Problem Solving (Different Operations with Fractions)

This lesson is designed for students to apply all of the fraction skills they have learned and practiced throughout our fraction unit.  Students solve multiple step word problems using a variety of strategies.  In solving these problems, students will have to switch between the different operations. As a warm-up to this lesson, students work together to complete these sentence starters.

• When you add fractions you always... (make common denominators)
• When you subtract fraction you always....(make common denominators)
• You might have to .... (Regroup or make improper fractions)
• When multiplying fractions you are finding a part of .... (a part)

Tip: Never multiply mixed numbers (make improper fractions).

These essential understandings summarize the very basic procedures for each of these operations. In each lesson, I have worked to help students develop the conceptual understanding for each of these operations.  Students learned and practiced with WHY these problems are solved each way. These statements are meant as a quick recap, not a deep understanding. 

To launch this lesson, I choose a challenging problem from the text to solve as a group. The guided practice problem is an example of rigorous mathematics that challenges students to demonstrate perseverance because of the content (profit) and multiple steps.

I choose this problem because I want to demonstrate to students that math is not "easy" but it is "doable" when you have the right attitude and you take a strategic approach. 

Using interactive modeling, the students and I break down this problem, make sense of the information provided, and then develop a strategy by finding two hidden questions to answer before solving the problem. 

Interactive modeling is beneficial for all learners in the classroom, because students learn from each others' comments, suggestions, and questions.  

The anchor chart for guided practice helps demonstrate how this problem was broken down and then the solution was found.

Multiple step problems with various operations are challenging.  For this lesson, I chose problems from the test book for students to solve.  Students work in their color groups (homogenous groups) to solve these problems.  Like the problem from the guided practice, the students are encouraged to focus on making sense of what each problem is asking and developing a plan to solve it. 

Rather than have students solve the problems from this lesson in sequential order, each color group is assigned four problems that are appropriate for their level.  When students solve the problems sequentially, students encounter problems that are too easy or too challenging for their level. 

These video clips show students working together to make sense of problems and persevere in solving them (MP1).

Following the group practice, students work independently to solve a problem involving adding and multiplying fractions on their own.  Students explain their thinking in writing.  This open response practice provides students with an opportunity to show what they know.