### Can you construct an expression for 100 which uses all the digits 1 to 9?

1

2

3

4

5

6

7

8

9

###### That's correct. Can you find any other ways of doing it?
• You can put numbers together to make larger numbers, for example. 53, 127 etc.
• Don't forget the order of operations, BIDMAS, when evaluating your expressions.
• Surprisingly there's a solution in which all of the digits remain in numerical order.

## A Mathematics Lesson Starter Of The Day

• Jake, Patana
•
• I have found 1+2+3+4+5+6+7+8x9 = 100
• Lewis Crosby, Doncaster
•
• I have found one too 198-73-26+5-4=100
•
• Another solution for this is 56+49-2-3+8-7-1=100
•
• I have got found another solution for this starter =
6x7x2+8-3+1+9-4+5
• Holly, Whitby High, Ellesmere Port
•
• Another Solution: (5x6)+(4x9)+(8x3)+7+2+1 = 100
• Reece & Ashlee, Ellesmere Port
•
• Two more solutions without brackets from Whitby High:

123-4-5-6-7+8-9 = 100

69+31+8+5-7-4-2 = 100
• James Wellington-Smith, Lea Moor High
•
• 231-(9x8)-(6x5)-7-4
• Mr Heeley's Krew, Rawthorpe in da Hudd of field
•
• We found (1+9+2+8) x 5 + (3+7) - (4+6).

We think that this is the best answer because simplicity is the key!

God bless you - Maths rocks
• Year 6, BIS Jakarta
•
• We found many solutions including
9 * 4 * 2 + 8 + 7 + 3 + 5 + 6 - 1 = 100
9 * 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100
9 * 8 + 4 * 7 - 5 * 2 + 6 + 3 + 1 = 100
• Year 11- Mr Kelly's class, Cross and Passion College
•
• We found another solution for ALL FOR 100

98+7-6+5-4+3-2-1=100
• Giovanni Fernandez, The British School of Quito, Ecuador
•
• 2 x (7 x 8 x 9 - 456) + 3 + 1
• Tim Channer, The British School of Quito, Ecuador
•
• (9 x 8) + (7 x 6) - (5 x 4) + (3 x 2 x 1)
• Montae, Mrs. Shelburne's Period 3/6 class, Hayward Middle School, Springfield, Ohio
•
• Here is Montae's solution...he found it in less than 5 minutes and creatively used exponents!

5^2 x 4 - 9 + 6 + 3 - 7 + 8 - 1
• Ashleigh Reid, S2 Lochend Community High School
•
• I found this way of getting the answer:

92 + 6 + 3 - 4 + 5 - 1 + 7 - 8
• Ciaran Donegan, Harrytown High School, Stockport, 8H
•
• I found (51+4+3) x 2 -9-8 + 7 -6
• Mrs Simpson, Torry Academy, Aberdeen
•
• 2D1 Maths Class at Torry Acadmey found this way:

89+7+6-5+(2*3)-4+1
• Andy Rowe, Knowles Hill School Devon
•
• Cameron Houdmont in Year 7 got this one

(7 + 3) x 9 + 5 + 4 + 1 + 8 - 6 - 2
• Ms Winters, Dubai English Speaking College
•
• Here are our answers from class 7DE...

9x8+1+2+3+4+5+6+7

6x3x5+12+4+(9-8)-7

9x8+7+1+5x6-(4x3-2)
• Miss Train, Saints Peter and Paul
•
• The first to get it in my class was Emma M in under 20 seconds - here's her solution:
[(1+2+3+4) x 9] + 5 + 6 + 7 - 8 = 100
• Jodie, Lauren, Hayley, Harrytown High School Stockport
•
• 123+45-67+8-9 Jodie Reilly 9T
98-7-6+5+4+3+2+1 Lauren Hill 9W
(1+2+3+4+5)x6-7+8+9 Hayley Ryder 9H
• Jack Houghton, Sydney, Australia
•
• I got 123+45-67+8-9
• Martin Vaughn, Central Sussex college haywards heath
•
• 8x9 +7 +1 +5 +6 +4 +3 +2 =100
•
12+34+59-6+8-7
• Miss Mian, Bishop Ramsey School, Ruislip
•
• Daniela got the total by doing
68 + 23 + 15 -4 +7 - 9

and Amy got it by doing

(9x8) + 1 + 2 + 3 + 4 + 5 + 6 + 7
• Josh Atkin, Dunbar Grammar
•
(98-7) +1 -4 +6 -2 +3+5=100
•

• Mark Daniels, Wissahickon Middle School
•
• Nicole from Mr. Daniels' Pre-Alg. Support class,WMS, Ambler,PA did this-
4(5+7+8) + 1(2+3+6+9)

