Quadratic Quest Unit PlanQuadratic Quest Algebra 2 • Unit 4 Overview & Pacing TEACHER GUIDE Unit Goals Students will master the properties of quadratic functions, exploring their multiple representations (tables, graphs, equations). By the end of this unit, students will confidently solve quadratic equations using various methods—factoring, completing the square, and the quadratic formula—and apply these skills to model real-world projectile motion. Pacing Guide (15 Days) DaysTopicKey Focus1–3Graphing QuadraticsStandard, Vertex, and Intercept forms; transformations.4–6Factoring Review & MasteryTrinomials ($a=1$ and $a>1$), difference of squares.7–8Complex NumbersImaginary unit $i$, simplifying radicals, operations.9–11Solving MethodsCompleting the square, Quadratic Formula, Discriminant.12–13ApplicationsProjectile motion, area problems, revenue models.14–15AssessmentUnit Review and Summative Exam. Vocabulary Parabola: The U-shaped graph of a quadratic. Vertex: The highest or lowest point of the graph. Axis of Symmetry: The line that divides a parabola into two mirror images. Discriminant: $b^2 - 4ac$; determines the number and type of roots. Zeros/Roots: The $x$-intercepts of the function. Key Standards CCSS.MATH.HSA.REI.B.4 CCSS.MATH.HSF.IF.C.7.A CCSS.MATH.HSA.SSE.B.3 Instructional Strategies Visual Connections Use Desmos daily to demonstrate how changing $a, h,$ and $k$ shifts the parabola. Students should see the movement as they change sliders. Scaffolded Solving Introduce the "Solving Tree" flowchart to help students decide which method (factoring, square roots, or formula) is most efficient for a given equation. Assessment & Differentiation Formative Checks "What's My Vertex?" Whiteboard Drills Rapid-fire identification of vertex from vertex form equations. Discriminant Sort Card sort activity where students group equations by their number of solutions. Error Analysis Tasks Students identify common mistakes in "worked examples" of completing the square. Summative Tasks The Pumpkin Launcher Project Students model the path of a projectile. They must write the equation in all three forms, find the maximum height (vertex), and determine when it hits the ground (roots). Differentiation Matrix Support (IEP/504) Provide "Step-by-Step" templates for the Quadratic Formula. Pre-graphed parabolas for analysis. Focus on $a=1$ for factoring initially. Extension (Advanced) Derive the Quadratic Formula from standard form. Explore optimization in business contexts. Solve systems of linear-quadratic equations. ELL/ESL Visual word wall with diagrams for "Vertex" and "Axis". Graphic organizers for solving steps. Collaborative pairs for application problems.
Logic Lab Proofs WorksheetLogic Lab Proofs Mastering Geometric Reasoning & Evidence NAME: DATE: 1 Prove the Segment Addition Theorem Application Given: $AC = 12, AB = x, BC = 2x+3$. Prove: $x=3$. A B C Diagram 1.0 StatementsReasons1. $AC = 12, AB = x, BC = 2x+3$1. Given2. $AB + BC = AC$2.3. $x + (2x + 3) = 12$3. Substitution Property4. $3x + 3 = 12$4.5. $3x = 9$5. Subtraction Property6. $x = 3$6. 2 Prove Triangle Congruence (SAS) Given: $AB \cong DE, \angle B \cong \angle E, BC \cong EF$. Prove: $\triangle ABC \cong \triangle DEF$. StatementsReasons1. $AB \cong DE$1.2. $\angle B \cong \angle E$2.3. $BC \cong EF$3.4. $\triangle ABC \cong \triangle DEF$4. Logic Challenge What is the difference between an Axiom and a Theorem? Explain why we can use a Theorem as a "Reason" in our proofs, but must prove the Theorem itself first.
Data Detectives Project GuideData Detectives 9th Grade Statistics Project Guide DUE DATE: ____/____/____ Your Mission Data is everywhere. From social media algorithms to sports analytics, information is being collected and analyzed to make decisions. Your task is to become a Data Detective. You will choose a research question, collect original data, analyze it using statistical measures, and present your findings in a visual report. Phase 1: The Question "Does the time spent on phones correlate with sleep quality?" or "Do older students carry heavier backpacks?" My Research Question: My Population & Sample Size ($n \ge 30$): Requirements Measures of Center: Mean, Median, Mode Measures of Spread: Range, IQR, Standard Deviation Visuals: Box-and-Whisker Plot & Histogram Analysis: Outlier check and Skewness description Grading Rubric Criteria4 - Mastery3 - Proficient2 - DevelopingData CollectionSample size > 40; bias clearly addressed.Sample size 30-40; bias mentioned.Sample size < 30; no bias check.CalculationsAll 6 measures calculated perfectly with work shown.4-5 measures correct; some work shown.Many errors or no work shown.VisualizationCharts are accurate, labeled, and color-coded.Charts are accurate but missing labels.Charts are messy or inaccurate.InterpretationDeep insight into what the numbers mean for real life.Summary provided but lacks depth.Minimal attempt at explaining results. Remember: Correlation does not equal causation! DETECTIVE_ID: MATH-9-STAT-001
Identity Insight Quiz AssessmentIdentity Insight Pre-Calculus: Trigonometry Quiz ID: SCORE: "Simplify each expression completely or verify the identity by working on one side only. Show all algebraic steps clearly for full credit." PART I Simplify the Expression 1. \(\sin(x) \cot(x)\) [3 PTS] 2. \(\frac{\sec^2(x) - 1}{\sin^2(x)}\) [4 PTS] PART II Verify the Identity 3. \(\cos(x) (\sec(x) - \cos(x)) = \sin^2(x)\) [6 PTS] 4. \(\frac{1}{1-\sin(x)} + \frac{1}{1+\sin(x)} = 2\sec^2(x)\) [7 PTS] Pythagorean • Quotient • Reciprocal • Even/Odd
Slope Intercept Anchor Chart ReferenceSlope-Intercept \(y = mx + b\) m The Slope STEEPNESS & DIRECTION \(\frac{\text{RISE}}{\text{RUN}}\) \(\frac{y_2 - y_1}{x_2 - x_1}\) Positive Negative Zero b The Y-Intercept THE STARTING POINT Where the line crosses the Y-AXIS. (0, b) Example: \(y = \frac{1}{2}x + 2\) RISE 1 RUN 2 START HERE (0, 2) TIP Always plot the y-intercept (b) first, then use the slope (m) to find your next points. If the slope is a whole number like 3, write it as \(\frac{3}{1}\) to see the rise and run!
