/154045/Numberline .swf. You will be given a number. Choose which range it lies in. Scroll across to find the correct range on the line, and click on it. Click on the correct range for each new ‘zoomed-in’ line, until you see the number at the bottom of the screen. Click ‘new number’ to repeat. Click ‘new number;’ again if necessary to make sure you have the chance to work with a number in each of the ranges at the top of the screen. This is a computer game
HSNP © Hamilton 2012 Page 76 Simmering Term 1 Week 2 Addition
Write as many pairs of numbers with a total of 100 as you can in one minute! E.g. 11 + 89; 23 + 77; 38 + 62; 42 + 58; 57 + 43; 65 + 35; 84 + 16
Play Speedy grid challenge at http://resources.oswego.org/games/SpeedGrid/Addition/urikaadd3res .html l. Try to answer 15 questions in three minutes! You will be given a number and asked to find a pair of numbers on the grid with this total. Write down how many questions you managed to complete. This is a computer game
Roll a dice four times and write the digits in this addition □□00 + □□00. Find the total. What is the biggest answer you could get using these digits? And the smallest? Repeat four more times. Now repeat with □□,000 + □□,000. E.g. They roll 4, 3, 3 and 5 4300 + 3500 = 7800 The biggest answer is 5300 + 4300 = 9600 The smallest answer is 3500 + 3400 = 6900 They roll 6, 2, 5 and 4 62,000 + 54,000 = 116,000 The biggest answer is 64,000 + 52,000 = 116,000 The smallest answer is 46,000 + 25,000 = 71,000 Use the digits 2 to 9 to make pairs of four-digit numbers. Find a pair with the greatest possible total, the least possible total and a total as close to 8000 as you can.
E.g. 9753 + 8642 = 18,395 (Greatest possible total) 3579 + 2468 = 6047 (Least possible total) 2348 + 5679 = 8027 3287 + 4695 = 7982 3269 + 4758 = 8027 3685 + 4297 = 7982 HSNP © Hamilton 2012 Page 77 Simmering Term 1 Week 3 Subtraction
Play Ghostblasters 3 at http://www.oswego.org/ocsd- web/games/Ghostblasters3/ghostsub3.html. Either play against another person, or just click begin to start. Play until one score is 10 points. This is a computer game.
Roll three dice (or roll one three times) to generate a three-digit number. Subtract this number from the next multiple of 100. Roll 3, 6, 6, work out 400 – 366. How many can you do in two minutes? Examples: Roll 5, 2, 1 600 – 521 = 79 Roll 3, 2, 6 400 – 326 = 74 Roll 5, 6, 6 600 – 566 = 34
Write digits in the subtraction 5□□ – 4□□ to give an answer of less than 100. Make four different subtractions. Repeat for 5□□□ – 4□□□ Examples: 535 – 482 = 53 584 – 499 = 85 527 – 497 = 30 563 – 472 = 91 511 – 488 = 23 547 – 458 = 89 576 – 495 = 81 523 – 460 = 63 5063 – 4972 = 91 5038 – 4973 = 65 5004 – 4949 = 55 5015 – 4990 = 25 5036 – 4978 = 58 5089 – 4999 = 90 5029 – 4983 = 46 5075 – 4988 = 87
HSNP © Hamilton 2012 Page 78 Simmering Term 1 Week 4 Multiplication
Play Are you a Math Magician? at http://www.oswego.org/ocsd- web/games/mathmagician/mathsmulti.html. Choose multiplication facts for the 6 times table and then for the 9 times table. Can you answer 20 questions in one minute? Write down the time for each set of multiplication facts. This is a computer game.
Find six multiplications of the form □□ × □ with answers between 250 and 350, e.g. 43 × 6. Examples: 93 x 3 = 279 57 x 5 = 285 65 x 5 = 325 28 x 9 = 252 47 x 7 = 329 34 x 8 = 272
Which of the following multiplications do you think will have the biggest answer? And the smallest answer? Work out the answers to each to check your prediction.
