Determining how to launch a middle school math class was a challenge for me. Having students coming in from various schools and backgrounds, I had no idea what baggage, good or bad, they were bringing with them. It is a great challenge to learn about each student, their learning styles as well as background while trying to teach them something new. For the month of September, I like my students of all levels, to feel successful in our math class. This helps create a positive feeling over the subject and also helps create a sense of community where we can all learn.
For the past two years I have started with percentages, rates and ratios. For some students this is an area of confidence, but for others it challenging due to confusing word problems and mechanical calculations that can become confusing. The goal is that we move from this into creating and balancing equations. Deeply understanding equality is very important for the start of algebra and balancing equations, and I felt that we could introduce this with percentages, rates and ratios.
To do this, our class focused on equivalent fractions. To solve each of their problems from rates, ratios or percentages, students created equivalent fractions. Identifying what is the part and whole in the problems and how they are equal to another part and whole.
It took two weeks, and three classes a week for the students to really grasp the idea. However, what I found was that students were reading the questions, analyzing the values and thinking about equality more than when we learned how to solve each of the problems in the traditional "divide the numbers and multiply by 100". Those students that came into the class with these calculation methods and didn't understand why they worked, found the equivalent fractions a longer thing to do, but they understood why they were doing these calculations.
Most importantly, students are identifying that what is on one side of the equal sign is equivalent to the other. They use the term equivalent in their explanations and when they are working on a problem. I know that this will be very helpful as we move forward to making one step equations where students rebel at the idea of writing an equation and just want to solve. So far it has helped those that are struggling, and given a new challenge to those students that already feel confident with their rates, ratios and percentages.
I have attached some questions that we did as a class later on to see how we set up and solve our fractions.
For the past two years I have started with percentages, rates and ratios. For some students this is an area of confidence, but for others it challenging due to confusing word problems and mechanical calculations that can become confusing. The goal is that we move from this into creating and balancing equations. Deeply understanding equality is very important for the start of algebra and balancing equations, and I felt that we could introduce this with percentages, rates and ratios.
To do this, our class focused on equivalent fractions. To solve each of their problems from rates, ratios or percentages, students created equivalent fractions. Identifying what is the part and whole in the problems and how they are equal to another part and whole.
It took two weeks, and three classes a week for the students to really grasp the idea. However, what I found was that students were reading the questions, analyzing the values and thinking about equality more than when we learned how to solve each of the problems in the traditional "divide the numbers and multiply by 100". Those students that came into the class with these calculation methods and didn't understand why they worked, found the equivalent fractions a longer thing to do, but they understood why they were doing these calculations.
Most importantly, students are identifying that what is on one side of the equal sign is equivalent to the other. They use the term equivalent in their explanations and when they are working on a problem. I know that this will be very helpful as we move forward to making one step equations where students rebel at the idea of writing an equation and just want to solve. So far it has helped those that are struggling, and given a new challenge to those students that already feel confident with their rates, ratios and percentages.
I have attached some questions that we did as a class later on to see how we set up and solve our fractions.
Yeah! Happy to see you are up and posting again! I'm so looking forward to connecting you with this year's Cohort team...they have so much to learn from you!
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