Computing Unit Rates with Complex fractions

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SWBAT compute unit rates with complex fractions.

Big Idea

Students will use mathematical practices 1, 2, 3, 4, and 6 to deepen their understanding with a difficult objective

Pre lesson Notes

When students walk in the, place them in their Individual Think Time seats.  Have students pull out their homework assignment from day 1 of the mini-unit (Computing Unit Rates).  Go over the homework to check for understanding.

Use same smartboard games from day 1.  Remember, consistency is the key with content area vocabulary.  Spend 15 minutes on the games. 

Proportional relationship

Constant of proportionality



Equivalent ratios

Unit Rate





Simple Interest








Percent off


Percent Increase

Percent Decrease


Percent Error




Better Buy

Coordinate Grid

Ordered Pairs

X and y axis





Bell Ringer

15 minutes

Bell Ringer:  Create a smartboard game(s) that will include the above listed terms.  Have students play the games in teams.  You can split your class into boys vs. girls, half and half, in teams of 4, 5, or 6.  This is open to what will be best for your classroom environment.  Playing the games as the bell ringer will boost student engagement, and excitement.  Students will have a reference to draw from when it is time to create their own definitions practicing MP 2, and MP 6.  During the bell ringer students will draw on MP 1, 2, 3, 4, and 6.  Some of these terms students may have mastered, some may have heard of the terms, some terms may have no understanding at all.  For this week, it will be helpful to start everyday with the same bell ringer.  I have found that it is helpful to start every day in a unit with content area vocabulary.  The growth you will see in mathematical student dialogue, as well as deeper understanding is tremendous. 

Being that there are 32 terms (You may want to add or delete terms depending on your learning targets for the unit) you will need at least 3 Smartboard games.  I will include an example game to give you a starting point on how I use vocabulary in the classroom.  It is important that the students are given the opportunity to apply content area vocabulary and not just copy and memorize.  The idea of placing a focal point on vocabulary is to build conceptual learning strategies within our students.  We want our student to draw heavily on the mathematical practices every moment in their learning experiences.  If students only know the memorized definition, they are not deepening their thinking, building strategies, and relying on personal experiences.  The first day, students may not know very many terms.  Please always use those open-ended questions to help facilitate student thinking.  As students enjoy the game, be sure to build classroom norms that are conducive to your classroom environment.

Examples of my classroom norms are:

1. Students must assign a speaker for the group that will relay the final response and discuss the group’s thinking and strategies.

2. All students must be engaged in the mathematical practices, discussions, and thinking processes during a question or the group forfeits its turn.

3. All students must have something to write on, and write with to be involved in the problem solving process.  Each student in my classroom is given a wipe board and dry erase marker. 

4.  There is no blurting out answers or you forfeit your group turn and lose all points.

5. All other teams must work on the same problem even if it is not their turn to be ready for a steal opportunity. 

These are example norms that are explained to the students before game play begins.  Students are aware of what the classroom game environment is.  They know if they want to engage in hands on activities they must uphold the expectations.  I usually take about 15 minutes to get through the content area vocabulary games.  Remember these games that are created are meant to deepen student understanding through application.  

Student Activity

15 minutes

Student Activity- Students will take the next 8 terms (students did the first 8 terms in the lesson yesterday, Computing Unit Rates), use the Frayer Model to write the explanations of the terms in their Interactive Math Journals.   

Once Students have completed their terms in their interactive notebooks, students should begin to work on the student worksheet.  Students will draw upon MP 1 and 2. Students will work on grappling through the problems on their own.  

Please see the reflection video included in this section that will give an explanation of how I start my students with this objective. 

Direct Instruction

15 minutes

Direct Instruction- Today’s learning target is to compute unit rates with complex fractions.  Use the process from day 1 to compute the unit rates.  This will build consistency.  Give students an example to grapple through on their own first.  This will allow them to practice MP1, MP2, MP 4, and MP6.

Computing the unit rate of complex fractions can be done using the same process of scaling the denominator to 1. When scaling the denominator to 1 with complex fractions, multiply the numerator and denominator by the reciprocal of the denominator.

An example I would give would be: Malissa can jog ¾ yards in ½ second, or (Malissa can jog .75 yards in .5 seconds, how long can Malissa jog in 1 second.)  To compute the unit rate scale the denominator to 1.  Setting up the rate may look funny to your students because there are fractions involved.  I always tell my students, “Don’t let the fractions scare you!”  This can be solved the same way as when the rate has whole numbers.  It is okay for the numerator and the denominator to be fractions. 

Important! When students are solving this, they will need to be aware of these terms and their application; numerator, denominator, reciprocal.  Students will need to know that a fraction that has the same numerator and denominator will total 1.  Students will need to know how to convert an improper fraction to a mixed number.  These may need to be review sessions held within the lesson for struggling learners.  Remember we are filling gaps.  Many students have been able to use the calculator up to this point and may not be aware of the processes involved in doing so.

Give students several examples to grapple through to help them understand the process of computing unit rates with complex fractions.  Have students work in groups to practice MP1, MP2, MP3, MP4, and MP6.  


10 minutes