Subtraction can be tricky.
Taking things away from six year olds is never a very popular idea.
But Quick Images, those are super fun!
So, I wanted to plan a Number Talk that would get us thinking about subtraction – but I wanted to change it up just a little bit from the 10’s frame and Rekenrek. I wanted to use the most “handy” tool that I had access too – a tool that we all ALWAYS have access too…
I am a huge fan of the Origo “Hands-on” approach where you spend time at the beginning teaching kids the special way of counting with their fingers- starting with the pinky, across both hands, ending at the opposite pinky, palms facing out. When you are facing someone who is using the method to count, you can group fingers, count on from 5, count up to make a 5 or a 10 – lots of wonderful thinking to be had.
So, I just started with one that they could use an addition strategy previously taught to quickly identify the number; I put up a full hand of 5 and my thumb, making six. After surveying the room, the general thought was that I showed the number 6. When I asked for how they knew it was six, here are some of the responses that I got…
“I counted by 1’s – 1, 2, 3, 4, 5, 6”
“I saw 5 on one hand and I counted on one more – 5, 6”
“There were 5 and 1 more – 5+1 equals 6”
From there, I moved on to my second flash of fingers; starting with the pinky, 4 fingers up, thumb down and zero on the second hand – showing 4. Again, the group was pretty certain there were only 4, and here is why they thought that…
“I counted by 1’s – 1, 2, 3, 4 – and that was all”
“I saw 2 and 2 more, and I know that 2 plus 2 is 4”
And, what I was looking for…
“If you had one more up, it would be 5. But it was 4.”
Inside, I was smiling everywhere, but outside, still, calm face.
“Can you tell me more about that?”
“Um…yeah. You have 5 fingers, but 1 is down. So, there are 4.”
So I recorded 5-1=4. And I asked someone else, someone who I knew was following that line of thinking, and I asked them to repeat what that student had just said.
“If you have 5 fingers, and 1 of your fingers is down, then you have 4 that are still up”
So I moved onto my last flash of fingers; 1 full hand up, then 4 fingers up on the second hand, pinky down, showing 9. This time, they were unable to wait to be called on – “Nine!” was being shouted all over the place. After checking to see if there was anyone with a different answer, I asked how they got to 9, and here is what I got…
“There was 5 on one hand, and I counted on the other fingers – 5, 6, 7, 8, 9.”
“5 and 4 more equals 9.” – so, before recording that, I asked for more information on the 4, and we got to go through again, 5 fingers on a hand, but 1 finger was down, so that left 4 up (YAY!)
The room quieted, and I asked, “Did anyone get 9 a different way?”
And then 1 brave hand went into the air, and he said, “Well, you have 10 fingers, and all of them were up, except that pinky, so it would be 10 minus 1 equals 9”
I saw this face sprinkled across the room…
(But older of course!)
…and I heard lots of “Oh yeah! I saw that too!”
It took 7 minutes. And then I could transition to my lesson about data.
But I introduced subtraction, the subtraction symbol, and the idea that subtraction can be a whole something, like a hand, spilt into 2 parts, fingers that are up and fingers that are down.
Lots of work to still do! But I’ll mark a win for Number Talks for today!