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.

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 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.

6th Grade Unit 4: Ratios

To introduce our unit on ratios this year, I started with the following picture and asked students to notice/wonder about it and if they could figure out what was meant by the word “ratio”

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I also had this one ready to follow up with if I needed to.

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Then I used a couple of Desmos activities.  This is one that I modified from something I found from Andrew Stadel.  Then I also created this card sort.  There are multiple correct options for the card sort I created.

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Then I used an I Spy activity.  I blogged about it here.

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I like this Which One Doesn’t Belong? around this time in the unit.

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Then we get into unit cost and finding the better buy.  Some years I have students look up items online and find the unit cost of the items, but I’m finding that more and more websites already give the unit cost on them.

Students always enjoy math fails, and they work great in this unit.  Sara shares a ton of them on her blog here, here, and here!

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I used Robert Kaplinsky’s “Which Ticket Option is a Better Deal?”  I definitely want to spend more time on this one next year and really focus on question 4.

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Don Steward also has some great ratio puzzles on his blog here and here.

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As I was going through my stuff when writing this post, I also came across this video.  I always forget about it and have never actually used it in my classroom.