Structure of HSNP Numeracy - Four levels of proficiency Booklet... · Web view– for those who...

Hamilton Secondary Numeracy Project

Numeracy

ShiningTerm 1

www.hsnp.org.uk

Published by Hamilton Trust1A Howard Street, Oxford, OX4 3AY

[email protected] tel: 01865 253980

Development team

Ruth Merttens, Jennie KerwinAlison Fahey, Deidre Holes, Jeanette Viney, Mike O’Regan

http://www.hamilton-trust.org.uk/

mailto:[email protected]

Contents

Contents i

Introduction to HSNP ii

Table showing different levels v

Content of HSNP vi

Weekly activities 1

Homework 43

Homework answers 55

HSNP © Hamilton 2012 Page i Shining 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 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 Shining 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.

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 Shining Term 1

HSNP © Hamilton 2012 Page iv Shining Term 1

Table showing how the different levels operate within HSNP

1st ‘Turn’ 2nd ‘Turn’ 3rd ‘Turn’ Y10/Y11

Stepping up

Between 15% and 40% of Y7

Between 5% and 10% of Y8

Keeping up

20% - 30% of Y7Y8 who were in Stepping-up in Y7

Y8 who need another go at this

Y9 who cannot move beyond this

Simmering

Around 50% of Y7Y8 who were in Keeping-up in Y7Y9 who were in Stepping-up and then in Keeping-up

Y8/Y9 who need to keep their skills on the boil

Y9 who need to keep their skills simmering

Y10 who need to keep their skills simmering

Shining

10% - 20% of Y7Y8/Y9 who have topped out of simmering

Y8, Y9 who are very good at numeracy but need something so they don’t forget it.

Y9 who are very good at numeracy but need something so they don’t forget it.

Between 20% and 40% of cohort

HSNP © Hamilton 2012 Page v Shining Term 1

Content of HSNP Wk Term 1 Term 2 Term 31 Place Value - Numbers

to 10 million, ordering on a line, comparing, even larger numbers – to a googol

Fractions - Concept of fraction, find fractions of fractions, divide by a fraction – what happens? Decimal and fraction equivalences incl 1/8

Decimals and Fractions - Round whole numbers & decimal numbers, using rounding to estimate answers to complex calculations

2 Addition - Mental addition and written addition; make up numbers to give hard additions to each other. What makes an addition difficult?

Addition of fractions - Explain why we need common denominator Introduce ‘smile then kiss’ – can they explain how it works?

Addition - Explore consecutive numbers (can each no. be made by adding consec nos?) Diffs between prime nos. Also Dig roots of primes

3 Subtraction - Mental subtraction & written subtraction. Revise methods Chn explain why a partic strategy is better than others. Make up ‘hard’ subtractions/ why are they hard?

Subtraction of fractions - Subtract fractions with related denominators (1/2 – ¼, ¼ - 1/8 etc. Or fractions in a sequence, ½ - 1/3, 1/3 – 1.4, etc. Look for patterns in subtraction

Subtraction – Explore 1089 investigation. Also explore palindromic numbers

4 Multiplication - Times tables, multiples and factors, mental strategies incl. doubling and halving – divisibility rules

Multiplication - Explore patterns: 7 x 7, 67 x 67, 667 x 667 etc. 99 x 11, 99 x 22, 99 x 33 etc. 999,999 X2, X3, X4 etc.

Multiplication - Binary numbers. Explore these – do ‘age trick’. Do Egyptian and Russian multiplication – why do they work.

5 Division - Reverse of multiplication = chunking, written division. Explore methods, Create harder divisions – what makes them hard?

Division - Explore patterns: What 5-digit no ÷ 4 gives an answer which is its reverse? Divide 2521 by 1, 2, …10 write down the remainder in each.

Division - Explore patterns: 22 – 1X3, 32 – 2X4, 42 – 3X5, 42 – 4X6 etc. And (11–2) ÷9, (111–3) ÷9, (1111–4) ÷9 etc. And 56÷11, 78÷11, 34÷11, 122÷11, 89÷11, 37÷11, 49÷11, 60÷11

HSNP © Hamilton 2012 Page vi Shining Term 1

6 Place Value - Decimal numbers to 3-places and beyond, order and compare using a line, PV calculations

Place value - Recurring decimals, non-recurring decimals. Converting fractions to decimals and vice versa

Place value - Natural nos, integers, Rational numbers and irrational numbers – explore these

7 Addition - Magic squares. Explore patterns include Durer’s and Franklin’s and diabolic squares

Addition - Pascal’s triangle and Fibonacci sequence. Explore patterns

Addition - Test Goldbach’s conjecture Every even no > 4 = sum of 2 odd primes, every odd no = sum of 3 odd primes. Test Chebyshev’s theorem

8 Subtraction - Subtract decimal numbers with different numbers of digits, include up to 4 places of decimals. Round to estimate first.

Subtraction - Find a difference between negative numbers; explore patterns in adding and subtracting negative numbers

Subtraction - Explore differences: between no & reverse 871 – 178 etcBetween square nos / cubic nosBetween nos in arithmetic series

9 Multiplication - Tables, multiples and factors, written multiplication including of two decimal numbers e.g. 34.57 x 23

Multiplication - Rehearse hard mults written method. Explore factorials. Explore reverse digits 12X42 &21X24 then 12X84, 13X62, 23X96, 24X63.

Multiplication -Explore indices. Work out 12 + 22, 12 + 22 + 32, etc.Work out 22, 23, 24, 25 etc. Work out 32, 33, 34, etc. Find ans’s digital roots

10 Division - Strategies for written division of decimals.

Division - Explore patterns in fractions to decimals: 1/9, 2/9, 3/9 etc. 1/11, 2/11. 3/11 etc. 3/7, 4/7, 5/7 etc.Explore patterns in factors Find prime factors. Perfect numbers and Amicable numbers

Division - Explore roots. Find square roots. Explore Chinese method for finding sq roots. Explore triangular nos and square nos. Test Diophantus’ rule: 8T +1 = sq no.

HSNP © Hamilton 2012 Page vii Shining Term 1

HSNP © Hamilton 2012 Page viii Shining Term 1

Numeracy

Shining

Term 1

Weekly Activities

HSNP © Hamilton 2012 Page 1 Shining Term 1

Week 1 overview Place value

Objectives

Understand place value in seven-digit numbers

Compare numbers to 10,000,000

Place numbers to 10,000,000 on a line

Be aware of really large numbers, e.g. a googol

For this week you will need:

a place value chart (see resources), dice, 0-9 digit cards, pdf of interesting facts involving large numbers (see resources), Mystery numbers at http://www.starrmatica.com/standalone/starrMaticaplaveValueMysteryNumbers.swf

Link to homework page

Watch out for pupils who:

are unsure what each digit represents in a seven-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 1,000,000 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. 4,201,056;

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.


http://www.starrmatica.com/standalone/starrMaticaplaveValueMysteryNumbers.swf


Week 1 Place value Day 1Objectives: Understand place value in seven-digit numbers

You will need: a place value chart (see resources), dice, Mystery numbers at http://www.starrmatica.com/standalone/starrMaticaplaveValueMysteryNumbers.swf

Teacher input with whole class Show the place value chart. Ring one number from each line. Ask

pupils to write the total on their whiteboards. Repeat. Ring numbers from only 3, 4, 5 or 6 lines on the place value chart, e.g.

4,000,000, 20,000 and 400. Ask pupils to write total.

Paired pupil work Pupils write a 7-digit number, each digit can only be used twice and

must be on the dice. They then roll the dice. If the number is in their 7-digit number, they subtract that number of 1,000,000s, 100,000s, 10,000s, 1000s, 100s, 10s or 1s, e.g., they write 3,244,126, 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 Play Mystery numbers. Ask pupils to read the clues and in pairs to

write the mystery number on their whiteboards. Ask a pupil to drag the digit to see if their number was correct.




Week 1 Place value Day 2Objectives: Compare numbers up to 10,000,000; Place numbers to 10,000,000 on a line

You will need: dice, 0-9 digit cards

Teacher input with whole class 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 7-digit number. Repeat 6 more times.

Who has made the biggest possible number? And the smallest? Ask five pupils who have made five different numbers to come to the front, and put themselves in order from smallest to largest.

Repeat as above. Ask pupils to compare their number with the person sat next to them. Choose several pairs and ask which sign (> or <), we could write between them.

Paired pupil work Pupils work in pairs. They each write a number of million, e.g.

5,000,000 and seven spaces □,□□□,□□□ . They then take turns to roll the dice and write the number they get in one of the spaces.

After seven rolls of the dice each, whose number is closest to the number of million they wrote? They win.

Repeat several times.

