The numbers on blue shapes are the sums of the two hidden numbers on red circles at the ends of the lines. What are the hidden numbers?

Hint: Begin by considering just the top triangle.

Think of a number that might go into the top red circle then subtract that number from the two blue totals on the sloping sides to find out what the other two red circle numbers would be. Do these two two red circle numbers add up to the blue total on the base of the triangle? Was your original guess too big or too small?

## A Mathematics Lesson Starter Of The Day

• Transum,
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• This is a nice lesson starter activity. It could be a matter of â€˜trial and improvementâ€™ or, for the more able, solved by naming the hidden numbers a, b, c, d and e then setting up ten simultaneous equations corresponding to the ten sums given. The button to reveal the answers can be found lower down this page along with a button to change the numbers used in this starter. Please let us all know how you get on with this activity.

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.

Previous Day | This starter is for 21 January | Next Day

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.

## Extension Puzzle

How difficult would the Pentadd puzzle be without the diagram? Imagine five numbers, randomly chosen, are added together in pairs to produce the following ten sums in no particular order. Can you figure out what those five numbers were?

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 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Transum.org/go/?Start=January21

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