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Algebra Essentials Sequence

A series of 8th and 9th grade Algebra lessons focused on linear relationships and systems of equations, with a focus on SPED/IEP support.

Ddeeohnny.jackson

Trend Trackers Lesson

An 8th grade Algebra lesson focused on interpreting slope and y-intercept in the context of scatter plots and lines of best fit, specifically designed for Special Education students with IEP supports.

Solution Detective Lesson

A 9th grade Algebra lesson focused on identifying the number of solutions in a system of linear equations (one, none, or infinite), specifically designed for Special Education students with IEP supports.

The Equal Point Lesson

A 9th grade Algebra lesson focused on interpreting the intersection point of a system of equations in a real-world context (media, sports, food), specifically designed for Special Education students with IEP supports.

Modeling with Systems Lesson

A 9th grade Algebra lesson focused on translating real-world scenarios (media, sports, food) into a system of two linear equations, specifically designed for Special Education students with IEP supports.

Algebra Essentials Sequence

A series of 8th and 9th grade Algebra lessons focused on linear relationships and systems of equations, with a focus on SPED/IEP support.

Ddeeohnny.jackson

Trend Trackers Answer Key

Teacher Answer Key

Unit 7.7 Linear Models | 8th Grade Algebra

North Star Academy

1. Do Now (Gaming)

(x): Hours Spent Gaming.

(y): Level Achievement.

Trend: UP (Positive Correlation).

2. Excellence (TikTok)

Starting Value: 200 fans.

Speed of Change: 50 fans per week.

3. Prior Knowledge

Slope = THE SPEED | Intercept = THE START.

Try This: Circle the 5 (it's the start point).

4. Guided Practice (Basketball)

Equation: y = 3x + 5

Slope: 3 | Intercept: 5.

5. Priority Practice

Taco Truck:

Starts with 50. Grows by 10 more per degree.

Hulu Cost:

Start (b) = 15 | Speed (m) = 5.

6. Mastery Challenge

Equation: y = 5x + 40

7. Exit Ticket

y = 0.75x + 5.00

8. Homework Answers

A. Start (b): 1 goal.

B. Speed (m): 0.5 goals per drill.

Match: Slope → Growth Speed | Intercept → Starting Point.

Trend Trackers Lesson Plan

Heart of the Lesson

"Interpreting the start and the speed helps us predict the future using data trends."

Unit 7.7 | Linear Models & Trends

North Star Academy

8th Grade SPED Algebra

Objective

Students will interpret slope (rate of change) and y-intercept (starting point) in real-world contexts using linear models.

Learning STAMP

"I can explain what 'm' and 'b' mean using the units in a real-world story."

Min	Section	Teacher Actions & Prompts	Expected Answers
5	Do Now	Observe Gaming Graph. "What variable is on the bottom? What happens to the Level as Hours increase?"	x = Hours. Trend = UP.
10	Excellence
Discovery Model:

TikTok Eq y = 50x + 200. Use checkboxes in packet.

"Look at Week 0. Did the user start at 50 or 200? Check that box."

Homework Walkthrough

Briefly check the Soccer Drills scenario. Remind them: "m" is the number with the x, "b" is the number alone.

Trend Trackers Student Packet

Trend Trackers Packet

Unit 7.7 | 8th Grade Algebra Concepts

Name: ______________________

Date: ______________________

Do Now (5 min)

The Gaming Trend: Look at the graph below.

HOURS (x) LEVEL (y)

1. Independent Variable (x):

2. Dependent Variable (y):

Trend: UP or DOWN?

Excellence (10 min)

The Discovery Case: TikTok Follower Growth

y = 50x + 200

1. Look at the number 200. If x is 0 (Week 0), what is the value of y?

This is our "Starting Point".

2. Look at the number 50. For every 1 week that passes, how many NEW fans are added?

This is our "Speed of Change".

Prior Knowledge (5 min)

Rate of Change (Slope)

The Speed

Y-Intercept (Start)

The Start

Try This!

"A pizza starts at $10.00 and adds $2.00 for each topping."

Identify the Speed (m):

Identify the Start (b):

Guided Practice (10 min)

Case Analysis: Basketball Training

"A player gains 3 points per game for every hour of extra practice. They started the season averaging 5 points."

Equation Scaffold:

y = ___x + ___

What is the Slope (m)?

What is the Intercept (b)?

Priority Practice (20 min)

1

The Taco Truck 🌮

y = 10x + 50

x = Degrees (F)

y = Tacos Sold

"At 0 degrees, the truck starts with ____ tacos. For every 1 degree warmer, the truck sells ____ more tacos."

2

Hulu Streaming 🎬

y = 5x + 15

x = Extra Devices

y = Total Cost

What is the START (b)?

What is the SPEED (m)?

Mastery Challenge

The Reverse Detective

"A gym membership costs $40.00 to join (the start) and then $5.00 for every class you take (the speed)."

y =

x +

Exit Ticket

STAMP Point

The Final Movie Case

Study: A ticket starts at $5.00. Each year, it increases by $0.75.

Write the linear model (y = mx + b):

Trend Trackers Student Packet

Trend Trackers Packet

Unit 7.7 | 8th Grade Algebra

Name: ______________________

Date: ______________________

Do Now (5 min)

The Gaming Trend: Look at the graph below.

HOURS (x) LEVEL (y)

1. Independent Variable (x):

2. Dependent Variable (y):

Trend: UP or DOWN?

Excellence (10 min)

The Discovery Case: TikTok Growth

y = 50x + 200

1. Look at the number 200. If Week = 0, what is the value of y?

"This is the starting point on the y-axis."

2. Look at the number 50. For every 1 week, how much does y grow?

"This is the speed of change (slope)."

Prior Knowledge (5 min)

Rate of Change (Slope)

THE SPEED

Y-Intercept (Start)

THE START

Detective Trial Case:

"A pizza starts at $10.00 and adds $2.00 for each topping."

Identify Speed (m):

Identify Start (b):

Guided Practice (10 min)

Case Study: Basketball Training

"A player gains 3 points per game for every hour of practice. They started the season averaging 5 points."

Equation Template:

y = x +

What is the Slope (m)?

What is the Intercept (b)?

Priority Practice (20 min)

1

The Taco Truck Mystery 🌮

y = 10x + 50

x = Degrees (F)

y = Tacos Sold

"At 0 degrees, the truck starts with ____ tacos. For every 1 degree warmer, the truck sells ____ more tacos."

2

Streaming Subscriptions 🎬

y = 5x + 15

x = Extra Devices

y = Total Cost ($)

Identify START (b):

Identify SPEED (m):

Mastery Challenge

The Reverse Detective Case

"A gym membership costs $40.00 to join (the start) and then $5.00 for every class (the speed)."

y =

x +

Exit Ticket

Teacher STAMP Zone

The Final Movie Case File

Study: A ticket starts at $5.00. Each year, it increases by $0.75.

y =

Trend Trackers Student Packet

Trend Trackers Packet

Unit 7.7 | 8th Grade Algebra Concepts

Name: ______________________

Date: ______________________

Do Now (5 min)

The Gaming Trend: Look at the graph below.

HOURS (x) LEVEL (y)

1. Independent Variable (x):

2. Dependent Variable (y):

Trend: UP or DOWN?

Excellence (10 min)

The Discovery Case: TikTok Growth

y = 50x + 200

1. Look at the number 200. If Week = 0, what is the value of y?

"This is the starting point on the y-axis."

2. Look at the number 50. For every 1 week, how much does y grow?

"This is the speed of change (slope)."

Prior Knowledge (5 min)

Rate of Change (Slope)

THE SPEED

Y-Intercept (Start)

THE START

Try This Case:

"A pizza starts at $10.00 and adds $2.00 for each topping."

Identify Speed (m):

Identify Start (b):

Guided Practice (10 min)

Basketball Training:

"A player gains 3 points per game for every hour of practice. They start at 5 points."

Equation:

y = x +

What is the Slope (m)?

What is the Intercept (b)?

Priority Practice (20 min)

1

The Taco Truck 🌮

y = 10x + 50

x = Degrees (F)

y = Tacos Sold

"At 0 degrees, the truck starts with tacos. For every 1 degree warmer, the truck sells more tacos."

2

Streaming Subscriptions 🎬

y = 5x + 15

x = Extra Devices

y = Total Cost ($)

Identify START (b):

Identify SPEED (m):

Mastery Challenge

The Reverse Detective

"A gym membership costs $40.00 to join (the start) and then $5.00 for every class (the speed)."

y = x +

Exit Ticket

STAMP Zone

Study: A ticket starts at $5.00. Each year, it increases by $0.75.

y = x +

Homework Assignment

Trend Detective

Soccer Drills vs. Goals

y = 0.5x + 1

A. The Start Value (b):

B. The Speed (m):

Concepts: Match the words

Systems Solutions Answer Key

Teacher Answer Key

Unit 8.4 Solutions Packet | 9th Grade Algebra

North Star Academy

1. Do Now Check

Meet Point: Coordinate (1, 3).

Verdict: 1 SOLUTION.

2. Excellence Model

Checklist: Slopes are DIFFERENT (3 vs 2).

Result: 1 SOLUTION.

3. Prior Knowledge

Rule: Same Slope + Different Intercept = Parallel.

Try This: "NEVER" cross.

4. Guided Practice (Gym)

Step 1: YES (Slopes are 4).

Step 2: NO (Starts 10 and -2).

Verdict: NO SOLUTION.

5. Priority Practice

Mystery 1 (Social):

1 Solution (Diff slopes 5 vs 2).

Mystery 2 (Burger):

Infinite Solutions (Identical equations).

6. Mastery Challenge

Example: y = 10x + 2 (Needs slope 10 and diff b).

7. Exit Ticket

Verdict: NO SOLUTION.

Reason: Slopes match (-3), starts don't (12, -1).

8. Homework Answers

Soccer: NO SOLUTION (Slopes are both 0.5).

Match: Slope → Growth Speed | Intercept → Starting Point.

Systems Solutions Student Packet

Solution Detective Packet

Unit 8.4 | North Star Academy

Name: ______________________

Date: ______________________

Do Now (10 min)

The Music App Mystery: Graph both lines on the grid below.

5 -5 -5 5 x y

Spotify (Line 1):

y = 1x + 2

Apple (Line 2):

y = -1x + 4

Verdict:

How many shared points?

Excellence (10 min)

Discovery: Netflix vs Hulu

y = 3x + 1

vs

y = 2x + 5

1. Look at the Slopes (the numbers with x). Are they the same or different?

2. If lines have different speeds, will they eventually cross each other?

YES NO

Prior Knowledge (5 min)

The Speed (m)

SLOPE

The Start (b)

Y-INTERCEPT

Try This Mystery:

"A pizza starts at $10.00 and adds $2.00 for each extra topping."

