Understanding Unit Rates with Holes

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SWBAT Compute unit rates associated with ratios of fractions in order to make beneficial decisions.

Big Idea

Students will appreciate how finding unit rates will enable them to make decisions that would benefit them in the real world.

Opening Video

2 minutes

Bell Ringer

15 minutes

Let’s dive into MP 1, and 2 right away.  As students walk through the door hand each student the Bell Ringer.  This bell ringer is meant for students to complete as individuals. The expectation for this bell ringer will be for students to use what they were taught in 6th grade. 

CCSS 6.RP.A1-3 taught students the concept of ratios and ratio language, the concept of unit rates associated with ratios, and the usage of ratios and rates to solve real world mathematical problems.  This bell ringer will formatively assess students on what understanding was gained through their 6th grade experience, and see how the students can build off of that understanding to determine a unit rate.  Tomorrow students will determine unit prices and compare the process in determining unit rates to unit prices.

In order for students to truly immerse in mathematical practice 1, instruct students to show their work and write a written explanation explaining the process they used to choose the appropriate response associated with the problem.  Empower students in finding the appropriate response on their own without direct instructing them first.  When students get stuck, ask questions such as:

“What is a rate?”

“How do we determine a unit rate from a rate?”

Once students recall this information taught in 6th grade, they should have a good starting point.

If you are in a district that was not Common Core aligned, I urge you to look at the 6th grade standards of 6.RP.A1-3.  It is quite ok to review with your students before going forward with CCSS 7.RP.A1.  I find it very useful to review with my students to fill the gaps. 

After giving your students about 5 minutes to grapple with the problem, pair them up with one another.  MP3 will come into play with this pair up session. 

Allow students to talk through their reasoning with one another.  Have students compare their strategies used, discuss their responses, and defend their work.  I find in this time students will be able to find mistakes, and teach one another through discussion of their work. I will allow my students 5 minutes for pair up time.

When I walk the room listening to conversations, I am looking to hear strategies used, and appropriate work to defend their chosen response.  In this time frame the correct answer is not what is at the forefront.  However, the correct answer is ultimately the end goal.  During the Bell Ringer, I am looking for critical thinking:

Where are the students coming into this lesson? 

Who are the students that have deep understanding? 

Who are the students that somewhat understand? 

Who are the students that lack understanding? 

This is how I will proceed with the remainder of the lesson.  Once the students have had about 5 minutes to discuss with their partner, we do come together as a group.  I ask for students to volunteer the strategy that they used to solve the problem, and also discuss any changes made during their discussion time with their partner.  This will allow the whole group to hear different approaches to the same problem.  I do in this time give the correct response and affirm any student strategies that were accurate in getting the correct answer.  


15 minutes

This activity is meant for whole group discussion and break out group work. For the student activity we will use Dan Meyer’s Holes.  The link for the activity is http://mrmeyer.com/threeacts/holes/ 

First show the clip for act 1.  The clip is taken from the 2003 film Holes, directed by Andrew Davis.  It is 59 seconds long.  T

here are 4 questions to accompany Act One. You may print out the questions for each group or have the link up on the Smartboard for students to refer back to.  If you are using your interactive notebooks, have the students write the questions in their notebooks and label the section Determining Unit Rates. Group students in groups of 4 or 5 students.  Give each group 5 minutes to grapple through the first 4 questions.  This will lend itself to MP 1, 2, 3, and 4.

Discuss the questions with the whole group and ask for a speaker from each group to share the group’s responses.  Compare the responses with one another.  During the whole group discussion have students defend their responses. This is a great MP 3 practice. Students should be prepared to share why they responded the way that they did, their thought process in their response and what from the clip led them to respond the way in which they did. 

When discussing the estimates the students came up with, this is an important time to discuss why they chose those estimates, and are the estimates reasonable.  If in the discussion you find that one group is extremely off from another group, have the students determine why they are so off from one another and defend which group is correct.  You can replay the clip however many times needed for students to listen to helpful information to defend their responses. 

Act Two ask for other information needed to correctly answer question number 1.  Allow students to discuss in their groups.  Give another five minutes, again you may replay the clip if needed.  Discuss as a whole group the responses each group gave. In the link, Dan Meyer chooses a file that is page 12 from the book, Holes written by Louis Sachar.  Dan Meyer does an awesome job with cross curricular activities. You may opt to print this file and pass it out to each group, or put it up on your Smartboard, or document camera.  You may have each table read the page as a group and discuss the accompany question, or you read the page and discuss the important information with your students that they may find useful in answering the questions.  This process is open to what would be best with your students.  Read page 12 and have your students use all information gained to answer the remaining questions. 

Discuss the questions with your students as a whole group.  Have your groups share their thinking and responses.  After all groups have shared, affirm any responses that were correct, and discuss mistakes made in responses in which were incorrect.  Have students discuss why incorrect responses were incorrect and what could be done to correct the mistakes.  Be sure to talk students through the correct answer of each question.  


5 minutes

Remember, our Big Idea for this lesson is to find unit rates to help make decisions that will benefit us.  Discuss question 7 as a whole group reflection. Questions that can be posed to the class are, “Who will benefit from question 7, X-Ray or Stanley?  Why?  How does he benefit?  What did he need to do in order to benefit?  What does the length of the shovel have to do with him benefiting?

How short would X-Ray's shovel have to be so that he was doing half of Stanley's work every day?


2 minutes

The homework question will lead into tomorrow’s lesson.  Students will need to answer one problem involving determining how to find a unit price.  Use the homework as your bell ringer discussion.  Please see Determining Unit Prices Lesson for the usage of the homework from today’s lesson.