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.

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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.

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)

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

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.

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.

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.

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.

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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Like Terms & Simplifying Expressions

To introduce the idea of like terms to my students.  I use this Desmos card sort.  Initially I have students group the card however they choose.   Students will inevitable group some cards that are like terms which leads us into talking about what it means for terms to be “like”.  Then I have students group the cards into groups that are like terms.

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Update 10/18

This year instead of using the card sort above, I had students do a stand and talk to introduce this idea.  I really liked how this went, and I’ll probably use the stand and talk in the future versus the Desmos activity.

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Then we play “Like Terms Uno”.  The version I use I got on Teachers Pay Teachers a while back, and it looks like it’s no longer available.  In a quick Google search of like terms Uno, several other versions came up.  I’m not sure if those versions are uploaded to the internet legally, which is why I haven’t included links to them.  So if you’re interested in a version of this, seriously just Google “Like Terms Uno” and several different options will come up.

After this we start talking about simplifying expressions.

I start with the video below.  A couple minutes in many of my students are groaning.  I may look at another option for next year, or cutting down the video clip somehow, because watching that video for over four minutes is torture, but it serves it’s point.  I tell students, “You know how your ears hurt after you watched that video for a few minutes? That’s what it’s like for mathematicians every time they see something like 5x + 7y + 3x + x + 8y.  How could we rewrite that so it doesn’t ‘hurt your ears’?”

We practice combining like terms one day, and then the next day we do practice with the distributive property.

Open Middle has some great problems for simplifying expressions.

I also made a One Incorrect worksheet for these types of problems.  You can download it here.

Update 10/18:  I also used this question stack from Sarah Carter.  In the future I would need to do some more work to set this one up than I did this year.  I did not do a good enough job of preparing students for terms with a power greater than 2.)

“One Incorrect” Worksheets

One of the things that’s a constant struggle for me every year is giving students access to answer keys for homework problems.  I want homework to be useful to students.  I want them to be able to check their work to know if they’re doing it right, but I go back on forth with whether I should just give students answers or worked out solutions.  I am also terrible at remembering to upload answer keys to Google Drive for students.  If anyone has a system that works for them, please share!

Last week in two of my classes, I assigned a worksheet like this:

I was introduced to this type of a worksheet this summer by Sara Van Der Werf.  She had us do the one below at one of her PD sessions this summer.  It was this activity from Don Steward.  All but one of the expressions simplifies to 5n + 3, and you need to find the expression that doesn’t and show that all the others do.  I like it because students know that 7 of the answers will be the expression in the middle.  I don’t have to worry about remembering an answer key for students!

I created similar versions for evaluating expressions and order of operations with integers that I used last week in two different classes.  It was easier to make 7 problems that all evaluated or simplified to the same answer than I anticipated.  For the problem that doesn’t work, I tried to create a problem that if students make a common error, the expression still equals what’s in the middle.  For example a problem might have -6² and if students say it is 36 the final answer will equal what’s in the center.

So far, I am really liking how well students have been working together on them.  For whatever reason, it seems that students are more engaged and are more willing to go back and find their own mistakes rather than asking me for help right away when they know that 7 of the answers are the same.  I’m not really sure how this is any different than having the answers in the back of the book, but I’ll take it!

I’m using this one this week for simplifying expressions because I was looking for slightly different types of problems than what I found on Don’s website.

You can find pdf files for the worksheets here.  I don’t know that the Publisher files would be of any use to anyone since I created the equations in Word and copied them to Publisher and used a random font for the other text, but if you want them let me know.  I can upload those too.

If anyone has created something similar to this or ends up creating similar things, I would love to share resources!