# Fraction Bars Represent Division

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## Objective

SWBAT recognize fractions as division equations and use this to convert fractions to decimals.

#### Big Idea

Students convert fractions into decimals using their knowledge of division.

## Launch

10 minutes

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.

## Guided Practice

15 minutes

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.

## Independent Practice

20 minutes

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.

## Group Share

5 minutes

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.