Working with Expressions and Equations Part 3

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SWBAT: • Create algebraic expressions and equations based on word problems. • Use substitution to evaluate algebraic expressions.

Big Idea

Ben’s mom gives him the option of grooming 3 horses or mowing 2 fields. Which job should Ben choose? Why? Students use their knowledge of algebraic expressions and equations to write expressions and equations.

Do Now

7 minutes

Part of my class routine is a do now at the beginning of every class.  Students walk into class and pick up the packet for the day.  They get to work quickly on the problems.  Often, I create do nows that have problems that connect to the task that students will be working on that day.  For this lesson I want students to start thinking about expressions that involve more than one operation.

I ask for a volunteer to read number 1.  I assert that I think that the answer is a. 8h + 2.  I tell students to discuss my answer with their neighbor and decide whether they agree or disagree.  I can on a few students to explain their thinking.  I want students to articulate that a. would be correct if it cost $2 to enter and $8 for every extra hour.  For number 3 I ask students to identify one answer choice that is incorrect and explain why it does not work.  Why might a student choose that answer choice?

Guided Practice

7 minutes

After the Do Now, I have a student read the objectives for the day.  I tell students that they will again be creating expressions and equations to model situations.   These expressions and equations will be more complicated than the ones that we created previously. 

Before students move into groups, we work through page 2 together.  I ask students who has ever ridden a horse before.  Students share out what they know about horses and we look at the picture about the tools that you need in order to groom, or clean, a horse.

We read #1 and I call on a student to share his/her answer.  If the student gives me 90 minutes, I ask for another way to write that answer (1 ½ hours or 1.5 hours).  How long would it take him to group 2 horses?  4?  9?  Using that data, I ask students to write an expression that shows how many minutes it will take Ben to groom h horses and to create an expression that is equivalent.  I want students to articulate that since it takes 30 minutes to groom each horse, you need to multiply the number of horses he grooms by 30 minutes and the order does not matter.

Students will be working in groups of 3-4 students on the rest of the packet.  I will review group expectations and using the Group Work Rubric.  See the Using the Group Work Rubric video in my Strategy Folder.

Group Work

31 minutes

I walk around and monitor student progress and fill out the group work rubric for each group.  I am also looking for student work that has different strategies for solving #4 on page 5 to use during the closure.

Some common mistakes are students incorrectly using substitution with the expression they have created.  Some students also get confused with number 6 on page 4, since both chores will take the same amount of time.  If students are struggling with pages 3-4, I may ask them the following questions:

  • What is going on in this situation?
  • How long would it take if he/she needed to groom 10 horses?  What operation did you use to figure that out?
  • How many unknowns are in the situation?  
  • What does your answer mean?  What units belong with your answer?  Could you write the answer in another way?

Some students may struggle when they get to the “Making Money” questions on page 5 and 6.  Here are some questions I may ask:

  • How many minutes are in an hour?
  • How much does he make for 1 hour of work?  How can you use that information to help you?
  • How many hours did it take Ben to complete that chore?

 For students who correctly work through problems I may ask them these questions and then have them work on the substitution practice on page 7:

  • Would Ben make more money grooming 11 horses or mowing 8 fields?  How do you know?
  • How much money would Ben earn if he mowed 3 ½ fields?
  • Ben has 4 ½ hours, how many fields can he mow?

Closure and Ticket to Go

15 minutes

I ask students to share and compare their answers to question 6 on page 6.  I want students to articulate that it doesn’t matter which chore he chooses, each of them will take 2 hours to complete.  Then we’ll move on to talk about #4 on page 5.  I will call up the students I identified during the group work time to put their work under the document camera and explain their thinking.  Some students may use equivalent rates to show that if he earns $6/1 hour than he’ll earn $15/2 ½ hours of work.  Other students may start with the rate $6/60 minutes and go from there.  Other student may create a unit rate that $1/10 minutes and use that to find the amount of money Ben earns.  Other students may use go through a similar process but not use rates.  Some students will use decimals.   If I did not see students using some of these strategies I will model them under the document camera.

 I will ask whether I could change 150 minutes --> 2 hours 30 minutes --> 2.3 hours to use in my calculations.  I want students to be able to articulate that 2 hours and 30 minutes is not equivalent to 2.3 hours, since an hour is out of 60 minutes, so 30 minutes represents 30/60 or ½ or .5.   

If I have time, I ask students to share struggles they had and how they overcame them.  I also ask students if there are still struggles they are having.  I ask other students to give advice.  In my classroom I try to consistently show students that they will struggle with different problems but that they need to use their creative problem solving minds to try a strategy.  If that strategy doesn’t work, try another one!  The main question in this lesson was a difficult one that required students to problem solve and persevere through challenges and set-backs.  I want to acknowledge my students hard work and their persistence.

With 5 minutes remaining, pass out the ticket to go.  Students work independently to complete it.