primary maths newsletter - spring 2010

Lancashire Primary Mathematics Newsletter

SpringTerm 2010

The Lancashire Primary Mathematics Team

Happy New Year and welcome to the Lancashire

Primary Mathematics Team newsletter.

We have included our usual selection of

information, guidance and resources to support

the teaching of mathematics in your classroom. Along

with these, and of course, our regular puzzle feature, the

majority of this term’s newsletter focuses on calculation.

There is a double page spread for each of the four operations;

addition, subtraction, multiplication and division. These contain key

vocabulary, vocabulary in context, an identified progression and activities

and resources to support learning.

As always, we would really appreciate any feedback

or suggestions you may have. If you would like to

submit an article about mathematical successes in

your schools – let us know!

In team news, we would

like to congratulate Sue Farrar,

Andrew Taylor and Peter Toogood who have

been appointed to permanent consultancy

roles within the mathematics team.

We would also like to welcome Kerry Swarbrick

from Belthorn Primary School to the team. She will be joining us on

secondment from January.

2 The Lancashire Primary Mathematics Team

The Lancashire Mathematics TeamTeam Leader / Alison HartleySenior Adviser

Primary Mathematics Lynsey Edwards (Senior Consultant), Sue Bailey, Consultants Tracy Dimmock, Sue Farrar, Anne Porter, Emma Radcliffe, Angeli Slack, Kerry Swarbrick, Andrew Taylor, Peter Toogood

Team Contact Details Phone: 01257 516102 Fax: 01257 516103 E-Mail: [email protected] Write to: LPDS Centre, Southport Road Chorley, PR7 1NG Website: www.lancsngfl.ac.uk/curriculum/math

ContentsFindings From End of KS2 Test 2009 3

How Can the Mathematics Team Support Your Professional Development? 4

National Centre for Excellence in the Teaching of Mathematics (NCETM) 5

Maths Specialist Teacher Programme (MaST) 5

One-to-One Tuition in Lancashire 6

Small Schools 6

Mathematics and EAL – Joined up thinking! 7

Securing Level 5 in Mathematics 7

Addition 8

Subtraction 10

Multiplication 12

Division 14

Puzzle Page 16

Team Information and Contents

The Lancashire Mathematics Team

Summary of strengths

Number• - doubling a 2-digit multiple of 10,

adding three 2-digit numbers, identifying

missing numbers on a number line (including

negative numbers), rounding and identifying

numbers greater than 1000. Recognising

simple fractions of shapes and identifying

where they fit on a number line.

Calculation• - simple division, rounding up

remainders when appropriate and making

some good use of the calculator. Problem

solving involving fractions.

Algebra• - following a rule and going on to use

the inverse.

Measures• – questions involving time and

temperature.

Shape• – visualising and drawing shapes and

identifying irregular shapes, including using

the properties of a range of quadrilaterals.

Identifying right angles accurately, working

out the size of angles from known facts and

properties, line symmetry, reflection and

rotation.

Handling data• - interpreting and using

information from tables and a range of graphs,

transferring data from a Carroll diagram to a

Venn diagram. Working out the most likely

event from given data.

Children need to be taught:

How and when to use • jottings and

annotations to help them to find solutions;

many opportunities to use jottings or

annotations on diagrams were missed by

children who gave incorrect answers.

To recognise and use the • most efficient

method for calculation, mental, written or

calculator, particularly when solving problems

where several calculations are involved; too

many children resorted to inefficient written

methods even when the calculator was

available and a significant number of children

used formal written algorithms for some of the

following calculations: 28 -19, doubling £1.40,

300+50, adding £1.99.

To• read and interpret questions correctly

and to recognise when a question has more

than one part; a significant number of children

successfully completed the first part of a

problem but then failed to answer the second

part when they were clearly confident with

the mathematics involved.

To • approximate first in order to check that

their answer to a calculation is sensible; too

many children had no checking strategies and

accepted unreasonable answers.

The • language and properties of number;

children were not confident about what

constitutes square, prime and odd numbers,

factors, perimeter, area and there was

significant confusion between percentages

and angle measurement when dealing with a

pie chart.

I’m sure you will agree that the first four of

these key messages are mathematical skills we

all regularly use as adults and are therefore

important life skills.

The Lancashire Primary Mathematics Team 3

Findings From End of Key Stage 2 Test 2009


In addition to providing Strategy Courses we also provide a wide range of marketed courses.

