Day 26 – More Division and Patterns

Today Math 6 students kept working on their division videos today using this planning sheet.

Math support students spent some time with the patterns that they had created from last week. A good mix of quadratic and linear growth, which is nice because 7th graders are beginning to graph proportional relationships and 8th graders have just transitioned to quadratics.

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For each problem they:

1) Cut it out and taped it in their notebook.
2) Described in words how they saw the pattern growing.
3) Showed on the picture how they saw the pattern growing.
4) Made a table for the pattern (variables should be term (x) and number of cubes/chips (y))
5) Made a graph from the table.
6) Wrote an equation that relates the term to the number of cubes/chips.

Day 25 – Division Videos

Today 6th graders began working on their division projects. They’ll be creating two videos, one with a grouping (measurement) story problem and one with a sharing (partitive) story problem. They’ll model each with an equation, explain the meaning of the dividend, divisor and quotient and solve each using partial quotients. We’re definitely spending lots of time on multi-digit division, but I’m hoping that it’ll pay off when we transition to fractions!


Day 24 – Mystery Heights, Division & Patterns

First day back from our middle school’s Week Without Walls trips. 6th graders headed down to Pench National Park while 7th & 8th graders headed up to the Rishikesh area for hiking and rafting. Good times.


Today all classes started off by beginning to unravel the mystery of how tall my colleague is. Mr. “Smith” doesn’t tell ANYONE how tall he is, so, naturally, it creates an incredible amount of intrigue. He knows that I start off each lesson with an estimation question and so a few weeks ago he sent me this picture:

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We took a look at it today and estimated what percent of Mr. Smith’s height Max’s height (the student) was,. We’ll use that information next class to try and get Max’s height from mine (our first estimation was guessing my height). Kids were super into it!


6th graders spent the rest of the period making sense of division situations by classifying them as “sharing” or “grouping”. Talking through the problems together definitely helped them to uncover the differences in structure between the two models. It was also interesting to notice that most of the students with education backgrounds in Western systems had sharing as their default model for division while most of the Asian students had grouping as their default model. I imagine that the lack of familiarity with the grouping model is what contributes to students’ difficulty in understanding division with fractions. Glad we’re spending such a long time on the different models, hopefully it will make it easier!


Math support students spend the rest of the period finishing up their claims for multiplying integers and creating patterns with linker cubes and integer chips. We’ll be exploring the patterns next class and will use them to talk about linear and quadratic relationships, stuff that they are seeing in their grade level classes.






Day 20 – Assessment & Intro Division Task

Math 6ers took a short assessment on the distributive property today and then completed an introductory division task in which I asked them to write a word problem for 225 / 22 and solve their problem using numbers and pictures. Trying to get an idea of how kids think about division before we start digging into some of the algorithms they’ve been exposed to. Most have been using partial quotients, and thankfully the folks at CMP who had been blogging the revision from the 2nd to 3rd editions provided some helpful input on how to transition students to long-division. Still i’m not totally convinced that knowing the long division algorithm is life-critical. I’d be curious to hear other peoples thoughts on this.


Math support students worked in pairs to revise their Laws of Arithmetic follow up assignments, as many had missed several of the expressions. The whole process seemed to be super helpful, and students got a lot of good practice explaining their thinking and building on their ideas by interacting with each other. At the end I gave each pair a blank copy and they put their revised thinking on it. Definitely worthwhile but boy this stuff takes up a lot of time! We’ll dig in to those integer multiplication claims that came up last class when we have more time next class.

Day 19 – The Distributive Property

Yikes! Busy week with the end of the quarter. Time to catch up with the 180 blog:


Math Support students took the follow up assessment for the MARS Laws of Arithmetic task and then engaged in an integer multiplication number talk for 4 x (-2). Though all the students got the correct answer their reasoning all referenced rules of which they were unclear, and which were disconnected from the models that I know students had used to develop rules for integer operations. We talked about how we noticed our reasoning not being super convincing and we all agreed that it would be worth our time to surface, and then explore, some of the things we thought to be true about integer multiplication. Here’s what they came up with:

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So its clear that they have correct rules for multiplying integers, but still lack some of the number sense behind them. Next class we’ll spend some time digging in and exploring them!


