Algebraic Equilibrium Lesson Plan LP Header
SWBAT... find market equilibrium algebraically by setting supply and demand equations equal.
45 Mins
Do Now
Student Questions (4 Tasks):
1. If y = 10 and y = x + 2, solve for x. (Ans: 8)
2. If y = 20 and y = 5x, solve for x. (Ans: 4)
3. Solve for x: 2x = 10. (Ans: 5)
4. Solve for x: 10 + x = 15. (Ans: 5)
Heart of the Lesson
Notebook Notes (Exact Student Text)
1. EQUILIBRIUM: The point where two lines meet.
2. THE RULE: To find where they meet, set Equation A = Equation B.
3. ALGEBRA: 1) Write side-by-side. 2) Move letters left. 3) Move numbers right. 4) Divide.
4. THE MATCH: The number found for X is the market price.
Teacher Script: "We set Supply equal to Demand to find the balance price."
Model: Cupcakes. y=2x+10 (Supply) and y=4x (Demand). 2x+10=4x -> 10=2x -> x=5.
Independent Practice
Individual Questions (8 Tasks):
1. 5x = 2x + 15 (Ans: 5)
2. 10x = 5x + 50 (Ans: 10)
3. 4x + 10 = 6x (Ans: 5)
4. 2x + 20 = 4x (Ans: 10)
5. y=3x; y=x+10 (Ans: 5)
6. y=5x; y=2x+12 (Ans: 4)
7. y=6x; y=3x+18 (Ans: 6)
8. y=8x; y=2x+48 (Ans: 8)
Exit Ticket
1. y=5x; y=2x+15 (Ans: 5)
2. y=4x; y=x+12 (Ans: 4)
3. y=10x; y=2x+80 (Ans: 10)
4. y=8x; y=4x+16 (Ans: 4)
Algebraic Equilibrium Student Handout Name:
Truth is Powerful and It Prevails- Sojourner Truth
NORTH★STAR
Quarter 1, Week 3, Day 1
Do Now
Directions: Solve each algebraic equation for x. Show your full work in the box provided.
1. y = 10; y = x + 2
2. y = 20; y = 5x
3. Solve: 2x = 10
4. Solve: 10 + x = 15
Notebook Notes
Directions: Record definitions for Equilibrium and Algebraic Steps into the area below.
Algebraic Equilibrium Page 1 of 2
Independent Practice
Practice Round 1
Directions: Set the equations equal to each other (y = y) and solve for the match point price x.
1. y = 5x and y = 2x + 15
2. y = 10x and y = 5x + 50
3. y = 6x and y = 4x + 10
4. y = 4x and y = 2x + 20
5. y = 3x and y = x + 10
6. y = 5x and y = 2x + 12
7. y = 6x and y = 3x + 18
8. y = 2x + 40 and y = 6x
Exit Ticket
Directions: Set equal and solve. Box your final x-value.
1. y=5x; y=2x+15
2. y=4x; y=x+12
3. y=10x; y=2x+80
4. y=8x; y=4x+16
Algebraic Equilibrium Page 2 of 2
Table Trends Lesson Plan Lesson Plan:
SWBAT... create data tables for linear equations to identify the market equilibrium price where quantities match.
45 Mins
Do Now
Yesterday's Algebra Quiz:
1. y=5x; y=2x+15 (Ans: 5)
2. y=4x; y=x+12 (Ans: 4)
3. y=10x; y=2x+80 (Ans: 10)
4. y=8x; y=4x+16 (Ans: 4)
Heart of the Lesson
Notebook Notes (Exact Student Text)
1. DATA TABLES: Organizers that list information row by row.
2. THE STEP: Pick a Price (X), then calculate Demand Y and Supply Y.
3. THE MATCH: Look for the row where both quantity numbers are the SAME.
4. THE SWEET SPOT: The price where quantities match is market balance.
Teacher Script: "We pick prices and check if shoppers and sellers agree. Watch as I fill this table. At $1, they don't match. But at $3, they both say 20. That is our 'X marks the spot'."