Why not take a look at the Learning Excellence Site to see if we are running a course which would benefit the professional development of a member of your staff?

You can access the Learning Excellence site directly www.learningexcellence.net or via a link on our own website www.lancsngfl.ac.uk/curriculum/math.

Watch out for the following mathematics courses…coming soon!

12/01/2010 ABL701c LPDS, Chorley Maths Boxes for the More Able

20/01/2010 MAT112b Woodlands Year 6 SATs revision - Mathematics

27/01/2010 MAT103b Woodlands Maths Teaching in Years 5 and 6 for new to phase teachers

23/02/2010 MAT102a Woodlands The Role of the Maths Subject Leader – Day Two

15/03/2010 MAT113a Woodlands Improving Maths Subject Knowledge: Number

05/05/2010 MAT117a LPDS, Chorley Guided Learning in Mathematics

26/05/2010 MAT120a Woodlands Support for Mathematics – Level 3

08/06/2010 MAT115a LPDS, Chorley Effective Use of the Starter Session in Mathematics Lessons

23/06/2010 MAT119a Woodlands Support for Mathematics – Level 2

01/07/2009 MAT111b Woodlands Improving Maths Subject Knowledge: Understanding Shape

Spring Term 2010

Summer Term 2010

How Can the Mathematics Team Support Your Professional Development?

4 The Lancashire Primary Mathematics Team


The NCETM has developed a number of resources on its website www.ncetm.org.uk.

There are many useful aspects, two of which are, the Primary Magazine and the Self-Evaluation Tools.

Once you register, you will be sent regular updates, including a monthly newsletter, with interesting articles, lesson ideas for the starter, children’s activities and in school CPD sessions.

There is also a subject knowledge self-evaluation. This takes very little time to complete, offers guidance on areas of mathematics that could be developed, and suggestions for how these could be addressed.

National Centre for Excellence in the Teaching of Mathematics (NCETM)

5The Lancashire Primary Mathematics Team

Maths Specialist Teacher Programme (MaST)

In his 2008 report 'Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools,' Sir Peter Williams emphasised the need for a combination of improved subject knowledge and pedagogical skills in order to promote effective learning of mathematics. The report recommended that:

‘There should be at least one Mathematics Specialist in each primary school, in post within 10 years, with deep mathematical subject and pedagogical knowledge, making appropriate arrangements for small and rural schools’

The Mathematics Specialist Teacher (MaST) Programme has been designed to address this need for an increase in the number of primary school teachers, the Mathematics Specialists, who can implement improvements in the teaching and learning of mathematics for all

children in their school.In Lancashire we have already recruited sixty teachers onto the Mathematics Specialist Teacher Programme and will be looking to recruit another sixty to begin the programme in September.

If you would like to apply for the Mathematics Specialist Teacher Programme, or for more information, please see the Lancashire Mathematics Team website (www.lancsngfl.ac.uk/curriculum/math/index.php?category_id=928).

All primary and secondary schools and most special schools in Lancashire now know their allocation of One to One Tuition places. These numbers range from a minimum of 2 places in primary to a maximum of 135 in one of our large secondary schools. We have allocated 6,500 places this year which is set to rise to 13,000 next year. The budget of £2.8 million will double to £5.6 million in 2010-11 - this money is ring-fenced.

These places are to be used over the year and schools will be in the process of selecting the students to receive the tuition and in employing tutors. The places are to tutor students in English/Literacy and mathematics who you feel will benefit from the opportunity of 10 hours individual tuition. Class teachers will want to be involved in supporting the tutor in setting tight targets for the children and discussing progress.

You may wish to be tutors yourselves. Tuition can take place within the school day or outside it. If you are interested, you should talk to your headteacher and express your interest in tutoring. There is already a large

database of trained tutors on the website.

There is a massive amount to take in about One To One and all the information to date can be found at our website. For more detailed information you can contact us through the site (www.lancsngfl.ac.uk/1to1tuition).

Hilary KingOne-to-One Project Lead, Lancashire

One-to-One Tuition in Lancashire

6

Have you seen the new Small Schools section on the LGfL primary mathematics website?

Here teachers can find support with mixed age planning. This includes:

PNS Renewed Framework mixed age •plans with ‘I can…’ statements added. Some objectives have been adapted to create coherent mixed age units.Progression maps to give teachers an •overview of strands of mathematics from YR to Y6. The ‘I can…’ grids for Y1 to Y6. Teachers •will find this useful for tracking through learning objectives.

