Pumphrey's Math

Patterns, everywhere


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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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Classkick Review – Thoughts from the first day

I first heard about Classkick through Dan Meyer’s blog and thought ‘I have to give this a try!’ The idea is simple but the implications could be huge. A platform that lets you see what students are thinking and writing, in real time! It is so simple I can’t believe it hasn’t been done before.

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So, as soon as I finished reading the article, I downloaded it onto my iPad and emailed my students to do the same ready for the next day. I didn’t want to go another day in my classroom without trying this out.

The punchline: It’s a great idea, but it needs some work.

The interface is clean and pleasant to use. The tutorial videos are helpful as some elements are more intuitive than others. For example, i assumed that students would sign up once to a class and after that would stay signed in (as is the case for many other education apps). But with Classkick, students will sign in to each assignment you set, separately with a different code. I think this could get a little cumbersome when I am setting activities every lesson.

The idea behind the app is phenomenal and when it worked it was magical. To be able to see what students are writing, provide immediate feedback and pointers is a very powerful tool. This could be used for in class work or for homework.

The students loved knowing that I could see their work, I could give them instant feedback and they responded very positively. They jumped into the learning from my feedback. I could not only look at their answers but circle and ask questions about mistakes in their thought processes. This is so exciting!

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However, on first use I did find the app a little slow, at least from the teachers side of things. In one lesson it took around 4 minutes for the students’ work to appear on the screen when the network was working just fine. Sometimes it took a while to recognize my writing, impeding my ability to give as many students as I could, feedback. It can also take a little getting used to writing with a stylus. I found if I wrote too quickly, it simply didn’t recognize my writing at all.

This is a new app; there are going to be bugs. I for one am excited to stick with it as the wrinkles are ironed out or I find something that is doing the same thing but better. One day, this sort of app will be part of every classroom and hopefully, very soon indeed. The best of luck to the Classkick team!