Math 6 students continue to investigate what it means to “Factor” and “Distribute”. Students focused on doing both geometrically using colored tiles and numerically, and I think that it helped some kids to make the connection a bit better. Using the tiles for factoring made me realize how helpful it would have been to use them when we first began discussing factoring,. Oh well, definitely a change to make for next year!

Day 18 – Making Rectangles

Today Math Support students continued their Laws of Arithmetic MARS task from last class. They got some feedback from their classmates on their pairings via sticky notes – orange to indicate matches that someone felt were incorrect and pink to provide some feedback on something that the person found helpful or really liked. Originally I only gave the orange but an 8th grader in the class asked for a different color because he wanted to provide some positive feedback on some good thinking that he saw at one table. Awesome!


We also did a fraction number talk and estimated the length of this song, which a student had e-mailed me to listen to and which I was surprised to discover was not, like lots of middle schoolers’ favorite songs, completely terrible. Screen Shot 2013-10-03 at 3.07.53 PM

As I’ve said already I’m really loving the daily estimation question, and am finding that it is doing wonders for my kids number sense and ability to judge the reasonableness of an answer.


Math 6 students did the same estimation, then broke into small groups for some targeted instruction related to their needs from the assessment. Some of us worked on GCF & LCM word problems that I snagged from IXL, while others extended their thinking by continuing on with the Seeing Stars task I took, and modified, from PCMI.


We then came together as a group and talked about what it means ” to factor”. We started by factoring with a whole number and I modeled how the students were factoring it with colored tiles. We then transitioned to looking at sums and discussed how factoring a sum meant to “join” the rectangles that could be made from each of the addends. I used 4 + 6 as an example:

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The kids then practiced by working on this task. They had square tiles at their table that they could use to help them, or they could just go directly to creating the rectangles in their notebooks, which have grid paper. It seemed to work well and I’m curious to see how they do with the transition to just dealing with the Distributive Property numerically!

Day 17 – Assessment Reflections & Ipad Battery Challenge

Since students took their first summative assessment last class we spent the majority of today setting up some of the routines that we’ll be using to react to the feedback provided on them. To help students get into “mistake detective” mode I took all of the common/interesting errors made by students in all three of my classes and “took” the test using all of those mistakes. I slapped a different teacher’s name on the top, asked permission to use them in this little story and then presented the assessment to students, who worked in groups to review the thinking on the assessment and answer the following questions:

-What does this assessment prove that this person knows?

-What is this person still struggling with or misunderstand?

-What questions could you pose to this person to help them revise their thinking?


In the process students identified errors that were made, conjectured about what they must have been thinking, and revised questions which were not full correct (all of them). The kids seemed to really enjoy trying to “get into someone else’s head” and it made it much easier for them to analyze their own assessments, which they did next. 


Math Support kicked off with the estimation question below. Again totally stole the idea from Andrew Stadel. ios 7 may make look more sleek but it makes this a bit harder with the light background color. May need to do the next one using itunes.   Image

The kids totally loved it, did some cool thinking, and were all really close.  I was about to transition when a student commented on the fact that I should plug my phone in. We all zoomed in on the battery indicator in the top right corner and got super excited, something else to estimate!


We started by estimating mine and then students had the idea to estimate each other’s (we’re a 1 to 1 ipad program). Just like that the Ipad Battery Challenge was born! Here’s how we did it:

1) Turn off the percent indicator on your own ipad then lock it.

2) Switch ipads with someone else.

3) Guess how much battery they have left. Sketch the battery indicator and explain your guess. 

4) Get your ipad back and turn on the percent indicator. Then lock it again.

5) Switch back and everyone press the home button on the count of 3 (so the screen lights up)

6) Revel is the sound of middle school squealing (delight, not pain).


It was totally fun, we’ll definitely do it again. They were still talking about it as we finished up our work on the Laws of Arithmetic MARS task we had started last class. 

Other thoughts:

1) It is ridiculous that every one of our students has an ipad.

2) The whole “how long do you have left?” question would be a cool one to explore. Anyone done this?

3) This totally came together in the moment, so how could it be better? 

4) Thanks again Andrew, this kind of stuff is super fun.