Breaking Down 2 Step Equations

Today I’m writing about a simple idea that makes 2-step equations easy for kids – a box “trick”.

Students obviously have already learned how to solve one-step equations before being introduced to two-step equations, so I introduce 2-step equations by giving students a simple one-step equation.  The only difference is that I use an index card instead of a variable in my equation.

Put an equation like the one pictured above on the board and tell students to solve it for the index card, which they should be able to do easily since it is a simple one-step subtraction equation.

Once they solve the equation for the index card, lift up the original card to reveal what is underneath it (in this case 8x).  It also works if you write 8x on the backs of the index cards and just flip them over.

So, since the index card = 8x they now need to solve the equation 8x = 56, which is another simple one-step equation that they should already know how to solve.

Do another example or two with the class and then discuss how to decide which part of the equation goes under the index card (whichever part comes first using the order of operations).  Have students replicate the process in their notebooks by giving them a 2-step equation.  They need to draw a box around the part that would be under the index card.  First solve the equation for the box and then solve the new equation for the variable.

I have found that this method really helps students make sense of solving 2-step equations by turning them into two 1-step equations.  How do you introduce 2-step equations in your class?  Do you do something similar?  Please share in the comments!

If you are in need of resources to supplement your lessons on one and two step equations you may be interested in the following activities in my TpT strore:

Christina

Fun (Free) Ways to Celebrate Valentine’s Day in the Middle School Math Classroom

With my school going from pre-k – 8th grade, I have always felt kind of bad for the “big kids” on Valentine’s Day because it is business for them as usual while the lower grades are having parties.  That’s why I always try to do something a little different than a normal math class, but still academic.  I thought I’d share a couple of the things I have done with my students on Valentine’s Day for other teachers who are looking for easy, free, no-prep ways to bring some holiday fun into their math classes.

I have shared before that I LOVE problem-solving and give my students word problems daily.  (You can read about my daily problem solving here).  On Valentine’s Day I use a set of Valentine’s word problems on fractions that I made a few years ago instead of the normal problem of the day.  (Download them free from my TpT store by clicking on the picture below).  The word problems are a great challenge because they combine two areas students typically struggle with – fractions and word problems.

I break the class into groups of 4 and have them work together on the problems.  I make it a contest – either the first group to get all the problems correct wins, or any group that gets at least 5 problems right within a set time limit wins, etc.  Students don’t necessarily love working on word problems (the understatement of the century), but working as a group and making it a contest definitely ups the fun-factor!

After the word problems, play a game of “Attack”, reviewing whatever concept you are currently studying.  On Valentine’s Day I have them draw hearts as the thing they are attacking and have them attack by drawing arrows on the hearts.  (If you missed my post explaining how to play, you can read it here – trust me, it’s worth the read because students absolutely LOVE this game!)

Finally, show your students some love by giving them a homework pass.  You can download mine free by clicking on the picture below.  (Write the student’s name on the 1st line and sign the 2nd line.)  Either give one to every student as a Valentine or use them as a prize for the groups that won the word problem race and “Attack” game.  (I use the point system of grading, and homework counts as 2 points a day in my class, so I personally allow my students to either use the homework pass to get credit on a night where they didn’t do their homework or they can turn it in at the end of the marking period for 2 extra credit points.)

I hope you are able to use some of these ideas in your class.  Please feel free to share what you do to have fun with your students on Valentine’s Day in the comments below!

Happy Valentine’s Day!

Christina

Turn Multi-Step Problems into Team Activities

Let me start by saying that relays are not an original idea..maybe you have been doing them for years…but they are new to me, (and i love them) so I figured I’d share in case anyone else has never tried relays with their class.

How they work:
Take a problem that requires multiple steps to solve, and break it up into however many steps you need to solve the problem.   Then break your class up into groups that are the same size as the number of steps in a problem.

For example: Multi-Step Equations

I came up with the following 5 steps:

• distribute to clear any parentheses in the problem
• combine like terms within each side of the equation
• add/subtract to isolate variable terms from constant terms
• multiply/divide to solve for the variable
• check by substituting answer in for variable

Since it is a 5 step process, I need to break the class up into groups of 5.  (If your class size doesn’t divide evenly by 5, you can make some groups of 4).

Give the class a problem, assign each student in a group a step of the process.  Student 1 completes the first step and passes it to student 2.  Student 2 checks student 1’s work and then does step 2, etc. until each student has completed a step and the problem has been solved (and checked.). For a group of 4, student 1 will also complete step 5.

Repeat this process 5 times with 5 different problems, each time shifting which student starts the problem, so that by the end every student has had a turn completing each step.

I love this activity because

• The students work cooperatively, but individually
• The students are checking each others’ work
• Relays really emphasize each step in a process

Make it a race if your class is competitive.  If you want to see who completed each part you can have them write in different colors.  Either have them sit in a circle if you want them to be able to help each other complete their steps or have them sit in a row if you want it to be a silent activity.

Do you use relays in your class?  If you have any tips, suggestions, or other ideas for them please share in the comments below!

If you don’t want to make your own relay and are looking for a pre-made one, I have one on writing and graphing linear equations (using point-slope and slope-intercept form) available for sale in my TpT store, which you can get to by clicking the image below.  I am planning to make several others on different topics in the near future, as well.