Teacher input with whole class Ask one pupil to hold 0 at the extreme left of the front of the

classroom and another to hold 10,000,000 at the other. Write six numbers such as 956,988; 1002; 9,462,884; 4,999,999; 2,345,897 and 6,023,455 on the board. Read each though together.

Ask a pupil to secretly choose one and stand approximately where this number should be on the line. The rest of the class work out which number was chosen. Repeat at least twice.

Ask pupils to Google a googol and other large numbers before the third session (see homework).


Week 1 Place value Day 3Objective: Be aware of really large numbers, e.g. a googol

You will need: pdf of interesting facts involving large numbers (see resources)

Teacher input with whole class Show pupils how to write a million, a billion, a trillion and discuss the

numbers of zeros in each. Challenge them to think of where we might need each number. Discuss the pdf of interesting facts involving large numbers. Ask pupils to report back interesting facts that they found.

If a million people were to stand side-by-side in a line, how long do you think the line would be? How could we work it out? Agree an estimate of the amount of space taken up by each person standing, e.g. 50cm. What should we do now? Agree that it might be better to think of 50cm as ½ a metre, and multiply this by one million. Half a million metres. How many kilometres is that? Show 500km on a map of Britain to give pupils a sense of the distance.

Paired pupil work Pupils choose one from: 1. If you could make a ladder to reach the

moon and the top of one rung was 25cm from the top of the previous one, how many rungs would be needed? (The distance from the Earth to the Moon is approximately 385,000km.) 2. If a million people held hands, how far round the world would they stretch? How many would it take to reach right round the world? (The circumference of the earth is approximately 40,000km.)

Teacher input with whole class Ask pupils to report back on what they found out about a googol. (E.g.

a googol is 1, followed by 100 zeros, more than the number of atoms in the universe, so, if you tried to write a googol lines on a piece of paper, for example, you couldn't do it, because you'd run out of atoms to use as paper and pencil. And it would take much longer than a lifetime to write all of it down. The name was suggested by the 9-yr old nephew of an American mathematician.) The Google search engine takes its name from the word googol. Why do you think this is?


Week 2 overview Addition

Objectives

Add pairs of two-digit numbers quickly and efficiently, both whole numbers and those with one or two decimal places

Use strategies for adding pairs of two-digit numbers to add larger numbers

Add large but ‘friendly’ numbers mentally

Use column addition to add whole and decimal numbers efficiently

Choose when to use a mental or written method according to the numbers involved


1-9 digit cards, Addition loop cards (see resources), an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a



have difficulty when the addition means passing through the next multiple of 100/1000/10,000, e.g. 84,998 + 10; give more practice counting in 10s/100s through multiples of 100/1000;

try to keep all the steps in their head and lose track; encourage them to use jottings, modelling how to use these if necessary;

use a written method automatically when adding numbers with three or more digits, rather than first looking at the numbers involved to see if they can work out the answer mentally.


http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a


Week 2 Addition Day 1Objectives: Add pairs of two-digit numbers quickly and efficiently, both whole numbers and those with one or two decimal places; Use strategies for adding pairs of two-digit numbers to add larger numbers; Add large but ‘friendly’ numbers mentally

You will need: 1-9 digit cards, Addition loop cards (see resources)

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. One person has to say the total. If correct, they get a point.

Continue, taking turns to be the one to say the total. If a person makes an error, they lose 2 points! After five minutes who has a minus score?!

Teacher input with whole class Shuffle the loop cards, and give one to each pupil. There are 30 cards,

so if you have more or fewer than 30 pupils, adjust accordingly giving some pupils two cards or one between two pupils, so that all cards are given out. Explain that a question is on one card, and the answer on another. So pupils will 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 as clearly as they can. Say that it is fine to write down the question so they can sit and stare at it whilst they work out the answer!

The pupil who has the card with ‘1 million! / 750 + 250’ starts. The pupil with 1000 at the top of their card says ‘1000’ and then reads the rest of the card. Eventually one pupil will read ‘650,000 + 350,000’ The pupil who read the first card answers ‘one million’ to complete the loop.

Time how long it takes to complete the loop and use the cards on another occasion to see if the pupils are any quicker.


Week 2 Addition Day 2Objectives: Use column addition to add whole and decimal numbers efficiently

You will need: none required

Teacher input with whole class Write the following additions on the board and ask pupils to list them

in order of size of answer, approximating to do so. Then they work as a pair to add the numbers and check their orders.

45,789 + 32,561; 78,456 + 2,397; 56.789 + 21.807; 65.723 + 8.24; 4587 + 8724 + 2937; 457 + 287 + 472 + 489

Paired pupil work Ask pupils to use only digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 to create

additions of two whole numbers, (no number with fewer than 4 digits). Challenge them to find the biggest and smallest answers.

Repeat, this time they can make numbers with 1, 2 or 3 decimal places.

Teacher input with whole class Discuss as a class what makes an addition harder than others. Discuss

that it is not just the number of digits (as 5,000,000 + 2,000,000 is easy!) but the numbers of ‘carries’, whether there are different numbers of decimals places etc.

Paired pupil work Ask pupils to work in pairs to make up five really hard additions for

another pair to work out, but before they hand over their list, they must have first worked out the answers themselves!


Week 2 Addition Day 3Objectives: Choose when to use a mental or written method according to the numbers involved

You will need: an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a

Teacher input with whole class Write the following additions on the board and ask pupils to agree a

ranking from easy to hard, writing them in order on their whiteboards: 42,000 + 35,000 768 + 299 + 879 32,453 + 24,302

25,983 + 39,897 192,200 + 4,100 3.678 + 36.884.233 + 2.331 456,879 + 874,789 456,374 + 199,999

Each pair compares their list with another pair’s, and justifies their order.

The four pupils divide the calculations between them and revise their order if necessary.

Take feedback and discuss what makes additions easier or harder, which pupils could work out in their heads, and for which they needed to use column addition.

Ask each group of four to come up with a really easy addition with lots of digits that they think the rest of the class can work out before you can work out the answer on a calculator. There must be at least two digits other than zero in each number! A pupil from each four comes out to the front of the class and shows the addition on a whiteboard to you and the class. If you can use a calculator to work out the answer first, you win a point. If the class work out the answer first, they win a point. Repeat for each four. Who won, teacher or class?!

Challenge each four to come up with an addition where they would really prefer to use a calculator! They must be able to explain why.



Week 3 overview Subtraction

Objectives

Subtract pairs of two-digit numbers quickly and efficiently, both whole numbers and those with one or two decimal places

Use strategies for subtracting pairs of two-digit numbers to subtract larger numbers

Subtract smaller numbers by counting back

Subtract large and decimal numbers by counting up

Use decomposition to subtract whole numbers efficiently

Choose when to use decomposition or counting up according to the numbers involved


1-9 digit cards, Subtraction loop cards (see resources), an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a



have difficulty when the subtraction means passing through the previous multiple of 100/1000/10,000, e.g. 90,000 – 10; give more practice counting in 10s/100s through multiples of 100/1000/10,000;

try to keep all the steps in their head and lose track; encourage them to use jottings, modelling how to use these if necessary;

use decomposition automatically when subtracting numbers with three or more digits, rather than first looking at the numbers involved to see if they can work out the answer mentally or use counting up if there are several zeros in the larger number.




Week 3 Subtraction Day 1Objectives: Subtract pairs of two-digit numbers quickly and efficiently, both whole numbers and those with one or two decimal places; Use strategies for subtracting pairs of two-digit numbers to subtract larger numbers; Subtract smaller numbers by counting back

You will need: 1-9 digit cards, Subtraction loop cards (see resources)

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. One person has to say the difference. If correct, they get a point.

Continue, taking turns to be the one to say the difference between the two numbers. If a person makes an error, they lose 2 points! After five minutes who has a minus score?!

Write the following numbers on the board: 1,000,000; 100,000; 10,000 and 1,000. Pupils create a number with consecutive digits and subtract this from one of the numbers on the board, e.g. 10,000 – 4567 = 5433. Repeat this to subtract a number with consecutive digits from each of the numbers on the board.

Teacher input with whole class Take feedback and discuss how pupils performed the subtraction.

Remind them that it is much easier to count up when subtracting from a multiple of 1000. E.g. 4567 + 33 + 400 + 5000 = 10,000.

Shuffle the loop cards, and give one or more to each pupil. Ensure that all cards are given out. Explain that a question is on one card, and the answer on another. Pupils need to listen carefully and read questions and answers clearly. Say that it is fine to write down the question so they can sit and stare at it whilst they work out the answer!

The pupil who has the card with ‘7.5 / 1,000,000 – 100,000’ starts. The pupil with 900,000 at the top of their card says ‘900,000’ and then reads the rest of the card. Eventually one pupil will read ‘9.4 – 1.9’. The pupil who read the first card answers ‘7.5’ to complete the loop.

