Math Standard:
Label
ordered pairs, finding domain and range, writing inequalities
Solve
polynomial systems by graphing
CTE Standard:
Define business related terms: demand (elastic), supply, equilibrium
point; Create an Excel chart from table data; Graph a set of points on Excel –
labeling via a text box; Change the axis formats in Excel as necessary
Teacher Notes/Materials
Needed:
Bags
of fun size candy (5 different types)
Excel
on a projector with a table file for each type of desired candy
White
boards, markers, & mini erasers
CTE Situation
The
day prior to this lesson ask students for their favorite fun size candy (given
them choices such as Skittles, Starburst, Twix, Milky Way, Reeses, etc) – take
a straw poll vote at the end of the class to find the most popular. Students may ask why and respond
with “you’re such a GREAT class I MAY have a treat for you tomorrow AND you may
have the chance to purchase candy from me on some days”. Write the choices on the board and leave
them overnight.
Upon
entry the next day, students will ask “do we get candy”. If possible, set up the various choices
in piles on tables and have students choose their favorite one piece as a free
sample. State the objectives. Now that you’ve had a nibble of the
delicious candy, would you like more?
However, you will have to buy them TOMORROW.
Day 1 Process:
Students
gather around the SmartBoard and teacher enters data as follows:
1. State that the teacher will offer some
Candy #1 (most popular) for $.01
2. Each student writes on his/her
whiteboard the number of pieces of Candy #1 desired to purchase for $.01
3. Total all of the student’s request to
purchase Candy #1
4. Enter the amount into the Excel table
5. Increase the amount to $.05 (make up a
story about why…. to offer at $.05”)
6. Repeat steps #2-5 until you have no
demand for the particular candy type, increasing $.05 for the purchase price.
7. Students return to computers and
together we create an Excel data series chart for the demand. Price will be the Y axis and quantity
desired will be the X axis. (CTE)
8. Label the ordered pairs using
textboxes, using proper mathematics language.
9. Below the chart, use set notation for
the domain and for the range
10. For an extra free piece of candy: State at the bottom of the chart, “what
is the meaning of the domain and range?”
11. Complete 4 candy charts (for the most
popular 4 candies) using steps #1-10. Create graphs using Excel or any other method.
DAY 2 Process
Prior
to class, teacher must determine the supply amounts for the prices determined
for the demand. “While I’m very
generous, I will be offering this candy at a specific price for each type.”
1. Open Candy #1 file and create a Column
C labeled Supply
2. Give students the figures (teacher
generates how much they will supply at each sale value), ask the students for
the reasons why at each increase of price, the teacher is willing to offer more
pieces of candy; lead the students to conclude that this is the inverse of
demand.
3. Give a piece of graph paper to each
student. Students will
duplicate the demand curve from previous day. Review concepts as necessary, restating domain and range.
4. Using the teacher generated numbers for
supply, have students graph the supply curve on the same piece of graph paper
5. Determine where the 2 curves meet
called the equilibrium point; “this is how you solved systems by graphing”
6. Use Excel to create a supply curve
(this is a repeat of #4 except now using technology.
7. Label the equilibrium point
8. Complete the remaining candy charts in
Excel; Sell the candy for the equilibrium price.
Using the table below write the ordered pairs.
How many pieces wanted
Price
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0.01
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0.05
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0.10
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0.15
|
|
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State the domain and range of the following relation.
Solve the following system by graphing:
Extension: Write the
equation of the supply and demand curves.
Solve the system by algebraic substitution.
Thanks
to Jean Keenan & Joanne Costa for sharing this lesson.
