Solving Equations: Variables on Both Sides vs Combine Like Terms

It seems pretty cut and dry to me - either the variables are on the same side of the equal sign or they aren't. But I can't tell you how many of my students confuse the procedures for these equations. I find that showing one of each of these types of problems side by side helps them. 


So I would show these two equations and ask them to compare and contrast them. I also have them draw a line down the equal sign when learning how to solve equations. This really helps them to remember to keep both sides balanced using the properties of equality


I created these notes to help walk students through the difference between the two types of equations. I like to use gradual release with these notes. We solve the equations at the top together (I Do). Then they try the matching in the middle with a partner (We Do). Then they try to problems at the bottom on their own (You Do). I usually project these notes onto the board and have students show their work on the board. 




Like any other math topic, practice helps them to improve so I created this puzzle (link). I love using self-checking activities so students can self- monitor as they go. If they don’t find their answer or the puzzle doesn’t make the correct shape, they know they made a mistake. I tell them the first thing they should check is whether they correctly combined like terms or used inverse operations.  
Often they will incorrectly use inverse operations when solving a problem where the terms are on the same side. They will say “I subtracted 7x from both sides.” Then it’s very easy to have them show me where they did that on the other side (spoiler alert - they didn’t) and then we can talk about a different strategy instead.

Graphing Equations from Standard Form

My students have such a difficult time keeping track of all the different methods of graphing lines from each form. I use this foldable to help them keep track of the various forms, but I also drill that they can always change it to slope-intercept form. And if they get really desperate, they can just use a table of values to graph everything. I think practicing converting from standard form to slope intercept form is a great way to practice literal equations as well.

I use these notes to practice rearranging equations from standard form to slope-intercept form. I have students glue them along the edge of the page and show all their work on the lines of the notebook paper. (They print four per page.)

I created this puzzle for students to practice converting between standard form and slope-intercept form. They find an equation in standard form, rearrange it to slope intercept form, and match the two pieces. There are several similar equations to keep students on their toes and "attending to mathematical precision."

 I love using these puzzles for practice activities, not only does it encourage students to work together, but students also receive immediate feedback - when they don't find their answers or their puzzle doesn't make the right shape, they know they have a mistake.

Translating a line

I will never forget one of my students telling me after a district exam, "One of the questions asked me to translate a line - what does that mean, write it in Spanish?" I thought I had done just a great job on the linear functions unit, but I had totally missed connecting the idea of translations for them. I had always waited until quadratic functions to talk about shifts in the parent function as transformations, but when I looked into the standards I realized I was missing a key part of linear functionsCCSS.MATH.CONTENT.HSF.BF.B.3: Identify the effect on the graph of replacing f(x) with f(x)+ k, … for specific values of k (both positive and negative); find the value of k given the graphs. 
So I created some doodle notes that compare various graphs to the parent function. Each graph already had y = x graphed, so seeing the transformation is easier. 

The standard specifically addresses translations, but I also wanted students to see that changing the slope is actually a dilation and making it negative is a reflection. 


After finishing the notes, we completed a dominoes activity to practice translations. I love these dominoes because they have an answer bank to work from. They start with the line y = x and perform the vertical translations up or down. Students match the graph and then perform the next translation.


For extra practice I had them write the equation of each line, again reinforcing the idea that the constant is the only thing changing in the equation. 


Both sheets made up a two-page spread in our interactive notebooks. 

I wrapped things up with this "Try It" question too. I know that before this lesson, my students would have had no idea how to even tackle it, but they were so confident in their answers. With any luck, when they see questions about "translating" on the next test, it will no longer think of a foreign language. 

The Most Magical Holiday


Hello! I'm spreading holiday cheer with a few of my math friends. Make sure to keep blog-hopping to find more giveaways!

My Favorite Holiday Activity

This year my favorite holiday activity was going to Disney World! I just returned from a three-day "Princess Trip" with my two-year old daughter and my mom - and it was the most magical vacation. I loved seeing Main Street all decorated with holly in the streets and the tallest tree plopped right at the end. My daughter was ecstatic when she caught her first glimpse of Cinderella's Castle and when Minnie Mouse held Elsa's hand while she sang, "Let It Go," it may have been the most exciting moment of her life so far. Something about being inside the bubble of Disney World makes all your other stresses and worries melt away and was just the break I needed to make it through the next five days of school (we are all counting at this point- right!?).


My Favorite Math Activity
The favorite of me and my students have to be my coloring activities. I find coloring to be so relaxing and soothing (and those are two words students don't usually associate with math!). In all my coloring activities, students get to pick their own colors., which means they do not all look the same. I also love self-checking activities, so that students don't practice incorrectly, and the coloring activities have an answer bank included, so students know when to ask for help. The opportunity to engage the right-brain is so important in math class, and I love giving the students a chance to show their creativity. Plus, with the holiday break so close, a few minutes coloring could be just the hook you need to get the kids to do their work and stop asking, "Can we just have a free day?"

My Favorite Teacher Tool 
My go-to daily teacher must-have is a nice strong cup of coffee. I love walking around helping students with their work as I sip it during 1st period. I usually brew my own at home and love to add some peppermint-flavored creamer this time of year. Only once in 10 years have I spilled any on a students' work and it was this year in her interactive notebook, while I was showing her work under the document camera (oops!). Now every time I ask to put her work on the document camera, she says, "Only if you make sure your mug is all the way closed first" 😁

Giveaway
So now it's time for your chance to win a present in a GIVEAWAY! I have a $15 Starbucks gift card that I will send to you via snail mail, and my Algebra Coloring Activities Bundle that you can use to keep your little elves engaged all year!

a Rafflecopter giveaway

Now it's time to hop over to Smith Curriculum and Consulting's blog to enter another giveaway! 
Giveaway ends Monday December 18, 2017 at 8PM EST! 

