Group Number Signs

Last year in this post I included a link to my group number signs inspired by Sara.

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These were truly one of the. best. additions to my classroom last year.  I absolutely loved them!  The only thing I didn’t like about them, was I hadn’t made enough!  I often like to have smaller groups or pairs, and often wished I had signs for more than 10 groups.

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SO I decided to make signs up to Group 17.  You can download the file here if you’re interested in using them in your own classroom.

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8th Grade Unit 6: Exponents (Part 2 Scientific Notation)

I shared part 1 of our unit on exponents here.


I got most of my notes from Sarah’s blog.  She also has a ton of activities on her blog here.

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As I was writing this, I remembered this image that Heather shared from one of Sara’s presentations.  I think this would be a GREAT way to introduce scientific notation next year.  I’ve got to remember to do that!

The last couple years, I’ve used tables similar to those below to help students notice patterns.

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After we talk about converting between standard form and scientific notation, I’ve used this Desmos activity.  I also like this Desmos activity.

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Then we get into multiplying and dividing numbers in scientific notation.

I made this Desmos activity for practice.

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The biggest thing my students struggle with at this point in the unit is when they multiply or divide and get a number that isn’t in scientific notation.  Something like 64 x 10^6.  They know the exponent will change by one, but many students get mixed up on whether it gets bigger or smaller.  I always, “Don’t try to memorize a “shortcut”.  Think about what 64 x 10^6 is.  Write it out in standard form, and then convert it to scientific notation.  Then you don’t have to try to memorize anything.”  The students that listen and follow my advice, usually have no issues with this, but it’s the students who want to take a “shortcut” that end up not getting these problems correct.  Please tell me I’m not the only one who has this issue!


I’ve got a couple Which One Doesn’t Belong? warm-ups for scientific notation.  I know I pulled the second one from Twitter.  I can’t remember who shared it.  If it’s yours, please let me know so I can give you credit for it.

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I’ve used this scavenger hunt as well.  I like that it gets students up and moving around.

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I created this worksheet for students to practice.  (I think I created it.  I may have modified it from somewhere.  Again, if you recognize it, please let me know so I can give credit to who originally created it.) . You can download it here.  I’ve created a few other worksheets of this format and like that it’s self checking for students.

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Transformations

I was able to squeeze a few days of transformations in with one of my 6th grade classes.  These are 7th grade standards in my state, but this is the group of students I will have again next year as 7th graders with the end goal of getting to all the 8th grade standards.


I started with this Which One Doesn’t Belong?

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And followed up with this Desmos Polygraph.

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I was able to borrow notes from a colleague for this unit.  Teaching in a small district this doesn’t happen often as none of us teach the same course as anyone else.  For each different type of transformation, I started with a Desmos activity.

Translations

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Rotations:  Students made a table of values of the pre-image and new image.  They created different images and looked for patterns to predict how to rotate an image 90 degrees clockwise, 180 degrees, and 90 degrees counterclockwise.

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Reflections

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And we ended with Transformation Golf.  I had so hoped to get to Robert Kaplinsky’s Skytypers or Pac-Man, but there just wasn’t enough time.  There’s always next year.

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I was amazed at how engaged students were with the Transformation Golf.  It was the second to last day of school, and we were doing locker clean outs.  I asked students to sit at the tables in the commons and work on this when they were done cleaning out their lockers, and they did!  They were having so much fun with it, it was great!  Desmos saves the day and prevents chaos at the end of the year!  I shouldn’t be surprised by that at all.

Similarity

I have a third of my 6th graders again next year as 7th graders.  In those two years, my goal is to teach them the 6th, 7th, and 8th grade standards.  It’s been somewhat of a slow process, but I’m making progress.

This year I was able to get a unit in on similarity at the end of the year with my 6th graders.  I definitely pushed them and challenged them in this unit, and my students rose to the challenge.  I was so proud of them for the challenging proportions they were solving.  Some of my students definitely noticed that I was pushing them a bit more and became frustrated that it wasn’t coming as easy to them, which wasn’t a bad thing.  We worked through that.


It had been a while since we had solved proportions, so I started the first day of our unit with a few review problems.  I knew I wanted to use Marcellus the Giant from Desmos at some point in the unit.  As I was planning, I wasn’t quite sure when I wanted to fit this in.  Should I intro with this and have them try it without telling them anything about similarity or scale?  Do I use it after we have talked a bit about both of these?  I ended up deciding to use it right away at the beginning and was glad I did.  Students may have been confused at some points throughout the activity, but by the end they were able to explain what it meant for a giant to be scale or not scale.

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After a couple days of notes on similar polygons and scale, we did this activity around the room.  I had done another Math Lib activity earlier in the year, and my students love it.  I fully admit that I could have created something, but I was end-of-the-year teacher tired and decided it was worth it to get the activity linked above.

