House Numbers

Houses next to each other

The numbers on five houses next to
each other add up to 70.
What are those five numbers?

A Mathematics Lesson Starter Of The Day


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Topics: Starter | Averages | Number | Puzzles | Sequences

  • Sarah Sergeant, djsergeant@blueyonder.co.uk
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  • My Year 5 students love these starters but how do I get the problem up full screen every day?
  • Transum,
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  • 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
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  • 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
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  • 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
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  • 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
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  • 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
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  • 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,
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  • 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
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  • 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
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  • 12,,,14,,,16,,18,,20.
  • Sarah, Taylor Swift
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  • 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
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  • 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
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  • 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,
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  • 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
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  • 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
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  • 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.

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