Class: Algebra I
Date: 3/22/15
Topic: Linear Equations In The World
Period: 1
Estimated Time: 50 minutes
1. Standard
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CC.2.2.HS.D.10: Represent, solve, and interpret equations/inequalities and systems
of equations/inequalities algebraically and graphically.
2. Materials/Equipment
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Three-acts Activity Worksheet (one per student)
Calculator
Pencil
Timer
3. Procedures:
The Three-acts Concept:
The topic for this three-acts concept is to use students’ knowledge of linear equations to explore
an application in real world hypotheticals. Students are presented with a picture in act one to
engage the students to pose questions on the pictures topic. Then there will be a class discussion
of these questions. The teacher will correct the students question to a central main question that
will cover linear equations. After, the students will start will asking what crucial information is
needed to solve the main question. After a class discussion upon this information the teacher will
present the necessary information to solve the problem. Furthermore, with the information the
students will set up an equation to solve the main question. Now, the class will move onto the
third and final act which the main questions answer will be revealed. The students will have time
to reflect and see if they were close to their original guess, back in act one. Through the three-acts
lesson the students will see the practical use of linear equations.
Complete Question for the three acts:
Dan got a job trimming trees. If he trims trees from 6a.m. to noon, with the exceptions of a 30
minute break, Dan can make 10.65 dollars an hour. How many hours with it take Dan to buy a
6,000 dollar Harley Davidson 1200 Sportster motorcycle?
Correct answer: 564 hours
a) Act One: (Time: 15 minutes)
 Act one the students will be presented a picture compilation of Dan looking at the
newspaper dreaming he had a motorcycle and then Dan getting a new job trimming
trees.
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The central question the students should ask is: “How many hours will Dan need to
work at his new job to get the motorcycle at a certain price?”
The teacher will set a timer for five minutes for the students to brainstorm ideas to
the Main Question, while also making a list of things they have noticed from the
pictures.
Once the timer goes off, the teacher will direct the students to write down their
questions and the things they noticed on the worksheet, which is provided. The
teacher will then lead a class discussion on what questions the students came up with
from the pictures. After the discussion, the teacher will need to demonstrate the Main
Question to be answered; which is, again, how many hours will Dan need to work to
get the motorcycle?
o Sample questions to ask the students:
- What financial problems could Dan run into with working at his new
job? (Taxes, overtime, raise of pay, or loss of employment)
- Will the price of the bike increase or decrease?
- Will Dan need to buy anything to be equipped for his new job, i.e. startup expenses?
The pictures that will be presented:
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Once the class starts to get close to having the correct answer to the Main
Question, the teacher should step in and direct the students to discuss
more upon the correct Main Question. During this time the teacher
should pose the correct Main Question to focus the lesson.
o The students’ questions will be anything and everything, so the
teacher needs to push along the discussion towards the correct
Main Question.
b) Act Two: (Time: 20 minutes)
 In act two the students continue to work on A Three Acts Mathematical Story
worksheet. They will write down what information they think they need to know and
the teacher will give the students the correct given information.
 The teacher will begin with instructing the students to write down what information
they think they need to answer their question that the students came up with from
viewing the first pictures. Then the teacher will open the floor to the students to go
over their Main Question, Guess, and What… information they thought is needed.
 The teacher should try to guide the students to request specific and important
information to solve the problem:
o Duration of work day?
o Break time?
o Wage?
o Cost of motorcycle?
 Once, the students ask a few of these questions the teacher should display the
PowerPoint on the Smart Board.
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Next, the students will be given ten minutes to use the newly acquire information to
solve the Main Question. The teacher will instruct the students to use the Workspace
on the “A Three Acts Mathematical Story” worksheet to solve the Main Question:
“How many hours will Dan need to work to get the motorcycle? “
 Once the students have an answer they should place their answer under the Answer
section to Main Question.
c) Act Three: (Time: 15 minutes)
 In act three, the students will take all their information, questions, and answers to
have a class discussion on how long Dan will need to work to afford the motorcycle.
 The teacher should go around the classroom and have the students give their answer
to the Main Question. The teacher should make a list of the answers of the students
on the board.
 Once the entire class gives their answer the teacher will present the last picture that
includes the answer of how long Dan will need to work.
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At this point the students can see Dan got his motorcycle after a many hours of
trimming trees.
Furthermore, the class can discuss the process in which they got their answer and
how the class set up a linear equation to find the unknown time.
If there is enough time the teacher can pose these follow-up questions:
o What problems could Dan run into with working at his new job? (Taxes,
overtime, raise of pay)
o Will the price of the bike increase or decrease?
o Will Dan need to buy anything to be equipped for his new job?
These questions can completely change the dynamic of the linear problem and are
important for real life decision making.
4. Adaptations:
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The students can be paired up such that a stronger student will be paired up with a weaker
one, so there is peer tutoring.
A Three Acts Mathematical Story worksheet can have hints or more guidance to help the
student see connections to the pictures with the mathematics of linear equations.
5. Evaluation of Students:
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The students will be evaluated on their participation during class discussion.
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The A Three Acts Mathematical Story worksheet will be collected and graded not on
correctness, but on completeness. This classroom activity will graded out of 30 points,
ten points per act.
6. Reflection:
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Use A Three Acts Mathematical Story to see the students work and to verify if the
students understood the tie to real world application with linear equations.
If the students were far from the correct Main Question with their own question then it
may be beneficial to change the pictures, as to be more explicit and informative.