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!

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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.

6th Grade Unit 2: Intro to Algebra (Part 4 -Inequalities)

The last part of our Introduction to Algebra unit in 6th grade is inequalities.  I also wrote about part 1, part 2, and part 3.

I don’t spend a ton of time with this.  I start with a few Desmos activities.  Polygraph is the first thing we do, and then I come back to it a day or so later after students have done more with inequalities.  Then we review the inequality symbols before students work on this Desmos activity.  It is a basic introduction to graphing, and it is usually the first time that my students see the greater than or equal to symbols and less than or equal to symbols.

The next day to review we start with this Which One Doesn’t Belong.

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Then we work a bit on graphing inequalities when given a situation.  This Desmos activity is one of the first things we do to practice this.

The last way we review is Mathketball.  My students LOVE this game.  They put their desks in a circle around the room.  I put a garbage can in the middle of the room.  I put a problem up on the board, and if students get it correct they get to try to shoot their paper in the basket.  Students would play this for every concept if I let them, but I try to save this for problems that I anticipate all students completing in the same amount of time compared to problems that have multiple steps to get the answer.

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I want to find more pictures like these that students can write inequalities for.

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The day before the test a student asked how many problems were going to be on the quiz.  I said, “8 problems tops.”  Another student said, “You should make us write an inequality for that.”  I just love these kiddos so much.

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.

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.

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Solving

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.

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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.

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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.

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

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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.

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

8th Grade Unit 1: Solving Equations (Part 1)

The first unit we do in 8th grade is on equations.  I start by reviewing order of operations, evaluating expressions, and simplifying expressions.  Then we get into solving more basic equations.  Here is a semi-brief overview of the first part of this unit.


Order of Operations

We start off with order of operations.  I use the following Notice/Wonder to lead into our discussion/review of order of operations.

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We also review absolute value as well as square roots as part of our order of operations practice.  These are great problems for vertical nonpermanent surfaces (#VNPS)

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This Desmos activity from Cathy Yenca is also a great review of squares and square roots.

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After a couple days of absolute value problems and square root problems, students work on a worksheet similar to the one below.  You can download it here.  I’ve thought about changing up this worksheet since it doesn’t include square roots or absolute value, but it is a good challenge for students, since students are only allowed to use the numbers 0 through 9 once, and I like that about it.

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Students also see their first Find the Flub warm-up in this unit.

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Evaluate Expressions

Then we spend a little bit of time on evaluating expressions.  I use the worksheet below as practice for students.  I blogged about this type of worksheet here.  You can find the link to download it in that post.

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Simplifying Expressions

Both years I’ve taught this, I forget that students aren’t as comfortable simplifying expressions as I expect them to be.  I start by having students simplify expressions that don’t involve the distributive property, and then I add that in a day or so later.  I found a Desmos activity in the Desmos Bank that I modified and uses on one of the first days on this topic.  Here is the link to the activity I modified.

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Then we do a couple days of simplifying expressions with the distributive property.  Again, I use a “One Incorrect” Worksheet.  You can download it in this post.

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The Notice/Wonder I used below was GREAT to discussion some common mistakes I was seeing students make when simplifying expressions.  For example, I had students who would say that 5x² was 25x.  We had a really good discussion about the differences in the expressions below and how that changed things.

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Solving Equations

Then we get start solving equations.  A few years ago, I had a group of students that struggled to plot points on a number line, so when we got to solving equations, I saw that as an opportunity for them to get more practice with that by having them graph the solution to the equation.  They also struggled with order of operations/evaluating expressions, so again,  I decided to have them practice this by checking their answers to the equations.  I’ve never looked back, and now I have students graph and check their answers to nearly every problem they do for me.

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If you’re interested in the worksheet I use, you can download it here.  Below are a couple of warm-ups we use when we’re talking about solving equations.

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A Day Full of “One Good Things”

I love reading the One Good Thing blog.  It always encourages me to find the positive in my day, regardless of what kind of a day/week I’m having.

Yesterday was one of those days that was full of One Good Things.

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I started with the following Which One Doesn’t Belong in my first 6th grade class.  The conversation was SO good, and I loved hearing all the vocabulary my students remembered.  The conversation went equally well in my other two sections.

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Then we used this Desmos activity.  It was the first time this group of students used Desmos.  It was love at first Class Code.  The groans when I paused the activity were music to my ears -I even gave them a 5 second warning.

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In my 8th grade classes I used Vertical Non-Permanent Surfaces (#VNPS) for the first time this year.  Whenever I do this, I ask myself why I don’t do this more often.  I’m always amazed at how much more engaged students are and how much more they participate when we do this compared to seat work.

After grouping students randomly for this, I saw that two students who I struggle to get to do anything on a lot of days ended up partners.  I had my doubts about how their group would function, but the 20 minutes those students worked together was by far the best either of them had worked all year!

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When it came time for my 5th hour class, I logged in to Desmos to find that none of my custom activities or history showed up in my account.  What could have been a disaster (my 30+ minute lesson plan with 6th graders, gone), ended up going just fine.

For whatever reason, my students were crazy patient and quiet while I tried to log in to Desmos and figure out what was going in.  Then I finally realized what happened.  My school email changed over the summer, and I had been trying to change my Desmos account to my new address.  I had contacted Desmos earlier in the week to help with this and saw in an email that they were able to make the change for me just before 5th hour.  The change didn’t quite go as expected, and I needed to change my password and wasn’t able to do this.

We had just set up something else on my students’ Chromebooks, so I had them work in that while I emailed Desmos to try to figure out the issue.  I spent the next 10 minutes or so emailing Denis from Desmos -we may as well have been live chatting for as quick as Denis was to respond to my emails.  (Have I mentioned that Desmos is awesome!  After my initial split second of panic when everything in my account was gone, there was never a doubt in my mind that Desmos would be able to fix the issue.)

The hour ended, and I still wasn’t able to get my stuff back in my account.  However, I tried the same thing I had been trying during class one more time, and it worked!  I was ready to go for 6th and 7th hours.

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After school I was able to go and support a colleague whose family is going through a difficult time.  While the situation isn’t a good thing, I was glad I could be there for her during this difficult time.