Time how long it takes to complete the loop and use the cards on another occasion to see if the pupils are any quicker.


Week 3 Subtraction Day 2Objectives: Subtract large and decimal numbers by counting up; Use decomposition to subtract whole numbers efficiently; Choose when to use decomposition or counting up according to the numbers involved


Teacher input with whole class Write the following subtractions on the board and ask pupils to list

them in order of size of answer, approximating to do so. Pupils then subtract each pair of numbers using column subtraction. Was their order correct? 45,739 – 32,561; 78,456 – 2,397; 56,732 – 21,807; 65,563 – 37,824

Repeat with the following subtractions, this time asking pupils to use counting up, drafting an empty number line to model counting up.

5000 – 3787; 4021 – 2789; 40,006 – 38,994; 4.23 – 3.78; 6.04 – 5.43, 7.2 – 3.78, 6.24 – 4.8, 4.356 – 2.789

As a class, discuss why the second group of subtractions might be easier to work out using counting up on a number line, whilst the first group are fine to work out using decomposition. For example, draw out that it might be easier to count up when there are zeros in the first number, or when subtracting decimals.

Paired pupil work Ask pupils to use only the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 to create

subtractions of two whole numbers, neither number with fewer than 4 digits. Challenge them to find the biggest and smallest answers. They choose to use either decomposition or counting up on the number line.

Repeat, this time they can make numbers with 1, 2 or 3 decimal places. They choose to use either decomposition or counting up on the number line.

Ask pupils to work in pairs to make up five really hard subtractions for another pair to work out, but before they hand over their list, they must have first worked out the answers themselves!


Week 3 Subtraction Day 3Objectives: Subtract large and decimal numbers by counting up; Use decomposition to subtract whole numbers efficiently; Choose when to use decomposition or counting up according the numbers involved


Teacher input with whole class Write the following subtractions on the board and ask pupils to agree a

ranking from easy to hard, writing them in order on their whiteboards: 42,000 – 39,000 768 – 301 32,453 – 24,387 45,007 – 39,897

192,200 – 4,100 36.78 – 6.45 4.231 – 3.7894.233 – 2.331 456,872 – 874,789 456,374 – 199,999

Each pair compare their list with another pair and justify their order. The four pupils divide the calculations between them and work out the

subtractions, either counting up or using column subtraction. Take feedback and discuss what makes subtractions easier or harder,

which pupils could work out in their heads, and for which they needed to use jottings or decomposition. Draw out that it is not just the number of digits (as 5,000,000 - 2,000,000 is easy!) but the numbers of ‘carries’, whether there are different numbers of decimal places etc.

Ask each group of four to come up with a really easy subtraction with lots of digits that they think the rest of the class can work out before you can work out the answer on a calculator. There must be at least two digits other than zero in each number! A pupil from each four will come out to the front of the class and show the subtraction on a whiteboard to you and the class. If you can use a calculator to work out the answer first, you win a point. If the class work out the answer first, they win a point. Repeat for each four. Who won, teacher or class?!

Challenge each four to come up with a subtraction where they would really prefer to use a calculator! They must be able to explain why.



Week 4 overview Mental multiplication

Objectives

Know all times tables up to 12 × 12

Find prime factors of two-digit numbers

Identify multiples of 2 to 12

Use tests of divisibility for 2, 3, 4, 5, 6 and 9

Use mental strategies for multiplication including doubling and halving


packs of 0 to 12 cards (see resources), packs of 1 to 9 digit cards or packs of playing cards, dice, Factor tree game at http://www.mathgoodies.com/factors/prime_factors.html



do not know their times tables. This lack of knowledge will really slow down their work in multiplication and division so use Simmering Term 1, week 4, day 1’s activities with tables as necessary; encourage them to turn the multiplication round, e.g. if they don’t know nine 6s, to use six 9s, or to use doubling, e.g. double four 6s to find eight 6s;

are unsure of equivalent calculations, e.g. 64 × 50 = 32 × 100.


http://www.mathgoodies.com/factors/prime_factors.html

Week 4 Mental multiplication Day 1Objectives: Know all times tables up to 12 × 12; Find prime factors of two-digit numbers

You will need: 0 to 12 cards (see resources), Factor tree game at http://www.mathgoodies.com/factors/prime_factors.html

Paired pupil work Pupils write six products on their whiteboard and draw a circle round

each one. E.g. 6, 24, 35, 56, 32 and 60. Shuffle a pile of 1-9 digit cards, place in a pile face down and turn over

the top two. Show the class. Any pair with the product of these two cards can cross it out. First to cross out all six products says ‘Bingo!’

Teacher input with whole class Play the Factor tree game. Ask pupils to suggest a factor of the given

number. Click on the white box, enter the number they suggest and press enter. Continue until all the prime factors are found.

Press ‘play again’ to choose a new number and repeat. If the given number only has a few factors, click ‘play again’ to change it.

Paired pupil work Click ‘play again’ and ask pupils to work in pairs to create their own

factor tree for the next number. Afterwards compare their factor trees, drawing out that they may have different trees but all give the same group of prime factors at the end.

Repeat.HSNP © Hamilton 2012 Page 15 Shining Term 1

http://www.mathgoodies.com/factors/prime_factors.html

Week 4 Mental multiplication Day 2Objectives: Identify multiples of 2 to 12; Use tests of divisibility for 2, 3, 4, 5, 6, and 9

You will need: packs of 1 to 9 digit cards or packs of playing cards

Paired pupil work Pupils play in pairs and use four packs of 1 to 9 digit cards, or use a

pack of playing cards, treating Aces as 1 and removing the 10s, Jacks, Queens and Kings.

They shuffle 1, 2, 3, 4, 5, 6, 7, 8 and 9, and place in a pile face down. They shuffle the remaining cards and deal eight each, face up.

Pupils turn over the top card and use their cards to make a two-digit multiple of this number, e.g. turn over 6, and try to make 12, 18, 24 etc. They place these pairs of cards to one side.

Then they take cards from the rest of the pack to fill their spaces so they still have 8 cards again and repeat. They carry on playing until there are no more cards left in the pack. The player with the most pairs of cards wins.

Teacher input with whole class Write the numbers 18, 24, 30, 27, 87, 117, 248, 4385 and 306 on the

board. Which are multiples of 2? How do you know? Write them on your whiteboards.

Which are multiples of 3? Remind pupils that if the sum of the digits in a number is divided by 3, then the whole number is also divisible by 3.

How can we tell if a number is divisible by 6? (Divisible by both 2 and 3).

And by 9? (Digit sum is divisible by 9). Challenge pupils to work in pairs to write really big multiples of 2, 3, 4,

5, 6 and 9.


Week 4 Mental multiplication Day 3Objective: Use mental strategies for multiplication including doubling and halving

You will need: dice

Paired pupil work Pupils play the following game in pairs. They take it in turns to roll a

dice twice to make a 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, so score 8 points. The winner is the person with the highest score when you ask them to stop.

Teacher input with whole class Discuss how pupils can multiply by 4 and 8 (using doubling). Ask pupils to explain to their partners how they would work out 64 × 5.

Draw out adding 60 × 5 and 4 × 5, but also multiplying 64 by 10 and halving. How might you multiply 64 by 50? And by 500?

Sketch a 64 × 50 rectangle, cut out and then cut in half and reassemble to form a 32 by 100 rectangle to show that both have the same area.

Repeat for 16 × 25. Also draw out the strategy of halving 16 and doubling 25, to give 8 × 50, and 4 × 100, which gives the same answer.

Paired pupil work Challenge pupils to work in pairs to come up with multiplications

which initially look quite difficult but because of the numbers involved but can be easily worked out using mental strategies, e.g. 248 × 250 (using 124 × 500, 62 × 1000).

Ask several pairs of pupils to share their ‘fiendish’ multiplications and the rest of the class work them out.


Week 5 overview Division

Objectives

Use multiplication facts to work out divisions

Use mental strategies to work out divisions with ‘friendly’ numbers

Divide two- and three-digit numbers by single-digit numbers

Divide three- digit numbers by two-digit numbers

Express remainders as fractions


Division bingo at http://www.topmarks.co.uk/Flash.aspx?f=BingoMultiplicationv9, Remainders after division bingo at http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/848/remainders.swf



do not know their multiplication facts and so can’t make use of them to solve divisions;

try to partition numbers into 100s, 10s and 1s to divide (as they would for multiplication), rather than into a multiple of 10/100 of the divisor and the rest, e.g. partition 372 into 300, 70 and 2 to divide by 4 rather than in 360 and 12;

do not know halves of odd numbers of multiples of 10/100, e.g. 70 and 90, 700 and 900 and so can only halve numbers with even digits.


http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/848/remainders.swf


http://www.topmarks.co.uk/Flash.aspx?f=BingoMultiplicationv9


Week 5 Division Day 1Objectives: Use multiplication facts to work out divisions; Use mental strategies to work out divisions with ‘friendly’ numbers

You will need: Division bingo at http://www.topmarks.co.uk/Flash.aspx?f=BingoMultiplicationv9, Remainders after division bingo at http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/848/remainders.swf

Teacher input with whole class Play Divisions bingo. Choose ‘random divisions missing number’ and

ask pupils to choose five numbers to write on their whiteboards. Click to show each question. Pupils ring the answer if they have it. Keep a record of the questions. The first to ring all five numbers wins.