Speed (Slope):

Start (Intercept):

Guided Practice (10 min)

Case Analysis: Gym Memberships

y = 4x + 10

vs

y = 4x - 2

Step 1: Slopes

Are they same? (4 vs 4)

Yes No

NO SOLUTION

(Parallel Lines)

Priority Practice (20 min)

1

Mystery Pair: Social Media Followers

y = 5x + 3

vs

y = 2x + 10

❌ 1 Solution 🛤️ No Solution 📏 Infinite

2

Mystery Pair: Burger Deal Pricing

y = 6x + 5

vs

y = 6x + 5

❌ 1 Solution 🛤️ No Solution 📏 Infinite

Mastery Challenge

The Custom Clue: Create your own mystery!

Write a second equation that would make this system have NO SOLUTION (Parallel lines).

y = 10x + 4

&

y =

x +

Exit Ticket

STAMP Zone

The Movie Ticket Mystery

y = -3x + 12

&

y = -3x - 1

ONE SOLUTION NO SOLUTION INFINITELY MANY PARALLEL SAME SLOPE

"This system has _________________ solutions because..."

Systems Solutions Lesson Plan

Solution Detective Lesson Plan

Heart of the Lesson

"Seeing where lines meet is the secret to solving the system puzzle."

Unit 8.4 | Determining Number of Solutions

North Star Academy

9th Grade SPED Algebra

Learning Objective

Students will determine if a system has 1, None, or Infinite solutions by comparing slopes and intercepts.

Learning STAMP

"I can use slope clues to predict if lines cross, never meet, or are the same."

Min	Section	Teacher Actions & Prompts	Expected Answers
10	Do Now	Students graph the Spotify vs Apple Music lines. "Where is the shared coordinate point?"	(1, 3)
ONE SOLUTION
10	Excellence	Scaffold discovery of Case 1 (Netflix). "Look at the numbers with the x. Are they different speeds?"	Slopes: 3 vs 2.
Verdict: 1 SOLUTION.
5	Prior Know.	Review icons. Match "Same Slope" to Parallel Tracks. Complete "Try This" (Pizza toppings).	m=2, b=10.
10	Guided	Gym membership case. "If speeds (slopes) match but starts don't, will they ever catch each other?"	No Solution
15	Practice	Mystery Pairs. Pair 1 (Diff m). Pair 2 (Everything same). Circle the 'm' values first.	1. One
2. Infinite
10	Exit & STAMP	Cinema Case. STAMP packet page 4 after "Because..." sentence is correct.	No Solution

Homework Walkthrough

Refer to Soccer Drills on Page 5. "If they practice at the same rate but one starts ahead, can they tie?"

Systems Solutions Student Packet

Solution Detective Packet

Unit 8.4 | North Star Academy

Name: ______________________

Date: ______________________

Do Now (10 min)

The Music App Mystery: Graph both lines on the grid below.

5 -5 -5 5 x y

Spotify (Line 1):

y = 1x + 2

Apple (Line 2):

y = -1x + 4

Verdict:

How many points do they share?

Excellence (10 min)

Discovery Case: Netflix vs. Hulu

y = 3x + 1

vs

y = 2x + 5

1. Look at the Slopes (the numbers with x). Are they the same or different?

2. If lines have different speeds, will they eventually cross each other?

YES NO

Prior Knowledge (5 min)

The Speed (m)

SLOPE

The Start (b)

Y-INTERCEPT

Trial Case:

"A pizza starts at $10.00 and adds $2.00 for each topping."

Speed (m):

Start (b):

Guided Practice (10 min)

Case Analysis: Gym Memberships

y = 4x + 10

vs

y = 4x - 2

Step 1: Check Slopes

Are they same? (4 vs 4)

YES NO

Step 2: Check Starts

Are they same? (10 vs -2)

YES NO

Verdict: NO SOLUTION (Parallel Lines)

Priority Practice (20 min)

1

Case: Social Media Followers

y = 5x + 3

vs

y = 2x + 10

❌ 1 Solution 🛤️ No Solution 📏 Infinite

2

Case: Burger Deal Pricing

y = 6x + 5

vs

y = 6x + 5

❌ 1 Solution 🛤️ No Solution 📏 Infinite

Mastery Challenge

Create your own mystery!

"Write a second equation that would make this system have NO SOLUTION (Parallel lines)."

y = 10x + 4

&

y =

x +

Exit Ticket

STAMP Zone

The Final Movie Case File

Cinema A: y = -3x + 12 | Cinema B: y = -3x - 1

ONE SOLUTION NO SOLUTION INFINITE PARALLEL SAME SLOPE

"This system has _________________ solutions because..."

Algebra Power Review Worksheet

Algebra Power Review

Independent Work | North Star Academy

Name: ______________________

Date: ______________________

Unit 7.8: Writing Inequalities

"At Least" / "Minimum"

$\geq$

"Less Than" / "Under"

$<$

Pizza Budget

"You have at most $20.00 to spend on lunch."

Write the inequality:

x

20

Point Guard Stats

"The player scores more than 5 points but no more than 15 points per game."

Write the compound inequality (Middle X):

5

x

15

Unit 8.1: Graphing Systems

"The solution to a system is the Intersection Point where the lines cross."

Equation 1:

y = 1x + 2

Equation 2:

y = -1x + 4

Solution Coordinate:

( , )

Unit 8.2: Substitution

"Substitution means replacing a variable with its equal value."

CLUE A

y = 2x

CLUE B

x + y = 6

Step 1: Replace 'y' in Clue B with '2x':

x + ( ___ ) = 6

Step 2: Solve for X (Remember: x + 2x = 3x):

3x = 6 → x = __

Step 3: Solve for Y (Double your X):

y = 2 × ( __ ) → y = __

Unit 8.3: Elimination

"Elimination means adding the rows to cancel a variable out."

x + y = 10

x - y = 2

y cancels!

Step 1: Add the Rows (x + x = 2x):

2x =

Step 2: Solve for X (Divide by 2):

x =

Step 3: Solve for Y (x + y = 10):

y =

Mastery & Final Stamp

The Review Challenge

"Choose the correct method for this mystery case and circle it!"

y = 10

&

y = x + 2

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA MASTER!"

Algebra Power Review Answer Key

Independent Work Answer Key

Units 7.8, 8.1, 8.2, 8.3 Review | North Star Academy

9TH GRADE ALGEBRA

Unit 7.8: Inequalities

1. Pizza Budget: $x \leq 20$

2. Point Guard: $5 < x \leq 15$

Note: "No more than" includes the number (equal to).

Unit 8.1: Graphing

Solution Point: (1, 3)

Both lines meet at x=1 and y=3.

Unit 8.2: Substitution

Step 1: $x + (2x) = 6$

Step 2: $3x = 6 \rightarrow$ x = 2

Step 3: $y = 2(2) \rightarrow$ y = 4

Final Solution: (2, 4)

Unit 8.3: Elimination

Step 1: $2x = 12$ (10 + 2)

Step 2: x = 6 (12 / 2)

Step 3: $6 + y = 10 \rightarrow$ y = 4

Final Solution: (6, 4)

Mastery Verdict

Answer: A (Substitution)

Reason: Since 'y' is already alone, it is easiest to plug it in.

Algebra Power Review Worksheet

Algebra Power Review

Independent Mastery | North Star Academy

Name: ______________________

Date: ______________________

Unit 7.8: Inequalities

"At Most" / "Maximum"

$\leq$

"Between" (Middle X)

$a < x < b$

Pizza Budget

"The total cost for your pizza order must be at most $20.00."

Write the inequality:

x

20

Average Points

"A basketball player scores more than 5 but less than 15 points each game."

Fill in the compound inequality:

5

x

15

Unit 8.1: Graphing Systems

"The solution to a system is the Shared Point where both lines meet!"

5 -5 -5 5 X Y

Equation 1:

y = 1x + 2

Equation 2:

y = -1x + 4

Find the meeting point:

( , )

Units 8.2 & 8.3: Solving Algebraically

8.2: The Substitution Case

"Replace the variable with its known value!"

y = 2x

x + y = 6

1. Rewrite Equation 2 using (2x) instead of 'y':

x + ( ) = 6

2. Solve for X:

3x = 6 → x =

8.3: The Elimination Case

"Add the rows together to cancel out 'y'!"

x + y = 10

x - y = 2

CANCEL!

Add them up: (1x + 1x) = (10 + 2)

2x =

→ x =

Units 8.5 & 8.6: Meaning & Modeling

8.5: Interpreting the Solution

"A system solution is (5, 50). $x$ is number of items and $y$ is total cost."

Explain the verdict in a story:

"When you buy items, both deals cost exactly dollars."

8.6: Modeling with Equations

"A food truck charges a $5.00 entry fee and then $2.00 per taco."

Translate the story into a model (y = mx + b):

y =

x +

Mastery & Final Stamp

The Detective's Choice

"If one equation has $y$ already alone (like $y=10$), which method is EASIEST to use?"

A

Substitution

Algebra Power Review Answer Key

Answer Key

Algebra Power Review | Monday & Tuesday

TEACHER USE ONLY

Monday (Day 1)

1. Sports Inequality:

x > 20

(Open circle at 20, arrow pointing right)

2. Media Inequality:

x <= 5

(Closed circle at 5, arrow pointing left)

3. Food Compound:

140 < x < 160

4. Sports Compound:

12 <= x <= 14

5. Graphing System (Media):

Solution: (1, 3)

6. Graphing System (Sports):

Solution: (1, 2)

Monday Mastery:

A: 10 < x < 20

B: NONE (Parallel lines never meet)

Tuesday (Day 2)

1. Substitution (Food):

Step 1: $x + (3x) = 20$

Step 2: $4x = 20$

x = 5

2. Substitution (Media):

$12 = 5x + 2$

$10 = 5x$

x = 2

3. Elimination (Sports):

$5x = 15$

x = 3

4. Elimination (Food):

$5y = 24$

y = 4.8

Tuesday Mastery:

A: y is eliminated (since $y + (-y) = 0$)

B: y = 10 ($2 \times 5 = 10$)

Algebra Power Review Worksheet

Algebra Power Review

Independent Practice | North Star Academy

Name: ______________________

Date: ______________________

Unit 7.8: Inequalities

"At Most" / "Maximum"

$\leq$

"Between" (Middle X)

a < x < b

Case 1: The Pizza Budget

"The total cost for your lunch must be at most $25.00."

x

25

Case 2: The Ticket Limit

"You need to sell at least 15 tickets to go on the trip."

x

15

Unit 8.1: Graphing

"Graph both lines and find the Intersection Point where they cross!"

y x 4 -4 -4 4

Spotify deal:

y = 1x + 2

Apple deal:

y = -1x + 4

Case Verdict:

( , )

Unit 8.2 & 8.3: Algebra Solver

Case 1: Substitution

y = 2x

&

x + y = 6

1. Replace 'y' in Eq 2 with (2x):

x + ( ) = 6

2. Solve for X (x + 2x = 3x):

3x = 6 → x =

Case 2: Elimination

x + y = 10

x - y = 2

Y CANCELS!

Add the columns together:

2x =

Now solve for X:

x =

Unit 8.5 & 8.6: Story Detective

8.5: Interpreting the Meaning

"The system solution is (5, 50).
$x$ is items bought and $y$ is total cost."

What does the '5' tell us about the story?

What does the '50' tell us about the story?

