Good Things: Volume 10

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My students have continued to enjoy our play table.

I got those on Amazon.

Those are Lego knock-offs from Target the dollar section.

I had a couple students who came early every day to class after lunch and each day they would try to balance a larger cube like that.

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I went to a math Ed Camp hosted by MCTM, and it was a great day of connecting with local math teachers!

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I’ve already tried a couple ideas people shared at the Ed Camp.  Jess Strom mentioned that she loves combining Open Middle problems with Vertical Non-Permanent Surfaces.  I tried it, and it was my favorite day of Open Middle problems yet! I found that students were more engaged and on task with the problem than when they do it on paper.

Students were working on this problem and this one.

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I pulled out Jay Chow’s Desmos Breakout activities recently for the first time this year.  Students always enjoy these so much.  You can find all of his activities here.  If you haven’t seen these yet, check them out!  They are awesome!

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The makers of Set came out with a new game, and it’s great!

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One of my students had an awesome way of thinking about converting 5/8 to a percent.

“Well, we already wrote 1/8 as a percent today and that was 12.5%, and I know that 4/8 is 50%.  I added 12.5% and 50% to get 62.5%.”

I use this method quite a bit with other types of problems, especially when finding percents of dollar amounts, but I hadn’t thought to use it in this direction – going from fractions to percents.  I love learning from my students!

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I had a couple of students debating over multiple days about whether 0/0 would be 100% or 0%.  In this class, we had not been covering percents and this debate was completely student initiated.  We did talk about 0/0 being undefined and sort of an irrelevant question, but they were debating that if you HAD to pick 0% or 100%, which would it be.  I loved listening to their arguments for which one they thought it was.

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The last couple years I’ve introduced the Pythagorean Theorem using Notice/Wonder, and I’ve liked how this has gone.  I really like how more of my students continue to think of the what is happening visually after introducing it this way.

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Last year I used Dan Meyer’s Taco Cart for the first time.  It was the first 3 Act I’d ever done and it was a spur of the moment decision to try it when I found out last minute that nearly half my class was gone for the day.  I used it again this year, and I felt like I facilitated it a little better than I did the first time.  I made adjustments to how we did this activity on the fly, and I was proud of myself for that.  Students are turning in their solutions on Monday, and I hope to write a short post on how this went soon.

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We used one of my favorite Polygraphs recently.  I absolutely love this one for angle pairs in 6th grade.

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We had a crazy couple months after Christmas break with several cold days, snow days, and late starts.  We had a brown Christmas, and ended February with normal amounts of  snow for MN.  It’s finally starting to warm up and the snow is melting.  Normally I don’t like this time of year when the snow gets muddy and the grass is brown; however, I’ve never been so happy to see brown grass as I have this year.

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Another idea shared at the MN EdCamp by May Vang was to give students examples of a vocal word and have them come up with the definition.  I tried this with rational and irrational numbers, and it didn’t quite go how I envisioned with my first class, so I changed things up with the second class.  It went better, but still not as well as I had hoped.  So I changed it slightly for the 3rd class, and it went much better.  I added some notice/wonder to the prompt, and it made all the difference.  No surprise there.  I don’t know why it took me three tries to add that to the prompt.

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A student stopped in my room after school one day this week with a baggie of seashells, “I keep forgetting to bring these to class.  I got these shells when we were on vacation, and they’re for you.”  She thought of her math teacher while on vacation.  How did I get so lucky to be apart of these kids’ lives??

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It was a work day in 8th grade this Friday, so I put on some of the NCAA basketball games.  A little math and some March Madness.  I can’t think of a better way to head into the weekend.

8th Grade Unit 5: Systems of Equations (Part 2 – Elimination & Choosing Method)

I shared here part 1 of our unit on systems of equations -solving by graphing and by substitution.


Elimination

I started this unit with the following warm-up.

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Then I followed it up with this notice/wonder.

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One of my students this past year noticed that, “These are like the problems we did for warm-up.”  I love when my students notice connections between the warm-up and the lesson for the day and that I’m not just having them do random stuff.

I was really pleased with how this led nicely into the lesson for the day.  Students noticed that in each problem there was a zero.  They were able to tell me why that happened.  When I told them that this is another method for solving systems of equations called elimination, at least someone in each class was able to explain why they thought that elimination was a good name for this method.

It had been a while since we had done Vertical Non-Permanent Surfaces, and these problems work great for that.

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Choosing Method

The last part of this unit was having students choose the best/most efficient method for solving a system of equations.

I started with this Desmos Activity.  I didn’t have students solve the systems the first day.  I wanted them to just think through what method they would want to use to solve each.  The next day they actually solved some of the systems.

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I love this Desmos Activity from Paul Jorgens.

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I’ve uploaded some of the worksheets and notes I used from this unit here.

Distributive Property

Earlier in the year my 6th graders talk about the distributive property without variables. Partway through this post I shared how I introduce that idea to students.

Later on in the year we start talking about the distributive property with variables.  I started by reviewing how they used the distributive property earlier in the year without variables.  I was so impressed with how many different ways my students came up with to use the distributive property to multiply 7×48.

