Pumphrey's Math

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Walk the Line – Adding and Subtracting with Negative Numbers

I wanted an activity that would give students a deep sense of adding and subtraction involving negative numbers. Both. At the same time. I figured the best way would be for them to actually walk through what happens to a number when it goes through these operations; so began ‘walk the line’.

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The idea is simple, have students walk through various sums increasing from adding two positive numbers, going through to subtracting two negative numbers, reviewing each time.

They will first need to stand in a line, then using sidewalk chalk, draw a zero on the floor and draw out a number line to the right and left of where they are in the positive and negative direction.

Here is the general dialogue that happens:

  • I am going to call out a sum and I would like to see how quickly you can get to the result. You start with the first number I call out and are permitted to move before I have finished calling out the sum.
  • 3 + 2 (call out slowly to give students time to move)
    • Review Questions
      • Now, what did you do when I first said 3? – Run to that number
      • What did you do when I said “add”? – Got ready to run away from zero
      • What did you do when I said 2? – Ran two spaces away from zero
  • Next:  5 – 8
      • Review Questions
        • Now, what did you do when I first said 5? – Ran to 5
        • What did you do when I said “subtract”? – Turned to face the zero (Why? etc)
        • What did you do when I said 8? – Ran 8 spaces and ended up at -3
  • What about  5 – ( -8)    (call out slowly)
    • Review: What was different when I said subtract -8 instead of 8? – Had to go the other way (Why? etc.)
  • At this point I bring student thinking together and explicitly clarify the rules:
    • Whatever number I say first is where you start
    • If I then say “add” you face this way (pointing in the positive direction) and if I say “subtract” you face the other way (pointing in the negative direction)
    • If my second number is positive you walk forward by that amount, if my second number is negative you walk backward by that amount (for example: 4 would be four steps forward, -4 would be 4 steps backward)
    • Let’s try this out
  • 3 – 8 (call out slowly to give students time to think and move)
  • -4 + 10
  • 2 + (-5)
  • -9 + 12
  • 2 – (-5)
  • -4 + (-7)
  • -6 – (-10)
  • etc
  • Then return to classroom and do the same sort of thing but students write (just) their answers on their mini whiteboards. We review each time going through the 3 step process.

This activity really worked and students were doing this all in their head by the end of 50 minutes which is what I was aiming for. There was no separation of addition and subtraction or positive and negative numbers. They were just different points on the number line and different ways to move.

How do you introduce adding/subtracting negative numbers?

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