8.6: Writing the Equation

"A food truck charges a $5.00 flat fee to enter and then $2.00 per taco."

Write the Model (y = mx + b):

y =

x +

Mixed Mastery Review

The Final Case File

"If one equation has y already alone (for example, $y = 10$), which solving method should a detective use?"

A

Substitution

B

Elimination

Learning STAMP

"I HAVE MASTERED ALGEBRA SYSTEMS!"

Algebra Power Review Answer Key

Teacher Answer Key

Algebra Power Review | Monday & Tuesday

9TH GRADE | SPED/IEP

M

Monday: Units 7.8 & 8.1

Do Now & Excellence

Do Now Match: > is Greater Than | ≤ is Less than or Equal.
Excellence 1-2: 13 is NOT allowed. 14 IS allowed.
Excellence 3: Correct Inequality: x ≥ 14.

Guided & Priority Practice

Guided (Netflix): Solution point is (1, 3).
Priority 1 (Taco): t < 6.
Priority 2 (Jersey): Solution point is (2, 4).

Mastery & Exit Ticket

Mastery (Range): 20 < x < 30.

Exit Ticket: Point is (2, 5).
(Substitute 5 for y: 5 = 2x + 1 → 4 = 2x → x = 2)

T

Tuesday: Units 8.2 & 8.3

Do Now & Excellence

Do Now Solve: Total = 5 + (10) = 15.
Excellence 1: YES (Replace y with 5).
Excellence 2: 5 + x = 12 → x = 7.
PK (Try This): 2x = 10 → x = 5.

Guided & Priority Practice

Guided 1: y + 2 = 11 → y = 9.
Guided 2: 9 = 3x → x = 3.
Priority 1: 3x = 30 → x = 10.
Priority 2: 5y = 30 → y = 6.

Mastery & Exit Ticket

Mastery (Taco): 4x = 16 → x = 4.
(Plug in: 2(4) + y = 10 → 8 + y = 10 → y = 2)

Exit Ticket: 2(4) + x = 20 → 8 + x = 20 → x = 12.

Instructional Note for Review

These independent worksheets are designed to be self-scaffolding. For students with lower reading comprehension, encourage them to highlight keywords like "at least", "start", and "speed". For the algebraic steps, ensure they are showing the divide operation clearly to avoid integer errors.

Algebra Power Review Worksheet

Algebra Power Review

Mastery Practice Packet

Name: ______________________

Date: ______________________

7.8: Linear Inequalities

"Maximum" / "At Most"

$\leq$

"Between" (Middle X)

$a < x < b$

1. Food Budget:

"You have at most $25 to spend on a burger and fries."

x

25

2. Points Scored:

"The star player scores more than 10 but less than 30 points."

10

x

30

3. Minimum Goal:

"You need to make at least 15 sales to win the prize."

x

15

8.1: Graphing Systems

5 -5 -5 5 X Y

Task: Graph both lines.

Line 1: y = 1x + 2

Line 2: y = -1x + 4

Where do they meet?

( , )

Algebraic Solving

8.2: Substitution Method

Eq A: y = 2x

Eq B: x + y = 6

1. Put (2x) where 'y' used to be:

x + ( ) = 6

2. Solve for X (Note: x + 2x = 3x):

3x = 6 → x =

3. Solve for Y (Use y = 2x):

y = 2 × ( ) → y =

8.3: Elimination Method

x + y = 10

x - y = 2

Y CANCELS!

Step 1: Add the columns (10 + 2)

2x =

Step 2: Solve for X (Divide by 2)

x =

Meaning & Modeling

8.5: Interpreting the Meanings

"A system solution is (5, 50). $x$ is items bought and $y$ is total cost."

What does the 5 mean?

What does the 50 mean?

8.6: Writing the Math Story

"A food truck charges a $5.00 entry fee and then $2.00 per taco."

y =

x +

Clue: Rate goes with X, fee is b alone.

Mixed Mastery Review

The Detective's Final Choice

"If an equation has y already alone (like $y = 10$), which method should you use?"

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA MASTER!"

Algebra Power Review Answer Key

Independent Review Answer Key

Review Packet | Units 7.8 - 8.6 | North Star Academy

9TH GRADE ALGEBRA

7.8: Inequalities

1. Pizza Budget: x ≤ 25

2. Points: 10 < x < 30

3. Sales Goal: x ≥ 15

8.1: Graphing Systems

Intersection Point:

(1, 3)

Check: 1 + 2 = 3 (Spotify) and -1(1) + 4 = 3 (Apple). Both match.

8.2: Substitution

Step 1: x + (2x) = 6

Step 2: 3x = 6 → x = 2

Step 3: y = 2(2) → y = 4

Final Point: (2, 4)

8.3: Elimination

Step 1: 2x = 12

Step 2: x = 6

Step 3: 6 + y = 10 → y = 4

Final Point: (6, 4)

8.5: Interpreting Meaning

Meaning: When you buy 5 items, both deals cost exactly $50.

8.6: Writing the Model

y = 2x + 5

($2 rate is slope; $5 fee is b)

Mastery Verdict

Answer: A (Substitution)

Teacher Scoring Note: For full credit on units 8.2 and 8.3, students must show the replacement step (substitution) or the combined row (elimination).

Algebra Power Review Answer Key

Mastery Review Answer Key

Independent Review | North Star Academy

9TH GRADE ALGEBRA

7.8: Inequalities

1. Pizza Budget: x ≤ 25

2. Points: 10 < x < 30

3. Sales Goal: x ≥ 15

8.1: Graphing Systems

Intersection Point:

(1, 3)

Verification: x=1, y=3 works for both deals.

8.2: Substitution

Step 1: x + (2x) = 6

Step 2: 3x = 6 → x = 2

Final: y = 2(2) → y = 4

Solution: (2, 4)

8.3: Elimination

Step 1: 2x = 12 (sum of rows)

Step 2: x = 6

Final: 6 + y = 10 → y = 4

Solution: (6, 4)

8.5: Meaning

Meaning: For 5 items, the total cost is $50 for both.

8.6: Modeling

y = 2x + 5

(Rate 2 next to x; fee 5 is b)

Final Mastery

Answer: A (Substitution)

Teacher Scoring Guide: Ensure students have shown the vertical addition step in Elimination and the parenthesis replacement step in Substitution for full credit.

Algebra Power Review Worksheet

Algebra Power Review

Independent Practice | North Star Academy

Name: ______________________

Date: ______________________

Unit 7.8: Inequalities

"At Most" / "Maximum"

$\leq$

"Between" (Middle X)

a < x < b

Case 1: The Pizza Budget

"The total cost for your lunch must be at most $25.00."

x

25

Case 2: Average Points

"A basketball player scores more than 10 but less than 30 points each game."

10

x

30

Unit 8.1: Graphing

"Step 1: Graph both lines. Step 2: Circle the Intersection Point where they cross!"

y x 4 -4 -4 4

Line 1:

y = 1x + 2

Line 2:

y = -1x + 4

Final Verdict:

( , )

Unit 8.2 & 8.3: Solver

8.2: Substitution Method

y = 2x

&

x + y = 6

Step 1: Replace 'y' in Eq 2 with (2x):

x + ( ) = 6

Step 2: Solve for X (x + 2x = 3x):

3x = 6 → x =

8.3: Elimination Method

x + y = 10

x - y = 2

Y CANCELS!

Add the columns together (sum of 10 and 2):

2x =

Final X Value:

x =

Meaning & Modeling

8.5: Interpreting the Meanings

"A system solution is (5, 50).
$x$ is items bought and $y$ is total cost."

What does the '5' represent?

What does the '50' represent?

8.6: Writing the Math Story

"A food truck charges a $5 fee and then $2 per taco."

y =

x +

Clue: Rate goes with X, Start Fee is alone!

Final Mastery Review

The Detective's Final Choice

"If an equation has y already alone (like $y = 10$), which method should a student use?"

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA SYSTEMS EXPERT!"

Algebra Power Review Answer Key

Algebra Power Answer Key

Independent Review | North Star Academy

9TH GRADE ALGEBRA

7.8: Inequalities

1. Pizza: x ≤ 25

2. Points: 10 < x < 30

3. Sales: x ≥ 15

8.1: Graphing

Shared Cross Point:

(1, 3)

Check: Both equations work with x=1 and y=3.

8.2: Substitution

Replaced: x + (2x) = 6

Solved X: x = 2

Solved Y: y = 2(2) → y = 4

Solution Pair: (2, 4)

8.3: Elimination

Sum: 2x = 12

Solved X: x = 6

Solved Y: 6 + y = 10 → y = 4

Solution Pair: (6, 4)

8.5: Interpreting Meaning

X = 5: 5 items bought.

Y = 50: $50 total cost.

Both deals are EQUAL at this point.

8.6: Modeling

y = 2x + 5

($2 rate is slope; $5 fee is start value)

Mastery Selection

Answer: A (Substitution)

Teacher Note: This worksheet is designed for independent mastery. Circulate to provide the Learning STAMP only after checking the "Case Verdict" on all pages.

Algebra Power Review Worksheet

Algebra Power Review

Mastery Practice | North Star Academy

Name: ______________________

Date: ______________________

Unit 7.8: Inequalities

"At Most" / "Max"

$\leq$

"At Least" / "Min"

$\geq$

1. Lunch Budget:

"The total cost for your lunch must be at most $25.00."

x

25

2. Points Scored:

"The player scores more than 10 points but less than 30 points."

10

x

30

Unit 8.1: Graphing

"Graph both lines. The Shared Point is your solution!"

Y X 4 -4 -4 4

Equation 1:

y = 1x + 2

Equation 2:

y = -1x + 4

Verdict:

( , )

Unit 8.2 & 8.3: Algebraic Solver

8.2: Substitution Method

y = 2x

AND

x + y = 6

Step 1: Replace 'y' in the 2nd Equation:

x + ( ) = 6

Step 2: Solve for X (x + 2x = 3x):

3x = 6 → x =

8.3: Elimination Method

x + y = 10

x - y = 2

Y CANCELS!

Add the rows (sum of 10 and 2):

2x =

Result: Solve for X.

Meaning & Modeling

8.5: Meaning of the Solution

"The system solution is (5, 50).
x is items bought and y is total cost in dollars."

What does the '5' represent?

What does the '50' represent?

8.6: Writing the Math Story

"A taco truck charges a $5.00 entry fee and then $2.00 per taco."

y =

x +

Rate goes with X, Start Fee is alone.

Mixed Mastery Review

The Final Case Choice

"If one equation has y already alone (like y = 10), which method should a detective use?"

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA MASTER!"

Algebra Power Review Answer Key

Algebra Mastery Key

Independent Review | North Star Academy

9TH GRADE ALGEBRA

7.8: Inequalities

1. Pizza Budget: x ≤ 25

2. Points range: 10 < x < 30

8.1: Graphing

Shared Cross Point:

(1, 3)

Check: x=1, y=3 works for both deals.

8.2: Substitution

Replaced: x + (2x) = 6

Solved X: x = 2

Final Solution: (2, 4)

8.3: Elimination

Sum: 2x = 12

Solved X: x = 6

Final Solution: (6, 4)

8.5: Interpretation

X = 5: 5 items bought.

