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.
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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 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.

8th Grade Unit 3: Functions (Part 3 – Point Slope Form & Standard Form)

Here’s part 1 and part 2 of unit 3.


I used this warm-up the first day after our test on slope-intercept form to get students thinking about equations and graphs again.

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Then I do notice/wonder with this.

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I heard things like:

  • There are two x’s and two y’s.
  • There are little 1’s by one of the x’s and one of the y’s.
  • There are parenthesis.
  • There’s an m (slope).
  • There’s no y-intercept
  • Is it another form of a linear equation?

It leads nicely into discussing point-slope form and students realize that it isn’t as scary as it may look at first because they recognize the similarities between slope-intercept form.

When going over point-slope form, I make a point to emphasize to students why it’s named point-slope form -we can see the coordinates of a point and the slope from the equation.  I remind them that this is similar to slope-intercept form where we saw the slope and the y-intercept.

Then we go over a few examples of writing equations in point-slope form before doing an activity similar to what Sarah shared here.  I didn’t have big foam die like Sarah used, but I do have double dice, which students always think are fun.  Students rolled the dice to create two ordered pairs and wrote an equation in point-slope form of the line between those two points.  Then they checked their answers using Desmos.  Having students check with Desmos was key to helping them see what they were doing when writing the equation of the line.

I also modified this Desmos marbleslides activity to rearrange the equation so that they looked like what my students were used to seeing.  My modified version can be found here.


Then after some more practice using point-slope form, students are introduced to standard form.

I use notice/wonder again to get students thinking about this.

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Again, students came up with the following things:

  • There’s 2’s in all of them.
  • The two is always by the x.
  • One of the equations is in slope-intercept form.
  • One of the equations is in point-slope form.
  • In the purple one, the x and y are on the same side.

We also talk about how, unlike slope-intercept form and point-slope form, we don’t see the slope, the y-intercept, or a point.


Of the three parts to this unit, this one is takes up the fewest number of class periods.  Writing up this post made me realize that I could probably use a few more activities on these concepts.  If you have any ideas for me, please share!

8th Grade Unit 3: Functions (Part 2 – Slope & Slope Intercept Form)

After talking about functions vs relations and linear vs nonlinear, we get into slope and slope intercept form in 8th grade.


Slope

To intro this I start by using a Desmos Polygraph.

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Then this year I tried this Desmos activity on steepness.  I liked we were able to move from talking about something students were familiar with, steepness, to a word students may not be familiar with in slope.

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Then I was able to use use this awesome activity Sarah shared here with some of my students, since they were a couple days behind the other class.  It was such a simple idea, but I absolutely LOVED how students figured out on their own how to find the slope of a line.  They also were able to explain when slope would be positive versus negative.  For next year, I might change some of the lines to include slopes such as 2/3 or 3/4.

And what would be a lesson on slope without Slope Dude?  I blogged about another activity I shamelessly stole from Sarah here.sd2

I used this Desmos activity I found online to have students practice finding the slope of lines.  After that, we talk about the slope of horizontal and vertical lines.  Students already know from playing Slope Dude that horizontal lines have a slope of zero and vertical lines have an undefined slope, but now we talk about why.

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Slope Intercept Form

A while ago on Twitter Mickie asked for ideas on introducing Slope Intercept Form to students.

I shared with her a worksheet I created a few years ago where students use Desmos to figure out slope-intercept form.  She had some great ideas of how to improve what I had created.  (Twitter and #MTBoS are so great!)  She shared with me what she and a colleague came up with.  I loved her addition of the table.  Here‘s the editable version of the worksheet she shared with me -I did make a few minor changes.

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When I’m teaching slope-intercept form, I try to make a big deal about how the name for this form of an equation makes sense based on the formula itself.  When we’re given an equation in this form, we can easily see the slope and the y-intercept, hence the name slope intercept form.  This is something that is obvious to me as the teacher, but I found that students don’t always make this connection.  Because of that, it’s important for me to help students make that connection.  This also helps later on when we talk about point-slope form.

One change I made this year to how I teach this is that I had students check their answers after graphing.  I decided to do this for a couple reasons.  One, I hoped that this would slow students down and help them catch mistakes they made when doing the slope of the line.  Two, I hoped that this would help students make the connection between the graph and the equation.  In the past, I don’t know that I have done a good job of helping students make this connection.

After students are comfortable with equations in slope intercept form, we go over writing an equation from a graph, writing equations for horizontal and vertical lines, as well as needing to get y by itself before graphing.

Here is the link to a Desmos activity I used to have students practice going from graph to equation.  I took the images from somewhere online, but I can’t remember where.  Sorry!  If anyone recognizes them, please share so that I can give whoever created them credit.

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You can download a worksheet and the test review here.

And last but certainly not least:  Desmos Marbleslides.  This is one of my absolute favorite activities from Desmos.

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8th Grade Unit 3: Functions (Part 1 -function vs relation, function notation, and linear vs nonlinear)

The first test in unit 3 for 8th grade covers the difference between a relation and function, function notation, and determining from a table whether something is linear or nonlinear.

I followed pretty closely to what I did last year.  You can read about that here.

I did use Sarah’s updated version of her representations of relations telephone activity.  I blogged about it here, and you can directly download her version here.

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Once we got into functions versus relations (again read more about what I did last year here), I used this Desmos Polygraph this year.  After I did it with one class, I ended up copying and editing the activity and changed the circle to another graph because my students kept thinking it was funny to pick the circle and have the other person guess on the first try…oh 8th graders!

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Then we started looking at tables and determined from a table whether or not the graph would be linear.  I feel like this portion of the unit is what I need to focus on improving the most for next year.  It went alright, but I didn’t love it.  I started with the following image and asked students what they noticed about the two and what made the green graph a straight line and not the red one.

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Usually someone will say that on the green one, the y’s go up by two’s.  Then I put this image up and ask why that theory doesn’t work in this case.

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We continued talking about what makes the graph linear, and the next day I used this Which One Doesn’t Belong? for a warm-up.

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When it came time to review for the test, I used a function vs relation Kahoot and this great open-middle type problem from Sarah to review functions versus relations.  I used it the same way Sarah did and had students use the numbers -4 to 4 and first had students place the numbers in the boxes so that the three relations were also functions.  Once students completed that, I had students place the numbers so that the three relations were not functions.

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I also have an Add ‘Em Up activity for function notation I created.  You can read about Add ‘Em Up here, and download the activity here.