Lesson 13

Break Even Day 1 of 2

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SWBAT set up and solve equations with two equivalent expressions.

Big Idea

Use cups of pennies to learn about setting expressions equivalent to find that magical "Break Even" point.

Bellringer: Homework Review

10 minutes

Spend about the first ten minutes allowing students to present their answers to the Spartan Pride Homework.  Take questions from anyone who is questioning a certain answer.  I sometimes encourage participation during homework review by offering a reward for putting solutions on the board with all work shown (I have everyone put up answers at the same time).  My rewards are sometimes school rewards and sometimes candy I bring in myself.  I also offer rewards such as candy to anyone in the audience who finds a mistake and can correct the mistake.  This really helps my homework completion percentage, as I do not grade homework.  


Scripting Strategy


Previous Preparation

To prepare for this lesson shouldn’t take very long.  Make copies of the paper balance scale and laminate them if you have time just to preserve them for later use.  I would not recommend trying to get really creative and brining in real balance scales from the science classroom, if your school has those.  Pennies have been made of two different materials through the years (cooper and zinc) and each have a different weight but same appearance.  The date on the penny determines the material used to create the inside of the coin.  I have a lab just for this in the systems of equations unit, so wait until then to actually weigh these coins. 


I went to the bank and cashed a ten-dollar bill for rolls of pennies.  I put a roll of pennies into a paper-drinking cup and gave each group a cup of pennies and a paper scale.

Beginning the New Activity

35 minutes

Clarify for students that today the focus of the lesson is to learn about breaking even.  What does it mean to break even, which is a finance word?  How do we find the break-even point visually, algebraically, and conceptually?  The whole context of the lesson today is about trying to just break even.

Pass out the activity papers first – no hands on materials until the students understand their purpose and the rules for properly caring for the materials.  Allow students one minute to read individually the instructions for table one and then discuss aloud the meaning of the directions.  This would be a good time to script this discussion on the board so students have clarification to look back to during the activity.  Common issues students might have include misunderstanding the rate of change (different for each partner but constant from turn to turn for the same partner) and misunderstanding the meaning of the word turn (each time pennies are added to the scale, a turn was used). 

Scripting Strategy

Then allow students to work in cooperative groups to complete questions one, two, and three.  Question three has a negative rate of change because partner two is taking pennies off the scale (adding a negative is the same as subtraction).  This may be an area where students ask a lot of questions but guide their thinking with questioning to consider what it means to add a negative.  Don’t tell them directly that it is subtraction.

As students work, move about the room assessing approaches and asking students to present various strategies during the mini wrap-up session.  Also, provide feedback to struggling students to help move their learning forward.  Feedback is good questioning to spark thought and discussion among partners.  Hold a student lead mini wrap-up of the first three tables after about 10-15 minutes and most groups are finished. 

Prepare students for the next sets of problems by saying that we are now going to begin focusing on the algebraic method of finding the break-even point but use the scales to check our work.  Allow students 10 minutes or so to complete questions four and five where you are asking them to find the break-even point algebraically before using the scales to check the solution.  Move about the room assessing student approaches and finding multiple entry points to present during the wrap-up session.  As you find multiple approaches, tell students what it is about their approach that you really want them to explain during the wrap up. 

Ultimately, you would like to see an equation with variables in each expression and then other students present equivalent equations as their approach.  Hold a full discussion over the algebraic solutions.

Activating students as owners of their own learning

Activating students as resources for one another

Cooperative Grouping Explained

Providing feedback that moves learning forward

Mini-Wrap Up Strategy Explained

Clarifying and Sharing Learning Intentions and Criteria for Success



5 minutes

After wrapping up the scale questions assign word problems six, seven, and eight for homework and collect the cups of pennies and paper scales. These problems are perfect for assigning in Edmodo for discussion because there are multiple entry points for students to begin working.  I would assign at least one or more of the problems for discussion in Edmodo that night.  You can post the questions you want students to discuss as an assignment.   


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