Y = 50: $50 total cost.

Both deals are EQUAL here.

8.6: Modeling

y = 2x + 5

Final Mastery Choice

Answer: A (Substitution)

Teacher Note: For 8.2 and 8.3, ensure students found both variables. For 8.5, ensure they used context units (items and dollars).

Algebra Power Review Worksheet

Algebra Power Review

Independent Mastery Review

Name: ______________________

Date: ______________________

7.8: Inequalities

"Maximum" / "At Most"

$\leq$

"Minimum" / "At Least"

$\geq$

"Total lunch cost must be at most $25.00."

x

25

8.1: Graphing Systems

y x 4 -4 -4 4

Step: Graph both lines.

y = 1x + 2 & y = -1x + 4

Shared Point:

( _ , _ )

8.2: Substitution Method

y = 2x

AND

x + y = 6

1. Replace 'y' in the 2nd Equation with (2x):

x + ( ) = 6

2. Solve for X (Note: x + 2x = 3x):

3x = 6 → x =

3. Solve for Y (Plug X back into y = 2x):

y =

8.3: Elimination Method

x + y = 10

x - y = 2

Y CANCELS!

1. Add the rows (10 + 2):

2x =

2. Now solve for X and Y:

x =

y =

8.5 & 8.6: Stories

8.5: Meaning of (x, y)

"A system solution is (5, 50).
x is items bought and y is total cost ($)."

What does the '5' mean?

What does the '50' mean?

8.6: Building the Model

"A food truck charges a $5.00 entry fee and then $2.00 per taco."

Write the Model (y = mx + b):

y =

x +

Mastery Review

Choice Detective

"If one equation has y already alone (like y = 10), which solving method should a detective use?"

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA MASTER!"

Algebra Power Review Answer Key

Teacher Answer Key

Algebra Power Review | Monday & Tuesday

9TH GRADE | SPED/IEP

M

Monday: Units 7.8 & 8.1

Do Now & Excellence

Do Now Match: > is Greater Than | ≤ is Less than or Equal.
Excellence 1-2: 13 is NOT allowed. 14 IS allowed.
Excellence 3: Correct Inequality: x ≥ 14.

Guided & Priority Practice

Guided (Netflix): Solution point is (1, 3).
Priority 1 (Taco): t < 6.
Priority 2 (Jersey): Solution point is (2, 4).

Mastery & Exit Ticket

Mastery (Range): 20 < x < 30.

Exit Ticket: Point is (2, 5).
(Substitute 5 for y: 5 = 2x + 1 → 4 = 2x → x = 2)

T

Tuesday: Units 8.2 & 8.3

Do Now & Excellence

Do Now Solve: Total = 5 + (10) = 15.
Excellence 1: YES (Replace y with 5).
Excellence 2: 5 + x = 12 → x = 7.
PK (Try This): 2x = 10 → x = 5.

Guided & Priority Practice

Guided 1: y + 2 = 11 → y = 9.
Guided 2: 9 = 3x → x = 3.
Priority 1: 3x = 30 → x = 10.
Priority 2: 5y = 30 → y = 6.

Mastery & Exit Ticket

Mastery (Taco): 4x = 16 → x = 4.
(Plug in: 2(4) + y = 10 → 8 + y = 10 → y = 2)

Exit Ticket: 2(4) + x = 20 → 8 + x = 20 → x = 12.

Instructional Note for Review

These independent worksheets are designed to be self-scaffolding. For students with lower reading comprehension, encourage them to highlight keywords like "at least", "start", and "speed". For the algebraic steps, ensure they are showing the divide operation clearly to avoid integer errors.

Algebra Power Review Answer Key

Mastery Review Answer Key

Independent Review | North Star Academy

9TH GRADE ALGEBRA

7.8: Inequalities

1. Pizza Budget: x ≤ 25

2. Points: 10 < x < 30

3. Sales Goal: x ≥ 15

8.1: Graphing Systems

Intersection Point:

(1, 3)

Check: 1+2=3 and -1(1)+4=3. Correct!

8.2: Substitution

Step 1: x + (2x) = 6

Step 2: 3x = 6 → x = 2

Step 3: y = 2(2) → y = 4

Solution: (2, 4)

8.3: Elimination

Sum: 2x = 12

Solve X: x = 6

Solve Y: 6 + y = 10 → y = 4

Solution: (6, 4)

8.5: Interpretation

Meaning: For 5 items, both options cost exactly $50.

8.6: Modeling

Taco Truck: y = 2x + 5

Burrito Bus: y = 2x + 10

(System uses both stories)

Final Mastery Choice

Answer: A (Substitution)

Easiest when a variable is isolated.

Confidential Answer Key for North Star Academy Staff

Algebra Power Review Worksheet

Algebra Power Review

Independent Mastery Review

Name: ______________________

Date: ______________________

7.8: Inequalities

"Maximum" / "At Most"

$\leq$

"Minimum" / "At Least"

$\geq$

"Total lunch cost must be at most $25.00."

x

25

8.1: Graphing Systems

y x 4 -4 -4 4

Step: Graph both lines.

y = 1x + 2 & y = -1x + 4

Shared Point:

( _ , _ )

8.2: Substitution Method

y = 2x

AND

x + y = 6

1. Replace 'y' in Equation 2 with (2x):

x + ( ) = 6

2. Solve for X (x + 2x = 3x):

3x = 6 → x =

3. Solve for Y (Plug X back into y = 2x):

y =

8.3: Elimination Method

x + y = 10

x - y = 2

Y CANCELS!

1. Add the rows (10 + 2):

2x =

2. Now solve for BOTH variables:

x =

y =

8.5 & 8.6: Real-World Modeling

8.5: Interpreting Meanings

"A system solution is (5, 50).
x is items bought and y is total cost ($)."

What does the '5' mean?

What does the '50' mean?

8.6: Write the System

Story 1: A taco truck charges $5 fee plus $2 per taco.

Story 2: A burrito bus charges $10 fee plus $2 per burrito.

Write the Model (y = mx + b) for both:

TACO TRUCK:

y = _x + _

BURRITO BUS:

y = _x + _

Mastery Review

Choice Detective

"If one equation has y already alone (like y = 10), which solving method should a detective use?"

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA MASTER!"

Algebra Power Review Worksheet

Algebra Power Review

Mastery Practice | North Star Academy

Name: ______________________

Date: ______________________

7.8: Inequalities

"Maximum" / "At Most"

$\leq$

"Minimum" / "At Least"

$\geq$

"Total lunch cost must be at most $25.00."

x

25

8.1: Graphing Systems

y x 4 -4 -4 4

Step: Graph both lines.

y = 1x + 2 & y = -1x + 4

Shared Point:

( ? , ? )

8.2: Substitution Method

y = 2x

AND

x + y = 6

1. Replace 'y' in Equation 2 with (2x):

x + ( ) = 6

2. Solve for X (Note: x + 2x = 3x):

3x = 6 → x =

3. Solve for Y (Plug X back into y = 2x):

y =

8.3: Elimination Method

x + y = 10

x - y = 2

Y CANCELS!

1. Add the rows (10 + 2):

2x =

2. Now solve for BOTH variables:

x =

y =

Meaning & Modeling

8.5: Interpreting Meanings

"A system solution is (5, 50).
x is items bought and y is total cost ($)."

What does the '5' mean?

What does the '50' mean?

8.6: Write the System

Story 1: A taco truck charges $5 fee plus $2 per taco.

Story 2: A burrito bus charges $10 fee plus $2 per burrito.

Write the Model (y = mx + b) for both:

Taco Truck:

y = x +

Burrito Bus:

y = x +

Mastery Review

Choice Detective

"If one equation has y already alone (like y = 10), which solving method should a detective use?"

A

Substitution

B

Elimination

Learning STAMP

"I AM AN ALGEBRA MASTER!"

Algebra Power Review Answer Key

Algebra Mastery Key

Independent Review | North Star Academy

9TH GRADE ALGEBRA

7.8: Inequalities

1. Budget: x ≤ 25

2. Points range: 10 < x < 30

8.1: Graphing

Shared Cross Point:

(1, 3)

Check: x=1, y=3 works for both deals.

8.2: Substitution

Replaced: x + (2x) = 6

Solved X: x = 2

Solved Y: y = 2(2) → y = 4

Solution: (2, 4)

8.3: Elimination

Sum: 2x = 12

Solved X: x = 6

Solved Y: 6 + y = 10 → y = 4

Solution: (6, 4)

8.5: Interpretation

X = 5: 5 items bought.

Y = 50: $50 total cost.

Both deals are EQUAL here.

8.6: Modeling System

y = 2x + 5

y = 2x + 10

Final Choice Case

Answer: A (Substitution)

Teacher Note: For units 8.2 and 8.3, ensure students found both variables. For 8.5, ensure they used context units (items and dollars).

Monday Algebra Power Review Worksheet

Monday Algebra Power Review

Units 7.8 & 8.1 | 55 Minute Independent Review

Name: ______________________

Date: ______________________

Do Now (5 min)

Match the symbol to its meaning:

>

<

Less Than

Greater Than

Excellence (10 min)

The Discovery: Compound Limits

"The Varsity football team requires players to be at least 14 years old but no older than 18 years old."

1. If $x$ is the age, and it must be 14 or higher, which inequality works? (Circle one)

x ≥ 14 x ≤ 14

2. If it must be 18 or lower, which works? (Circle one)

x ≤ 18 x > 18

3. A "Compound" inequality puts them together. Look at the number line. Shade between 14 and 18!

14 18

Prior Knowledge (5 min)

Recall: y = mx + b

m (Slope)

The Movement / Speed

b (Y-Intercept)

The Start Point

Try This: Plot the point (2, 3)

"Go right 2, go up 3. This is where two lines MIGHT meet."

Guided Practice (10 min)

Case: Netflix vs. Disney Cost

Option 1: $y = 1x + 2$ | Option 2: $y = -1x + 4$

Step 1:

Graph both lines.

Step 2:

Circle the intersection.

Final Solution:

( ___ , ___ )

Priority Practice (20 min)

1

Inequality Challenge: Food Truck Prices

"The Taco Truck only sells meals that cost more than $10. Write the inequality for meal price ($p$)."

p

10

"Does it include 10? No! Just MORE THAN."

2

Graphing Challenge: Sports Jersey Orders

"Graph the system and find the tied point."

y = 2x + 0

y = 1x + 2

Solution:

( ___ , ___ )

Mastery Challenge

The Combined Case

"A player scored more than 20 points but less than 30 points. Write the compound inequality for points ($x$)."

20

x

30

Exit Ticket

STAMP Zone

The Ultimate Solution Check

"If two lines are parallel (like train tracks), how many solutions do they have?"

Tuesday Algebra Power Review Worksheet

Algebra Power Review: Day 2

Tuesday Independent Practice | North Star Academy

Name: ______________________

Date: ______________________

Unit 8.2: Solving by Substitution

Substitution Rule Book:

1. Find the "lonely variable" (already equal to something).
2. Plug that value into the other equation.
3. Solve for the missing letter.

