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.

Screen Shot 2018-02-03 at 11.26.24 AM.png

Then I do notice/wonder with this.

Screen Shot 2018-02-03 at 11.26.34 AM.png

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.

Screen Shot 2018-02-03 at 11.41.21 AM

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.


To intro this I start by using a Desmos Polygraph.

Screen Shot 2018-01-21 at 4.32.48 PM.png

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.

Screen Shot 2018-01-21 at 4.29.51 PM

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.

Screen Shot 2018-01-21 at 4.47.55 PM.png

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.

Screen Shot 2018-02-02 at 11.42.51 PM.png

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.

Screen Shot 2018-01-30 at 7.08.09 PM

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.

Screen Shot 2018-01-21 at 5.13.25 PM

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.


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!

Screen Shot 2017-12-30 at 10.35.09 AM.png

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.

Screen Shot 2017-12-30 at 10.29.19 AM

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.

Screen Shot 2017-12-30 at 10.29.26 AM.png

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.

Screen Shot 2017-12-30 at 10.30.02 AM

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.

Screen Shot 2017-12-30 at 10.30.32 AM

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.

Screen Shot 2017-12-08 at 6.56.27 PM

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


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.

Screen Shot 2017-12-08 at 7.00.38 PM

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.

Screen Shot 2017-12-08 at 7.21.38 PM.png

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.

Screen Shot 2017-12-08 at 7.15.38 PM.png

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.

Screen Shot 2017-12-08 at 7.25.58 PM

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.

Screen Shot 2017-12-01 at 9.17.32 PM.png

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?

Screen Shot 2017-12-01 at 9.18.16 PM

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.

Screen Shot 2017-12-01 at 9.19.09 PM

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?” 😉

Screen Shot 2017-12-01 at 9.33.59 PM.png

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.

Screen Shot 2017-12-01 at 9.30.02 PM.png

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.

Screen Shot 2017-11-19 at 5.48.55 PM

Here is the link to download the test review.

8th Grade Unit 2: Inequalities (Part 1)

After solving many different types of equations in 8th grade, inequalities are up next.  We start by reviewing graphing inequalities before getting into solving them.  Then we also work on inequalities that have all real numbers and no solution as answers.

Review of Graphing

Although students have seen inequalities and graphed them in the past, I’ve found that it is worth my time to spend a day or so giving students a quick refresher on this.  There are several great Desmos activities for this.  Here are a few that I’ve used and like.

Screen Shot 2017-11-19 at 5.20.16 PM


In the past I had an activity I used to get students to discover when the inequality symbol needs to be switched when solving inequalities.  It was sort of lengthy and cumbersome, but I didn’t know how to improve it more than I already had.  Then I saw Sarah Tweet the picture below.  It was EXACTLY what I was looking for!  Thanks Sarah!  Here is the link to download Sarah’s file.

Screen Shot 2017-11-19 at 5.02.55 PM.png

Then for practice students do a Tarsia puzzle.  I created the puzzle a while ago and don’t know where the file is that I can share.  If you’re unfamiliar with Tarsia puzzles, you can learn more about them here.

Screen Shot 2017-11-19 at 5.17.20 PM

I also have a question stack that I use for these types of problems.  You can read about Sarah Carter’s question stacks here.




All Real Numbers/No Solution

To introduce inequalities that have No Solution or All Real Numbers as the solution, I went back to what students already knew about equations like these.  I had students solve a problem similar to the one below and then asked them what inequality symbol we could replace the equal sign with that would make the inequality have no solution and the same for all real numbers.


Then for practice, I had students work on this Desmos activity.

Screen Shot 2017-11-19 at 5.26.34 PM

I also tried creating an Open Middle problem for these types of problems after seeing a similar one Sarah created for equations.  I had one of my co-workers take a look at a different Open Middle problem I made, and he had a great idea from when he has used Open Middle problems in the past.  He suggested to start by letting students use whatever numbers they want, and then after they come up with a solution to restrict them to only using certain numbers.  I thought this was a great idea, so that’s what I did.  I started by telling students they could use any integers they wanted as long as they didn’t repeat any of the 12 numbers.  When a student came up with a solution, I said they could only use the integers -6 to 6.

Screen Shot 2017-11-19 at 5.31.35 PM

You can download the files for the Open Middle puzzle here.

Math Telephone

I used Sarah Carter’s Representations of a Relation Telephone activity last year.  You can read all about the activity in her blog post.  In short, it works just like the game of “telephone”.  A student starts by writing six ordered pairs on the bottom, passes the paper to the next person who creates the graph, who passes it on the the next person who creates the table from looking at just the graph.  This continues until you get to the top of the paper with the ordered pairs again.  If done correctly, the ordered pairs should be the same.

I really liked it, but I knew there were some tweaks I wanted to make the second time around, and it went much better this time.  Part of it could have been that I had already explained the activity once, so I did a better job of explaining it and anticipating where students would struggle.  The first year I did this I actually had one group start whispering ordered pairs into each other’s ears.  I don’t know if they just weren’t listening or if my directions were that bad…probably a combination of both.  Thankfully that didn’t happen this year!

Sarah also shared an updated version of her activity here which also helped as she’s included more instructions on the sheet itself.

Screen Shot 2017-12-06 at 6.54.20 PM

The first time I did this I made the mistake of having one piece of paper per group of 4-5 students.  What was I thinking?!  That meant for 10+ minutes about 6 students in my class were working while the others were supposed to wait patiently?!  Not my brightest move ever.  This year all students had their own paper so everyone was doing something at all times.  This went MUCH better.


As I watched the activity with my first class of the day, I noticed that it was taking students FOREVER to just fold the paper, and one student commented, “Folding the paper was the hardest part of this!”  I found that rather than folding it in an accordion at first it worked better for my students if each person just folded the bottom representation under before passing their paper on to the next person -these instructions are also on Sarah’s updated version.


Overall it was a big success.  I loved watching students look at where the mistakes were made when they were done, and the second time they did it several students were thinking ahead when they created their ordered pairs to try to make it “easier” or linear -which will lead perfectly into what we’re getting to later in this unit.  I even had a student who doesn’t usually get too excited about much of anything say, “This is actually fun.”

I was thinking today what other concepts this could be used for and remembered one I made last year for my 6th graders on exponents.  Since last year, I lost the editable version of the document I made, so I recreated it and added some of Sarah’s instructions to it.  You can download the file here.

Screen Shot 2017-12-06 at 7.35.41 PM.png

What other concepts could this idea be used for?