Linear Functions and Relationships II
Name: Brian Youn
Title of lesson: Linear Functions and Relationships II
Length of lesson: 50 minutes(?)
Description of the class:
Name of course: Algebra
Honors or regular: Either
Source of the lesson:
Give specific information.
TEKS addressed:
(b) Foundations for functions: knowledge and skills and performance descriptions.
(1) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. Following are performance descriptions.
(A) The student describes independent and dependent quantities in functional relationships.
(B) The student gathers and records data, or uses data sets, to determine functional (systematic) relationships between quantities.
(C) The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations.
(D) The student represents relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.
(E) The student interprets and makes inferences from functional relationships.
Students will be able to:
III. Resources, materials and supplies needed
IV. Supplementary materials, handouts.
Five-E Organization
Teacher Does Probing Questions Student Does
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Engage: Imagine
that your family – parents and siblings – decide you want to all go out and
watch an NBA basketball game in |
Critical questions that will establish prior knowledge and create a need to know |
Expected Student Responses/Misconceptions |
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Explore: What are some factors that affect how much money it will cost in total?
We should come up with things such as ticket prices (obviously),
parking, refreshments and concessions.
For this lesson, we’ll take an example where we are selling tickets to
the school drama team’s musical. We have tickets from two different sections
of the theatre – the balcony (b), and the floor (f).
There are 2000 seats in the theatre (600 on the floor and 1400 in the
balcony).
Now you have the freedom of setting the respective prices for the floor
seats (f) and the balcony seats (b), however as a regulation, the sum of f
and b must not exceed $200 (otherwise people will start to revolt).
As the manager of the venue, how can we ensure that we maximize the
revenues from ticket sales?
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Critical questions that will allow you to decide whether students understand or are able to carry out the assigned task (formative) On the topic of tickets, how many seats are in a typical basketball arena? From our first few days in this NBA project, how much money does your team feel it needs to raise from ticket sales? Would you want to make every ticket the same price, or would you want to set variable pricing (tiered pricing)? How many different tiers of ticket prices do you want to set?
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Expected Student Responses/Misconceptions |
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Explain: We can start by writing out two expressions.
The first will be an equation for the revenue:
600f + 1400b = revenue
where “f” represents the cost of
floor seats and “b” represents the cost of balcony seats (both in
dollars).
A second equation we can write involves the requirement for the limit
on the cost of ticket prices.
b + f = $200
One way we can figure out the optimal ticket prices is to simply fill
out a table… go in increments of about $10 and calculate out the total
revenue using the first equation above.
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Critical
questions that will allow you to help students clarify their understanding
and introduce information related to concepts to be learned Why are we using 600 and 1400? What do those represent? What are some reasons that there is a
limit to the ticket prices? What if we
just didn’t have any limit on the prices of tickets? What would happen? And what is a good guess for the optimal
balance of prices? (take some guesses
from the class) Where did we find the optimal balance
point? |
Expected Student Responses/Misconceptions |
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Extend / Elaborate: Now that we have gone over how to approach the problem of optimizing revenue in this situation, let’s explore some things that we might not have thought of. What assumptions are we making with this approach of solving for optimal ticket prices? What are some of the things that might happen in a real-life scenario that would prevent this from actually giving us the maximum revenue possible? Talk this out with your group members to see what you can come up with.
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Critical
questions that will allow you to decide whether students can extend
conceptual connections in new situations We are assuming that all the tickets in
both sections will sell out. What happens if we sell all the tickets on
the floor but only half the tickets in the balcony? If we knew this to be the case, how can we
change our formula to reflect this change/ There’s probably other things to factor in… what about group discounts?, etc… |
Expected Student Responses/Misconceptions |
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Evaluate: Lesson Objective(s) Groups will present their solutions to the example problem on the board. We will discuss the different solutions presented.
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Critical questions that will allow you to decide whether students understood main lesson objectives |
Expected Student Responses/Misconceptions |
Percent effort each team member contributed to this lesson plan:
___%___ ____Name of group member_____________________
___%___ ____Name of group member_____________________