The weather in Minnesota was FINALLY nice, so I decided to do this activity outside with students.

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Then I saw this and knew I had to make this happen in my classroom.

Lisa used the game Clue and incorporated scale factors into the activity for students to figure out who was intentionally making math mistakes.  😉  Read Lisa’s post on how she set up the activity with her students.

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I ended up doing it slightly different than how Lisa described in her post.  I printed out Clue boards that Lisa shared and the Clue cards.  I wrote different numbers on all of the cards.

Students started by finding the area of each of the rooms on the clue board.  Once they had done that I gave them one Clue card with a scale factor on it and had them pick which room to use that scale factor for.  After they found the new area, I checked their work.

Nearly every group did what I expected them to do.  They took the area and multiplied it by the scale factor, rather than multiplying by the scale factor squared.  That was one of my main reasons for doing this activity -I wanted students to see how scale affected area since prior to this we had just talked about how scale affected length.IMG_7592

I let students struggle with that for a little bit before giving them a hint to help them out.  I put a grid up on the board and we looked at a 1×1 square.  Then I picked an easy scale factor, I think it was 2, and we talked about what the new dimensions of the square would be.  Then I asked students what the new area of the square would be?  I saw the lightbulbs go off for some students, and then I asked how that would apply to the problem they were working on.  It was enough for all groups to eventually figure out what to do in the Clue activity.

In the future when I do this, I would be more intentional about the numbers that I picked for the scale.  I used some pretty small numbers for some of the cards so after applying the scale factor the areas of the rooms were pretty unrealistic.  Overall though, it was a great activity and I am looking forward to using it again next year.

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.

8th Grade Unit 5: Systems of Equations (Part 1 – Graphing & Substitution)

Graphing

Even though this is Unit 5 in 8th grade, this is the unit I’ve done last the past couple years I’ve taught it.  It just worked out that way my first year teaching 8th grade, and I liked it that way so I did it again this past year.  I like having it at the end of the year because it’s a good way to review graphing lines.

I start the unit by spending a half day or so on just a review of graphing lines.  I almost didn’t do that this year, but was SO glad that I did.

Then we do Desmos Polygraph and this Desmos activity to intro systems of equations.

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Then we spend some more time practicing.  I’ve used this Desmos activity in the past.

After that we get into systems of equations that have no solution or infinite solutions.  I usually start by putting up one of those types of problems without giving students any explanation.

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Students have had a lot of experience solving problems with no solution or infinite solutions by this point in the year, so I usually have some students who come up with the fact that because both equations are the same line, there are infinite solutions.


Substitution

I blogged here about how I introduce substitution to students.  I’ve used this method 3 years in a row and am still amazed every. time. how smoothly it goes.


Here is the link to download some of the worksheets I use for this portion of our unit.

8th Grade Unit 4: Applications of Lines

We start our unit on applications of lines by discussing independent and dependent variables.  I have a note to myself to remember to use the following language next year because it worked well this year.  Nothing earth shattering, I know.

  • “(independent variable) causes change to (dependent variable)”
  • “(dependent variable) depends on (independent variable)”

I use a lot of Sarah’s resources found here for my notes, and I’m pretty sure that’s where I got the problems for this Desmos activity.

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The next day we do Sarah’s Ghosts in the Graveyard activity with independent and dependent variables.  Every time I use that activity I think to myself, “Why don’t I do this more often?  It’s great!”

After students have a pretty solid understanding of defining the dependent and independent variable, writing linear equations from word problems goes a lot better.


Then we get into parallel and perpendicular lines.  I blogged briefly about what I did last year here.

I start with parallel lines and use this Desmos activity.  One of the downfalls of starting with that activity is that when students are asked to solve problems where they need to write the equation of a line parallel to a given line through a specific point, they want to use Desmos to guess and check.  This is a good strategy, but I also want them to know another method.  I start the next day with a couple problems like these.

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After spending another day or so on parallel lines, we finally get into perpendicular lines.  I start with this Desmos activity.

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We spend another day or so practicing with perpendicular lines.  I’ve used this activity before and like how it brings back different forms of lines.

We also talk a little bit about parallel and perpendicular lines and quadrilaterals using this Desmos activity.

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Then we get into scatter plots.  I start with this Notice/Wonder

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We do Desmos Polygraph next.  Last year I had a student ask if there were two “loners”, and I will forever think of outliers as loners.

After students do that activity, I put the graphs up on the board and ask students to put them in groups.  They end up describing the different correlations to me.

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This Which One Doesn’t Belong? is great around this time in the unit.

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I took a couple tasks from this page and turned them into Desmos activities.  (I know she tweeted out links to the activities at one point, but I couldn’t find them.

Here’s one on correlation.

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And another on lines of best fit.

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Here is the link to download some of the worksheets I use in this unit.