Now play Remainders after division bingo. Pupils again choose five numbers, but this time ring them if they have the remainder after each given divisions.

Paired pupil work Pupils work in pairs to write 11 divisions, each with a different

remainder from 1 to 11. Each division must have a different divisor! They compare their list of divisions with a neighbouring pair.

Teacher input with whole class Write the following divisions on the board and ask pupils to discuss

how they might solve them: 420 ÷ 5, 448 ÷ 8, 872 ÷ 4, 560 ÷ 7, 4200 ÷ 6 Draw out strategies such as dividing by 10, then doubling to divide by

5, and halving 2/3 times to divide by 4/8. Pupils solve each.






Week 5 Division Day 2Objectives: Divide two- and three-digit numbers by single-digit numbers; Express remainders as fractions


Teacher input with whole class Write 96 ÷ 6 on the board. Ask pupils if there are more than ten 6s in

96. Subtract 60 from 96 and write 10 at the top. How much is left? How many 6s in 36? Write 6 at the top and subtract 36. Agree that there is no remainder.

10 + 6 = 16 6 ) 96 - 60 36 - 36 0

Repeat for 115 ÷ 8. Agree that there is a remainder of 3.

Paired pupil work Write the following divisions on the board:

92 ÷ 4, 55 ÷ 4, 85 ÷ 6, 93 ÷ 8, 100 ÷ 7, 127 ÷ 5, 87 ÷ 3, 150 ÷ 6, 159 ÷ 3 , 191 ÷ 7, 106 ÷ 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! Ask them to keep a record of all the divisions with answers.

Teacher input with whole class Ask pupils what the answer was to 106 ÷ 8. Agree that the remainder

was 2 and remind pupils how we can also divide this 2 by 8 instead of leaving it as a remainder, to give the fraction 2/8, which can be simplified to ¼. Ask pupils to write the remainders to the other divisions as fractions, simplifying where possible.


Week 5 Division Day 3Objective: Divide three-digit numbers by two-digit numbers


Write 896 ÷ 26 on the board. Ask pupils to list multiples of 26 to 10, using the previous multiples of 26 to help them, e.g. adding 26 and 52 to give three lots of 26, doubling four lots of 26 to give 8 lots of 26. Are there are more than ten 26s in 796? More than 20? More than 30? More than 40? Pupils use this list of multiples to help. Subtract 780 from 896 and write 30 at the top. How much is left? How many 26s in 116? Use your list of multiples to help. Write 4 at the top and subtract 104. Agree that the remainder is 12.

30 + 4, r12 34 r12 26 ) 896 - 780 116 - 104 12

Repeat for 715 ÷34.

Paired pupil work Write the following numbers on the board:

456 756 432 945 634 Pupils take it in turns to choose a number and divide it by a number

between 10 and 50 of their choice – the number may not be a multiple of ten! If the answer is between 10 and 20 they win 10 points, if the answer is between 20 and 30 they win 20 points and if the answer is between 30 and 40 they win 30 points, otherwise they score nothing! Ask them to keep a record of all the divisions with answers.

Teacher input with whole class Discuss how pupils could check their work. Draw out using

multiplication and adding on the remainder. Pupils check three of their divisions using multiplication.


Week 6 overview Decimals

Objectives

Know what each digit represents in numbers with three decimal places

Use place value for tenths, hundredths and thousandths to complete additions and subtractions

Compare and order numbers with three decimal places

Place numbers with three decimal places on a line

Round to the nearest whole unit

Write numbers with four decimal places


dice, calculators, large digits cards and a card with a decimal point, a counting stick, an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a, Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx?f=DartboardRoundingv2



think that 3.145 is more than 3.7 because 145 is more than 7;

write 3.450 when multiplying 3.45 by 10 saying that we add a zero when multiplying by 10; encourage them to see how the value of each digit changes according to its place in a number and that whilst adding a zero is a useful shortcut, it only applies to whole numbers.


http://www.topmarks.co.uk/Flash.aspx?f=DartboardRoundingv2



Week 6 Decimals Day 1Objectives: Know what each digit represents in numbers with three decimal places; Use place value for tenths, hundredths and thousandths to complete additions and subtractions

You will need: 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 Enter the number 3.572 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 0.5, five tenths.

Repeat with 7.256 and 8.625.

Paired pupil task Pupils write a four-digit number with three decimal places, all digits

different and on the dice, e.g. 5.263. They roll the dice. If the number is in their number, they subtract that number of 1s, 0.1s, 0.01s or 0.001s. E.g., they write 5.263, roll 6, so subtract 0.06. They write the answer (5.203).

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 the number 5.545 on the board. Ask pupils what must be added

to make 5.555. Repeat with 5.325, 5.541 and 5.352. Write the numbers 5.758 and ask what must be subtracted to make

5.555. Repeat with 5.859, 5.675 and 6.589.

Paired pupil task Pupils take it in turns to roll a dice to make four-digit numbers with

three decimal places. They work out what must be added to make all 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.



Week 6 Decimals Day 2Objectives: Compare and order numbers with three decimal places; Place numbers with three decimal places on a line: Round to the nearest unit

You will need: dice, Dartboard rounding at http://www.topmarks.co.uk/Flash.aspx?f=DartboardRoundingv2

Teacher input with whole class Write 3.7 and 3.145 on the board. Which number is larger? Why?

Agree that it has 7 tenths whereas the 2nd number only has one tenth. Paired pupil work Pupils work in pairs to roll a dice to get three different digits. They use

the digits to write six different numbers less than 1 each with three decimal places and write them in ascending order.

Teacher input with whole class Use Dartboard rounding, choosing ‘nearest kilogram’. Click on the

green segments and ask pupils to round each weight (mass) to the nearest whole kilogram. If necessary, draft a line between neighbouring whole kilograms and discuss where the measurement should be placed. Ask pupils to round to the nearest 0.1 of a kilogram.

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 initials. Continue until one person has three numbers in a line without their opponent’s marks in between.



Week 6 Decimals Day 3Objective: Write numbers with four decimal places

You will need: large digit cards and a card with a decimal point, a counting stick

Teacher input with whole class Ask six pupils to hold the cards to show the number 4728.9. Ask them

to divide the number by 10 and move accordingly (showing 472.89). Repeat so that they show 47.289. What do you think will happen if we divide by 10 again? Write the number on your whiteboards. Ask the six pupils to move to show 4.7289. Discuss what each digit is worth.

Draw a place value grid with headings 100s, 10s, 1s, 0.01s, 0.001s and 0.0001s. Write the number 45.678 in the grid and ask pupils to divide this number by 10. Discuss the new value of each digit. Write the number 0.3446 and ask pupils to multiply the number by 10. Repeat with other numbers, multiplying by 10 and by 100 giving lots of practice at writing numbers with four decimal places.

Paired pupil work Write 4320, 14572, 124, 7421, 6, 13.58 and ÷10, ÷ 100 and ÷1000 on

the board. Pupils choose a number, divide by 10, 100 or 1000 and show their partner the answer. Can the partner guess what division they have done? Repeat.

Teacher input with whole class Use the counting stick to quickly support counting in tenths from 0 to

1. Point to between 0.1 and 0.2 and ask pupils to write a number that goes between 0.1 and 0.2, e.g. 0.15, 0.12 etc. Repeat with other neighbouring divisions.

Use the counting stick to quickly support counting in hundredths from 0 to 0.1. Point to between 0.01 and 0.02 and ask pupils to write a number which goes between 0.01 and 0.02, e.g. 0.015, 0.012 etc. Repeat with other neighbouring divisions.

Repeat, this time counting in steps of 0.001 from 0 to 0.01. Point to between 0.001 and 0.002 and ask pupils to write a number which goes between 0.001 and 0.002. Repeat for other neighbouring divisions.


Week 7 overview Addition patterns

Objectives

Add several numbers mentally

Identity patterns

Solve mathematical puzzles


calculators, copies of Franklin’s magic square (see resources), animation at http://www.math.wichita.edu/~richardson/8x8-ani.html



are not fluent in adding two-digit numbers;

are not confident to play with numbers but when solving puzzles for example give up if their first attempt is not successful; make it clear that trial and improvement is part of the mathematics!


http://www.math.wichita.edu/~richardson/8x8-ani.html

Week 7 Addition patterns Day 1Objective: Solve mathematical puzzles


Teacher input with whole class Draw the following square on the board and ask pupils to work in pairs

to place numbers 1, 2, 3, 4, 6, 7, 8 and 9 in it to make each row, column and diagonal add up to 15:

5

Ask each pair to compare their solutions with another pair. Can they see any patterns? Where are the even numbers? Odd numbers? Can they see a z-shape of consecutive numbers? Why do they think 5 goes in the middle?

