Unit Rates for Ratios of Fractions - Additional Practice

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SWBAT find the unit rates associated with ratios of fractions using a model

Big Idea

Keep students engaged and accountable by presenting one problem at a time.


10 minutes

We'll start the lesson by reviewing the exit ticket from the previous lesson.  Today's lesson is a continuation of the previous day; students are given more time to practice.

When we review the exit ticket I will bring out some mistakes.  The most likely errors will be caused by the following:

1) Students fail to find the correct unit rate

2) Students fail to label the number lines with units.

3) Students to do not make sure to vertically align ticket marks for each number line.

4) Students fail to increment the fractions by the correct amount.

To alleviate these problems I will tell students to do the following:

First create the double number line without placing any numerical values.  Make sure to keep the tick marks vertically aligned.  

Secondly, label the unit for each number line.

Third, start with 0 on both number lines - the leftmost tick mark.

Fourth, make sure to increment each number line correctly.  For example if a number line increases by 4/5 we should add 4/5 to each new value.  This +4/5 can be drawn in between each interval of tick marks.  For students who have a difficult time with intervals of mixed numbers, I will tell them to convert them to improper fractions.   

Problem Solving

20 minutes

For the practice problems, I will present one problem at a time.  Students will do the work on individual white boards.  I will have to remind students of a few basic expectations when working on white boards:

1) All writing must pertain to the problem - no doodling.

2) Do not erase your work until asked to do so.

3) Write quickly and neatly.

These rules are designed to mitigate issues I have experienced in the past when working with white boards.  

To help enforce the rules and general classroom behavior, this would be a good lesson for Teacher VS Class.  The class earns points when they work well and follow expectations.  The teacher earns points when the class fails to work well and follow expectations.  If the class ties or loses to the teacher, there will be a homework assignment.  In this game, I will try to keep the score close but ultimately give the class plenty of opportunities to win.

Problems 3,4,6, and 10 all ask students to find two different unit rates.  These are good opportunities for MP3. Students can briefly discuss situations where it may be helpful to find one rate vs another (ie  miles per gallon vs gallons per mile).

I will set a timer for about 1 minute per problem.  While students are working, I will circulate the room to check how the work is going.  On the first 3-4 problems, students will be allowed to check in with a neighbor.  I will also be more helpful. On the last few problems, students will be expected to solve problems independently.

Exit Ticket

5 minutes

Before we begin the exit ticket.  I will ask students the keys to making a good model.  This is basically a summary of what we discussed at the beginning of the lesson.

Students will have 4 problems to solve today.  3 out of 4 correct answers will be the sign of a successful exit ticket.  

Some students may not need to use the double number line anymore.  That is fine as long as they show how they came up with the unit rate.