Computing Unit Rates

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Objective

SWBAT deepen their understanding of proportional reasoning through application of content area vocabulary. Day 1 students will focus on identifying and computing unit rates.

Big Idea

Students will be given the opportunity to fill in any gaps of missing information through applying content area vocabulary into investigative mathematical scenarios, problems, and games.

Pre Lesson Notes for Teacher

Examples of CONTENT AREA VOCABULARY students must have mastered before starting the proportional reasoning unit, in order to draw on mathematical practices and deepen their understanding of proportional reasoning.

Proportional relationship

Constant of proportionality

Linear

Non-Linear

Equivalent ratios

Unit Rate

Quadrants

Quantities

Ratio

Percent

Simple Interest

Tax

Markup

Markdown

Gratuity

Tip

Discount

Commission

Percent off

Fees

Percent Increase

Percent Decrease

 

Percent Error

Table

 

Sale

Better Buy

Coordinate Grid

Ordered Pairs

X and y axis

Interest

 

proportion

comparison

 

 

 

 

 

 

 

 

 

This explains the importance of content area vocabulary in the Common Core State Standards.

 

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 1

15 minutes

Student Activity Part 1:  It is important students have the opportunity to build a resource to draw from throughout the unit.  One of my main resources is the use of the Interactive Math JournalsStudents will use the Frayer Model to place the first 8 content area vocabulary words into their notebooks.  Please refer to my strategy folder for the use of the Frayer Model in my classroom. 

Direct Instruction

15 minutes

Direct Instruction: The learning target for this part of the lesson is for students to identify and compute unit rates. 

Give students several ratios.  For example, If Billy can jog 30 yards in 10 seconds ask the students how far can Billy jog per second.  Using the term per is important for students to figure out “per” means one.  Allow students to attempt to figure out on their own how far Billy can jog per second.  Once students have had an opportunity to practice MP1 and MP2, go through the correct process with the whole group.  Students should write down the process in their interactive notebooks. 

To compute the unit rate, students can be shown that dividing the numerator and denominator by 10 will get the result wanted.  Students will need to know how to set up the rate in fraction form.  Please do not take for granted that some students will not know how to do this.  Once the students set the rate up in fraction form, 30 yards/ 10 seconds (be sure to place emphasis on labeling the rates) It is important for the students to understand unit rates will have a denominator of 1.  Ask students “How can we use division to get the denominator to 1?”  Students should know that you must divide a number by itself to get to 1.  Please do not take for granted many struggling learners may not know this.  Give students several examples to practice this process.  Tomorrow we will practice this same process using complex fractions.  You may opt to give student examples that they will work through on their own, in pairs, or as a whole group.  

Closing

5 minutes

Homework

Give your students several examples that mirror the lesson examples given in today's lesson.