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.

6th Grade Unit 8: Probability

Another new unit and another Which one Doesn’t Belong? to start out.

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Then we did notice/wonder with tree diagrams.

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After doing some practice with tree diagrams, I encourage students to start looking for a pattern to figure out the total possible outcomes each time.  Most often students are able to notice the counting principle.  Sometimes students will notice the pattern before I even mention it.  They’ll ask, “Can’t you just…”  I usually nearly scream at them, “Wait! Not yet!  Don’t ruin it for those that haven’t noticed the pattern yet!”

Tree diagrams are good opportunities for students to make up the problems as they go.

One problem I like to give students is “A tree diagram has 16 possible outcomes.  What could the tree diagram be?”


Then we start talking more about probability.  After spending a day on theoretical probability we start talking about experimental probability.  I know there have to be some awesome probability activities for 6th grade, but I haven’t found them yet.  (If you’ve got some, please send them my way!)  What I’ve done the past several years is set up 5 different stations for students to work through:  coin toss, dice, deck of cards, box with different colored cubes in it, and a wheel with different colors on it.  Then students compare their experimental probabilities with the theoretical probability.

Here’s an example of one of the stations for experimental probability.

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I also use this as an opportunity to review converting between fractions, decimals, and percents.  Another way that I like to spiral concepts in this unit is to give a problem like the following:

The following numbers are written on cards and put into a box:  1, 1, 3, 4, 5, and 8.  What is the probability of randomly picking a prime number?  a factor of 20?  A multiple of 4?

To review we play mathketball.  Students LOVE this simple game.  Students make a circle around the room with their desks, and I put a trash can in the middle of the room.  Students answer a question I put up on the board, and if they get it correct, they get to crumple up their 1/4 sheet of paper and try to make a basket.

Here’s an example problem from that.

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Here’s a different class playing mathketball, but you get the idea of what it is.  I do try to pick topics for mathketball where the problems shouldn’t take students too long to solve and/or have fewer steps.  I don’t want students to feel rushed, but I also don’t want students who complete problems quickly to be waiting a long time.

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6th Grade Unit 7: Surface Area and Volume

As I’m writing posts on each unit I teach, I’m noticing a theme.  I often start a new unit with Which One Doesn’t Belong?  This unit was no different.

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Then because it had been since the beginning of the year since we had our unit on area, we reviewed with the worksheet pictured below. (Link to download is at the bottom of this post.)  I’ve thought about restructuring the order in which I teach the units, but I like that by having my unit on area at the start of the year and my unit on surface area and volume at the end, it forces students to go back and remember what they learned at the start of the year.

I actually had a parent compliment me on that worksheet at conferences.  The parent liked that it forced the kids to get the answer correct rather than just move on to the next problem right away.

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Surface Area

When we talk about surface area, I really stress that the name “surface area” makes sense based on what we’re finding -the area of the faces.  I have students count the number of faces in the figure and number their paper accordingly.  I’ve found that this really helps some students keep track of their work as they work through the process of finding the surface area.


Volume

I remember the first couple years I taught volume one of the confusions for students was all the vocab, and I wasn’t really expecting that.  Then all of a sudden the lightbulb went off for me, and I realized where the confusion was coming from.

My students were getting confused between the base of the faces of the prism and the base of the prism itself.  Same goes with the height of one of the faces of the prism and the height of the prism itself.  Up until that point when we talked about the “base” we were talking about a side length, but now the “base” was a face itself.  Also, within the same problem we were talking about multiple different heights.

Once I realized where students were getting confused, I started changing how I described what we were doing. When I talk about finding the volume of a prism, I talk about how we first need to find the area of one of the bases of the prism.  I always make sure to say “base of the prism” instead of just “base”.  We talk a lot about how the bases of the prism are two faces that are parallel to each other and are congruent.

Then, once students have found the area of the base of the prism, instead of telling them to multiply by the height, I say, “Now we need to multiply by the height of the prism -the distance between those two parallel bases of the prism.”


Last year I shared a couple of the activities I did in this unit in this blog post.  I really like loop activities because it gets students up and moving around.  It’s even better when the weather is fantastic and we can go outside! 🙂

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I use this Desmos activity prior to having students start solving word problems involving surface area and volume.

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6th Grade Unit 6: Angles and Triangles

Angle Pairs

I used this Which One Doesn’t Belong? to start our unit on angles and triangles.  I love how starting with something like this gives me insight on where students are at with this topic based on their answers and the vocabulary they are using.

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After taking some notes on different vocab words we came back to the same image at the end of the day, and I asked students to use the new vocabulary to describe the images.

I also had students do this Desmos Polygraph several times throughout the unit as they learned new vocab words.

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Sum of Angles of a Triangle

In one of my classes, I had students cut out a triangle, rip off the angles, and put those pieces together to form a line.  It didn’t go quite as I hoped with that class, so in the other classes I was the only one who cut the triangle.  I would like to figure out a way so that more students see what I want them to see as they’re cutting the triangles and putting the angles together.

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Jo Morgan shared several good Angle Chase activities in this Math Gems post.

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Interior Angles of Polygons

After talking about the sum of the angles in a triangle, I have students Notice/Wonder with polygons divided into triangles for them to figure out the sum of the interior angles of polygons.

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After they’d done some practice with that we made a table to come up with the general formula.

 

6th Grade Unit 5: Percents

We start our unit on percentages by talking about converting between fractions, decimals, and percents.

I start with this Which One Doesn’t Belong? to get students thinking about percents and for me to see where my students are at in their understanding of this.  Then I ask them to brainstorm everything they know about percentages.

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I created matching cards for converting between decimals and percents years ago.  I intentionally picked numbers with lots of 2s and 4s in them so students can’t just say, “These are the only two cards with a 5 and a 6, so they have to match”.  You can download the file here.

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I spend several days letting students practice converting between fractions, decimals, and percents with different puzzles I’ve found over the years.  If I remember where I’ve found them, I’ll link to them here.

This is one puzzle I like for fractions and percents.

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From Chris Smith‘s newsletter via Jo Morgan’s blog.

Here is an Open Middle problem too.

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And yet another good Open Middle problem on percents.

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Then we get into applications of percents:  finding tip, tax, and discount.  I think this was the first year that I didn’t have a student do a discount problem with an answer greater than the original cost of the item.

One of my students favorite things to do during this part of our unit is for me to pull up a store’s website, find an item, and then calculate tax, discount, or tip.  (Side note:  Little Caesar’s website was super nice for adding things students wanted to the cart and finding the price.)

We used this loop activity for practice.