This is the third post in a series about my magic elevator animations. In my last post I started to describe a teaching sequence. We had just reached the point where students were finding answers by translating number sentences such as ‘-3++4′ to magic elevator scenarios (‘starting on the third basement level, 4 happy people get on the elevator’). Here’s what I do in the next lesson (after revising those number sentences!).

1. Draw the elevator diagram on the board again. Ask questions like: “If the elevator is on the second floor, what are two ways that it could move to the fifth floor?”. When students provide the answers I translate them into number sentences on the board (’2++3=5′, ’2- -3=5′). In this step I only ask questions where the elevator moves upwards. By the end of this step I have several pairs of equations on the board (e.g. ’2++3=+5′, ’2- -3=+5′  and ’1++2=+3′, ’1- -2=+3′ and ‘-2++4=+2′, ‘-2- -4=+2′.
2. I ask the class to tell me what they can learn from these equations? What do the pairs have in common? We draw a conclusion together that subtracting a negative has the same effect a adding a positive (with the same magnitude).
3. I repeat step 1 but ask questions that involve the elevator moving downwards. For example “If the elevator is on the second floor, what are two ways that it could move to the ground floor?”. Again I end up with several pairs of equations on the board (e.g. ’2+-2=0′, ’2-+2=0′ and ‘-1-+3=-4′,’-1+-3=-4′ and ’5-+2=+3′,’5+-2=+3′).
4. I ask the class what we can learn from these new equations? What do the pairs have in common? We draw a new conclusion that adding a negative has the same effect as a subtracting a positive (with the same magnitude)
5. At this point I write ’2       =-3′ on the board and ask the class to find two ways to complete the number sentence (in this case ’2+-5=-3′, ’2-+5=-3″). They will need to add an operation and a second number. I then organise the students into groups and ask them to create similar ‘fill in the blanks’ questions for each other.

I try to give the class an opportunity to sleep on this before I do more. I will continue this teaching sequence in a later post.