Please contact the Lancashire Primary Mathematics team if:

You have any ideas for items to be •

included on the small schools section.You have useful resources or ideas we •may be able to share with other small schools.

[email protected]

Small Schools


Mathematics and EAL – Joined up thinking!

We are holding a series of workshops aimed at developing mathematical understanding for children learning English as an additional language.

The aims of the workshops are:

To understand some of the •key language issues for EAL and mathsTo experience a range •of strategies and activities which develop mathematical talk and support mathematical understanding

Everyone who attended the first session left with plenty of ideas to trial out back at school and are already down to attend the next session! If you feel that your school might benefit from these workshops and you would like to be included in the next sessions, contact Julia Page at LPDS on 01257

516160. The next dates are...

26/01/10 - 1.30-3.45 at The Oaks, Burnley20/05/10 - 1.30-3.45 at The Oaks, Burnley

As usual the powerpoint used will be available on our website.

7


Coming Soon!

A further chapter in the ‘Securing Level’ series of publications will be available from the teachernet website in early Spring term. Ref: 00866-2009BKT-EN. Securing level 1 in mathematics is due to be released later in the year.

Also on the horizon is Overcoming barriers in mathematics – Helping children move from level 4 to level 5. This will complement the existing ‘Overcoming barriers’ materials – level 1-2, level 2-3 and level 3-4.

Finally, an exciting resource called ’Numbers and Patterns: Laying Foundations in mathematics’ is due for release this term. The resource looks at the development of early number sense, counting and calculation and operates in a similar way to the ‘Letters and Sounds’ materials for phonics development.

Securing Level 5 in Mathematics

Addition

The Lancashire Primary Mathematics Team8

double 6 is 12

half of 6 is 12

Gordon puts 2p in his piggy bank. He gets 2p more. How much has Gordon got altogether?

0 1 2 3 4 5 6 7 8 9 10 11 12

3 + 2 = 5

Key vocabulary + add, addition, more, plus, make, increase, sum, total, altogether, score, double, near double Vocabulary in Context Can you tell me one more? Two more? Ten more? How many more to make ……? Roll two die, count how many spots there are altogether. 6 plus 2 equals 8 I can count on 3 from 8 to show how many there are altogether. 12 twice is the same as double 12. Tom threw a bean bag in to target hoops. He got 3, 2 and 6. What did he score? The sum of 12 and 35 is 47. Sum is the outcome of addition and not to be used for ‘calculation’ or ‘number story’. For example, 3 x 5 = 15 is a calculation.

Progression Through Addition Counting forwards / counting on Children should have experience of counting forwards in ones, from different starting points, including crossing 10s and 100s boundaries. Use number tracks, number lines, hundred squares and counting sticks to model. Combining groups

Combine real objects then images using number lines to support where necessary. Record the addition number sentence alongside the practical activities.

Commutativity - addition can be done in any order

Use dominoes to model that addition

can be done in any order e.g. this domino has 5 spots on one side and 2 on the other, making 7 altogether. If I turn it around, will there still be 7?

This is a particularly important law of arithmetic. When children understand commutativity, decisions can be

made to rearrange the order of the numbers being totalled to help with efficiency e.g. 12 + 5 + 6 + 8 + 4 could be arranged as 12 + 8 + 6 + 4 + 5

(20) + (10) + 5

7 8 9 10 11


It is imperative that children experience practical resources alongside written methods when the methods are becoming more and more compact and abstract.

67 This example of adding the + 24 least significant digits first

11 (7 + 4) leads on better to the compact + 80 (60 + 20) method. It helps children to 91 realise where numbers that are ‘carried’ refer to in the compact method.

Both of these methods should be taught alongside the use of Base 10 apparatus.

Using both methods would help children to bridge the gap between informal methods for addition, supported by the number line and the compact written method.

Add – number line

Diennes and Coins

Add Horizontal – PV cards V3 Add Vertical Expanded – PV cards V3 Add Expand

Expanded written method to compact written method

Activities and Resources to Support Addition There are a number of Gordon ITPs that help to model some of the different stages in the progression through addition. There is a link to all the Gordon ITPs on our website. Whilst these ICT programmes are incredibly useful to support the teaching and learning of addition, they do not replace the practical activities that children should experience.