Building Community While Taking Attendance


Is there anything more awkward for the first day of school than calling the role? Standing with a clipboard trying to put together letters into a way that doesn't butcher too badly the name their parents had in mind, all while the other students listen, laugh. Not only is this embarrassing for me, but it robs my students of valuable class time. So I have created a system that works better for me and helps build community in my classroom.

I tell students from the first day of school that teamwork is essential in my class. My desks are arranged in groups of three and these people are your first resource for anything from pencils to help with the assignment. So I have them turn to their neighbors and introduce themselves. At minimum, you need to know the names of the two people you are sitting with, but I tell them to learn something else about them too.

Then during the work period, I circulate with my clipboard. I pick someone at random in the group and ask, "What are your group members' names?" And the student tells me their names. Then I ask another student the same question, then the last student. At that point, I have heard the students say each name twice, which is plenty for me to mark down the attendance. The kids are also more likely to correct each other (even though I beg them to correct me if I pronounce their name wrong, they are usually hesitant to). The best part is that it builds the classroom culture of relying on each other from the beginning. I have already found that students are way more likely to strike up a conversation about a tricky word problem or ask for help finding a mistake if they know the person's name. It makes me sad when, in December, I ask someone to pass out papers and they tell me they don't know anyone's name. I am going to make a point to rotate the groups too and always emphasize that you need to know the names of your group member ... and rely on them for help. Teamwork!

Why I made Warm Ups extra credit

Warm-Ups were always a struggle for me - I like the idea of having something for the kids to work on immediately, but logistically, I had trouble with motivating kids to do it. Some would take forever to get out a Warm Up journal, some would wait until the answer was on the board and just copy, some would ignore it all together.  After nine years of trial and error, I finally found a Warm-Up routine that I like: 

I create a Warm Up question that will take about three minutes to answer and project it on the board as students enter (it may be review from earlier in the school year or earlier in the unit). I stand at the door greeting students and hand out scrap paper as they walk in. I LOVE recycling, so I just re-use some of the extra paper that I have laying around - old memos, extra copies, and if I ever run low, I just ask in the copy room and they usually have a stack of paper in the recycle bin. Each student gets 1/4 sheet of paper from me as they enter. I also keep an extra container of it on my back table for students who walk in after the bell. 

I usually give students about three minutes after the bell rings to complete the problem, and I give a 30 second warning. They must show ALL work to receive credit, but they don't have to copy down word problems. Then I or a student volunteer walk around and pick them up. But here is the kicker that makes students actually WANT to try it - after students get five Warm-Up points for the quarter, the rest are EXTRA CREDIT! Just the idea of bonus points is usually enough to get students to try even a challenging problem, plus it takes the pressure off if they get one wrong or are absent or tardy to class. 


I can quickly separate the right answers from the wrong and then I make a check-mark on my roster next to everyone who answered correctly. I usually put in Warm-Up grades twice a quarter (once before progress reports and once before the end of the quarter). Students love seeing a score like 7/3 and the bonus points aren't enough to bring up a quarter of slacking, but do help balance out late work or other missed points.

Depending on the nature of the Warm-Up, I may use it to launch into instruction, put a correct answer under the document camera, have a student work it out on the board, or work it out myself. 

Linear Inequalities

I usually teach linear inequalities right after systems of equations, but this year I ended that unit right before Thanksgiving break, then we spent the time between Thanksgiving and Christmas on Radicals and Rational Exponents. Then when we came back in the new year, it was on to polynomials and quadratics. Although I kept meaning to find a few days to fit in linear inequalities, it kept getting lost. Then we had a four day week right after we wrapped up the quadratics unit where it fit perfectly. I actually liked having this topic here for a few reasons: 1. Coming off using the quadratic formula to find irrational solutions, this seemed like a breeze! 2. It was a great refresher of graphing linear functions. I reminded them how we graphed one-variable inequalities on the number line with open and closed circles and then we extended that to dashed and solid lines.

I developed these fun interactive notes for students to practice graphing linear inequalities, writing linear inequalities from a graph and solving word problems involving linear inequalities. Students really liked shading their graphs with colored pencils and markers. We did the first one together, then they graphed the second one on their own and we talked about how to shade together.



With both these problems projected on the board, at least one student in each class would point out that > are shaded above the line and < are shaded below. Just like any other shortcut, we talked about the limitations and specifically how this only works if y is on the left side of the equation. Some of my students liked to use this shortcut and some preferred to test a point. I modeled with testing (0,0).

Next we took on the word problem together, rearranging the equation in standard form to graph it in y-intercept form. Then we jumped to the other word problem and students tried it on their own. These word problems helped my students understand the shading in context.


Then I had the students complete the other problems on their own. I projected them onto the board and had students work them out.



Students practiced with this coloring activity. I love all the variety of my creative students!

At the end of the class, I passed out this exit ticket. {click to download for free!}

After class, I quickly sorted them into those who answered it perfectly and those who made a mistake. I used my single-hole-punch to make a hole in the stack that answered perfectly. At the start of the next class, I passed back the ones who answered perfectly with a student who needed help and had them assist the student in finding and correcting their error. This method has worked really well for engaging everyone and getting students instant remediation.

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