83 4

1 5 96 7 2

Using these patterns, ask them to create another magic square, using the same nine numbers and total.

Paired pupil work Challenge pupils to create their own magic square where every row,

column and diagonal has a total of 18 using numbers 2 to 10. Suggest they first think about what number might go in the middle (6).

9 4 52 6 10


7 8 3


Week 7 Addition patterns Day 2Objectives: Add several numbers mentally; Identity patterns


Teacher input with whole class Show Albrecht Dürer’s magic square:

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

Say that Dürer produced this square in 1514 (can they see they date in the square?) and this is probably the first example seen in Europe although similar squares existed in China 250 years earlier.

Ask pupils to find the total of each row.

Paired pupil work Pupils work in pairs to look for other groups of four numbers which

have a total of 34. They then swap ideas with another pair.

Teacher input with whole class Take feedback. Draw out the totals of squares of numbers, columns,

diagonals, the four corners, four corners of 3×3 squares and also squares linking numbers as below.

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1


Week 7 Addition patterns Day 3Objectives: Add several numbers mentally; Identify patterns

You will need: calculators, copies of Franklin’s magic square (see resources), animation at http://www.math.wichita.edu/~richardson/8x8-ani.html

Teacher input with whole class Explain that in 1750, Benjamin Franklin constructed a 8×8 magic

square (he later produced other larger squares). Describing his invention Franklin stated, "I was at length tired with sitting there to hear debates, in which, as clerk, I could take no part, and which were often so unentertaining that I was induc'd to amuse myself with making magic squares or circles" (Franklin 1793).

Give each pair a copy of the square and ask them to find the total of each row.

Paired pupils work Pupils work in pairs to find other patterns of numbers which also have

a total of 260. encourage them to look at ‘bent diagonals’, e.g.

Teacher input with whole class Take feedback and then play the animation to show many

combinations of numbers which have 260 as a total. Which did they spot? Did they spot any others?


52 61 4 13 20 29 36 45

14 3 62 51 46 35 30 19

53 60 5 12 21 28 37 44

11 6 59 54 43 38 27 22

55 58 7 10 23 26 39 42

9 8 57 56 41 40 24 24

50 63 2 15 18 31 34 47

16 1 64 49 48 33 32 17



Week 8 overview Subtraction of decimals

Objectives

Say how much is needed to make a decimal number up to the next whole number

Subtract pairs of numbers with one or two decimal places by counting up

Subtract pairs of numbers with two or three decimal places

Subtract pairs of numbers with three or four decimal places


stopwatch or clock/watch with second hand



think that 0.47 needs to be added to 0.63 to make 1, because they look for tenths which add to 1, not 0.9;

have difficulty adding the jumps together when using counting up, particularly if the numbers have different numbers of decimal places;

do not align digits correctly when using decomposition.


Week 8 Subtraction of decimals Day 1Objectives: Say how much is needed to make a decimal number up to the next whole number; Subtract pairs of numbers with one or two decimal places by counting up

You will need: stopwatch or clock/watch with second hand

Individual practice Ask pupils to find how many are needed to make the next whole

number for the numbers in the table below. Challenge them to see how many they can find in two minutes.

2.89 6.49 1.35 7.638.71 3.75 5.48 4.546.85 5.38 7.25 8.42

Teacher input with whole class Remind pupils how they can use counting up to solve subtractions such

as the following: 7.34 – 4.89, 6.2 – 3.78, 8.35 – 4.7. Ask pupils up to the board to draw a number line jotting to show the steps for each, e.g.

Paired pupil work Ask pupils to discuss in pairs which of the following subtractions will

have the greatest and least answers, and then to work each out:

4.23 – 2.67 9.2 – 5.83 7.35 – 4.6 8.78 – 4.59 6.7 – 4.44 7.8 – 5.62


3.78 6.2

2.2

4

0.22

0.22 + 2.2 = 2.42, so 6.2 – 3.78 = 2.42

Week 8 Subtraction of decimals Day 2Objectives: Say how much is needed to make a decimal number up to the next whole number; Subtract pairs of numbers with two or three decimal places

You will need: stopwatch or clock/watch with second hand

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 4.235 – 3.678. Draw a number line jotting to show the steps. Say that some pupils may combine the first two steps.

Also show how the same calculation can be done using decomposition. Repeat, showing both ways for 5.67 – 3.673, showing how it is helpful

to write a zero in the thousandths place when using decomposition. Emphasise the importance of aligning digits correctly.

Individual practice Ask pupils to find how many are needed to make the next whole

number for the numbers in the table below. Challenge them to see how many they can find in three minutes.

2.895 6.798 1.354 7.6388.971 3.756 5.482 4.5436.859 5.383 7.254 8.422

Teacher input with whole class How could you check your answers? Draw out using addition. Ask

pupils to use addition to check two of their subtractions.

Paired pupil work Pupils work in pairs to complete each of these using any method they

choose: 6.348 – 5.823 6.235 – 5.789 8.485 – 7.593 9.25 – 8.839 4.512 – 3.79 7.462 – 6.34


3.678 4.2353.68

0.002 0.235

4

0.32

Week 8 Subtraction of decimals Day 3Objective: Subtract pairs of numbers with three or four decimal places


Teacher input with whole class Remind pupils how they can use decomposition to work out

subtractions such as 6.0492 – 3.5418. Agree an estimate as a class first (e.g. 2.5) and then talk through each ‘carry’ involved in the subtraction.

Paired pupil work Ask pupils to use the digits 0 to 9, to create their own subtraction, e.g.

3.6159 – 2.4807. They repeat this three times. They must estimate the answer to each subtraction before doing it.

Challenge pupils to use the digits to create the smallest answer that they can and the largest answer that they can.

Take feedback.

Teacher input with whole class Discuss where pupils used the digit zero, drawing out that 6.4920 for

example is 6.492 but that in a subtraction such as 6.492 – 3.5418, it can be helpful to write a zero in the ten thousandths place. Model using decomposition for this subtraction, emphasising the importance of aligning digits correctly, 0.1s under 0.1s, 0.01s under 0.01s etc.

Individual practice Pupils use the digits 1 to 9 to create three subtractions of the form

□.□□□□ – □.□□□ and three of the form □.□□□ – □.□□□□. They estimate the answer to each, work them out and then use

addition to check two of them


Week 9 overview Multiplication

Objectives

Know all times tables up to 12 × 12

Find factors of two-digit numbers

Multiply three- and four-digit numbers by two-digit numbers

Multiply numbers with one or two decimal places


packs of 0 to 12 cards (see resources for week 4)



do not know their times tables. This lack of knowledge will really slow down their work in multiplication and division so use Simmering Term 1, week 4, day 1’s activities with tables as necessary; encourage them to turn the multiplication round, e.g. if they don’t know nine 6s, to use six 9s, or to use doubling, e.g. double four 6s to find eight 6s;

make place value errors when multiplying decimals, e.g. 6 × 0.7 = 0.42, or 0.3 × 0.2 = 0.6; encourage them to estimate the answer first; they might find it helpful to multiply 0.3 by 2 for example, and then divide by 10 to find 0.3 × 0.2.


Week 9 Multiplication Day 1Objectives: Know all times tables up to 12 × 12; Find factors of two-digit numbers

You will need: packs of 0 to 12 cards (see resources for week 4)

Paired pupil work Pupils work in pairs to each shuffle a pack of 0 to 12 cards and place in

a pile face down. They each take a card and turn over on the count of 3. The first person to say the product wins both cards. They continue playing until all the cards are gone. Who won most cards?

If time, play again.

Teacher input with whole class Ask pupils to choose six numbers between 1 and 100 and to write

them on their whiteboards. Call out times table questions up to 12 × 12, keeping a record of each. If they have the answer they ring it on their boards. The first person to ring three numbers wins.

Play again. Do they want to change their numbers this time?! Why? What sorts of numbers would be good to choose? Why is a number like 48 better than 31 or 15?

This time, use a variety of vocabulary, e.g. What is the product of 9 and 7? What is 6 multiplied by 4? 8 times 8 is?

Paired pupil work Ask pupils to work in pairs to investigate which number from 1 to 50

has most factors. (48 has the most with 10 factors) Take feedback. Discuss which numbers they immediately discounted

and why.