Independent Practice Key
Scenario 1 (Pizza): $2, 6
Data: (0,10,2), (1,8,4), (2,6,6), (3,4,8), (4,2,10)
Scenario 2 (Cookies): $3, 15
Data: (1,25,5), (2,20,10), (3,15,15), (4,10,20), (5,5,25)
Scenario 3 (Pens): $4, 30
Data: (2,50,20), (3,40,25), (4,30,30), (5,20,35), (6,10,40)
Scenario 4 (Soda): $3, 20
Data: (1,30,10), (2,25,15), (3,20,20), (4,15,25), (5,10,30)
Exit Ticket Key
Eraser Market Table Analysis:
1. Row $3 Demand? (Ans: 15)
2. Row $3 Supply? (Ans: 15)
3. Match Price? (Ans: $3)
4. Match Coord? (Ans: (3, 15))
Table Trends Student Handout Name:
Truth is Powerful and It Prevails- Sojourner Truth
NORTH★STAR
Quarter 1, Week 3, Day 2
Do Now
Directions: Solve for the match point x-value. Show all algebraic steps.
1. y = 5x and y = 2x + 15
2. y = 4x and y = x + 12
3. y = 10x and y = 2x + 80
4. y = 8x and y = 4x + 16
Notebook Notes
Directions: Record definitions for "Data Tables" and steps for the "Match Point".
Table Trends Handout Page 1 of 3
Independent Practice
IP: Table Match-Up
Directions: Use the rules to calculate quantities. Circle the matching row.
Scenario 1: Pizza (y=-2x+10 & y=2x+2)
<table class="w-full text-center text-sm border-collapse border border-slate-400 bg-white"><tbody><tr class="bg-slate-200 font-bold uppercase text-[9px]"><td>Price (X)</td><td>Dem</td><td>Sup</td></tr><tr><td>$0</td><td>10</td><td>2</td></tr><tr><td>$1</td><td>8</td><td>4</td></tr><tr class="font-black bg-blue-50"><td>$2</td><td>1. _____</td><td>2. _____</td></tr><tr><td>$3</td><td>4</td><td>8</td></tr><tr><td>$4</td><td>2</td><td>10</td></tr></tbody></table>
3. Match Price:
$
Scenario 2: Cookies (y=-5x+30 & y=5x+0)
<table class="w-full text-center text-sm border-collapse border border-slate-400 bg-white"><tbody><tr class="bg-slate-200 font-bold uppercase text-[9px]"><td>Price (X)</td><td>Dem</td><td>Sup</td></tr><tr><td>$1</td><td>25</td><td>5</td></tr><tr><td>$2</td><td>20</td><td>10</td></tr><tr class="font-black bg-blue-50"><td>$3</td><td>4. _____</td><td>5. _____</td></tr><tr><td>$4</td><td>10</td><td>20</td></tr><tr><td>$5</td><td>5</td><td>25</td></tr></tbody></table>
6. Match Price:
$
Scenario 3: Pens (y=-10x+70 & y=5x+10)
<table class="w-full text-center text-sm border-collapse border border-slate-400 bg-white"><tbody><tr class="bg-slate-200 font-bold uppercase text-[9px]"><td>Price (X)</td><td>Dem</td><td>Sup</td></tr><tr><td>$2</td><td>50</td><td>20</td></tr><tr><td>$3</td><td>40</td><td>25</td></tr><tr class="font-black bg-blue-50"><td>$4</td><td>7. _____</td><td>8. _____</td></tr><tr><td>$5</td><td>20</td><td>35</td></tr><tr><td>$6</td><td>10</td><td>40</td></tr></tbody></table>
9. Match Price:
$
Scenario 4: Soda (y=-5x+35 & y=5x+5)
<table class="w-full text-center text-sm border-collapse border border-slate-400 bg-white"><tbody><tr class="bg-slate-200 font-bold uppercase text-[9px]"><td>Price (X)</td><td>Dem</td><td>Sup</td></tr><tr><td>$1</td><td>30</td><td>10</td></tr><tr><td>$2</td><td>25</td><td>15</td></tr><tr class="font-black bg-blue-50"><td>$3</td><td>10. ____</td><td>11. ____</td></tr><tr><td>$4</td><td>15</td><td>25</td></tr><tr><td>$5</td><td>10</td><td>30</td></tr></tbody></table>
Market Meaning Lesson Plan Lesson Plan:
SWBAT... interpret the point of intersection, surplus, and shortage in a real-world market context.
