6th Grade Unit 2: Intro to Algebra (Part 2 -Evaluating Expressions)

I blogged about the first part of our Intro to Algebra unit in 6th grade here.  In this part of the unit, we finally get into the algebra stuff.

Word Phrases

Before we start evaluating expressions, we talk about what variables are and what the purpose of them is.  We review word phrases.  I started this year by putting these words up on the board and having students classify them based on their operation.

After we have done a bit of large group practice with that, I have students do a card sort/matching activity.  Once I have checked their answers, they can play memory.  Some students have also played Go Fish with the cards as well.

I also use this Desmos card sort on another day to review this concept.

Evaluate Expressions

Then we get into evaluating expressions.  This year I made a small tweak to how I introduce this to students.  In the past,  I would stand up in front of the class and tell students what you do when you’re asked to evaluate an expression.  I’m really trying to get away from being the teller of information in my classroom and instead be the asker of questions to get students to explain the mathematical concepts to each other.  Here’s the small change I made this year.

It was a small change, but it felt SO much better than standing up in front of the class telling them a process to follow.

The first activity I do is something I created several years ago, and I realized last year when I did this that it’s pretty similar to Sara’s Add-Em-Up activity.  I created 4 different sets of 5 cards.  Each set of cards is printed off on a different color paper so that I can tell which set students are working on.  Below is a picture of the first page of the document for this activity which has 4 copies (each column) of the first set.  I have 8-10 copies of each set.  Because all 8-10 sets are the same color, before I laminated the cards, I wrote a number on the back of each card in a set.  This way, when I find a random card on the floor I can ask, “Who has the red 3s?” and easily figure out where the card goes.

Students are put in groups of 2-3 and in their group they work together to evaluate each of the cards.  When they are done, they add up their 5 answers and come tell me what they got.  If they are correct, I will give them the next set.  If they are incorrect, I don’t tell them which one they got wrong, and they go back to their group and work to figure out what they did wrong.  I’ve tried to level the cards so that each set gets increasingly difficult.  Set 1 has one to two operations on each card.  Set 2 has three steps to each problem.  The next set incorporates decimal operations and the final set has the variable in the problem more than once.

One of the reason I like having a different color for each of the sets is that it is easy for me to see where students are when we are doing this activity.  If I look around my room and see one group on the red set (the first set for me) and every other group is on orange or green (the 2nd and 3rd set for me), I know I need to check in with the group working on the red cards.

Below is an example of each of the four sets.

As I was looking through my stuff to find the file for that activity, I came across another activity I created and had forgotten about.  For this activity, I put students in groups and have them start at a problem.  They can choose to solve either problem on the card.  I encourage all students to try at least one of the more challenging problems.  Once students solve the problem, they look for the answer on another card that I have hanging around the room and then solve either problem on that card.  Eventually, they will loop through to all of the problems and end back where they started.

I also used this Desmos card sort towards the end of the unit to review with students.

Find the Flub warm-ups are great for evaluating expressions.

Tables

In the past, I haven’t done much with tables in any of my classes, and I know that this is something I should do more of.  I added this Desmos activity to this unit, and overall I was pleased with how it went.  It was challenging for some of my students, which was my goal when creating it.

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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.

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.

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.

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.

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.

“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!