Trend Trackers Answer KeyTeacher 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 PlanTrend 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." MinSectionTeacher Actions & PromptsExpected Answers5Do NowObserve Gaming Graph. "What variable is on the bottom? What happens to the Level as Hours increase?"x = Hours. Trend = UP.10ExcellenceDiscovery 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." | Start=200, Speed=50. | | 5 | Prior Know. | Review matching visual anchors. Students attempt "Try This" (y = 10x + 5). "Which one is alone? That's the start!" | Circle 5. | | 10 | Guided | Basketball Story. Model building y = 3x + 5. "Where do they start before practice? Which number is that?" | b = 5, m = 3. | | 15 | Practice | Students work through Taco Truck and Hulu Cost. Circulate and check if they used "y = mx + b". | 1. 50+10x / 2. 15+5x. | | 15 | Mastery/Exit | "Architects: build the gym equation. Then solve the Movie Mystery for your final stamp!" | Gym: 5x+40. Movie: 0.75x+5. | 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 PacketTrend 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 PacketTrend 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 PacketTrend 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 KeyTeacher 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 PacketSolution 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 PlanSolution 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." MinSectionTeacher Actions & PromptsExpected Answers10Do NowStudents graph the Spotify vs Apple Music lines. "Where is the shared coordinate point?"(1, 3)ONE SOLUTION10ExcellenceScaffold discovery of Case 1 (Netflix). "Look at the numbers with the x. Are they different speeds?"Slopes: 3 vs 2.Verdict: 1 SOLUTION.5Prior Know.Review icons. Match "Same Slope" to Parallel Tracks. Complete "Try This" (Pizza toppings).m=2, b=10.10GuidedGym membership case. "If speeds (slopes) match but starts don't, will they ever catch each other?"No Solution15PracticeMystery Pairs. Pair 1 (Diff m). Pair 2 (Everything same). Circle the 'm' values first.1. One2. Infinite10Exit & STAMPCinema 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 PacketSolution 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 WorksheetAlgebra 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 KeyIndependent 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 WorksheetAlgebra 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 KeyAnswer 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 WorksheetAlgebra 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 KeyTeacher 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 WorksheetAlgebra 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 KeyIndependent 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 KeyMastery 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 WorksheetAlgebra 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 KeyAlgebra 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 WorksheetAlgebra 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 KeyAlgebra 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 WorksheetAlgebra 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 KeyTeacher 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 KeyMastery 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 WorksheetAlgebra 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 WorksheetAlgebra 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 KeyAlgebra 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 WorksheetMonday 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 WorksheetAlgebra 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 WorksheetAlgebra 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 WorksheetAlgebra 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 KeyTeacher 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 WorksheetAlgebra 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 KeyTeacher 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 WorksheetAlgebra 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 WorksheetAlgebra 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 KeyTeacher 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 WorksheetAlgebra 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 WorksheetAlgebra 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 WorksheetMonday 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 WorksheetTuesday 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 KeyTeacher 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 WorksheetMonday 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 WorksheetTuesday 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 WorksheetTuesday 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 WorksheetMonday 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 PlanInterpreting 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'." MinSectionTeacher Actions & PromptsExpected Answers10Do NowReview solving for \(y\) when \(x\) is given. "If Spotify is \(y = 10x + 5\), how much for 2 months?"\(y = 25\)10ExcellenceDiscovery: Show a graph with an intersection at (4, 20). "In this context, what happened at month 4?"Both cost $20.5Prior Know.Define "Solution" visually as the X and Y coordinate. Complete "Try This" (Gym deals).(2, 40)10GuidedTaco vs Burrito sales. "At how many days are they equal? What is that equal amount?"10 days, 100 sold15PracticeMystery Scenarios (Netflix/YouTube, Pizza/Burger). Check for proper units (Months, Dollars).Check Answer Key10Exit & STAMPThe "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 PacketThe 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 KeyTeacher 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 PacketThe 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 PlanWriting 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 \(y = mx + b\)." MinSectionTeacher Actions & PromptsExpected Answers10Do NowIdentify m and b from a single story (Music App). "Which number happens once? Which repeats?"m=5, b=20.10ExcellenceDiscovery: Show two gym deals. "Underline the starting fees in red. Underline the monthly rates in blue."Scaffolding check.5Prior Know.Review \(y=mx+b\) template. Complete "Try This" (Pizza vs Burrito cost).\(y = 2x + 10\)10GuidedNetflix vs Hulu Case. Model color-coding keywords (per, each, starts at).Check Packet15PracticeMystery Scenarios (Soccer Drills, Burger Joints). Check that both equations have the same variables.Check Answer Key10Exit & STAMPThe "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 PacketSystem 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 KeyTeacher 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 PacketSystem 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."