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This year I used Illustrative Math Unit 6 Lessons 10 and 11 to introduce the distributive property with variables.

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Illustrative Math Grade 6 Unit 6 Lesson 10

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Illustrative Math Grade 6 Unit 6 Lesson 10

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Illustrative Math Grade 6 Unit 6 Lesson 11

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Illustrative Math Grade 6 Unit 6 Lesson 11

As we were working through the resources from Illustrative Math, I loved how they incorporated the idea of factoring, without explicitly calling it that.  I had done a little bit of that in the past with this puzzle from Open Middle.

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Again, I was super impressed with all the different solutions they came up with.  I didn’t quite use the “rule” of the Open Middle problem and allowed students to use fractions and decimals.

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After going through that, students worked on this distributive property puzzle.  When students finished that, they started working on some Yohaku style puzzles I created.  This was my first time creating my own puzzles like this, so I had no idea how it would go over with students.  When I made the puzzles, I found two solutions for each.

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This activity went over SO much better than I even imagined, and my students found solutions that were much more creative than the ones I had found!

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When I was explaining how these puzzles worked to students I told them that if I did it correctly when I made them, each one should have at least two solutions.  One student asked, “But what if you did it wrong?”  I told them that very well could have happened. I’m human, and it’s May.  I’m tired.  😉

After the first group found two solutions for the same puzzle, one student told me, “You did it right!  You didn’t make a mistake.”

My students were so engaged while working on these puzzles.  They were so persistent.  I loved seeing all the eraser marks on their paper as evidence of them trying again and again and again until they found something that worked.  Students were cheering when they found a solution.  I wish I had recorded them working on these.  It was fantastic.

After the bell rang one student said, “Could you make some more of these for next week? Maybe nobody else liked them, but I thought they were fun.”

I also am looking forward to have a conversation with this student about the right column.

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I completely understand the student’s thinking.  This is the same student who came up with this solution earlier in the week.

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Here is the link to the puzzles I created.

If you create more, I would love to see what you come up with.  After sharing a picture of the puzzles on Twitter, Yohaku created a few similar.  You can find them here.


Solving Equations

Then we start solving equations using the distributive property.

I gave them a couple review problems prior to starting this.  The problems were similar to the following.

  1. 3(x + 4)
  2. 3x + 12 = 24

Then I told them we were going to use both of those ideas today and put the following problem up:  3(x + 4) = 24.

As students were working on this one student goes, “Oh Ms. Bergman, you are so smart.”  Another example of a student noticing that I am intentional about the problems I put in front of them, and I love it.

(Also, yes I know we don’t need to use the distributive property to solve 3(x + 4) = 24.  We talk about that too.)

I made an Add Em Up activity for this.  You can download the file here.  Add Em Up is an activity I got from Sara Van Der Werf.  You can read her post on this activity here and a post I wrote here.  Students are always super engaged when doing this!  We also spent some time doing Vertical Non-Permanent Surfaces with these problems and students were also super engaged in the math they were doing.  Here are some of the problems we used for VNPS.

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VNPS Variation

(VNPS: Vertical Non-permanent surfaces)

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This is a different time we did VNPS, but my classroom looks like this nearly every time we do this.  Why don’t I do this more often??

Last year I created a “Two Truths and a Lie” worksheet on exponent worksheets.  Students simplify three problems.  Two of the answers are the same, and the third answer is similar but not quite the same.  I was really happy with how the worksheet turned out and how it went last year.

The day I had this worksheet in my lesson plan, I realized I wasn’t really looking forward to another worksheet with my 8th graders.  I try to mix things up, but lately they’ve had worksheets pretty consistently.  I was thinking through other options and was trying to come up with a way to change things up less than 2 hours before I had students in my room.

Screen Shot 2018-04-05 at 8.33.32 PMScreen Shot 2018-04-05 at 8.33.43 PMScreen Shot 2018-04-05 at 8.33.49 PMScreen Shot 2018-04-05 at 8.33.54 PMWhiteboards!  I realized it had been a while since I’d had students work at the whiteboards.  I took screenshots of the problems, projected them on the board, and had students work in groups through the four problem sets.

In the past when students worked at the whiteboards, I had them do one problem at a time and get it checked by me.  This time, I had students do all three problems in each set before I would check their answers.  They knew that two of the answers were going to be the same and one would be slightly different, so they already were doing some self-checking as they went along!  When students called me over to check their answers, I would tell them how many problems they had wrong but wouldn’t tell them which one.  I really liked the small change in how I had students do these problems.  This is something I do a lot when they’re working in Desmos or with other activities, but I hadn’t done it in this situation before and loved how it went.

I had more students engaged for more of the hour by doing the problems this way, and my students were talking through the problems more than they would have if they were working on the worksheet.  I actually had students cheer when I said we were going to the whiteboards.  🙂 It was a good reminder that I don’t have to always come up with some fancy activity to switch things up.  Something as simple as taking problems from a worksheet and having students complete them in a different way is enough sometimes.


Here’s the link to download the worksheet and others on exponents.  Here is where I shared other things I did in this unit last year.