The crucial points are to remember when working through an example like this are: 1. Positioning the digits in the correct place value columns. 2. Knowing which digit to write in the answer and which digit to ‘carry’. 3. Recognising the value of the ‘carried’ digit so that when adding up the tens column the

children say 20 + 40 + 10 =70 rather than 20 + 40 + 1 = 61

67 This example of adding the + 24 most significant digits first 80 (60 + 20) leads on better from the mental + 11 (7 + 4) method of partitioning the numbers 91 involved, adding the tens, then the units before recombining.

Something Strange! A teacher recently noticed that some children in her class were doing strange things when carrying out column addition of three or more numbers. If the units digits were, for example, 7, 9 and 6, the children correctly gave the total of 22. However, when it came to writing the total in the calculation, only 1 was carried into the ‘tens’ place and 12 was squeezed into the units place. Needless to say, the final answer was incorrect. Those children have probably not had to ‘carry’ more than 1 into the tens place and therefore built up a misconception that only 1 can ever be ‘carried’ into the next place value column. The moral of this story is to ensure that children are adding three or more numbers together from an early age so that misconceptions like this can be prevented.

10

Subtraction


Key Vocabulary how many more to make… ? how many more is… than…? take (away), leave, how many are left/left over? how many have gone? one less, two less… ten less… how many fewer is… than…? difference between, how much more is…? subtract, minus, subtraction, inverse Vocabulary in Context You have 3 apples. How many more to make 5 ? How many more is 7 than 4? Take away 2 from 8. 9 take away 3 leaves 6; You had 6 cakes and you ate 2. How many are left/left over? How many have gone? What is one less, two less, ten less than 12? How many fewer is 3 than 8? What is the difference between 18 and 11? How much more is £5 than £1.50? Subtract 1.9 from 3.2; What is 24 minus 5? How much less is 3 than 10? I know subtraction means I have to take away or find a difference. 235 is one hundred less than which number? Decrease 256 by 13. I can explain how I know that subtraction is the inverse of addition.

Progression Through Subtraction Counting backwards Children should have experience of counting backwards in ones including crossing 10s and 100s boundaries. Use number tracks, number lines, hundred squares and counting sticks to model. Taking Away

Remove objects one by one from a set Record subtraction alongside the practical

activities. Relate the removal of objects to counting backwards on a number line.

Difference When asking children to calculate the difference between two numbers, we need the children to compare the numbers in terms of their size. Working out how much greater or smaller one number is compared to another is finding the difference. Decomposition

Use Diennes apparatus (base 10) and place value arrow cards to model decomposition and exchange Move onto the expanded method of decomposition When children are ready introduce the compact method

Representing numbers as towers can support children in calculating difference.

When calculating difference on a number line, we need the children to understand that this is the span between the two numbers. This is a crucial element to children’s understanding as counting back from the larger to the smaller number finds the difference, as does counting on from the smaller to the larger number.

When counting on, to find the difference between two numbers, the related number sentence will be an addition, as in the example.

This method should continue to be used throughout Key Stage 2, for particular cases e.g. 3002 – 1997, and calculating time intervals.


Make two towers using Multilink or Unifix. Write the number of cubes in each tower on a piece of paper.

Put the two towers next to each other to see the ‘difference’ in height.

Break off the top part of the larger tower so that the part remaining is the same size as the small tower. The part that has been broken off is the ‘difference’ itself.

Write the number of cubes in the difference on the piece of paper with the other two numbers.

Ask the children to create a number sentence using the three numbers they have written down.

Discuss why some children have a subtraction number sentence and some people have an addition number sentence.

Difference ITP can be used to illustrate this

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 1 2 3 4 5 6

Activities and Resources to Support Subtraction Practical difference

Using a marked number track, identify two different numbers (4 and 9). Recognise that the ‘amount’

of the smaller number is within the larger number. Cut off the smaller amount (4) so you are left with the difference between the smaller and larger amounts (5)

Difference as a span between two numbers

Using a marked number line, cut off a given difference from 0, e.g. from 0 – 7. Use this as a difference of 7 checker to identify a range of numbers that have a difference of 7, such as 4 and 11.

Number Line ITP can illustrate span between two numbers and prompt discussion about how the difference would be altered by moving one or both of the numbers involved.

When children have this understanding of difference, ensure they have experience of questions such as, the difference between two numbers is 1.58. One of the numbers is 4.72. What is the other number? Is this the only answer?

