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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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.

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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.

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.

8th Grade Unit 2: Inequalities (Part 3 -absolute value special cases and word problems)

The last part of our unit on inequalities covers absolute value special cases and word problems.  You can read about part 1 here and part 2 here.


Absolute Value Inequality Special Cases

To introduce solving absolute value inequalities that have no solution or all real numbers as the answer, I tried a couple different things this year.  In a couple classes I put this up on the board and we talked about each of them, which is what I had done in the past.

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In another class I put the following up on the board and asked how we could write an inequality that would never be true.

|x|______________

Then I asked how we could write an inequality that would never be true.  Once students gave me answers for that and understood, we talked about if it mattered what was inside  the absolute value bars.  Both ways worked fine, but I almost think I liked think I liked this new way better.  I liked that students were coming up with the inequalities.

The next day I started with the following warm-up problem.  I always like to include absolute value inequalities that don’t have all real numbers or no solution as the answer so that students don’t forget what they already knew about those types of problems.

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Here is the link to download a worksheet with these types of problems.

I also created an Open Middle type problem for these types of inequalities.  You can download it here.

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Absolute Value Inequality Word Problems

One of the things that my students need to know is how to solve word problems involving absolute value inequalities.  In the past, I just jumped into these types of problems, but this year I took a day to go over setting up the absolute value inequalities given a graph.  The day before this I had each student solve an absolute value inequality to use as this introduction.  You can download the problems I used here.

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I took several of these and had students find the midpoint of each graph and the distance from the midpoint.  Then students looked for a pattern.Screen Shot 2017-12-08 at 7.10.45 PM.png

Then I had students practice writing absolute value inequalities when given a graph and practice finding the midpoint of the graph and distance from the midpoint when given an absolute value inequality.

The next day when we got to solving word problems went so much better than it did last year having spent a day on this ahead of time.

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You can download the test review here.

8th Grade Unit 2: Inequalities (Part 2 -Compound Inequalities and Absolute Value Inequalities)

You can read about the first part of our unit on inequalities here.  In the next part of the unit we do some word problems, compound inequalities, and absolute value inequalities.


Word Problems

I know the word problems I give students aren’t very “real world” and that this is an area I need to work on -finding/creating better word problems for students and doing a better job of teaching them as well as incorporating them into class.  I don’t have anything fancy I do for these other than a couple examples together as a class and then partner practice.

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Compound Inequalities

I use Notice/Wonder to start our conversation on compound inequalities.  Then we do this Desmos activity.  I also like this Polygraph activity for compound inequalities.

This year I also realized I could make a connection between “compound inequalities” and “compound words” and “compound sentences” that students are familiar with already from their English classes.  Why did it take me so long to do this?

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The following day I use this Which One Doesn’t Belong? for a warm-up and then we go back to the image from the notice/wonder the day before.  I put numbers on the graphs and students write inequalities for each.

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I used one of Sarah Carter’s awesome questions stacks for practice on solving these types of inequalities.  You can download the file she shared here.

One of my classes got to Point Collector.  This was my first time using this activity with students.  It’s SO fun!

One of my students came up with this for the last challenge.  He didn’t quite follow the directions exactly, but I love that he wanted to get the maximum number of points.  I overheard him telling another student about it later on during the class period when they were working on something else.  His friend goes, “Oh, so you cheated the system?” 😉

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Absolute Value Inequalities

I tried a couple different ways of introducing absolute value inequalities this year.  In a couple classes I started with Notice/Wonder.  Then in another class I started with an absolute value equation such as 3|x – 1| + 4 = 19 and had students solve that.  Then I changed it to an inequality and asked students what they thought would be the same/different about solving the problem.  Both ways of introducing the topic were good for different reasons.  I think for next year I may try to find a good combination of both.

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We did some vertical non-permanent surface practice with solving absolute value inequalities at the whiteboards around my room.

I also used this Open Middle type problem I made.  You can download the file here.

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Here is the link to download the test review.