1. FOOD: Total cost (y) for sandwiches (x) is given by:

y = 3x

Lonely Variable Case

x + y = 20

Step 1: Replace 'y' with '3x'

x + ( ) = 20

Step 2: Solve for x

x = ________

2. MEDIA: Solving for shared monthly cost.

y = 5x + 2

y = 12

Substitution:

12 = 5x + 2

Solve for x (Show work):

x = ________

Unit 8.3: Solving by Elimination

Detective Rule:

Add the equations vertically to DELETE one variable!

3. SPORTS: Total equipment bill elimination.

2x + y = 10
3x - y = 5

5x + 0 = 15

Finish the solution:

Divide by 5 on both sides:

x = ________

4. FOOD: Solving for drinks (x) and fries (y).

4x + 2y = 20
-4x + 3y = 4

0 + 5y = 24

Solve for y (Show work):

y = ________

Tuesday Mastery

The Power Check

A. ELIMINATION: What happens when you add these equations? (Circle one)

x + y = 10
x - y = 4

y is eliminated

x is eliminated

B. SUBSTITUTION: If $x = 5$, what is the value of $y$ in $y = 2x$?

y = ________

TUESDAY POWER STAMP

Monday Algebra Power Review Worksheet

Algebra Power Review: Day 1

Monday Independent Practice | North Star Academy

Name: ______________________

Date: ______________________

7.8

Unit 7.8: Simple Inequalities

Detective Clue: Keyword Matching

>
More than

<
Less than

≥
At least

≤
At most

1. SPORTS: A team needs to score more than 24 points to break the record.

Write the inequality (Use x):

x _________________

Graph it below:

24

2. FOOD: A safe oven temp must be at most 450 degrees.

Write the inequality (Use x):

x _________________

Graph it below:

450

7.8

Unit 7.8: Compound Inequalities

Detective Clue: The "AND" Sandwich

When a value is BETWEEN two numbers, we put 'x' in the middle.
Example: 5 < x < 10 (X is more than 5 but less than 10).

3. MEDIA: A video length must be between 10 and 20 minutes.

Write the compound inequality:

< x <

4. SPORTS: Age limit is at least 15 AND at most 18.

Write the compound inequality:

≤ x ≤

8.1

Unit 8.1: Graphing Systems

Graphing Checklist:

1. Start at b (y-axis).
2. Move with m (slope).
3. Circle where they CROSS.

5. MEDIA: Subscription Cross-Over.

5 -5 -5 5 x y

Line 1:

y = 1x + 2

Line 2:

y = -1x + 4

Meet Point:

( __ , __ )

6. SPORTS: Score Match-Up Duel.

5 -5 -5 5 x y

Team A:

y = 2x + 0

Team B:

y = -1x + 3

Meet Point:

( __ , __ )

Monday Mastery Review

The Final Cases

Compound Inequality Case:

"A ticket costs more than $10 but less than $20."

________ < x < ________

System Result Check:

"If two lines never cross (Parallel), how many solutions?"

NONE

ONE

Tuesday Algebra Power Review Worksheet

Algebra Review: Day 2 (Part B)

Tuesday Independent Practice | North Star Academy

Name: ______________________

Date: ______________________

8.2

Unit 8.2: Solving by Substitution

The Substitution Guide:

1. Find the "lonely variable" (like y = 3x).
2. Plug that value into the other equation.
3. Solve for the missing letter.

1. FOOD: Find the cost of burgers (x) and drinks (y).

y = 3x

Step 1: The Lonely Variable

x + y = 20

Step 2: The Plug-In Eq

Substitution Move:

x + (

) = 20

Work Space to Solve for x:

x = ________

2. MEDIA: Solving for shared monthly cost.

y = 5x + 2

y = 12

Substitution Result:

12 = 5x + 2

Solve for x (Show each step):

x = ________

8.3

Unit 8.3: Solving by Elimination

The Elimination Trick:

Add the equations vertically to DELETE a variable that matches but has an opposite sign (+ and -).

3. SPORTS: Total equipment bill elimination.

2x + y = 10
3x - y = 5

5x + 0 = 15

Final Calculation:

"Divide by 5 on both sides to find x"

x = ________

4. FOOD: Solving for orders.

4x + 2y = 20
-4x + 3y = 5

0 + 5y = 25

Solve for y (Show steps):

y = ________

Tuesday Mastery Review

The Final Case File

Elimination Logic Check:

"What happens to the Y when you add these equations together?"

x + y = 10
x - y = 4

Y is Deleted (0)

X is Deleted (0)

Substitution Calculation:

"If you know x = 5, what is the value of y in y = 2x?"

y = ________

TUESDAY POWER STAMP

Algebra Power Review Answer Key

Teacher Answer Key

Algebra Power Review | Monday & Tuesday Review

FOR TEACHER USE ONLY

Monday (Day 1)

1. Sports Inequality:

x > 24

(Graph: Open circle at 24, arrow pointing Right)

2. Food Inequality:

x ≤ 450

(Graph: Closed circle at 450, arrow pointing Left)

3. Media Compound:

10 < x < 20

4. Sports Age Limit:

15 ≤ x ≤ 18

5. Media Graph Solution:

(1, 3)

6. Sports Graph Solution:

(1, 2)

Monday Mastery:

A: 10 < x < 20

B: NONE (Parallel lines have no solution)

Tuesday (Day 2)

1. Substitution (Food):

Move: x + (3x) = 20

Combine: 4x = 20

x = 5

2. Substitution (Media):

12 = 5x + 2

10 = 5x

x = 2

3. Elimination (Sports):

5x = 15

x = 3

4. Elimination (Food):

5y = 25

y = 5

Tuesday Mastery:

A: Y is Deleted (y + -y = 0)

B: y = 10 (since 2 * 5 = 10)

Tuesday Algebra Power Review Worksheet

Algebra Power Review: Day 2

Tuesday Independent Practice | North Star Academy

Name: ______________________

Date: ______________________

8.2

Unit 8.2: Solving by Substitution

The Substitution Rule Book:

1. Find the "lonely variable" (like y = 3x).
2. Plug that value into the other equation.
3. Solve for the missing letter.

1. FOOD: Find the cost of burgers (x) and drinks (y).

y = 3x

LONELY VARIABLE

x + y = 20

THE PLUG-IN EQ

Step 1: Substitution Move

x + (

) = 20

Step 2: Work Space (Solve for x)

x = ________

2. MEDIA: Monthly App Cost.

y = 5x + 2

y = 12

Plug-In Equation:

12 = 5x + 2

Solve for x:

x = ________

8.3

Unit 8.3: Solving by Elimination

Detective Trick: Add equations vertically to DELETE one variable!

3. SPORTS: The Equipment Bill.

2x + y = 10
3x - y = 5

5x + 0 = 15

The Final Move:

"Divide by 5 on both sides to find x"

x = ________

4. FOOD: The Order Case.

4x + 2y = 20
-4x + 3y = 5

0 + 5y = 25

Work Area (Solve for y):

y = ________

!

Tuesday Mastery Review

The Final Evidence

Elimination Logic:

"What happens to the Y when you add these together?"

x + y = 10
x - y = 4

Y is DELETED (0)

X is DELETED (0)

Substitution Check:

"If x = 5, find y in the equation y = 2x."

y = ________

POWER STAMP

Algebra Power Review Answer Key

Teacher Answer Key

Algebra Power Review | Monday & Tuesday Review

FOR TEACHER USE ONLY

Monday (Day 1)

1. Sports Inequality:

x > 24

(Graph: Open circle at 24, arrow pointing Right)

2. Food Inequality:

x ≤ 450

(Graph: Closed circle at 450, arrow pointing Left)

3. Media Compound:

10 < x < 20

4. Sports Age Limit:

15 ≤ x ≤ 18

5. Media Graph Solution:

(1, 3)

6. Sports Graph Solution:

(1, 2)

Monday Mastery:

A: 10 < x < 20

B: NONE (Parallel lines have no solution)

Tuesday (Day 2)

1. Substitution (Food):

Move: x + (3x) = 20

Combine: 4x = 20

x = 5

2. Substitution (Media):

Combine: 12 = 5x + 2

Subtract 2: 10 = 5x

x = 2

3. Elimination (Sports):

Step: 5x = 15

x = 3

4. Elimination (Food):

Step: 5y = 25

y = 5

Tuesday Mastery:

A: Y is Deleted (y + -y = 0)

B: y = 10 (since 2 * 5 = 10)

Monday Algebra Power Review Worksheet

Algebra Power Review: Monday

Part 1: Inequalities & Graphing | North Star Academy

Name: __________________________

Date: __________________________

Unit 7.8: Simple Inequalities

Detective Clue: Keywords to watch for!

>
More than

<
Less than

≥
At least

≤
At most

1. SPORTS: A team needs to score more than 24 points to break the record.

Write the inequality (Use x):

x _________________

Graph it below:

24

2. FOOD: A safe oven temp must be at most 450 degrees.

Write the inequality (Use x):

x _________________

Graph it below:

450

Unit 7.8: Compound Inequalities

The "Between" Strategy

When an answer is BETWEEN two numbers, write Number < x < Number.
Example: 10 < x < 20 means "x is between 10 and 20".

3. FOOD: The temperature of a fresh burger should be between 140 and 160 degrees.

Write the compound inequality:

< x <

Show the range on a number line

4. SPORTS: Players in the elite league must be at least 15 AND at most 18 years old.

Write the compound inequality:

≤ x ≤

Unit 8.1: Graphing Systems

5. MEDIA: Subscription Cross-Over.

5 -5 -5 5 x y

Line 1:

y = 1x + 2

Line 2:

y = -1x + 4

Shared Solution:

( __ , __ )

6. SPORTS: Points Match-Up Point.

5 -5 -5 5 x y

Team A:

y = 2x + 0

Team B:

y = -1x + 3

Shared Solution:

( __ , __ )

Monday Mastery Review

The Final Analysis

Compound Check:

"A ticket costs more than $10 but less than $20."

________ < x < ________

Visual Logic Check:

"If two lines are PARALLEL and never touch, how many solutions?"

None

One

Infinite

MONDAY POWER STAMP

North Star Academy | 9th Grade Algebra

Tuesday Algebra Power Review Worksheet

Algebra Power Review: Day 2

Tuesday Independent Practice | North Star Academy

Name: __________________________

Date: __________________________

8.2

Unit 8.2: Solving by Substitution

The Substitution Logic:

1. Find the "lonely variable" (like y = 3x).
2. Plug that value into the 'y' spot of the other equation.
3. Solve for the missing variable.

1. FOOD: Burgers (x) and Drinks (y) system.

y = 3x

The lonely y

x + y = 20

The plug-in case

The Substitution Move:

x + (

) = 20

Work Space: Solve for x

x = ________

2. MEDIA: Monthly App Shared Cost.

y = 5x + 2

y = 12

Plug-In Connection:

12 = 5x + 2

Solve for x (Show work):

x = ________

8.3

Unit 8.3: Solving by Elimination

Detective Rule: Add the equations vertically to DELETE (ELIMINATE) a variable that has opposite signs (+ and -).