8020 6

3-

701

750= 57

8 5 3 8 – 5 = 3 3 + 5 = 8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

12

Multiplication


Key Vocabulary pairs, groups, lots of…, multiplied by, repeated addition, times, twice as many, three times as many, double, array, row, column, product, scale up by a factor of… Vocabulary in Context There are 4 pairs of socks on the washing line. How many socks is this? Show me 5 groups of 3. How many is this altogether? The giant is three times taller than the tree. The tree is 5 metres tall, so how tall is the giant? Show the number 12 as an array. How else can it be shown? What is the product of 4 and 5? There are 4 cubes in this tower. How many cubes would be in a tower that has been scaled up by a factor of 5?

Progression Through Multiplication Counting in equal steps

Whenever illustrating a concept, begin with real

life examples, then use models and images. It is important to relate these examples to the

number system e.g. on a number line.

Repeated addition Show how the groups of cubes could be represented on a number line alongside the corresponding number sentence.

5 x 3 = 5 + 5 + 5

Arrays and commutativity Children need to have a good understanding of what an array is – an arrangement of objects in equal rows or columns. Multiplication Facts ITP can demonstrate this particularly well. Children’s understanding of multiplication as an array is crucial for their progression into the grid method.


This could be made into a game between two children. Using a cup of counters, one child picks a handful out and arranges them as a rectangular array (not a

single line). If 12 counters are picked out, they could be arranged as a 2 x 6 array. The other child then tries to arrange the same set in a different array such as a 3 x 4. This continues until all the possible arrays have been created. If a number of counters taken from the cup cannot be arranged as a rectangular array, then the children

will have chosen a prime number of counters.

Grid method Children need experience of ‘breaking up’ a larger array into more manageable arrays, such as partitioning into tens and ones. 10 3

4 This image leads to children understanding the layout of the grid method.

X 10 3 4 40 12

There are many prerequisite skills for this approach and these need to be secure for children to understand the grid method. These should also be built up over a series of lessons, rather than asking children to work through the entire method in a single lesson. The prerequisite skills are:

Partition numbers into tens and ones Derive multiplication facts Multiply by multiples of 10 and 100 Position numbers correctly in the grid Addition

Once this method is secure, it can be used for any size of number, including decimals.

Activities and Resources to Support Multiplication Allow children to explore arranging a number of objects in different ways e.g. 8 counters can be arranged as a random group or an array. The array supports children’s identification of the groups e.g. 4 x 2 and 2 x 4.

Use real examples of arrays such as:

Bun trays Ice cube trays

Egg boxes Lego bricks

40 12

14

Division


Key Vocabulary share, share equally, one each, two each, three each…, group in pairs, threes…tens, equal groups of, divide, divided by, divided into, left, left over, division, remainder, factor, quotient, divisible by, inverse

Vocabulary in Context Can we share out these cakes fairly? How shall we do it? If you share 6 counters equally between 2 people, how many does each one get? In PE the teacher needs groups of 4 children. There are 24 children in the class how many groups will there be? Divide 25 by 5. What is 45 divided by 9? What is 14 divided into 2? How many are left over when you share 18 pencils between 5 children? What numbers have a remainder of 1 when divided by 3? What are the factors of 30? Tell me two numbers with a quotient of 5. Are there other possibilities? Explain how you know that 75 is divisible by 3. Use the knowledge that division is the inverse of multiplication to check the answer to 23 x 8.

Progression Through Division Sharing Ensure that children experience sharing out

different objects in a variety of contexts and purposes.

This understanding would still be used throughout Key Stage 2 when finding fractions of quantities or amounts.

Counting back in equal steps Ensure children experience counting from different starting numbers and steps e.g. count back in 4s

from 24; 24, 20, 16… Use number tracks, lines, hundred squares and counting sticks to model.

Move on to starting with numbers that aren’t multiples of the number being subtracted e.g. count back

in 3s from 20; 20, 17, 14… This will support children’s understanding of remainders. Repeated Subtraction / Grouping Use practical apparatus and number lines to show the constant step sizes of repeated subtraction.

Use Grouping ITP to demonstrate organising an amount

into equal groups. This is an important strategy and supports the chunking method.

(Please note the Grouping ITP counts forward so therefore does not show repeated subtraction on the number line).

24


Ask children to work in pairs, one playing the role of the banker and the other playing the role of the person wanting to exchange some coins.