356 × 6 = 2136 729 × 4 = 2916 (Largest answer) 562 × 3 = 1686 (Smallest answer) 275 × 9 = 2475 473 × 6 = 2838
HSNP © Hamilton 2012 Page 79 Simmering Term 1 Week 5 Division
Play Hit the button at http://www.wmnet.org.uk/resources/gordon/Hit %20the%20button%20v9.swf. Choose ‘division facts’ and ‘÷6’. You’ll be asked division facts for the 6 times table. Click on as many answers as you can in one minute. Write down your score. Repeat for ‘÷9’. This is a computer game.
Use ‘chunking’ to work out the following divisions: 53 ÷ 3, 123 ÷ 8, 92 ÷ 5, 73 ÷ 4, 84 ÷ 6, 126 ÷ 9 and 103 ÷ 6
(30 ÷ 3 = 10, 21 ÷ 3 = 7) 53 ÷ 3 = 17, r 2 (80 ÷ 8 = 10, 40 ÷ 8 = 5) 123 ÷ 8 = 15, r 3 (50 ÷ 5 = 10, 40 ÷ 5 = 8) 92 ÷ 5 = 18, r 2 (40 ÷ 4 = 10, 32 ÷ 4 = 8) 73 ÷ 4 = 18, r 1 (60 ÷ 6 = 10, 24 ÷ 6 = 4) 84 ÷ 6 = 14 (90 ÷ 9 = 10, 36 ÷ 9 = 4) 126 ÷ 9 = 14 (60 ÷ 6 = 10, 42 ÷ 6 = 7) 103 ÷ 6 = 17, r 1
Write two other divisions with an answer between 10 and 20. Examples: 97 ÷ 6 = 16, r 1 142 ÷ 9 = 15, r 7
Use halving to solve the following problems: . A pack of 4 pens cost £1.56. How much does each pen cost? 156 ÷ 2 = 78; 78 ÷ 2 = 39 Each pen costs 39p . A cyclist is cycling 288 miles for charity. If she takes four days and cycles the same distance each day, how far does she need to cycle each day? 288 ÷ 2 = 144; 144 ÷ 2 = 72 She must cycle 72 miles each day . A pack of 8 desserts costs £4.48, how much does one dessert cost? 448 ÷ 2 = 224; 224 ÷ 2 = 112; 112 ÷ 2 = 56 Each dessert costs 56p
HSNP © Hamilton 2012 Page 80 Simmering Term 1 . 248 pupils are split into eight equal classes. How many are in each class? 248 ÷ 2 = 124; 124 ÷ 2 = 62; 62 ÷ 2 = 31 Each class has 31 pupils Use dividing by 10 and doubling to divide each of the following numbers by 5: 70, 170, 95, 230 and 145. 70 ÷ 10 = 7; 7 x 2 = 14 70 ÷ 5 = 14 170 ÷ 10 = 17; 17 x 2 = 34 170 ÷ 5 = 34 95 ÷ 10 = 9.5; 9.5 x 2 = 19 95 ÷ 5 = 19 230 ÷ 10 = 23; 23 x 2 = 46 230 ÷ 5 = 46 145 ÷ 10 = 14.5; 14.5 x 2 = 29 145 ÷ 5 = 29
Week 6 Decimals
Help Builder Ted to order bricks at http://www.bbc.co.uk/education/mathsfile/shockwave/games/ladder game.html. Choose level 1. This is a computer game.
Work out what needs to be added to each of the following numbers to make all the digits 9: 9.59, 9.92, 9.45, 4.59, 4.92, 3.46 0.4, 0.07, 0.54, 5.4, 5.07, 6.53
HSNP © Hamilton 2012 Page 81 Simmering Term 1 Sketch a line from 0 to 1 and place the numbers on it. 0.45, 0.79, 0.15, 0.28, 0.63, 0.92
Round each of the capacities to the nearest litre: 3.678l 1.294l 2.712l 8.492l 4l 1l 3l 8l
Week 7 Addition of decimals
6 7 3 2 . . . . 7 6 3 1 Use the above numbers to make an addition with an answer . of exactly 10 6.7 + 3.3 . more than 10 6.7 + 7.6 = 14.3; 7.6 + 3.3 = 10.9 . less than 10 6.7 + 2.1 = 8.8; 7.6 + 2.1 = 9.7; 3.3 + 2.1 = 5.4
HSNP © Hamilton 2012 Page 82 Simmering Term 1 Play Decimal addition at http://www.sheppardsoftware.com/mathgames/decimals/matchingDe cimalsAdd.htm. Match the additions to their answers, and level up each time! What level did you reach and how many correct matches did you make? This is a computer game.
