To launch students thinking about fractions as a division notation, I write 3/4 on the board and ask students to read what it says. I call on students to hear as many different possibilities as they can come up with.
• three fourths
• three out of 4
• less than 1
• more than 1/2
These are the most common responses students come up with.
By directing their thinking to the fraction bar itself, students add "division". (Important!)
Note: Earlier in the year, I introduced fractions as division notation when playing a math game online. I intentionally come back to this idea throughout the year, so students are familiar with this idea, but it hasn't been a formal lesson.
Today, when working with fractions we'll be thinking about them as division equations.
Students turn and talk about 3/4. What division sentence would this be? 3 divided by 4.
First I write it horizontally.
Which number represents the dividend? (4) and the divisor? (3).
After labeling the divisor and dividend, I ask students to write 3/4 as a division problem in the "algorithm" format.
I draw attention to the fact that students might think it looks wrong to have the 3 in the dividend place with the 4 is in the divisor place. This reflects thinking from prior grades, and even though we have worked with dividing to get decimal quotients, some students have a hard time moving past the misconception "the big number goes in the house".
I make sure to address this misunderstanding right at the beginning of the lesson. I also keep the model 3/4 also written as a division problem in the "standard algorithm) format on the board for students to reference throughout the class.
I use the text book as a jumping off point for this lesson. To make the lesson more rigorous and to provide an opportunity to connect decimals, division, and fractions in one lesson I extend the expectations. Rather than asking students rewrite each fraction as a division expression, I have the students use this to then covert the fraction to a decimal (thousands place only).
I choose a few problems from the book and we complete these using interactive modeling.
Throughout the interactive modeling, I focus on identifying the dividend and the divisor, then placing them in the correct places in the division notation.
Students practice writing fractions as division equations and converting fractions to decimals, working in pairs to complete problems.
I circulate around the room to monitor student progress. While doing this, I look for students who have misplaced the divisor and dividend then meet with them to help adjust their thinking. A video of this error is included in the resources.
To wrap up the lesson I ask students to consider what they learned today. They share their thoughts with the group and then we write the 2 most important understandings of today's lesson on the board.
1. Fraction is a way to represent division
2. You can use division to convert fractions to decimals.