Solving Systems of Equations by Graphing

I love solving Systems of Equations! It is one of my favorite units to teach because the students get to use so many of things we have been learning all at once. 

We have already learned how to graph equations, but spent a day reviewing it before beginning this. We did a lot of talking about "solutions" and how they fit into equations. I struggle the most with students not understanding that the points on the line actually fit in the equation! We talk about that everyday during this unit, it eventually sticks with most of them. 

After a little exploration of just drawing graphs all over our coordinate plane, we finally realized that sometimes the lines will cross (one solution), sometimes they will never touch (no solution), and sometimes they will be the exact same line (infinite solutions).  From that we discussed slopes and y-intercepts and how they affect how our 2 lines will look. 

This is the final piece to our graphing systems discussion. Notes that we do together to show one of each type of solutions. We do this for graphing, substitution, and elimination.

Once the notes were done, they created pockets to sort the notes. This makes it easy to look back and see the commonality between one set of solutions.

The following day, after an assignment that turned out okay, I posted different systems of equations around the room. Each student had a graphing white board and worked through all 9 systems, they found their answer and then went to the sheet that had that answer. I was able to see their work and assist them if needed. It turned out to be a great activity that reinforced those who already got it and established a better foundation for those who were struggling.

 Some students worked faster than others, but because they had different starting spots, they couldn't tell what step their peers were on. It allowed everyone to work at their own pace. I also allowed the student who finished first to get out of the assignment that day.

Complex Fractions

We spent a day in 7th grade talking about complex fractions. I wanted a way to review fractions and understand that complex fractions do not mean they are harder to do. After a lot of searching for other people's ideas...I decided I was going to have to come up with my own. 

Here's what we did. I wrote on post-it notes and gave each student one note. I had three different groups of post-its: first group was simple addition and subtraction problems, second group was fractions, third group was addition and subtraction problems involving fractions. Each group contained a few whole numbers.

In their journals they drew a big division bar and we talked about what that line means; it makes a fraction, it means divide.

They then paired up and each put their post-it in either the numerator or denominator and then solved that problem below. Once all the groups finished, one partner rotated to the next group and they solved the new problem. I always had one group work their problem on the board so I could see their work.

I loved this activity. It was a nice change from the mundane, "let's do these examples in your journals". Not everything can have a fancy foldable or project...but mixing up the review and practice sure seemed to help my students stay engaged. 

Candy Wrappers to Scale

We ended our unit of Scale with 7th grade by putting our art skills to the test. I found this idea on Pinterest...where most of my really great ideas come from. Check out Fast Times of a Middle School Math Teacher for more great ideas. I modified it a little to meet the needs of my students and am really excited about how it turned out. 

I had originally planned on two days for the project, but some of the students went a little large and so I extended their time. They had 3 days in class to work plus a week to work outside of class. 

Although we had done an entire unit on learning about Ratios and Proportions with several lessons on Scale, they had a tough time getting started. We had a discussion about the best way to go about creating our candy bar wrappers so that they looked like REAL candy bar wrappers. We eventually came to the conclusion that a grid was the best way to make sure all parts were proportional, this idea actually stemmed from the grids you sometimes find in coloring books when asked to redraw a picture. 

We learned that markers made it look more real than colored pencils.

Some students chose large scale factors.

This one is pretty cool, love the colors!

What I really enjoyed about this project was the assessment. As a class we decided what the rubric would look like to grade their wrappers. Each student was then able to grade their own. I followed by using the same rubric and their grade came from the average of the two grades. Grading their own work was a great learning tool to hold themselves accountable to the rubric.

I am so happy with how they turned out! 

Just getting started....

3 out of 2 people have trouble with fractions!