Students use 100ths grids to model .5 x .2 and then .6 x .4 . This is a review from our multiplying decimals unit at the beginning of they year. This warm- up provides a concrete connection for students between multiplying decimals and multiplying fractions.
When we go over these two examples together, I ask students to rewrite the equations with fractions rather than decimals. Through this experience, they see the connection between multiplying fractions and multiplying decimals. First, students rewrite the decimals as fractions on their own, then share with a partner, and finally groups share out to the class. Students are reminded and encouraged to write the answers in simplest from. The purpose of this transition is to help students connect what they know about multiplying fractions with what they know about multiplying decimals. If students struggle with converting these decimals to fractions, I use this opportunity to review the procedure with them, then make a note to revisit this again later.
Working with the models helps students develop the conceptual understanding of multiplying numbers less than 1. I connect these models to arrays (3 rows of 4 makes 12). However, when working with numbers less than one, the 100s grid that students work with now becomes 1 whole, not 100 wholes. Students need support in this transition. As you saw in the warm-up, students have trouble modeling multiplication and sometimes revert back to accidentally modeling addition. Don't be discouraged by the students' challenges, grappling with this complexity allows them to better understanding the WHY behind the procedures.
To launch this lesson, I show a short clip about multiplying fractions (I only show the first 1:07 because the second part is about dividing). I choose this clip because it is easy to understand and it cuts right to the chase of the procedure.
For this lesson, it is my priority to help the students understand why this procedure for multiplying fractions is reasonable. I use the phrase "find a piece of a piece" throughout this lesson.
Note: Since I want to focus on the meaning more than the procedure, I have decided to introduce this quick and easy procedure first. I debated whether I should teach students to simplify with cross canceling common factors or not. I think it is important to get their minds thinking algebraically, so I chose to imbed it into include that part of this video. I will spend more time teaching this part of the procedure because the video is very brief.
The guided practice of this lesson focuses on the "why" behind the procedure for multiplying fractions. I use interactive modeling to connect the warm-up (modeling multiplying decimals) with two examples of multiplying fractions. I choose two problems where cross canceling to simplify is not possible. (Since the video clip exposes students to the cross canceling approach to simplifying, I know it will come up, but I want all students to be able to feel comfortable and successful with multiplying fractions and then simplifying afterwards. I don't want to overwhelm any students by teaching too much at once.)
I encourage students to do the math procedure first, then we model together. Based on the students' comfort level, I walk them through the first example and then let them work together on the second. If they need more support, we will do more of these together before they try it with the group.
• 3/4 x 7/8
• 3/5 x 3/4
For the 3rd example
• 1/4 x 2/3
We walk through cross canceling together (interactive modeling). I make it clear to students that they can choose to use the short cut or not when multiplying fractions.
Students work in pairs to solve problems involving the multiplication of fractions. Today's warm-up and guided practice took longer than I originally planed, so this lesson will be spread over 2 days.
During the short time that students are multiplying fractions, they use "math and models" for each problem they complete.
I circulate and support students as needed.
Note: Some students may struggle with the modeling portion of this lesson working in pairs can help surface some of these challenges.