Estimate the answers to the following addition, then use column addition to find the exact answers:
4.56 + 2.72 25.6 + 17.5 4.56 + 3.28 78.6 + 23.7 7.28 43.1 7.84 102.3
Week 8 Subtraction
Write a pair of four-digit numbers and find the difference between the two. You can only use each digit once in each subtraction. Try to get an answer as close to 1600 as possible. E.g. 4860 – 3259 = 1601
Write digits in the subtraction 6.□□ – 3.□□ to give an answer of less than 3. Make three different subtractions. Repeat for 6.□ – 3.□□ and 6.□□ – 3.□. Examples: 6.45 – 3.92 = 2.53 6.24 - 3.3 = 2.94 6.67 – 3.78 = 2.89 6.02 – 3.9 = 2.12 6.21 – 3.85 = 2.36 6.59 - 3.81 = 2.78 6.4 – 3.72 = 2.68 6.7 – 3.96 = 2.74 6.3 – 3.45 = 2.85
HSNP © Hamilton 2012 Page 83 Simmering Term 1 Three of these subtractions are wrong! Which do you think they are and why? Find the correct answers. Use addition to check your answers to make sure you aren’t wrong too! 7246 – 2378 = 5132 4868 8542 – 6327 = 2215 4236 – 2152 = 2084 6278 – 3489 = 3211 2789 8432 – 5071 = 3061 3361 7252 – 2431 = 4821
Week 9 Multiplication
Play Ghostblasters at http://www.oswego.org/ocsd- web/games/Ghostblasters1/gbcd.html.. Choose multiples of 7. Click on any ghost with a multiple of 7. How long did it take you to spot 100 multiples? Write down the time. Repeat for multiples of 8. This is a computer game.
Use grid multiplication to find the area of these rectangles: 35 x 24 = 840 54 x 18 = 972 76 x 14 = 1064
Multiply each of these numbers by a number between 1 and 10. Try to get an answer as close to 20 as you can. Which answer was closest? 3.26 x 6 = 19.56
HSNP © Hamilton 2012 Page 84 Simmering Term 1 Week 10 Division
Play Are you a Math Magician? at http://www.oswego.org/ocsd- web/games/mathmagician/mathsmulti.html. Choose division facts for the 7 times table and then for the 8 times table. Can you answer 20 questions in one minute? Write down the time for each set of division facts. This is a computer game.
Use 1-9 digit cards or take the 10s, Js, Qs, Ks and Jokers out from a set of playing cards and shuffle the remaining cards. Take two and use them to make a two-digit number, using the cards in either order. An Ace counts as 1. Divide the number by a single-digit number of your choice. If the answer is more than 10, you score the remainder. If the answer is less than 10, you score nothing. For example, you could use the cards 3 and 5 to make 35 or 53, and divide by 4. If you divide 35 by 4 you score nothing because the answer is less than 10. If you divide 53 by 4, the answer is 13 r 1, so you score 1. Repeat, and add your remainder to your previous score. Keep going. Can you reach a score of 30 in fewer than 10 goes?
Examples:- 6 and 8; 68 ÷ 5 = 13, r 3 Score 3 86 ÷ 7 = 12, r 2 Score 3 5 and 7; 57 ÷ 9 = 6, r 3 Score 0 57 ÷ 4 = 14, r 1 Score 1 75 ÷ 6 = 12, r 3 Score 3
HSNP © Hamilton 2012 Page 85 Simmering Term 1 Optional week 1 Percentages Play Number invaders at http://www.mathplayground.com/balloon_invaders_percent.html. Choose 10%. Use the arrow keys to move from side to side and the space bar to pop the balloons with the correct answers on. You’ll need to be quick! Write down your score. Play again. Did you improve your score? This is a computer game.
Sarah has being selling unwanted items on an online auction site and has worked out 10% of each item sold as she’s going to give 10% to her favourite charity. But she’s spilt coffee over the prices she got for each item! Help her by working out the prices.
