I was originally supposed to co-teach a performing arts elective, but as things started falling into place it was determined that I needed to teach intervention, and I partnered up with the 7th grade math teacher to do so. The nice thing about it is that we get full control over what we do and which kids we get and when. So we decided to run various themed intensive interventions with kids from 6-8th grade.
While I am STILL trying to figure out how to keep up with the rest of 8th grade math in my district with one less day of instruction every week, I am actually incredibly grateful for these times with students. I get to do the things I know students really need, and I have the time to work on mindset, exploration, inquiry, and lots of number sense.
This past Wednesday was particularly fun, and since I spend so much time thinking about the things that need fixing, I thought I would indulge myself and think about the things that were good!
So, here's a little run-down:
Group 1: Number Sense focused on Multiplication and Building Rational Numbers
My first group is mostly made up of kids that I also had during last trimester and they are the ones who struggle the most in their classes. We focused really heavily on number sense with multiplication last trimester (as well as mindset), and most of them actually requested to be in our class again! We had done work on whole number place value and operations before, but this trimester, we are working towards dealing with rational numbers.
During our number talk the prior week, one of the students happened to question whether 0.9 and 0.90 were the same thing. We had a pretty big discussion and the class convinced itself that they are in fact the same value, even though the numbers are different.
Because this idea of equivalence and place value came up, I wanted to start with that, so I made a list of equations and students had to discuss and determine whether they were true or false and why. Part of the way down the list, I had the equation "0.10 = 0.010" and boy, was that controversial! One group of kids was convinced that the two sides were equivalent and they put up quite the argument. The rest of the kids went through 4 or 5 different ways of looking at the numbers to try to prove the statement false. I had kids jumping out of their seats in excitement over what other students said. Students were at the board drawing, explaining, justifying, asking their peers questions. I WISH I had thought to take a picture of my whiteboard at the end - it was COVERED with math from students. And these are the kids who are supposed to be "bad at math" - what a bunch of hooey. At the end, one of the students looked at me wide-eyed and said, "That discussion was CRAZY!" I asked if he thought it was important and I got "Yeah!" right away. Then he asked if we could do number talks again next week. This is a student who was loudly complaining about being placed in this class at the first meeting (the prior session).
Group 2: Place Value
Our second group is the only one that includes 6th graders (because of timing). My partner teacher and I decided to ask the 6th grade teacher what he would like us to focus on, and he requested place value.
I had done some research on various routines and strategies for place value, but instead of trying to "teach" place value, I decided to do an exploration with "Exploding Dots" from James Tanton (you can check out the entire course here). At the first session, I showed this animation and we did notice and wonder (we did this twice, since it's hard to tell what's happening in the video right away). Then, students worked on answering their list of wonderings. This time, I showed the video again (there were a couple kids absent), and then had the students work on creating the code AND the boxes for 1-20 (in base 2). Our focus was on finding patterns. As students were working, I just wandered around and asked them what they noticed and if they found any patterns.
6th graders are really cute and small by the way.
Anyway, the 6th graders take the longest to warm up to me because I am TOTALLY new to them and I also seem really weird because I make them do things like watch weird videos and make them look for patterns instead of taking notes. But, as different kids started to see patterns, they totally lit up and wanted to tell me about it. Some of the more notable noticings:
- As you count up consecutively, the last digit will always alternate 1, 0, 1, 0, etc.
- There is a pattern of circling back around to all the things that happened before every time a new place value happens
- Any double is the same number, but with a zero at the end (basically, shifting place value).
We didn't have time to get to talking about what "1" dot is worth in each box, but that is where we will go next week.
Group 3: Number Sense in Application
My last group is more focused on heading into grade-level work, but they struggle with application. They tend to sort-of get and do procedures, but they don't really have the background of how/why things work and they get confused. We are working on making sense of problems and connecting representations.
I just stole Steve Leinwand's suggested plan for improving problems from the curriculum (from his Asilomar 2016 presentation) - sorry... I can't find a link, but here is a link to his twitter page and his blog. Here's the basic idea: Give a one piece of info from the story (math problem). Ask the kids what three things they can tell you? Allow them to make inferences (they think this is hilarious). Then give them the next piece. Ask what three things they know... etc. Then, ask them for the question. They solve the questions the class posed.
This went pretty much as expected, except that the kids went WILD with wanting to make up stories for their word problems. One of my squirrely boys who complained about being put in my class was ALL excited to make up stories about the boring word-problem-people. He would get so involved, he would often have to solve most of the possible questions as part of his story. This rubbed off on my MOST reluctant student, who begged me to let him make a word problem story to share with the class (part of the plan for the next session).
So yeah - it was a fun day - lots of questions, lots of smiles, and lots of math. Who knew that math intervention could be such a magnet for joy :)
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