Welcome back from break! To ease my students back into a school mind set, I ask them to spend time working in their math journals. They are to think about some fractions they encountered over vacation. They can draw, cartoon, list, write, etc. their fractional thinking. To demonstrate a fractional model, I share my "journal" entry with them.
Today I am going to spend time helping students really master the basics of finding equivalent fractions. Based on some formative assessment data, I see that students are able to create equivalent fractions, but they have little understanding of the concept.
When I ask what equivalent fractions are, they say "the same", "equal". I am expecting students to have a deeper understanding of what they are doing, and why they are doing it. This lesson is to help them build that understanding. I also expect students to understand that simplifying fractions is one way of making equivalent fractions.
To begin, I explain the goals of the lesson.
1. To understand the meaning of equivalent fractions.
2. To understand the procedures for making equivalent fractions (including simplifying fractions).
3. To practice both of these skills.
These skills are the foundations of working with fractions. We are going to spend time today strengthening the basic skills that have been developed in the past few grades. It's important to pay careful attention as we review, because this lesson will push your thinking past what you already know.
This lesson is split into three parts, an overview, understanding equivalence, and simplifying fractions. Between each part, I have students practice a problem or two on their own, so I can check in on their understanding as I go. This helps break up the long direct instruction.
I ask the students to think, and share, what the terms equivalent fractions means. Students answers are vague, but suggest that they have some understanding of the term. To help students visualize their understanding and to support their explanations, I use interactive fraction models. I ask a student to come up and create an example of equivalent fractions.
The image "What are equivalent fractions?" demonstrates what the student made. She made 1/2, 4/8 and 2/4 with the support of the manipulatives and probing questions. The students collectively explain equivalent fractions as "fractions that have the same size and the same value, but look different because they have different sized pieces".
Next I ask the students, How did ___ make equivalent fractions using the fraction tiles?
How can you make equivalent fractions if you do not have tiles?
Using learning from the previous lesson, students explain that they use multiplication and division to make equivalent fractions.
I put a non-example on the board to help students articulate what they mean when they say "use multiplication". I ask students if these fractions are equivalent, and provide an opportunity for them to discuss this in small groups. Then students explain - You have to multiply a fraction (or divide it if simplifying) by a fraction that equals 1 (5/5) so that you don't change the value. I emphasize the importance of this by asking multiple students to repeat it, and write it on the board. I tell students that this is an essential understanding of working with fractions.
To break up the length of this direct instruction, I ask students to find 3 fractions equivalent to 6/10 and circulate to check on their strategies. Students who are writing 8/10, 12/20, 24/40, and so on, are encouraged to use the original fraction each time, rather than using the strategy of continuously multiplying the new fraction by 2/2. This is emphasized again during the share out.
I ask students to share their equivalent fractions to 6/10 and also to share their thinking. I call on students until someone shares 3/5. Then I ask students why this fraction is different from the others on the board.
Students recognize that this equivalent fraction is simplified.
Next, we are going to take a close look at simplifying fractions. I tell students that I am going to help them remember what they have learned in the past about simplifying fractions, and then show them something new. Helping the students connect their current learning to prior knowledge allows for them to more easily build on these understandings.
Again, I go back to the online fraction strips. I ask students to explain why 3/4 is a simplified form of 6/8. What does simplified mean (see image). Using the tiles, students are able to articulate that simplified fractions have fewer parts.
Next, I briefly mention the difference between simplified and simplest form. This will be part of tomorrows lesson, but I want to get the students to start thinking about it.
I model (using 6/8) how to use common factors to simplify fractions.
In pairs, students practice using assigned questions from their text book to simplify fractions and find equivalent fractions. Students must show their thinking. As I'm still closely monitoring student thinking, I slowly circulate to each pair of students and assess their various approaches.
We will continue working with equivalent fractions tomorrow. I ask students to do a quick self reflection on their work before passing it in.
Smile Face - I've totally got this
Serious Face - I am feeling a little confused and could use some help from a friend or teacher
Sad Face - HELP ME!
There were no sad faces passed in!