3. SPORTS: The Equipment Bill Elimination.

2x + y = 10
3x - y = 5

5x + 0 = 15

The Solution Finisher:

"Divide by 5 on both sides to find the value of x!"

x = ________

4. FOOD: Solving for the Combo Order.

4x + 2y = 20
-4x + 3y = 5

0 + 5y = 25

Final Case Work Area (Solve for y):

y = ________

!

Tuesday Mastery Case Review

The Final Detective Verdict

ELIMINATION LOGIC:

"What happens to the Y when you add these two equations together?"

x + y = 10
x - y = 4

Y is Deleted (0)

X is Deleted (0)

SUBSTITUTION CHECK:

"If you know x = 5, find the value of y in the equation: y = 2x."

y = ________

TUESDAY POWER STAMP

Algebra Power Review Answer Key

Teacher Answer Key

Algebra Power Review | Monday & Tuesday review

FOR TEACHER USE ONLY

Monday (Day 1)

1. Sports Inequality:

x > 24

(Graph: Open circle at 24, arrow right)

2. Food Inequality:

x ≤ 450

(Graph: Closed circle at 450, arrow left)

3. Media Compound:

10 < x < 20

4. Sports Age Limit:

15 ≤ x ≤ 18

5. Media Graph Solution:

(1, 3)

6. Sports Graph Solution:

(1, 2)

Monday Mastery:

A: 10 < x < 20

B: NONE (Parallel never meet)

Tuesday (Day 2)

1. Substitution (Food):

Steps: x + (3x) = 20 → 4x = 20

Full Solution: (5, 15)

2. Substitution (Media):

Steps: 12 = 5x + 2 → 10 = 5x

Full Solution: (2, 12)

3. Elimination (Sports):

Step: 5x = 15 → x = 3

Find y: 2(3) + y = 10 → y = 4

Full Solution: (3, 4)

4. Elimination (Food):

Step: 5y = 25 → y = 5

Find x: 4x + 2(5) = 20 → 4x = 10

Full Solution: (2.5, 5)

Tuesday Mastery:

A: Y IS DELETED (0)

B: y = 10 (since 2 * 5 = 10)

Monday Algebra Power Review Worksheet

Algebra Power Review: Monday

Part 1: Inequalities & Graphing | North Star Academy

Name: __________________________

Date: __________________________

Do Now (10 min)

The Music App Case: Graph the lines below.

x y

y = 1x + 2

y = -1x + 4

Verdict:

Where do they meet?

( ____ , ____ )

7.8

Unit 7.8: Simple Inequalities

>
More than

<
Less than

≥
At least

≤
At most

1. SPORTS: A team needs more than 24 points to break the record.

INEQUALITY: x _________________

2. FOOD: A safe temp must be at most 450 degrees.

INEQUALITY: x _________________

7.8

Unit 7.8: Compound Inequalities

3. FOOD: A safe burger temp is between 140 and 160 degrees.

Write as: Number < x < Number

< x <

140 160

4. SPORTS: Tournament age is at least 15 AND at most 18.

Write as: Number ≤ x ≤ Number

≤ x ≤

15 18

!

Monday Power Review

Compound Analysis Case:

"A movie ticket costs more than $10 but less than $20."

< x <

Visual Reasoning Check:

"If two lines are PARALLEL and never cross, how many solutions are there?"

None

One

Infinite

MONDAY POWER STAMP

North Star Academy | 9th Grade Algebra Concepts

Tuesday Algebra Power Review Worksheet

Algebra Power Review: Tuesday

Part 2: Algebraic Solutions | North Star Academy

Name: __________________________

Date: __________________________

8.2

Unit 8.2: Substitution

The Substitution Move:

1. Find the variable that is alone (like y = 3x).
2. PLUG that value into the other equation.
3. SOLVE for the missing variable.

1. FOOD: Total cost for Burgers (x) and Drinks (y).

y = 3x

The Alone y

x + y = 20

The system equation

The Substitution Move:

x + (

) = 20

Solve for x (Show each step):

x = ________

2. MEDIA: Solving for shared monthly cost.

y = 5x + 2

y = 12

Connect the Equations:

12 = 5x + 2

Solve for x:

x = ________

8.3

Unit 8.3: Elimination

Detective Rule: Add equations vertically to DELETE (ELIMINATE) a variable that has opposite signs (+ and -).

3. SPORTS: The Equipment Bill.

2x + y = 10
3x - y = 5

5x + 0 = 15

Final Solve:

"Divide by 5 on both sides to find x!"

x = ________

4. FOOD: The Combo Box Case.

4x + 2y = 20
-4x + 3y = 5

0 + 5y = 25

Solve for y (Final Case Work):

y = ________

!

Tuesday Mastery Review

The Final Case File

ELIMINATION LOGIC:

"What happens to the Y when you add these together?"

x + y = 10
x - y = 4

Y is DELETED (0)

X is DELETED (0)

SUBSTITUTION CHECK:

"If you know x = 5, find the value of y in the equation: y = 2x."

y = ________

TUESDAY POWER STAMP

Monday Algebra Power Review Worksheet

Monday Algebra Power Review

Part 1: Inequalities & Graphing | North Star Academy

Name: __________________________

Date: __________________________

Do Now (10 min)

The Music App Case: Graph the lines below.

5 -5 -5 5 x y

y = 1x + 2

y = -1x + 4

Verdict:

Solution Point:

( ____ , ____ )

7.8

Unit 7.8: Simple Inequalities

>
More than

<
Less than

≥
At least

≤
At most

1. SPORTS: A team needs more than 24 points to win.

INEQUALITY: x _________________

2. FOOD: A safe temp must be at most 450 degrees.

INEQUALITY: x _________________

7.8

Unit 7.8: Compound Inequalities

3. FOOD: A safe burger temp is between 140 and 160 degrees.

Write as: Number < x < Number

< x <

140 160

4. SPORTS: Tournament age is at least 15 AND at most 18.

Write as: Number ≤ x ≤ Number

≤ x ≤

15 18

Monday Mastery Review

The Case Final Review

Compound Case Analysis:

"A movie ticket costs more than $10 but less than $20."

< x <

Visual System Detective:

"If two lines are PARALLEL and never cross, how many solutions?"

None

One

Infinite

MONDAY POWER STAMP

North Star Academy | 9th Grade Algebra

Tuesday Algebra Power Review Worksheet

Tuesday Algebra Power Review

Part B: Algebraic Solutions | North Star Academy

Name: ______________________

Date: ______________________

8.2

Unit 8.2: Substitution

The Substitution Move:

1. Find the variable that is alone (like y = 3x).
2. PLUG that value into the 'y' spot of the other equation.
3. SOLVE for the missing variable.

1. FOOD: Total cost for Burgers (x) and Drinks (y).

The Alone y

y = 3x

Target Equation

x + y = 20

The Substitution Move:

x + (

Plug 'y' here

) = 20

Solve for x (Show work):

x = ________

2. MEDIA: Monthly App Case.

y = 5x + 2

y = 12

The Combined Equation:

12 = 5x + 2

Work Space (Solve for x):

x = ________

8.3

Unit 8.3: Elimination

Detective Move: Add equations vertically to DELETE (ELIMINATE) a variable that has opposite signs (+ and -).

3. SPORTS: The Equipment Elimination.

2x + y = 10
3x - y = 5

5x + 0 = 15

The Final Solve:

"Divide by 5 on both sides to find x!"

x = ________

4. FOOD: The Combo Box System.

4x + 2y = 20
-4x + 3y = 5

0 + 5y = 25

Work Space (Solve for y):

y = ________

!

Tuesday Mastery Case Review

The Final Detective Case

ELIMINATION LOGIC CHECK:

"What happens to the Y when you add these together?"

x + y = 10
x - y = 4

Y is DELETED (0)

X is DELETED (0)

SUBSTITUTION CALCULATION:

"If you know x = 5, find the value of y in the equation: y = 2x."

y = ________

TUESDAY POWER STAMP

Algebra Power Review Answer Key

Teacher Answer Key

Algebra Power Review | Monday & Tuesday

FOR TEACHER USE ONLY

Monday (Day 1)

1. Sports Inequality:

x > 24

(Graph: Open circle at 24, arrow right)

2. Food Inequality:

x ≤ 450

(Graph: Closed circle at 450, arrow left)

3. Media Compound:

10 < x < 20

4. Sports Age Limit:

15 ≤ x ≤ 18

5. Media Graph Solution:

(1, 3)

6. Sports Graph Solution:

(1, 2)

Monday Mastery:

A: 10 < x < 20

B: NONE (Parallel never meet)

Tuesday (Day 2)

1. Substitution (Food):

x + (3x) = 20 → 4x = 20

x = 5, y = 15 → (5, 15)

2. Substitution (Media):

12 = 5x + 2 → 10 = 5x

x = 2, y = 12 → (2, 12)

3. Elimination (Sports):

Step: 5x = 15 → x = 3

Find y: 2(3) + y = 10 → y = 4

Solution: (3, 4)

4. Elimination (Food):

Step: 5y = 25 → y = 5

Find x: 4x + 2(5) = 20 → 4x = 10

Solution: (2.5, 5)

Tuesday Mastery:

A: Y IS DELETED (0)

B: y = 10 (since 2 * 5 = 10)

Monday Algebra Power Review Worksheet

Monday Power Review

Unit 7.8 & 8.1 | Independent Practice

Name: ______________________

Date: ______________________

Do Now (5 min)

Match the symbol to its meaning:

>

≤

Less than or Equal to

Greater than

Excellence (10 min)

Discovery Case: Stadium Limits

"The stadium rules say you must be at least 14 years old to enter. If x is your age, which ages are allowed?"

1. Is 13 allowed? __________________

2. Is 14 allowed? __________________

Circle the math model:

x < 14 x ≥ 14

Prior Knowledge (5 min)

Graphing Tip

Start at "b"

The Secret

Cross Point

Trial Plotting Check:

"Draw an Open Circle at 5 and shade RIGHT for: x > 5"

5

Guided Practice (10 min)

Streaming Battle: Netflix vs. Disney

Line A: y = 1x + 2 | Line B: y = -1x + 4

5 -5 5 -5

The Mission:

"Graph both lines. Circle the point where they meet. Write that coordinate below!"

Final Solution:

( ____ , ____ )

Priority Practice (20 min)

1

Inequality Challenge: Taco Truck

"The taco truck only serves meals that cost more than $10. Write the inequality for price (p)."

p

10

2

Graphing Challenge: Jersey Tie

The Mystery System:

y = 2x + 0

y = 1x + 2

Meeting Point:

( ___ , ___ )

Mastery Challenge

The Range Case

"A sports player scored more than 20 points but no more than 30 points."

20

x

30

Exit Ticket

Learning STAMP

Find the solution point for this case:

y = 2x + 1

&

y = 5

The Final Verdict:

( ____ , ____ )

Monday Homework

Unit 7.8 & 8.1

Problem 1: Sports Eligibility

Tuesday Algebra Power Review Worksheet

Tuesday Algebra Power Review

Unit 8.2 & 8.3 | Independent Practice

Name: ______________________

Date: ______________________

Do Now (5 min)

The Substitution Swap:

"If a burger costs $5 (b = 5), what is the total cost of 2 burgers plus a $2 drink?"

