Review 5: Walking Trip - Using Expressions and Equations to Represent Situations

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Objective

Students will be able to represent a situation with an expression, represent a situation with an equation, create a graph/table that demonstrates the relationship between two variables, use rates to solve multi-step word problems.

Big Idea

How long will it take two girls to finish their 10 mile charity walk? Students stretch their knowledge of rates, expressions, equations, and measurement conversions to answer this question.

Do Now

5 minutes

See the Do Now video in my Strategy Folder for more details about how I begin class.  During this review unit, I have selected multiple choice questions that cover as variety of topics. 

To check the do now, I display a step by step answer for #1.  Students check and correct their work.  I ask student to share their strategy for answering #2.  Some students may convert 1/5 and 2/5 to decimals.  Other students may convert the decimals to fractions and then change the fractions to have a common denominator of tenths. 

 

Expressions + Equations Practice

10 minutes

After the Do Now, I have a student read the objectives for the day.  I tell students that they will be connecting their knowledge about rates, expressions, equations, and measurement conversions to answer a question: How long will it take 2 girls to complete their 10 mile charity walk?  

I have students work in partners to complete the problems on page 2.  Students can check in with the partner if they have a question, and check in and compare answers when they have completed the five questions.  After about 7 minutes I call on students to quickly share their thinking and answers to questions 1-4.

Walking Trip

35 minutes

I move students into heterogeneous groups of 4 students.  I pass out group rubrics and explain expectations.  See the Group Work Rubric video in my Strategy Folder for more details.

 A student reads the opening paragraph and we text mark the important information.  I tell students that they will use all of this information in some part of the problem.   I ask, “What is the unit rate that expresses the girls’ speed?”  Together we create a table (time in sec/ distance) next to the graph, from 0 to 9 seconds.  Then we create the graph showing the distance the girls travel over time. I ask, “Is this walking rate data proportional?”  I am looking for students to tell me that yes it is proportional because for every second that passes the girls walk 1.5 meters. 

I have students work on pages 4-7 in their groups.  I post a key for each page around the room.  See the Posting A Key video in my Strategy Folder.  Students are engaging with MP1: Make sense of problems and persevere in solving them and Reason abstractly and quantitatively.  This is a complex problem that requires students to dig into what the units mean and how to navigate between them. 

If students struggle with #2, I ask them what they know about the girls’ walking rate.  Once they tell me that the girls are traveling 1.5 meters per second I ask them to tell me about the variables.  Some students can narrow it down to (b) and (c) but don’t notice the difference in the variables.  For #3 and #4 if a group is struggling I’ll ask them how many seconds are in 1 minute?  Then I’ll encourage them to set up a ratio with the unit rate and what they are trying to figure out (____ m / 60 seconds).

For #5 I am looking that students are correctly extending the pattern and are able to express that for each additional hour, the girls walk 5,400 more meters.  If students struggle with the equation for 5b I direct them to the equation question for #2.  How should these equations be similar?  How should they differ?

Students who struggle with multiplying/dividing with decimals will struggle on #6-10. I have calculators available for students to use to check their work. 

For students who complete the problem I will pose one or more of the following questions:

  • How would increasing the girls’ walking rate affect the values in the table?  How would it affect the graph?
  • How would decreasing the girls’ walking rate affect the values in the table?  How would it affect the graph?
  • If their walking rate was 1 meter/ 1.5 seconds, how could you find out how fast they were walking per second?
    • How far could they walk in a minute?  An hour?
    • How long would it take them to complete the 10 mile charity walk at this pace?

 

Closure

10 minutes

I ask students to share their equation for #9 and how their group came up with it.  I ask students to explain what the equation means, what is it telling us?  Then I ask students to share out their answers to the question, “How long will it take the girls to finish the charity walk?”  Depending on rounding, some student answers may vary.   Then I’ll ask students how accurate they think their prediction is.   What factors might make the girls’ actual finish time different than your prediction?  I am looking for students to share that the girls are humans (not machines/take breaks/etc) so it would probably be nearly impossible for them to maintain a constant rate for that long of time.  Many people do use rates like minutes per mile to set goals when they are training for a long distance walk or run.  See the Closure video in my Strategy Folder for more details.

I collect students’ work to analyze their progress with the problem.