Week 9 Multiplication Day 2Objective: Multiply three- and four-digit numbers by two-digit numbers


Teacher input with whole class Write on the board: 542 × 38. Discuss how we can estimate the

answer, e.g. 540 × 40 = 21,600. Remind pupils how to use the grid method to keep track of the steps. Take particular care when discussing 30 × 500, e.g. working out 3 × 500 and then multiplying the answer by 10.

× 500 40 230 15,000 1200 60 16,260

8 4000 320 16 + 4336 20,596

Say that the first row records the steps in finding 30 × 542 and the second row records the steps in finding 8 × 542, and then we add these two products together to find the answer to 38 × 542.

Individual practice Ask pupils to practise using the grid method, using the same five digits

to create a different three-digit by two-digit multiplication. Next challenge them to find the largest possible answer (832 × 54 =

44,928).

Teacher input with whole class Remind pupils how we can use the same method to work out

calculations such as 4854 × 23, asking pupils to estimate the answer and then to find the exact answer. Ask them to use the same digits to find at least three other multiplications.

Show the following grid and ask pupils to work in pairs to work out what two numbers were multiplied together (2347 × 84):

×160,000 24,000 3200 560 187,760

8000 1200 160 28 + 9388197,148


Week 9 Multiplication Day 3Objective: Multiply numbers with one or two decimal places


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 them that the answer to 3 × 0.6 is a tenth of the answer to 3 × 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 □.□□ × □ and □□.□ × □. What was the largest answer they found? And the smallest?

Teacher input with whole class Demonstrate using the grid method to work out 34.52 × 24. Ask pupils to work out 3452 × 24 and to compare the two answers.

Draw out that the answer to 34.52 × 24 is 1/100 of the answer to 3452 × 24. How might you work out 72.35 × 63? Draw out using the grid method keeping the numbers as they are, or using the grid method to work out 7235 × 63, and then dividing the answer by 100. Ask pupils to choose which way they prefer and to work out the answer. Emphasise that making an estimate will help them to avoid making place value errors.

If the answer to 34.52 × 24 is 828.48, what do you think the answer to 34.52 × 2.4 might be? And 34.52 × 0.24?

Paired pupil work Pupils work in pairs to work out 34.52 × 16, 34.52 × 1.6, 34.52 x 0.16

and other related facts.


Week 10 overview DivisionObjectives

Divide three- and four-digit whole numbers by single-digit numbers

Divide three- and four-digit whole numbers by two-digit numbers

Express remainders as fractions

Express some remainders as decimals

Divide decimal numbers


counting stick, division grid (see resources), an IWB calculator, e.g. the one at http://www.crickweb.co.uk/ks2numeracy-tools.html#Toolkit%20index2a



do not know their multiplication facts and so can’t make use of them to solve divisions;

try to partition numbers into 1000s, 100s, 10s and 1s to divide (as they would for multiplication), rather than into a multiple of 10/100 of the divisor and the rest, e.g. partition 2572 into 2000, 500, 70 and 2 to divide by 4 rather than in 2400 and 172, then partitioning 172 into 160 and 12;

do not know the decimal equivalents for fifths and quarters;

are not secure in multiplying and dividing by 100.




Week 10 Division Day 1Objectives: Divide three- and four-digit whole numbers by single-digit numbers; Divide three- and four-digit whole numbers by two-digit numbers; Express remainders as fractions; Express some remainders as decimals


Teacher input with whole class Write 2896 ÷ 6 on the board. Ask pupils to estimate how many 6s

there might be in 2896. Agree that there are between 400 and 500 6s in 2896. Model the division on the board, subtracting 2400 and writing 400 at the top. How much is left? How many 6s in 480? Use how many 6s are in 48 to help. Agree that there are 80 6s, and write 80 at the top and subtract 480. Agree that there two 6s in 16 leaving a remainder of 4. What is 4 divided by 6? Draw out that 4/6 can be simplified to 2/3.

400 + 80 + 2, r4 Ans 482 2/3 6 ) 2896 - 2400 496 - 480 16 - 12 4

Repeat for 3815 ÷ 4, agree a remainder of 3 and discus how this can be written as ¾ or as 0.75, giving an exact answer of 953.75.

Individual practice Ask pupils to divide 3277 by 4, 5, 6 and 7 expressing the remainder as a

decimal fraction where they can.

Teacher input with whole class Ask pupils to list multiples of 16 to 10 × 16, using the previous

multiples of 16 to help them and then talk through the division 2898÷ 16. Write the reminder as 2/16, simplifying to 1/8.

Ask pupils to divide 2898 by 12, 14 and 15, expressing the remainder as a fraction or decimal where they can.


Week 10 Division Day 2Objective: Divide decimal numbers


Teacher input with whole class Ask pupils to work out 3456 ÷ 6. Show 345.6 ÷ 6 on the calculator and compare the two answers. So

how do you think you could work out 345.6 ÷ 6 without a calculator? How do you think you could work out 34.56 ÷ 6 without a calculator?

Agree that they could divide the answer to 3456 ÷ 6 by 100. Check with the calculator to see that this is correct.

Ask pupils to work out 3456 ÷ 16, and use this to find the answers to 345.6 ÷ 16 and 34.56 ÷ 16.

Take feedback.

Paired pupil work Ask pupils to work out the following divisions and then work in pairs to

use the answers to derive related decimal division facts:4528 ÷ 8 3428 ÷ 4 1792 ÷ 7 2224 ÷ 8

2958 ÷ 14 3136 ÷ 13 Take feedback.

Teacher input with whole class How could we find the answer to 3456 ÷ 1.6? Will the answer be bigger

or smaller than the answer to 3456 ÷ 16? Why? Take pupil’s suggestions and test them out using the calculator.

Ask them to use some of their previous divisions to work out other related divisions, i.e. 2958 ÷ 1.4 and 3136 ÷ 1.3.

Take feedback.



Week 10 Division Day 3Objective: Divide decimal numbers

You will need: counting stick, division grid (see resources)

Teacher input with whole class Count along the counting stick in steps of 0.3. Stop and ask questions

such as: so how many 0.3s are in 1.2? How many 0.3s are in 2.1? Explain that Alfie makes friendship bracelets by threading beads on

pieces of elastic. He has 0.8m of elastic and each bracelet needs 0.2m. Ask pupils to discuss in pairs how many bracelets he can make with 0.8m. Agree that there are four 0.2s in 0.8. Record 0.8 ÷ 0.2 = 4.

Point out that if we multiply BOTH numbers by 10, we do not alter the division (what we are dividing into and what we are dividing are both ten times larger and so the answer is the same). Hence we could check our answer to 0.8 ÷ 0.2 by 8 ÷ 2 = 4.

What if he had 1.2 m of elastic? 1.8m? Ask pupils to record the corresponding division sentences (1.2 ÷ 0.2 which is same as 12 ÷ 2).

Write 0.9 ÷ 0.3. How can we work out the answer to this? Agree that we can think of this as how many 0.3s there are in 0.9, answer 3.

Individual practice Pupils work out: 0.4 ÷ 0.2; 1.5 ÷ 0.3; 1.6 ÷ 0.4; 3.5 ÷ 0.5; 2.8 ÷ 0.7. Suggest that they then create similar divisions for each other to solve.

Teacher input with whole class Display grid and play Three in a line. Divide class into 4 teams, assign a

colour to each. Each team take turns to choose a number from the grid, and say which two numbers below the grid have this number as a quotient. If correct, ring the chosen grid number in their colour. Carry on playing until one team has three ringed numbers in a line.

2 3 7 3 98 6 5 6 24 12 2 9 127 3 6 4 8

1.4 2.4 4.8 1.2 2.7 5.4 3.5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9



ShiningTerm 1

Homework

Name ___________________________


Week 1 Place value

Write the value of the digit 5 in each of the following numbers:4,653,199 2,992,503 6,523,469

Add 100,001 to each number.

Subtract 10 from 1,000,000, 100,000 and 10,000.

Roll a dice six times and use the digits to record two numbers. Write a number in between. Repeat four more times.

Use books and/or the internet to find interesting facts that include large numbers. Google a googol! Be ready to report back in the next session.Write a googol, and time how long it takes you to write all the digits.


Week 2 Addition

Draw a pyramid of boxes, beginning with five on the bottom row. Use the numbers 0.5 to 0.9 in the bottom row in any order. Add neighbouring numbers and write the number in the box that overlaps the pair of numbers. Continue up the pyramid until they reach a total at the top.

What number did you get at the top of the pyramid? Move the numbers around in the bottom row. Can you get a bigger total at the top?

Write six additions of pairs of numbers. Each number must have six digits. Write three that you could work out in your head, and three where you would prefer to use a written method. You can use whole numbers or decimal numbers. Find the answer to each.


0.5

0.6

0.7

0.8

1.1

1.3

1.5 0.