45 Mins
Do Now
Yesterday's Graphing Quiz:
1. Ex A Match Pt? (Ans: (4, 6))
2. Ex A Quantity? (Ans: 6)
3. Ex B Match Pt? (Ans: (5, 10))
4. Ex B Quantity? (Ans: 10)
Heart of the Lesson
Notebook Notes (Exact Student Text)
1. EQUILIBRIUM: The "Sweet Spot." When Supply = Demand.
2. SURPLUS: Price is TOO HIGH. Items are left over on shelves.
3. SHORTAGE: Price is TOO LOW. The store runs out of stock.
4. BUSINESS GOAL: Always stay at the Sweet Spot to make the most money and keep customers happy.
Teacher Script: "Look at the graph. Match is $300. At $500, customers won't buy it. That's a SURPLUS. At $100, everyone wants one but I only have 10. That's a SHORTAGE."
PRICE Ref
Independent Practice
8 Individual Logic Tasks:
1. Price > Sweet Spot? (Ans: Surplus)
2. Price < Sweet Spot? (Ans: Shortage)
3. At $500 (high price)? (Ans: Surplus)
4. At $100 (low price)? (Ans: Shortage)
5. Surplus = Leftover? (Ans: Yes)
6. Shortage = Out of Stock? (Ans: Yes)
7. Name of match point. (Ans: Equilibrium)
8. Goal of owner? (Ans: Equilibrium)
Exit Ticket
1. Define Surplus. (Ans: Too much stuff)
2. Define Shortage. (Ans: Out of stock)
3. Game Match Price? (Ans: $300)
4. Why stay at match? (Ans: No waste)
Market Meaning Student Handout Name:
Truth is Powerful and It Prevails- Sojourner Truth
NORTH★STAR
Quarter 1, Week 3, Day 4
Do Now
Directions: Use your notes from yesterday's graphing exit ticket to complete the match point details for Exercise A and Exercise B.
1. Ex A Match Point (X, Y):
Answer...
2. Ex A Matching Quantity (Y):
Answer...
3. Ex B Match Point (X, Y):
Answer...
4. Ex B Matching Quantity (Y):
Answer...
Notebook Notes
Directions: Record definitions for Surplus, Shortage, and the Sweet Spot as presented by your teacher.
Market Meaning Page 1 of 2
Independent Practice
IP: Market Logic
Directions: Analyze the Video Game market graph. Use the Match Point ($300) to answer the questions.
Quantity (50) Price ($300)
1. If Price > Sweet Spot? (Surplus/Shortage)
2. If Price < Sweet Spot? (Surplus/Shortage)
3. Why is a Surplus bad for the store owner?
4. Why do we need the 'Match Point'?
5. Result of $500 price (high)?
6. Result of $100 price (low)?
Exit Ticket
Directions: Define the terms in 3-5 words based on today's lesson.
1. Surplus Definition:
2. Shortage Definition:
3. Equilibrium Price ($):
4. Why find the match?
Market Meaning Page 2 of 2
Market Meaning Student Handout Name:
Truth is Powerful and It Prevails- Sojourner Truth
NORTH★STAR
Quarter 1, Week 3, Day 4
Do Now
Directions: Use your notes from yesterday's graphing exit ticket to complete the match point details.
1. Ex A Match Point (X, Y):
2. Ex A Matching Quantity (Y):
3. Ex B Match Point (X, Y):
4. Ex B Matching Quantity (Y):
Notebook Notes
Directions: Record definitions for Surplus, Shortage, and the Sweet Spot as presented by your teacher.
