Add 'Em

Add up all of the numbers from
1 to 52

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A Mathematics Lesson Starter Of The Day

Topics: Starter | Algebra | Number | Problem Solving | Sequences

  • Kerei James, NZ
  • It is an excellent resource.
  • S.W, Redbourn Junior
  • I would have this starter up when the children enter the room. They work out the answer on white boards and as soon as they have finished they write their initials against the highest number available in a list of numbers from 1 to 10 on another board - the TOP TEN list. When the TOP TEN is full up we stop and look at the answer together.
  • Nicola, Neilston Primary School
  • My class counted them all up and got the answer 703 then double checked it with a calculater and they were correct.
  • Class A, Furness Vale Primary School
  • We get 1176 doubled checked on a calculator.
  • Cody Reimer, Acadia Junior High, Canada
  • The correct answer is 820 like it says at the bottom. The formula you use is for consecutive sum.
    sum = 40(40+1)/2
    sum = 1640/2
    sum = 820.
  • Ray Dunne, Ireland
  • Answering the question as written ,assuming there is no word play and using universal basic addition I concur with 1176. I would prefer your method though as my sallery would be greatly increased.
  • Ray Dunne, Ireland
  • While Cody from Canada has the formula correct he has inputted the wrong information . if you change 40 and 41 for 48 and 49 then you get 1176 which is the correct answer.
  • Jonathan, Wales
  • The triangular number formula is correct.
    However I would like to point out that the numbers used sometimes differ hence why different people are saying different results.
  • Mrs Zaker - Teacher Of Maths, Tolworth Girls' School, London UK
  • Using Carl Friedrich Gauss's method: we have 22 pairs that add to 46 (half of 45 is 22) PLUS the 23rd number (which is 23)
    45 + 1 = 46
    44 + 2 = 46
    43 + 3 = 46
    so 22 x 46 = 1012
    add on 23 that gives 1035.
  • Transum,
  • Please note that each time this page is loaded the number of numbers in the question changes. Consequently the solutions suggested here in the comments will refer to different variations of this starter. Thanks Jonathan for pointing this out. Thanks also for the comments and explanations of the methods you used. keep them coming!
  • Angus Dresner, O.K.C.M.S
  • Just today I found this method myself. If you half the biggest number which in my case is 56 you get 28. then add .5 to get 28.5. Multiply the two numbers together to get 1596.
  • Uzma, Barking
  • Hi all
    I found it 1176 . I want to tell you the way I followed. I think it is the easiest method. First add all th 10s in the sum. Then find how many 1s,2s.......8s in the sequence. These numbers coming 5 times in the sequence, so multiply each number from 1-8 with 5.and add all in the sum of 10s. Finally add 9x4, as 9 appear only 4 time in the sequence.
  • G Morkel, Albany Junior High School NZ
  • The answer is 1711. Follow the formula for adding consecutive numbers thus:
    OR, you split the numbers in half and pair them up as 58+1, 57+2, 56+3, etc, you will then have 29 groups of 59 which is 1711.
  • Alan, Australia
  • The answer to the question as asked is "infinite" !!
    The question did NOT say to just add the whole numbers
    if just whole numbers, the answer is 990 ( 45 x 22 ).
  • James Streeter, Luton
  • None of you are correct!
    It is 1081
    There are 23 pairs of 47
    Until you reach the middle - which is
    Exactly twenty three pairs!
    23 x 47 = 1081
    Definitely correct.
  • Eamon,
  • It has already been pointed out that the 2nd number changes via a random number generator when the page is loaded/reloaded. From what I can see, the random number generator has 3 rules
    - The number has to follow this expression: ൦ is less than or equal to n" and "n is less than 60"
    - The number has to be an integer
    - The number has to be even
    With these rules, if you decide to pair numbers together as your method of choice, there should be nothing remaining as a "stray" or "middle", unless you are going to attack the wording choice of "number" instead of "integer".
  • Rey, Vietnam
  • The sum of each pair of numbers is 53. There are 26 pairs. 26 x 53 = 1378. So, the sum is 1378.
  • Ramu Chikkala, Visakhpatnam
  • Suppose if we want to find the sum of first 54 terms we can formula n(n+1)/2 or we can the forumula n/2(a+b) where 'a' and 'b' are first and last term of the sequence
    so sum of first 54 natural numbers = 54/2 (1+54)
    = 27 x 55
    = 1485.

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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Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

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.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

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 Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more... #ad

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

Apple iPad Pro

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.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more... #ad

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

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

"The ideas come from two sources. First, from the wonderful guests on his Tips for Teachers podcast - education heavyweights such as Dylan Wiliam, Daisy Christodoulou and Tom Sherrington, as well as talented teachers who are not household names but have so much wisdom to share. Then there's what he has learned from working with amazing teachers and students in hundreds of schools around the world.

Another Craig Barton Book

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.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more... #ad

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

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

Math with Bad Drawings

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.

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Laptops In Lessons

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:

However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a related student activity.

Student Activity

The famous Mathematician Carl Gauss found a quick way to perform this type of calculation when he was a boy; a long time before calculators! Can you find more details of this story?

Carl Gauss


Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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