9

1.7

Week 3 Subtraction

Play Speed grid challenge at http://www.oswego.org/ocsd-web/games/SpeedGrid/Subtraction/urikasub2res.html. See if you can answer 10 questions in two minutes!

Roll a dice and subtract the number from 100,000. Repeat rolling the dice and subtract the number from the previous answer. What number can you get down to in two minutes?

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.□.

Which of these subtractions will have the smallest answer? And the largest? Find the answers to each to check.

5002 – 3877 40,005 – 39,997 6379 – 4572 524 – 378

7284 – 2874 12,723 – 9,487 45.2 – 27.8


http://www.oswego.org/ocsd-web/games/SpeedGrid/Subtraction/urikasub2res.html


Week 4 Mental multiplication

Play Hit the question at http://www.wmnet.org.uk/resources/gordon/Hit%20the%20button%20v9.swf. Choose ‘hit the question’ and choose the 7 times table or the times table you need to practise. Answer as many questions as you can in one minute. Repeat for the 8 times table or another times table you need to practise.

Follow the instructions at http://www.bored.com/mysticalball/.

Can you fathom out how it works? Choose several numbers, what do the final numbers have in common? Look for other numbers on the grid which have the same symbol. What do you notice?

Work out the following multiplications mentally (you can make some jottings). They are not as difficult as they might seem at first, you don’t need to use a written method but remember your halving and doubling tricks!

67 × 4, 112 × 8, 72 × 50, 248 × 25, 36 × 15, 84 × 75


http://www.bored.com/mysticalball/

http://www.wmnet.org.uk/resources/gordon/Hit%20the%20button%20v9.swf


Week 5 Division

Play Are you a Math Magician? at http://resources.oswego.org/games/mathmagician/mathsdiv.html. Choose division by 6, 7, then 8. Can you answer 20 questions in one minute? Write down the time for each set of division facts.

See if you can reach a score of 100 by answering divisions correctly at http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html. Choose Level 3. Record both your score and how many you got correct and incorrect.

A farmer has 346 eggs. She can store them in trays of 12, 15 or 18. She wants as few eggs left over as possible. Which size tray would be best?


http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html

http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html

http://resources.oswego.org/games/mathmagician/mathsdiv.html

Week 6 Decimals

Write what must be subtracted to eliminate the digit 5 in each of the following numbers:

7.256 3.615 4.05 5.582 4.565 5.855

Write □.□□□, □.□□□, □.□□□. Roll a dice and choose where to put the digit rolled in one of the three numbers. You are aiming to make three numbers each with three decimal places such that the first number is the smallest and the last is the greatest. But you must write in each digit after each dice roll!

Write a number in between each pair of numbers below:

4.1 □.□□ 4.2

3.45 □.□□□ 3.46

6 □.□□□ 6.01

5.06 □.□□□ 5.07

3.725 □.□□□□ 3.726


Week 7 Addition patterns

In this arrangement of eight dominos the sum of dots in each column, row and diagonal is 7.

Use a set of dominoes (or draw them) to see if you can find another arrangement of dominoes which has 7 as a total of each row and column. If you can also make each diagonal have a total of 7, that would be really impressive! Also try and make each row and column add up to 8 or 9.

Read about Dürer’s square at http://www.mathcats.com/explore/puzzles/magicsquare.html.

Then use the Magic carpet at http://www.mathcats.com/explore/puzzles/magiccarpet1.html to try and find other magic 4× 4 squares. Each row, column, diagonal, four corners, each 2×2 square should all have a total of 34.


http://www.mathcats.com/explore/puzzles/magiccarpet1.html

http://www.mathcats.com/explore/puzzles/magicsquare.html

Week 8 Subtraction of decimals

Use 1-9 digit cards or shuffle a set of playing cards, first removing the 10s, Js, Qs, Ks and Jokers. Use the Ace as 1. Place face down and take 3. Use them to make at least two numbers less than 1 with three decimal places, e.g. use 4, 8 and 1 to make 0.148 and 0.841. Work out how many more are needed to make 1, e.g. 0.841 + □ = 1. Repeat five more times.

Repeat, but this time making four-digit numbers and finding how many more are needed to make 10, e.g. 4.782 + □ = 10. Write four additions like this.

Use pairs of these numbers to make subtractions where the answer is less than 2. How many can you find?


3.4 5.024 4.17 3.89

2.879 5.2244

7.834 6.78

3.5789

6.4 4.72 9.89

8.389 8.05 4.387 6.2

Week 9 Multiplication

Find which number between 50 and 100 has the greatest number of factors.

Use grid multiplication to find the area of these rectangles:

Multiply each of these numbers by a number between 15 and 30. Try to get the answer as close to 100 as you can. Which answer was closest?


24cm

54.7cm

18cm

7.6cm

4.54 3.26 6.24 5.78

32.4cm

1.4cm

Week 10 Division

Work out the first division in each group, and then use the answers to work out the remaining divisions:

3024 ÷ 7 302.4 ÷ 7 30.24 ÷ 7

3204 ÷ 6 320.4 ÷ 6 32.04 ÷ 6

4032 ÷ 8 403.2 ÷ 8 40.32 ÷ 8

3302 ÷ 13 330.2 ÷ 13 33.02 ÷ 13

3584 ÷ 14 358.4 ÷ 14 35.84 ÷ 14

Copy and fill in the missing numbers:

□ × 0.2 = 0.6 □ × 0.4 = 3.2 4 × □ = 2.4 □ × 0.4 = 2

0.6 ÷ 0.2 = □ 2.5 ÷ 0.5 = □ 1.8 ÷ 0.3 = □ 2.1 ÷ □ = 0.7

Which of the following divisions can’t be right and why? 2547 ÷ 6 = 424.5 3456 ÷ 17 = 203 17/5

284.8 ÷ 8 = 35.6 37.76 ÷ 16 = 23.6 2.4 ÷ 0.4 = 0.6

Find the correct answers to each.



Numeracy

Shining

Term 1

Homework answers


Week 1 Place value

Write the value of the digit 5 in each of the following numbers:4,653,199 2,992,503 6,523,469

50,000 500 500,000Add 100,001 to each number.

4,753,200 3,092,504 6,623,470

Subtract 10 from 1,000,000, 100,000 and 10,000.999,990, 99,990 and 9,990

Roll a dice six times and use the digits to record two numbers. Write a number in between. Repeat four more times. E.g. 451,462 and 244,561 325,999 is in between.

Use books and/or the internet to find interesting facts that include large numbers. Google a googol! Be ready to report back in the next session.Write a googol, and time how long it takes you to write all the digits.

A googol is a 1 with one hundred 0s after it. It is hoped that pupils willdiscover a range of interesting facts.


Week 2 Addition

Draw a pyramid of boxes, beginning with five on the bottom row. Use the numbers 0.5 to 0.9 in the bottom row in any order. Add neighbouring numbers and write the number in the box that overlaps the pair of numbers. Continue up the pyramid until they reach a total at the top.

What number did you get at the top of the pyramid? Move the numbers around in the bottom row. Can you get a bigger total at the top?

For pupils to get the biggest total (12.5), 0.5 and 0.6 should start on the outside and 0.9 in the centre.

Write six additions of pairs of numbers. Each number must have six digits. Write three that you could work out in your head, and three where you would prefer to use a written method. You can use whole numbers or decimal numbers. Find the answer to each.

E.g. 245,684 + 375,250 = 620,934 (written method)470,985 + 199,999 = 670,984 (in their head)


0.5

0.6

0.7

0.8

1.1

1.3

1.5

2.4 2.8

5.2

0.9

1.7

3.2

6

11.2

Week 3 Subtraction

Play Speed grid challenge at http://www.oswego.org/ocsd-web/games/SpeedGrid/Subtraction/urikasub2res.html. See if you can answer 10 questions in two minutes!

This is a computer game.

Roll a dice and subtract the number from 100,000. Repeat rolling the dice and subtract the number from the previous answer. What number can you get down to in two minutes?

E.g. 100,000 – 5 = 99,995; 99,995 – 4 = 99,991; 99,991 – 4 = 99,987…

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: 6.245 – 3.789 = 2.4566.823 – 3.904 = 2.9196.428 – 3.763 = 2.6656.5 – 3.678 = 2,8226.258 – 3.5 = 2.758

Which of these subtractions will have the smallest answer? And the largest? Find the answers to each to check.

5002 – 3877 = 1125 40,005 – 39,997 = 8 (smallest)

6379 – 4572 = 1807 524 – 378 = 146

7284 – 2874 = 4410 (largest) 12,723 – 9,487 = 3236

45.2 – 27.8 = 17.4




Week 4 Mental multiplication

Play Hit the question at http://www.wmnet.org.uk/resources/gordon/Hit%20the%20button%20v9.swf. Choose ‘hit the question’ and choose the 7 times table or the tines table you need to practise. Answer as many questions as you can in one minute. Repeat for the 8 times table or another times table you need to practise.


