House Numbers

Houses next to each other

The numbers on five houses next to
each other add up to 65.
What are those five numbers?

A Mathematics Lesson Starter Of The Day

Topics: Starter | Averages | Number | Puzzles | Sequences

  • Sarah Sergeant,
  • My Year 5 students love these starters but how do I get the problem up full screen every day?
  • Transum,
  • Hi Sarah, If you are using Internet Explorer press the F11 key to hide the toolbars. Press F11 a second time when you want to show them again. Alternatively the View menu has a Toolbars option you can use to hide elements of the browser.
  • Looby Loo, England
  • Well done, you've got me here, I haven't got a clue. Is there a way of working out the answer?
  • Lara k, England
  • If you find the average by dividing the total by 5 this gives you the number of the middle house and then the rest is easy, hope this helps.
  • Holyrood sec school Glasgow, Mrs O'Hagan's 3rd yr class
  • Enjoyed the starter which led to a discussion about delivering papers!
    We moved on to talking about seven houses etc
  • Anne Carlill, Adult Tutor, Leeds City College
  • What a good starter! One of my group was working on odd and even numbers and another one on algebra. With some hints for the learners who are not so far along on their maths journey, this starter works for everyone at all levels.
  • Mark Edgar, Lincoln Christ's Hospital School
  • Thanks for this starter which has produced a nice discussion in my classes. The normal rule for numbering streets is that they start from the end nearest the city/town/village centre and have the odd numbers on the left. Few streets have the nubers consecutively on one side, but one notable exception is Lincoln High Steet which is numbered consecutively starting from the southern end on the left hand side, going to the northern end then returning on the right hand side (finishing in the 500s, I think). This causes no end of confusion!
  • Vicki,
  • Or if you think of the first house as x then x + x + 1 + x + 2 + x + 3 + x + 4 = 45.
    So 5x + 10 = 45
    5x = 35
    x = 7.
    So the first house is 7.
  • Scott, New Jersey
  • Assuming streets are either odd or even on a single side, we must be on the 'even' side to have five numbers result in an even total of 90.
    90 divided by 5 is 18 which must be the house in the middle. To maintain the distribution of 5 house number weights adding up to 90, we need to have numbers above and below 18 all averaging out to 18.
    Take houses 2 higher and 2 lower than eighteen. Add in houses 4 higher and 4 lower than eighteen and you have the result:
    18, 20, 16, 22, and 14 or:
    14 + 16 + 18 + 20 + 22 = 90.
  • Sam, Suva Fiji
  • 12,,,14,,,16,,18,,20.
  • Sarah, Taylor Swift
  • If the houses are numbered consecutively they could be:

    23, 24, 25, 26 and 27

    If however, the street has odd numbers on one side and even numbers on the other they could be:

    21, 23, 25, 27 and 29.
  • Matthew, 3D, Craigslea State School
  • If the total of the numbers (consecutively) is 135, the house numbers are 25, 26, 27, 28, 29. If it isn't consecutively, then the numbers are 23, 25, 27, 29, 31.
  • Room 11, HPS
  • Primary 5/6 thought the answer could be:
    16,18,20,22 and 24 or 18,19,20,21,22.
    Our class enjoyed this activity.
  • Transum,
  • Please Note: This starter, like many other Starter Of The Day, is generated using a random numbers each time the page is loaded. Consequently the comments above will probably be referring to a different house number total than the one on the version of the page you are looking at now. The randomness means that all you have to do is refresh the page to get another challenge for your students so that they can practice using the problem solving strategies they have developed. Thanks to everyone for their comments and enjoy!
  • Jg, St Lucia
  • Assuming the roads have even and odd sides, the difference between each number is 2. Let x be the first house then we have: x, x + 2, x + 4, x+ 6, and x +8.
    When added gives 5x + 20 = 45 (the question I believe said they add up to 45)
    Solving gives 5x = 25 (subtract 20 from both sides)
    So x = 5
    Substituting gives the house numbers- 5, 7, 9, 11 and 13.
  • Katy Pillman, Kansas City Metro
  • This is an easy question. Houses are odd numbers as the sum is an odd number. Common knowledge is odd addresses on one side and even on the other.
    They are also in a sequence, so just divide the total by the amount of buildings. That will give you the average as well as it being a medium as the houses have a sequence.
    17, 19, 21, 23, and 25 is the solution.
  • Als, Camden London
  • The numbers have to be one after another in a sequence and so I started by thinking like that, what numbers in a sequence add up to 120? to work that out, you need to know that 24x5 is 120 and from then you need to find numbers to substitute for 24 as you can only have that once thus I got the answer, 22+23+24+25+26=120.
  • Mrs K, Maths Cadets
  • We found this fun but also it was easier than we thought. More of these please.

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.

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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.

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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.

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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

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



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