Market Meaning Page 1 of 2
Independent Practice
IP: Market Logic
Directions: Analyze the Video Game market graph. Use the Match Point ($300) to determine the result of different prices.
Quantity (50) Price ($300)
1. If Price > Sweet Spot? (Surplus/Shortage)
2. If Price < Sweet Spot? (Surplus/Shortage)
3. Why is a Surplus bad for the store owner?
4. Why do we need the 'Match Point'?
5. Result of $500 price (high)?
6. Result of $100 price (low)?
7. Match Point Name:
8. Goal of Owner:
Exit Ticket
Directions: Define the terms in 3-5 words based on today's lesson.
1. Surplus Definition:
2. Shortage Definition:
3. Equilibrium Price ($):
4. Why find match?
Market Meaning Page 2 of 2
Market Graphing Lesson Plan Lesson Plan:
SWBAT... plot two market trends on one coordinate grid to find the intersection point visually.
45 Mins
Do Now
Yesterday's Eraser Market Table:
<table class="w-full border-collapse border text-[9px] text-center mb-1"><tbody><tr class="bg-slate-200"><td>Price</td><td>Dem</td><td>Sup</td></tr><tr><td>$1</td><td>25</td><td>5</td></tr><tr><td>$2</td><td>20</td><td>10</td></tr><tr class="bg-blue-100"><td>$3</td><td>15</td><td>15</td></tr><tr><td>$4</td><td>10</td><td>20</td></tr><tr><td>$5</td><td>5</td><td>25</td></tr></tbody></table>
Match Pt (Q, P): (15, 3)
Heart of the Lesson
Notebook Notes (Exact Student Text)
1. GRAPHING EQUILIBRIUM: Drawing two market trends on one coordinate grid.
2. THE AXES: Price is Vertical (UP). Quantity is Horizontal (SIDE).
3. THE MATCH: Look for the 'X' where the lines cross.
4. THE COORDINATE: Record as (Quantity, Price) to match standard math.
Teacher Script: "Watch me plot (15, 3). Quantity first, then Price."
Independent Practice Key
4 Practice Scenarios (Q, P):
Task 1 (Pizza): (6, 2)
Task 2 (Cookies): (15, 3)
Task 3 (Pens): (30, 4)
Task 4 (Soda): (20, 3)
Exit Ticket Key
Summative Review:
1. Demand Start (y-int): 10
2. Supply Start (y-int): 2
3. Match Pt (Q, P): (6, 2)
4. Eq Quantity: 6
Market Graphing Student Handout Name:
Truth is Powerful and It Prevails- Sojourner Truth
NORTH★STAR
Quarter 1, Week 3, Day 3
Do Now
Directions: Use your notes from yesterday's pencil market exit ticket to complete the 4 summary points below.
1. Pencil market match price?
Answer here...
2. Pencil market match quantity?
Answer here...
3. If Demand=50 and Supply=10, match?
Answer here...
4. Pencil Match Coordinate (X, Y)?
Answer here...
Notebook Notes
Directions: Copy the steps for graphing market equilibrium as demonstrated by your teacher. Use your ruler for the grid lines.
Market Graphing Page 1 of 2
Independent Practice
IP: Visual Equilibrium
Directions: Plot both linear trends on the grid. Find the 'X' where they cross and label the Match Point coordinates.
1-2. y = -x + 10 & y = x + 2
1. Pt: (___,___) 2. Q: ___
3-4. y = -2x + 12 & y = 2x + 0
3. Pt: (___,___) 4. Q: ___
5-6. y = -x + 15 & y = x + 5
5. Pt: (___,___) 6. Q: ___
7-8. y = -5x + 50 & y = 5x + 10
7. Pt: (___,___) 8. Q: ___
Exit Ticket
Directions: Graph each pair and identify the intersection point.