Follow the instructions at http://www.bored.com/mysticalball/.

Can you fathom out how it works? Choose several numbers, what do the final numbers have in common? Look for other numbers on the grid which have the same symbol. What do you notice?

Every possible answer shares the same symbol, so whatever number you choose, the symbol in the crystal ball will be the same! NB: The symbols change sometimes but all the possible answers will be the same as one another!

Work out the following multiplications mentally (you can make some jottings). They are not as difficult as they might seem at first, you don’t need to use a written method but remember your halving and doubling tricks!

67 × 4 = 268, 112 × 8 = 896

72 × 50 = 3600, 248 × 25 = 6200

36 × 15 = 540, 84 × 75 = 6300


http://www.bored.com/mysticalball/



Week 5 Division

Play Are you a Math Magician? at http://resources.oswego.org/games/Mathmagician/mathsdiv.html. Choose division by 6, 7, then 8. Can you answer 20 questions in one minute? Write down the time for each set of division facts.


See if you can reach a score of 100 by answering divisions correctly at http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html. Choose level 3. Record both your score and how many you got correct and incorrect.


A farmer has 346 eggs. She can store them in trays of 12, 15 or 18. She wants as few eggs left over as possible. Which size tray would be best?

346 ÷ 12 = 28, r 10

346 ÷ 15 = 23, r 1 (the best option!)

346 ÷ 18 = 19, r 4


http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html.%20Choose%20level%203

http://www.amblesideprimary.com/ambleweb/mentalmaths/dividermachine.html.%20Choose%20level%203

http://resources.oswego.org/games/Mathmagician/mathsdiv.html.%20

http://resources.oswego.org/games/Mathmagician/mathsdiv.html.%20

Week 6 Decimals

Write what must be subtracted to eliminate the digit 5 in each of the following numbers:

7.256 3.615 4.05 5.582 4.565 5.855

0.05 0.005 0.05 5.5 0.505 5.055

Write □.□□□, □.□□□, □.□□□. Roll a dice and choose where to put the digit rolled in one of the three numbers. You are aiming to make three numbers each with three decimal places such that the first number is the smallest and the last is the greatest. But you must write in each digit after each dice roll!

This will depend on the dice rolls: E.g. 1.452, 3.641, 6.553

Write a number in between each pair of numbers below:

4.1 □.□□ 4.2 E.g. 4.17

3.45 □.□□□ 3.46 E.g. 3.452

6 □.□□□ 6.01 E.g. 6.004

5.06 □.□□□ 5.07 E.g. 5.069

3.725 □.□□□□ 3.726 E.g. 3.7253


Week 7 Addition patterns

In this arrangement of eight dominos the sum of dots in each column, row and diagonal is 7.

Use a set of dominoes (or draw them) to see if you can find another arrangement of dominoes which has 7 as a total of each row and column. If you can also make each diagonal have a total of 7, that would be really impressive! Also try and make each row and column add up to 8 or 9.

Examples:


Read about Dürer’s square at http://www.mathcats.com/explore/puzzles/magicsquare.html.

Then use the Magic carpet at http://www.mathcats.com/explore/puzzles/magiccarpet1.html to try and find other magic 4× 4 squares. Each row, column, diagonal, four corners, each 2×2 square should all have a total of 34.



http://www.mathcats.com/explore/puzzles/magiccarpet1.html

http://www.mathcats.com/explore/puzzles/magicsquare.html

Week 8 Subtraction of decimals

Use 1-9 digit cards or shuffle a set of playing cards, first removing the 10s, Js, Qs, Ks and Jokers. Use the Aces as 1s. Place face down and take 3. Use them to make at least two numbers less than 1 with three decimal places, e.g. use 4, 8 and 1 to make 0.148 and 0.841. Work out how many more are needed to make 1, e.g. 0.841 + □ = 1. Repeat five more times.

Examples: 0.841 + 0.159 = 1; 0.148 + 0.852 = 1

Repeat, but this time making four-digit numbers and finding how many more are needed to make 10, e.g. 4.782 + □ = 10. Write four additions like this.

Examples: 4.782 + 5.218 = 10; 7.248 + 2.752 = 10

Use pairs of these numbers to make subtractions where the answer is less than 2. How many can you find?

5.024 – 3.4 = 1.624; 5.024 – 4.17 = 0.854; 5.024 – 3.89 = 1.1345.024 – 3.5789 = 1.4451; 6.4 – 5.024 = 1.376; 5.024 – 4.72 = 0.3045.024 – 4.387 = 0.637; 4.17 – 3.4 = 0.77; 4.17 – 3.89 = 0.28; 4.17 – 2.879 = 1.291; 4.17 – 3.5789 = 0.5911; 3.89 – 3.4 = 0.49;


3.4 5.024 4.17 3.89

2.879 5.2244

7.834 6.78

3.5789

6.4 4.72 9.89

8.389 8.05 4.387 6.2

3.89 – 2.879 = 1.011; 3.89 – 3.5789 = 0.3111; 5.2244 – 3.4 = 1.8244; 5.2244 – 5.024 = 0.0204; 5.2244 – 4.17 = 1.0544; 5.2244 – 3.89 = 1.3344; 5.2244 – 3.5789 = 1.6455; 5.2244 – 4.72 = 0.5044; 5.2244 – 4.387 = 0.8374; 7.834 – 6.78 = 1.054; 6.78 – 5.024 = 1.756; 6.78 – 5.2244 = 1.5556; 6.78 – 6.2 = 0.58; 3.5789 – 3.4 = 0.1789; 3.5789 – 2.879 = 0.6999; 4.72 – 3.4 = 1.32; 4.72 – 4.17 = 0.55; 4.72 – 3.89 = 0.83; 4.72 – 2.879 = 1.841; 4.72 – 3.5789 = 1.1411; 4.72 – 4.387 = 0.333; 9.89 – 8.389 = 1.501; 9.89 – 8.05 = 1.84; 8.389 – 7.834 = 0.555; 8.389 – 6.78 = 1.609; 8.389 – 8.05 = 0.339; 8.05 – 7.834 = 0.216; 8.05 – 6.78 = 1.27; 8.05 – 6.2 = 1.85; 4.387 – 3.4 = 0.987; 4.387 – 4.17 = 0.217; 4.387 – 3.89 = 0.497; 4.387 – 2.879 = 1.508; 4.387 – 3.5789 = 0.8081; 6.2 – 5.2244 = 0.9756; 6.2 – 5.024 = 1.176; 6.2 – 4.72 = 1.48; 6.2 – 4.387 = 1.813; 6.4 – 5.2244 = 1.1756; 7.834 – 6.4 = 1.434;6.78 – 6.4 = 0.38; 6.4 – 4.72 = 1.68; 8.389 – 6.4 = 1.989; 8.05 – 6.4 = 1.65; 6.4 – 6.2 = 0.2

Week 9 Multiplication

Find which number between 50 and 100 has the greatest number of factors.

60, 72, 84, 90 and 96 each have 12 factors

Use grid multiplication to find the area of these rectangles:

777.6cm² 984.6cm² 10.64cm²

Multiply each of these numbers by a number between 15 and 30. Try to get answer as close to 100 as you can. Which answer was closest?

4.54 x 22 = 99.88 (this is the closest to 100)HSNP © Hamilton 2012 Page 65 Shining Term 1

Week 10 Division

Work out the first division in each group, and then use the answers to work out the remaining divisions:

3024 ÷ 7 = 432 302.4 ÷ 7 = 43.2 30.24 ÷ 7 = 4.32

3204 ÷ 6 = 534 320.4 ÷ 6 = 53.4 32.04 ÷ 6 = 5.34

4032 ÷ 8 = 504 403.2 ÷ 8 = 50.4 40.32 ÷ 8 = 5.04

3302 ÷ 13 = 254 330.2 ÷ 13 = 25.4 33.02 ÷ 13 = 2.54

3584 ÷ 14 = 256 358.4 ÷ 14 = 25.6 35.84 ÷ 14 = 2.56

Copy and fill in the missing numbers:

3 × 0.2 = 0.6 8 × 0.4 = 3.2 4 × 0.6 = 2.4 5 × 0.4 = 2

0.6 ÷ 0.2 = 3 2.5 ÷ 0.5 = 5 1.8 ÷ 0.3 = 6 2.1 ÷ 3 = 0.7

Which of the following divisions can’t be right and why? 2547 ÷ 6 = 424.5 3456 ÷ 17 = 203 17/5 (Should be 5/17) 284.8 ÷ 8 = 35.6 37.76 ÷ 16 = 23.6 (Should be 2.36) 2.4 ÷ 0.4 = 0.6 (Should be 6)

Find the correct answers to each.


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