Total = 2 ( ___ ) + 2

Excellence (10 min)

Discovery: The Substitution Secret

"A system gives you y = 5. The second equation is y + x = 12."

1. If you know y is 5, can you erase the 'y' in the second equation and write '5' instead? ____________

2. Solve the new mystery sentence for x:

5 + x = 12

Prior Knowledge (5 min)

Algebra Review: Opposite Operations

+ ↔ -

× ↔ ÷

Try This: Solve for X

2x = 10

x = ___

Guided Practice (10 min)

Case Analysis: Substitution Swap

Equation 1: y = 3x

Equation 2: y + 2 = 11

Step 1: Solve for Y first!

Step 2: Plug Y back into y = 3x to find X.

Priority Practice (20 min)

1

Substitution: Netflix Sharing

"One app costs y = 2x. Together they cost y + x = 30."

2x + x = 30

Combine the X's and Solve:

2

Elimination: Order Cancellations

5x + 3y = 20

-5x + 2y = 10

The 5x and -5x
"cancel out" to ZERO.

What is the result when you add the Y's?

Mastery Case

The Taco Truck Elimination

2x + y = 10

2x - y = 6

"The y and -y will disappear!"

"Total 4x = __________"

"Wait! Find X first, then plug back in for Y!"

Exit Ticket

Learning STAMP

"A detective finds that y = 4. If the case says 2y + x = 20, what is x?"

The Verdict:

x = ____

Tuesday Homework

8.2 & 8.3 Review

Jersey Order

"One jersey is y = 5x. If y = 50, how many months ($x$) were paid?"

50 = 5x

Tuesday Algebra Power Review Worksheet

Tuesday Power Review

Unit 8.2 & 8.3 | Independent Practice

Name: ______________________

Date: ______________________

Do Now (5 min)

Substitution Swap: If you know x = 10, solve the math sentence below.

Total Cost = 5 + ( ___ )

Excellence (10 min)

Discovery: The Substitution Secret

"A case file says y = 5. The second case says y + x = 12."

1. If you know y is 5, can you erase the 'y' and write '5' in the second sentence? ____________

2. Solve the new sentence for x:

5 + x = 12

Verdict:

Prior Knowledge (5 min)

Substitution

REPLACE

Elimination

DELETE

Try This Trial Solve:

"Solve for X by dividing both sides by 2."

2x = 10

x = ___

Guided Practice (10 min)

Substitution Step-by-Step

Solve the system: y = 3x | y + 2 = 11

1. Solve the easy equation for y:

y + 2 = 11 → y = ________

2. Plug your Y answer into y = 3x to find X:

_____ = 3x → x = ________

Priority Practice (20 min)

1

Substitution: Netflix Account Sharing

"One app costs y = 2x. Together they cost y + x = 30. Find X!"

2x + x = 30

"Combine the 2x and 1x first!"

2

Elimination: Order Cancellations

5x + 3y = 20

-5x + 2y = 10

The 5x and -5x
cancel to ZERO!

What is the result when you add the Y's and numbers?

Mastery Challenge

The Taco Truck Elimination

2x + y = 10

2x - y = 6

Total: 4x = __________

"The y and -y disappear! Solve for X!"

Exit Ticket

STAMP Zone

"A detective finds that y = 4. If the case equation says 2y + x = 20, what is x?"

The Final Solve:

x = ____

Tuesday Homework Sheet

8.2 & 8.3

Problem 1: jersey order

"One jersey is y = 5x. If y = 50, how many months ($x$) were paid?"

Monday Algebra Power Review Worksheet

Monday Power Review

Unit 7.8 & 8.1 | Independent Practice

Name: ______________________

Date: ______________________

Do Now (5 min)

Match the symbol to its meaning:

>

≤

Less than or Equal to

Greater than

Excellence (10 min)

Discovery Case: Stadium Limits

"The stadium rules say you must be at least 14 years old to enter. If x is your age, which ages are allowed?"

1. Is 13 allowed? __________________

2. Is 14 allowed? __________________

Circle the math model:

x < 14 x ≥ 14

Prior Knowledge (5 min)

Graphing Tip

Start at "b"

The Secret

Cross Point

Trial Plotting Check:

"Draw an Open Circle at 5 and shade RIGHT for: x > 5"

5

Guided Practice (10 min)

Streaming Battle: Netflix vs. Disney

Line A: y = 1x + 2 | Line B: y = -1x + 4

5 -5 5 -5 X Y

The Mission:

"Graph Line A and B. Circle the point where they cross. Write the shared point below!"

Final Solution Point:

( ____ , ____ )

Priority Practice (20 min)

1

Inequality Challenge: Taco Truck

"The taco truck only serves meals that cost more than $10. Write the inequality for price (p)."

p

10

2

Graphing Challenge: Jersey Tie

X Y

Find the Tied Point:

y = 2x + 0

y = 1x + 2

Meeting Point:

( ___ , ___ )

Mastery Challenge

The Sports Points Range

"A player scored more than 20 points but no more than 30 points."

20

x

30

Exit Ticket

Learning STAMP

Find the CROSS POINT for this case:

y = 2x + 1

&

y = 5

The Final Verdict:

( ____ , ____ )

Monday Homework

Units 7.8 & 8.1

Systems Meanings Lesson Plan

Interpreting Systems Lesson Plan

Heart of the Lesson

"The intersection is the only place where both stories are perfectly equal."

Unit 8.5 | Meaning of a Solution

North Star Academy

9th Grade SPED Algebra

Learning Objective

Students will interpret the intersection point $(x, y)$ as the time or quantity where two real-world options cost the same or have the same value.

Learning STAMP

"I can explain that $(x, y)$ means 'At X amount of time, both things equal Y dollars'."

Min	Section	Teacher Actions & Prompts	Expected Answers
10	Do Now	Review solving for $y$ when $x$ is given. "If Spotify is $y = 10x + 5$, how much for 2 months?"	$y = 25$
10	Excellence	Discovery: Show a graph with an intersection at (4, 20). "In this context, what happened at month 4?"	Both cost $20.
5	Prior Know.	Define "Solution" visually as the X and Y coordinate. Complete "Try This" (Gym deals).	(2, 40)
10	Guided	Taco vs Burrito sales. "At how many days are they equal? What is that equal amount?"	10 days, 100 sold
15	Practice	Mystery Scenarios (Netflix/YouTube, Pizza/Burger). Check for proper units (Months, Dollars).	Check Answer Key
10	Exit & STAMP	The "Equal Point" verdict. Teacher STAMPS after context sentence is complete.	Context check

Homework Guidance

Ensure students explain the meaning of BOTH coordinates: the 'when' and the 'what'.

Systems Meanings Student Packet

The Equal Point Packet

Unit 8.5 | North Star Academy

Name: ______________________

Date: ______________________

Do Now (10 min)

The Spotify Mystery: Solve for y.

"If Spotify costs $y = 10x + 5$ where $x$ is months..."

HOW MUCH DOES IT COST FOR 2 MONTHS?

y = 10 (

) + 5

y =

Excellence (10 min)

Discovery: The Netflix vs Hulu Cross

(4, 20)

X-COORDINATE (4):

What does this represent? (Time? Amount?)

Y-COORDINATE (20):

What does this represent? (Cost? Total?)

"The green dot is the only place where the blue and red deals are EQUAL!"

Prior Knowledge (5 min)

The Solution (x, y)

The Cross Point

The Context

The Meaning

Try This Context Case:

"A system solution is (2, 40). $x$ is hours of work and $y$ is total pay."

Complete the sentence:

"After hours, the total pay is dollars."

Guided Practice (10 min)

Case Analysis: Taco vs. Burrito Sales

"A truck sells tacos ($y=10x$) and burritos ($y=5x+50$). The lines cross at (10, 100)."

What does '10' mean?

What does '100' mean?

"at 10 days, both foods have 100 sales!"

Priority Practice (20 min)

1

YouTube vs. Hulu Case

"The system solution is (5, 25). $x$ is months and $y$ is cost."

Explain the meaning:

2

Sports Points Case

"Team A and B tied at (15, 60). $x$ is minutes played and $y$ is total points."

Explain the meaning:

Mastery Challenge

The Choice Detective

"Option A is better for the first 3 months. Option B is better after 3 months."

At what Month are they EXACTLY EQUAL?

Exit Ticket

Learning STAMP Spot

The Movie Mystery Solution

"The solution to the ticket price system is (4, 25)."

Write the Meaning Context:

Homework: Solving Stories

9th Grade Algebra

The Food Court Mystery

"Subway and Chipotle have the same price at (5, 45). $x$ is sandwiches bought and $y$ is cost."

Systems Meanings Answer Key

Teacher Answer Key

Unit 8.5 Interpreting Systems | North Star Academy

9TH GRADE ALGEBRA

1. Do Now (Spotify)

Substitution: $y = 10(2) + 5$

Solution: y = 25

(Cost for 2 months is $25)

2. Excellence (Discovery)

X (4): 4 Months.

Y (20): $20 Cost.

Meaning: At 4 months, both streaming apps cost exactly $20.

3. Prior Know. (Try This)

After 2 hours, the total pay is 40 dollars.

4. Guided Practice (Tacos)

10: 10 days of sales.

100: 100 total items sold.

Meaning: On day 10, both trucks have sold 100 items total.

5. Priority Practice

Case 1 (YouTube):

At 5 months, both apps cost $25.

Case 2 (Sports):

At 15 minutes, both teams have 60 points.

6. Mastery Challenge

At Month 3.

7. Exit Ticket Solution

Meaning: After 4 years, both movie ticket deals cost exactly $25.00.

8. Homework Answers

5: 5 sandwiches bought.

45: $45 total cost.

Context: For 5 sandwiches, both restaurants charge $45.

Systems Meanings Student Packet

The Equal Point Packet

Unit 8.5 | North Star Academy

Name: ______________________

Date: ______________________

Do Now (10 min)

The Spotify Mystery: Solve for y.

"If Spotify costs $y = 10x + 5$ where $x$ is months..."

HOW MUCH DOES IT COST FOR 2 MONTHS?

y = 10 (

) + 5

y =

Excellence (10 min)

Discovery Case: Netflix vs. Hulu

(4, 20) MONTHS COST ($)

X-COORDINATE (4):

This 4 represents the total...

Y-COORDINATE (20):

This 20 represents the total...

"At Month 4, both Netflix and Hulu cost exactly $20!"

Prior Knowledge (5 min)

The Intersection (x, y)

The Meeting Point

Interpretation

The Meaning

Context Trial:

"The solution to a system is (2, 40).
$x$ is hours of work and $y$ is total pay in dollars."

COMPLETE THE CASE SUMMARY:

"After hours, the total pay is dollars."

Guided Practice (10 min)

Case Analysis: Food Truck Duel

"A truck sells tacos and burritos. The system solution is (10, 100).
$x$ is days in business and $y$ is items sold."

What does '10' represent?