1-2. y = -x + 10 & y = x + 2
1. Pt: (___,___) 2. Q: ___
3-4. y = -x + 15 & y = x + 5
3. Pt: (___,___) 4. Q: ___
Market Graphing Page 2 of 2
Market Graphing Student Handout Name:
Truth is Powerful and It Prevails- Sojourner Truth
NORTH★STAR
Quarter 1, Week 3, Day 3
Do Now
Directions: Analyze the Eraser Market table. Identify the match price and point.
<table class="w-full text-center text-[12px] border-collapse border-4 border-slate-950 bg-white uppercase"><tbody><tr class="bg-slate-200 font-black tracking-tight"><td>Price ($)</td><td>Dem (Q)</td><td>Sup (Q)</td></tr><tr><td>$1</td><td>25</td><td>5</td></tr><tr><td>$2</td><td>20</td><td>10</td></tr><tr class="font-black"><td>$3</td><td>15</td><td>15</td></tr><tr><td>$4</td><td>10</td><td>20</td></tr><tr><td>$5</td><td>5</td><td>25</td></tr></tbody></table>
1. Match Price:
$ _____
2. Match Pt (Q, P):
( , )
Notebook Notes
Directions: Record steps for graphing market equilibrium from a data table.
Market Graphing Handout Page 1 of 3
Independent Practice
IP: Visual Equilibrium
Directions: Use the 5-row data tables to plot your lines. Label the match point 'X'.
Task 1: Pizza Market
<table class="text-[9px] border-collapse border border-slate-400 bg-slate-50 w-2/3 uppercase text-center font-bold"><tbody><tr class="bg-slate-200"><td>P</td><td>D</td><td>S</td></tr><tr><td>$0</td><td>10</td><td>2</td></tr><tr><td>$1</td><td>8</td><td>4</td></tr><tr><td>$2</td><td>6</td><td>6</td></tr><tr><td>$3</td><td>4</td><td>8</td></tr><tr><td>$4</td><td>2</td><td>10</td></tr></tbody></table>
Quantity (Q)
Price ($)
Match Pt (Q, P): (____,____)
Task 2: Cookie Market
<table class="text-[9px] border-collapse border border-slate-400 bg-slate-50 w-2/3 uppercase text-center font-bold"><tbody><tr class="bg-slate-200"><td>P</td><td>D</td><td>S</td></tr><tr><td>$1</td><td>25</td><td>5</td></tr><tr><td>$2</td><td>20</td><td>10</td></tr><tr><td>$3</td><td>15</td><td>15</td></tr><tr><td>$4</td><td>10</td><td>20</td></tr><tr><td>$5</td><td>5</td><td>25</td></tr></tbody></table>
Match Pt (Q, P): (____,____)
Market Graphing Handout Page 2 of 3
Independent Practice (Cont.) & Assessment
Task 3: Pen Market
<table class="text-[9px] border-collapse border border-slate-400 bg-slate-50 w-2/3 uppercase text-center font-bold"><tbody><tr class="bg-slate-200"><td>P</td><td>D</td><td>S</td></tr><tr><td>$2</td><td>50</td><td>20</td></tr><tr><td>$3</td><td>40</td><td>25</td></tr><tr><td>$4</td><td>30</td><td>30</td></tr><tr><td>$5</td><td>20</td><td>35</td></tr><tr><td>$6</td><td>10</td><td>40</td></tr></tbody></table>
Match Pt (Q, P): (____,____)
Task 4: Soda Market
<table class="text-[9px] border-collapse border border-slate-400 bg-slate-50 w-2/3 uppercase text-center font-bold"><tbody><tr class="bg-slate-200"><td>P</td><td>D</td><td>S</td></tr><tr><td>$1</td><td>30</td><td>10</td></tr><tr><td>$2</td><td>25</td><td>15</td></tr><tr><td>$3</td><td>20</td><td>20</td></tr><tr><td>$4</td><td>15</td><td>25</td></tr><tr><td>$5</td><td>10</td><td>30</td></tr></tbody></table>
