House Numbers

Starter of The Day Transum Mathematics Topics

Topics: Starter | Averages | Number | Puzzles | Sequences

Sarah Sergeant, djsergeant@blueyonder.co.uk
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.
There-for:
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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Answers

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.

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Graphic Display Calculator

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Apple iPad Pro

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

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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.

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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?

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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

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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

Maths T-Shirts on Amazon

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=January26

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.

Transum.org/go/?to=Consecutive