Mr. Daniels offered this-
2^5 + (8x9-4) + 13-(6+7)
• Mrs Simpson and class 4M4, Torry Academy, Aberdeen
•
• Vincent found 963-852-7-4x1
Emma found 6x9x2-8+4+1-3+5-7
Shelby found 9x6+34+7+8-5+2x1
Jasmine found 9x7+(6x8)-5-4-3-1+2
• Liam Hutchison, Lochend Community High School in Glasgow
•
• I calculated it this way

(9x7) + 6 + 1 + (5 x 2) + (4 x 3) + 8
• Ellen Moore, KNGS, Birmingham,UK
•
• This works!
(9+1)-(2+8)+(3+7)+(4+6)*5=100
• Miss Samantha Rhodes, Filsham Valley school, Hastings
•
• In 1 class, I had 5 different correct solutions.
8x9+67+1-45+2+3 =100 (Charlotte Avery, year 8)
5x19+34-28-7+6=100 (Sam Davies, year 8)
3x4x6+2x9+(8-7+1)x5=100 (Sophie Fairall, year 8)
8x9+1+2+3+4+5+6+7=100 (Charlotte Rudd, year 8)
156-78+29-3-4=100 (James Bisson, year 8)
• Mr Jordan Fry, Laurence Jackson School, Guisbrough
•
• We got 5*9=45, 45+7=52, 52*2=104, 104-6=98, 98+4=102, 102-3=99, 99+1=100
•
• 78+24+9-6-5+3-2-1=100
• Soumya, Croydon
•
• 1+8x9+2+7+6+5+3-4=100.
• Form 7Y, Harrytown Catholic High School, Stockport
•
• Amy Booth found 9x8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100
James Wilson (9x8) + 7 + 6 + 5 + (4 x 3) - (2 X 1) = 100.
• Miss Marcham And 10f1, Prince Henry's High School, Evesham
•
• We got (6+4)x(8+9-7+5-3-2)x1 = 100.
• Mrs J A Thompson, Mexborough School Specialist Science College
•
• Two different answers were found in 10 minutes. 7P SPECTRUM group
The first was 1 + 2 + 3 + 4 + 5 +6 + 7 + (8x9) = 100 by Ashley Finney
and (1+7+2) x 9 + 8 + (4x5)- (3x6) = 100 by Emma Rodgers.
• Mitchel, Brocket
•
• Another way of doing it is
9-1=8, 8-2=6,7-3=4, 6-4=2, then
8+6+4+2=20x5=100.
• Y Ramsamy, Phoenix College, Reading, UK
•
• My pupils came up with the following solutions:
(124-3-5-6-8-9)+7 = 100 Ryan Walsh
(5x7x2x1)+3+4+6+8+9 = 100 Moin Khan
Y Ramsamy
• Jerry & Tom, Fukien School (HK)
•
• (1+2x3x4)x5-6*7+8+9=100.
• Thomas, Cabrach
•
• This wasn't easy but I found
9x8+7+(6x4)-5+1+3-2=100.
•
• Connor found 4x5x6-7-8-9-1+2+3
Brandon found 24x5-9-8-7+6+1-3
Brandon found 9x8+1+2+3+4+5+6+7.
• Mrs Barnett & 8x1, Bredon Hill Middle School, Evesham
•
• Our simplest answer was (9x8)+7+6+5+4+3+2+1 = 100.
• Greg Patko Yr8, Murray Park, Derby
•
• (9+8) x 7 - 6 x 5 + 4 x 3 + 1 - 2
(1 + 9 + 2 + 8 + 3 + 7 - 6 - 4) x 5.
• Mike Drewniak, Kewaskum Middle School
•
• Dinara found: 91+82-67-5-4+3.
• Beacon Community College, Crowborough, 8XMa3
•
• (6+4)x9+7+3+1+2+5-8=100.
• David Clowes, St Peter's Academy
•
• I got 7x5x4-9x3-8-6+2-1.
• Max, Hethersett Junior
•
• 12x5+39+6-8+7-4=100.
• 9 (the Better Half) 1, Chellaston Academy, Derbyshire
•
• Anneli and Molly: 9(6+3)+1+8+7+2+(5-4)
May: 2(6x9-3-1+8-5-7+4)
Rhys: 7x9+4x3+5+6x2+8x1
David: 1(932-845)+6+7
Eve: 5x6+87+1-9-4-3-2
Ashley: 9x8+7+6+5+4x3-2x1.
• 7ax1, Alexandra Park School, London
•
• Susie, Vinesha and Tommy : 8 x 9 + 7 + 1 + 6 + 5 + 4 + 2 + 3 = 100
Semi (1 + 2 + 3 + 4 + 5) x 6 + (8 + 9) - 7 = 100
Kira and Simon 341 - 265 + 9 + 7 + 8 = 100
Ben 91 + 7 + 2 + 5 + 8 - 3 - 4 - 6 = 100
Seb 123 - 45 - 67 + 89 = 100
Lottie 8 x 9 x 2 - (4 x 5) - (6 x 3) - 7 + 1 = 100
Peter (1 + 2 + 3) x 6 - 7 - 5 - 8 + 9 x 4 = 100.
• Australia Class, Cottam, Preston, England
•
• Our class found 2 ways to solve this puzzle:
8x9=72+(5x4)=92+(7+1)=100-6=94+2x3=100
The next idea is:2+8= 10X9=90+5=95+6=101+4=105+3=108-1=107-7=100.
•

