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?
Topics: Starter  Arithmetic  Problem Solving  Puzzles  Simultaneous Equations
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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.
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 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=January21 However it would be better to assign one of the student interactive activities below. 

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