Item Sold for 10% Scarf £6.50 65p Jumper £7.20 72p Hand held game £36 £3.60 School trousers £3.20 32p DVD box set £28 £2.80
Tom says that if a price goes up by 10%, and then goes down by 10% it will be the same price as it was at the beginning. His mate Jimmy says he is talking rubbish. What do you think? Make up an example to show who is right. Jimmy is right. For example: 100 goes up by 10%, it becomes 110, 10% of 110 is 11, 110 – 11 = 99
HSNP © Hamilton 2012 Page 86 Simmering Term 1 Optional week 2 Ratio
Green paint is made by mixing blue paint and yellow paint. A limey shade can be made using a ratio of yellow to blue, 2 : 1. Fill in the missing amounts in the following table to make sure each batch of paint is the same colour.
Yellow paint Blue paint
100ml 50ml
150ml 75ml
400ml 200ml
300ml 150ml
Draw five different size rectangles so that the ratio of the longer side to the shorter side is 3 : 1. Examples: 1 x 3; 2 x 6; 3 x 9; 4 x 12; 5 x 15; 6 x 18; 7 x 21
This list of ingredients makes enough tomato soup for four people. Scale it up so that it will be enough for 6 people.
1 and a half onions, peeled and finely chopped 1 and a half cloves of garlic, peeled and finely chopped 3 carrots, peeled and coarsely grated 1 and a half handfuls of fresh basil, leaves picked, stalks finely chopped 1 and a half tablespoons of olive oil 9 tablespoons double cream 1.5kg super-ripe tomatoes 1.5 litres vegetable stock sea salt and freshly ground black pepper to taste HSNP © Hamilton 2012 Page 87 Simmering Term 1 Optional week 3 BIDMAS
Mark the following pupil’s work. Write the correct answers by the side and ring where you think the person might have gone wrong.
1. 4 + 22 × 6 - 2 = 94 26
2. 5 + (2 × 3) – 7 = 4
3. 9 + 7 – 12 ÷ 2 = 2 10
4. 3 × 4 + 10 ÷ 2 - 7= 10
5. (4 + 2)2 × (12 – 2) = 360
6. 16 – 8 ÷ 22 + 6 = 8 20
7. 30 – 42 + 8 × 2 = 30 -2
8. (70 + 2) ÷ (2 × 3)2 = 2
9. -10 + 4 = 6 Use the numbers 2, 3, 4 and 6 and any operations and brackets to see if you can create10. calculations-5 – 3 = 2 with every answer from 1 to 15. You don’t have to use all four numbers in each calculation, but must use at least three and you cannot use any number more than once in one calculation. You can use 2 as a power to square a number. Make sure your calculations follow the BIDMAS rules and add brackets where necessary. Examples: 3 + 4 – 6 = 1 4 × 3 ÷ 2 = 6 2 + 3 + 6 = 11 4 × 3 ÷ 6 = 2 4 + 6 – 3 = 7 3 × 6 – 4 – 2 = 12 6 × 2 ÷ 4 = 3 6 × 4 ÷ 3 = 8 32 + 4 = 13 6 × 2 ÷ 3 = 4 6 × 3 ÷ 2 = 9 3 × 4 + 2 = 14
HSNP © Hamilton 2012 Page 88 Simmering Term 1 (4 + 6) ÷ 2 = 5 42 – 6 = 10 32 + 6 = 15
HSNP © Hamilton 2012 Page 7 Simmering Term 1 Optional week 4 Converting between units
Copy and complete the following tables:
mm cm m m km 360 36 0.36 600 0.6 750 75 0.75 8300 8.3 4250 425 4.25 7259 7.259
Find four tins/packets of food that weigh between 100g and 2kg. For each write their weight (mass) in grams and then in kilograms. Round each to the nearest whole kilogram. Answers will depend on the tins/packets chosen.
Find four bottles which contain between 100ml and 2 litres of liquid. Write the amount in millilitres, and then in litres. Round each to the nearest whole litre. Answers will depend on the containers chosen.
HSNP © Hamilton 2012 Page 89 Simmering Term 1