Math class the other day – I had 5 students in grades 6,7,8 with math abilities ranging from 3rd to 5th grade. They started with this:
(Sorry about the writing . . .started jotting their comments on the paper – had to switch to writing elsewhere.)
So – here’s what I heard: -it goes up one – it goes down one, -they all have 2 at the bottom, the are all shaped like an ‘L’., they ‘step’ up, like stairs – or they go down like stairs – depending on where you start.Then we talked about – does it matter where you start? – some said yes, some said no Why? Why not? – because you can still see the same things – the up or down, the 2 at the bottom where ever you start, so it doesn’t matter.The 8th grade girl, who writes so you have to use a microscope to read it, says, “I want to label them, I NEED to label them!” – ok – how ?- everyone agreed to the steps written above. Ok, now what? –
An 8th grade boy, who is normally quite talkative sat with his elbows on the table staring silently at the cubes for a bit. Then says – well, they all have the two on the bottom and, so, you could add from there. Great – nudge, nudge for a little more . . . he thinks – the other 8th grade boy, who is fairly quiet – says very loudly – “They all have 3 in the tower, so then you just add 3.” I was so excited to hear this, especially from him. It was really hard not to add my 2 cents and further the conversation. Keeping my mouth shut is not one of my strengths, but I find I’m getting more capable of doing so as I just wait and let them mull things over. Then he quickly says, “I don’t know, never mind.” Urgh!!! – I said – no, your being brilliant, you’re totally on to something – just let it simmer a bit. (say what? then we had to discuss what that meant – ha!). So, As the 2 8th grade boys are simmering . . . my 6th grade boy, who is famous for having his head on the table in avoidance, says, “You just take the number of the step and add 2 to the tower and make sure you have the little piece at the bottom, that’s all.” The first 8th grader is back – “Yes!, that’s the add 3 part – 2 on the top and the little one at the bottom!” While this was going on, I had given the 2 girls some steps to build – step 17 and strep 12. They built, then listened to the boys, then changed their mind and would add one, take one off etc. So, we decided to write a formula: step +3 = your whole building, or – step +2 on the tower + 1 net to it = your whole building – then we ended up with: the base of 2 + step -1 = the tower . . . One student really wanted to add to the one at the bottom as the tower was added to because it was not equal and looked wrong and would fall over 🙂 I told him we could get back to that another day, as, at this point, we were out of time 😦 There was a ton of good conversation not written here – but it was an awesome class – and everyone was engaged!!