• RM, UK
•
• I have found: 1 x 7 x 9 + 2 x 6 + 4 x 5 + 8 + 3 = 100.
• Abi T, St Peter's Y6 Maths Group
•
• (9x8)x1 +6 +7 + (5x4)- (3+2).
• Miss Brook, Crick Primary School
•
• William - Year 6 - 9x8=72 + 5x6 - 7 - 2 - + 3 + 4 x 1
Ethan - Year 6 - 7x9 x 2 - 8 - 6 - 5 - 3 - 4 x 1.
• Taeh, Croydon
•
• I found out that you can do 8x9 which equals 72 and then you add 7+6+5+4+3+2+1=28 then 28 and 72 equals 100.
• Sophie Tune, Kingswinford England
•
• I got 1+2+3+4+5x7(105)-6+9-8.
• Matthew Zhao, 4AD, Craigslea State School
•
• Matthew Zhao here, coming with with a personal answer in two minutes!
47*2+1+3+6+9-8-5=100.
•
• Sarah here in Jersey Year 8.1 came up with (93+7)+(8x6)-45-2-1
Some of the others came up with answers like 99.2, which aren't 100 last time I checked!
•
• I found 9x8+7+6+5+4+3+2+1 which makes 100.
• Mr. Van, Sweden
•
• We did it!
• Shaa, India
•
• It's really cool, do you want to see more?

_ _ +_ _+_ _ = _ _+ _=100

Fill in the blanks with the numbers from 1 to 9 without repeating.
• , Myrtleford
•
• I have managed to find a way of getting so many firstly you two numbers to be a ninety type number aka 9 and 6 then you add to make 100 so in this case 4 then you the rest of the numbers to add and subtract what you have added on so now it's 96+4+8-7-1+5-3-2 making countless ways of doing it!!

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

## Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

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Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more... #ad

## How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes GĂ¶del's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

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## Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more... #ad

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

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## Craig Barton's Tips for Teachers

Teaching is complex. But there are simple ideas we can enact to help our teaching be more effective. This book contains over 400 such ideas." more... #ad

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## The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

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## Christmas Maths

This book provides a wealth of fun activities with a Christmas theme. Each photocopiable worksheet is matched to the Numeracy Strategy and compatible with the Scottish 5-14 Guidelines. This series is designed for busy teachers in the late Autumn term who are desperate for materials that are relevant and interesting and that can be completed with minimun supervision.

All the activities are suitable for use by class teachers, supply teachers, SEN teachers and classroom assistants and cover topics such as 'How many partridges did the true love give all together?' and 'Filling a sleigh with presents by rolling a dice!'. Children will have lots of fun working through the Christmas Maths themes but also gain valuable skills along the way.

A great source of ideas and another reasonably priced stocking filler. more... #ad

## A Compendium Of Mathematical Methods

How many different methods do you know to solve simultaneous equations? To multiply decimals? To find the nth term of a sequence?

A Compendium of Mathematical Methods brings together over one hundred different approaches from classrooms all over the world, giving curious mathematicians the opportunity to explore fascinating methods that they've never before encountered.

If you teach mathematics to any age group in any country, you are guaranteed to learn lots of new things from this delightful book. It will deepen your subject knowledge and enhance your teaching, whatever your existing level of expertise. It will inspire you to explore new approaches with your pupils and provide valuable guidance on explanations and misconceptions. more... #ad

I had been tutoring the wonderful Betsy for five years. When the day came for our last ever session together before the end of her Year 13, I received this beautiful book as a gift of appreciation.

This a very readable book by Ben Orlin. I'm really enjoying the humour in the writing and the drawings are great.

Ben Orlin answers maths' three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that mathematics should belong to everyone. more... #ad

Click the images above to see all the details of these gift ideas and to buy them online.

## Maths T-Shirts

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

 Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments: Transum.org/go/?Start=October6 However it would be better to assign one of the student interactive activities below.

Here is the link which will take them to a student version of this activity with different levels for which they can earn Transum Trophies!

Transum.org/go/?to=Centex

## Extension Activity

Use the digits zero to nine to make the first ten digits (one at a time!)