Two Numbers

Find two numbers whose sum is 12 and product is 35.

Add Multiply

Find two numbers whose sum is 30 and product is 224.

Add Multiply

Find two numbers whose sum is 15.5 and product is 59.5.

Add Multiply

A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic | Number | Simultaneous Equations

  • Mr Jankowski, Haydock Sports College
  • Very nice as it can be used to lead into factorising quadratics.
  • Matt Robey, Brighton Hill School
  • This was really easy. I got the last one on the first guess!
  • Chris And Phillip, Swansea
  • The first question is really easy and can be spotted quite quickly.
    The third question always has to be an even number multiplied by a number ending in 0.5
  • Mr Spanion, Ejs
  • I thought it was brilliant.
  • Mr M Shepherd, St Lawrence Academy, Scunthorpe
  • Easiest way to solve these we found was to double the "sum" number. This means that both the two original numbers have doubled so we need to multiply the product number by 4. This gave us all whole numbers to deal with. Once solved, half both the numbers.
    (Prime factor breakdown is the best way to look at combinations systematically if needed to, although most of year 8 relied on trial and error to find the abswer once they'd found the whole numbers).
  • Transum,
  • This one of those starters that is generated with random numbers. Each time you load this page a new set of numbers appear in the statements above. You can use it many times over the course of the year so that your pupils are reminded of the techniques and have regular practice applying them.

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.
Click here to enter your comments.

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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.

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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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