What does '100' represent?

Final Verdict Sentence:

"At day , both items have sold total units!"

Priority Practice (20 min)

1

Mystery Case: Media Subscriptions

"The system solution for two media apps is (5, 25).
$x$ is months and $y$ is total cost."

Explain the Context Meaning:

2

Mystery Case: Sports Points Duel

"Team A and Team B are tied at (15, 60).
$x$ is minutes played and $y$ is total points scored."

Explain the Context Meaning:

Mastery Challenge

The Choice Detective Logic

"Subscription A is cheaper for the first 3 months. Subscription B is cheaper after 3 months."

Question: At what month do both cost the EXACT SAME?

MONTH:

Exit Ticket

STAMP Point

The Final Movie Case File

"The solution to the ticket price system is (4, 25)."
(x = years, y = dollars)

Writing Systems Lesson Plan

Heart of the Lesson

"Translating stories into equations is the first step to becoming a math detective."

Unit 8.6 | Writing Systems of Equations

North Star Academy

9th Grade SPED Algebra

Learning Objective

Students will write a system of two linear equations in slope-intercept form to model a real-world situation involving two variables.

Learning STAMP

"I can find the 'Start' (b) and the 'Rate' (m) for two stories and write them as $y = mx + b$."

Min	Section	Teacher Actions & Prompts	Expected Answers
10	Do Now	Identify m and b from a single story (Music App). "Which number happens once? Which repeats?"	m=5, b=20.
10	Excellence	Discovery: Show two gym deals. "Underline the starting fees in red. Underline the monthly rates in blue."	Scaffolding check.
5	Prior Know.	Review $y=mx+b$ template. Complete "Try This" (Pizza vs Burrito cost).	$y = 2x + 10$
10	Guided	Netflix vs Hulu Case. Model color-coding keywords (per, each, starts at).	Check Packet
15	Practice	Mystery Scenarios (Soccer Drills, Burger Joints). Check that both equations have the same variables.	Check Answer Key
10	Exit & STAMP	The "Final Model" verdict. Teacher STAMPS after both equations are written correctly.	Correct Eq pair

Homework Guidance

Remind students that 'y' usually represents total cost or total amount in these models.

Writing Systems Student Packet

System Modeler Packet

Unit 8.6 | North Star Academy

Name: ______________________

Date: ______________________

Do Now (10 min)

The Music App Story: Identify the variables.

"Spotify charges a $20 starting fee and then $5 per month."

WHICH NUMBER IS THE START (b)?

WHICH NUMBER IS THE RATE (m)?

y =

x +

Excellence (10 min)

Discovery: The Gym Membership Duel

Deal A: "Pay $50 to join and $10 every month."

Deal B: "Pay $10 to join and $50 every month."

1. Circle the words that mean "Rate of Change" (m) in both stories.

Hint: Look for words like 'every', 'each', or 'per'.

2. Why are these stories different if they use the same numbers (50 and 10)?

Prior Knowledge (5 min)

y = mx + b

m = the rate (speed)

b = the start (fee)

Try This Template:

"A pizza costs $10 plus $2 per topping."

y = x +

Guided Practice (10 min)

Modeling Case: Streaming Subs

Netflix: Starts at $15 and adds $5 per screen.

Hulu: Starts at $10 and adds $10 per screen.

Netflix Model:

y = x +

Hulu Model:

y = x +

Priority Practice (20 min)

1

Sports Points Duel

Team A: Starts with 10 pts, gains 5 pts each quarter.

Team B: Starts with 0 pts, gains 10 pts each quarter.

Eq for Team A:

y = x +

Eq for Team B:

y = x +

2

Food Truck Costs

Taco Truck: $5 flat fee plus $3 per taco.

Burrito Bus: $10 flat fee plus $2 per burrito.

Eq for Tacos:

y = x +

Eq for Burritos:

y = x +

Mastery Question

The Variable Challenge

"In the equations you've been writing, what does the variable X usually represent in most stories?"

Total Cost

Time or Items

Exit Ticket

STAMP Point

The Final Movie Mystery

"Cinema A costs $5.00 to enter and per popcorn. Cinema B costs to enter and per popcorn."

Writing Systems Answer Key

Teacher Answer Key

Unit 8.6 Writing Systems | North Star Academy

9TH GRADE ALGEBRA

1. Do Now (Spotify)

Start (b): 20

Rate (m): 5

Equation: y = 5x + 20

2. Excellence (Gym Duel)

Rates (m): 10 (Deal A) and 50 (Deal B).

Starts (b): 50 (Deal A) and 10 (Deal B).

Conclusion: The numbers are swapped, changing which gym is cheaper long-term.

3. Prior Know. (Try This)

Equation: y = 2x + 10

4. Guided Practice (Netflix)

Netflix: y = 5x + 15

Hulu: y = 10x + 10

5. Priority Practice

1. Sports Points:

Team A: y = 5x + 10

Team B: y = 10x + 0

2. Food Trucks:

Taco: y = 3x + 5

Burrito: y = 2x + 10

6. Mastery Question

Correct Answer: Time or Items (The Independent Variable).

7. Exit Ticket Solution

Cinema A: y = 1x + 5

Cinema B: y = 0.5x + 10

8. Homework Answers

Planet Fitness Eq: y = 10x + 1

b (Start): 1 | m (Rate): 10

Writing Systems Student Packet

System Modeler Packet

Unit 8.6 | North Star Academy

Name: ______________________

Date: ______________________

Do Now (10 min)

The Music App Mystery: Identify the clues.

"Spotify charges a $20 starting fee and then $5 per month."

CLUE 1: START FEE (b)

CLUE 2: RATE (m)

y =

x +

Excellence (10 min)

The Discovery Case: Gym Memberships

Deal A: "Pay $50 to join and $10 every month."

Deal B: "Pay $10 to join and $50 every month."

1. Underline the words that tell you how much to pay MONTHLY. Are they the same in both deals?

2. Why does the number with "month" or "each" always go next to the X in our equations?

Prior Knowledge (5 min)

y = mx + b

m = the rate / speed

b = the start / fee

Trial Case Builder:

"A pizza costs $10.00 base price plus $2.00 per extra topping."

y = x +

Guided Practice (10 min)

Modeling Case: Streaming Subs

Netflix: Starts at $15 and adds $5 per screen.

Hulu: Starts at $10 and adds $10 per screen.

Netflix Equation:

y = x +

Hulu Equation:

y = x +

Priority Practice (20 min)

1

Sports Points Duel

Team A: Starts with 10 pts, gains 5 pts each quarter.

Team B: Starts with 0 pts, gains 10 pts each quarter.

Equation for Team A:

y = x +

Equation for Team B:

y = x +

2

Food Truck Costs

Taco Truck: $5 flat fee plus $3 per taco.

Burrito Bus: $10 flat fee plus $2 per burrito.

Equation for Tacos:

y = x +

Equation for Burritos:

y = x +

Mastery Challenge

The Variable Detective Case

"In all the stories we modeled today, what did the X variable represent most often?"

A

TOTAL COST (y)

B

TIME / ITEMS (x)

Exit Ticket

Learning STAMP Spot

The Movie Mystery Model

"Cinema A costs $5.00 to enter and $1.00 per popcorn. Cinema B costs to enter and per popcorn."

y =

x +

Homework: Data Detectives

Unit 7.7 Review

Soccer Drills vs. Goals

y = 0.5x + 1

A. The Start Value (b):

B. The Speed (m):

Concept Match Up

SLOPE

Y-INTERCEPT

STARTING POINT

THE GROWTH SPEED

x +

Homework: Data Review

Unit 7.7

Soccer Drills vs. Goals

y = 0.5x + 1

A. The Start Value (b):

B. The Speed (m):

Detective Concepts

Slope

Intercept

STARTING POINT

THE GROWTH SPEED

SLOPE

INTERCEPT

STARTING POINT

THE GROWTH SPEED

Homework: Detective Review

Unit 8.4

Soccer Drills vs. Goals

"If two teams practice at the same rate but one starts with more goals, will the scores ever be tied?"

y = 0.5x + 1 & y = 0.5x + 3

The Verdict:

The Evidence (Reason):

Vocabulary Match Up

Slope

Y-Intercept

STARTING POINT

THE SPEED

Homework Review

Unit 8.4

Soccer Drills vs. Goals

"If two teams practice at the SAME RATE but one starts with MORE GOALS, will the scores ever tie?"

y = 0.5x + 1 & y = 0.5x + 3

The Verdict:

The Evidence:

Vocabulary Match Up

Slope

Intercept

STARTING POINT

THE GROWTH SPEED

B

Elimination

Learning STAMP

"I HAVE MASTERED ALGEBRA SYSTEMS!"

1 Solution

No Solution

Infinite

Monday Homework

7.8 & 8.1 Review

Problem 1: Inequality Sketch

"The burger deal is for anyone under 12 years old. Write it!"

x

12

Problem 2: Graphing System

y = 1x + 1

y = 0x + 3

Solution: ( __ , __ )

INFINITE

POWER STAMP

"A wrestler must weigh more than 100 lbs but no more than 150 lbs."

100

x

150

Problem 2: Solution Sketch

"Two lines are graphed. They cross exactly at (3, 5). What is the solution to the system?"

( ____ , ____ )

Divide both sides by 5!

🔍 Algebraic tip

"Substitution means REPLACE.
Elimination means DELETE!"

50 = 5x

Verdict: x = ________

🔍 Algebraic secret

"Substitution means REPLACE.
Elimination means DELETE!"

Problem 1: Sports Rules

"A wrestler must weigh more than 100 lbs but no more than 150 lbs. Write the compound model!"

100

x

150

Problem 2: Shared point Sketch

"Two lines cross exactly at (3, 5).
What is the solution to the system?"

( ____ , ____ )

What does the 5 mean?

What does the 45 mean?

🔍 Context Tip

"In a system solution, both options are EXACTLY THE SAME at that specific point!"

Write the complete context meaning:

Homework: context detective

Unit 8.5

The Food Court Mystery

"Subway and Chipotle have the same price at (5, 45).
$x$ is sandwiches bought and $y$ is total cost in dollars."

What does the 5 mean?

What does the 45 mean?

🔍 Final context tip

"A system solution is the only point where both deals are perfectly equal!"

$1.00

$10.00

$0.50

Eq for Cinema A:

y = x +

Eq for Cinema B:

y = x +

Homework: Model Creators

Unit 8.6

The Gym Model

"Planet Fitness has a $1.00 sign-up fee and costs $10.00 per month."

y =

x +

What is the b (Start)?

What is the m (Rate)?

🔍 Writing Tip

"The RATE goes with the X. The STARTING FEE is the B alone!"

$10.00

$0.50

Eq for Cinema A:

y = x +

Eq for Cinema B:

y = x +

Homework: Model Creators

Unit 8.6 Review

The Gym Model Review

"Planet Fitness has a $1.00 sign-up fee and costs $10.00 per month."

y =

x +

What is the b (Start)?

What is the m (Rate)?

🔍 Writing detective tip

"The RATE (m) goes with the X.
The STARTING FEE (b) is the number alone!"

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