Take a number of 1p coins to the bank manager and ask them to exchange the coins for 5p coins. How many 5p coins should you get for twenty 1p coins? 20 in groups of 5 = 4 or 20 ÷ 5 = 4

Using 12 counters, group these

into 4’s and record as 12 ÷ 4 = 3. Ask what would happen if you

had 13 counters? What about 14, 15, 16 or 17 counters?

What do you notice about the

remainders? Can you generalise about the size of the remainder in relation to the divisor?

Chunking

The highlighted multiples total 84, which shows you that 7 x 2 and 7 x 10 collectively make 7 x 12. So 84 ÷ 7 = 12

7 x 1 = 7 7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 35 7 x 6 = 42 7 x 7 = 49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 70

Activities and Resources to Support Division Grouping

Grouping and Remainders

The Key Element of Chunking Grouping or chunking is quite simply considering the dividend (the number being divided) in terms of multiples of the divisor (the number in each group). For example: When dividing 84 by 7, it is helpful to recognise how 84 can be made up using multiples of 7. If the 7x table was listed, children could select a combination of answers that would total 84 (there is no single correct answer, though some are more efficient than others).

32 r 46 ) 196

- 180 30x 16

- 12 2x 4

3 ) 72

- 30 10x42

- 30 10x12

- 6 2x6

- 6 2x0

24

This method progresses to subtracting multiples of 10 of the divisor.

72 ÷ 3

r 32 r 4

196 ÷ 6

This method progresses to subtracting larger multiples of the divisor.

12 ÷ 4 = 3 Read as 12 in groups of 4 equals 3 groups

13 ÷ 4 = 3r1 Read as 13 in groups of 4 equals 3 groups with 1remainder/remaining

6 x 50 6 x 10 6 x 3

378 ÷ 6 = 63

With plenty of practise at partitioning numbers in different ways (Y2 objective), children will be able to consider 378 ÷ 6 without too much difficulty. 378 considered as multiples of 6 could be: 300 + 60 + 18

By showing the calculation alongside a practical demonstration using cubes or counters, children should realise that subtracting single groups each time is inefficient

200- 6

- 6

- 6

- 6

194

188

182

. . . .

. . . .8

- 62

1x

1x

1x

1x

1x

33r2

200 ÷ 6

Puzzle Page

Sets of four numbers

Miss Brown was working with Becky's group

on numbers that share a certain property. She

wrote twelve numbers on the board.

2, 3, 4, 5, 7, 9, 10

15, 21, 25, 28, 49

"You can all find a different set of just four

numbers that go together," she said, "And they

must have a proper mathematical name. They

can't be just a set of numbers that you like!"

The children stared at the numbers. Alan put up

his hand. "Like odd numbers?" he suggested.

"That's the right idea," said Miss Brown, "but you

can't choose just odd numbers because there

are more than four of them. You must use all the

numbers in my list which fit your set. Anyone

else got an idea?"

Becky put her hand

up. "Numbers in the

5 times table? There

are four of those."

"That's right. But

what would be

a good name for

them?"

"Multiples of 5?"

suggested Becky.

"Good," said Miss Brown and she wrote on the

board:

2, 3, 4, 5, 7, 9, 10

15, 21, 25, 28, 49

Becky’s set is multiples of 5 (5, 10, 15, 25)

There are ten children in Becky's group.

Can you find a set of numbers for each of them?

Are there any other sets?

Solution to last term's puzzle...

...(W)Holy numbers

Digit How many? Reason

0 8There can only be two zeros in each row because there is no 000 or 1000 in the hymn book

1-5 9There can only be one triple digit number repeating the same single digit three times (e.g. 111, 222, 333). The rest can only repeat it twice at most (e.g. 011, 110, 101, 211, 311) because the numbers 111, 222, etc. cannot be repeated.

6 12Even though there cannot be a triple digit that repeats 6 three times, the extra 6s would be needed to be turned in to 9s (e.g. 696, 669, 699, 996). You must not for-get that 6s can be turned into 9s.

7-8 8There can only be two, at maximum, of this number in each row (e.g. 177, 277, 377, 477, 070, 007). There cannot be 777 or 888 because the hymns only stop at 700.

9 09 would work like 7 and 8 because it too cannot be written as 999. But the 9s do not need their own numbers because the numbers for 6 can be turned around to make 9.

2, 3, 4, 5, 7, 9, 1015, 21, 25, 28, 49


primary maths newsletter - spring 2010

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