Overview

Grade Level: Algebra 1 (Approximate ages 14–15)
Class Duration: 90 minutes
Class Size: 30 students
Curriculum Framework: International Baccalaureate (IB) Middle Years Programme (MYP) Mathematics Criterion A & B alignment

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IB Curriculum Alignment

MYP Mathematics Objectives:

• Criterion A: Knowing and Understanding
  • Explain mathematical concepts, processes, and results clearly and confidently using appropriate terminology (using standard forms such as quadratic equations).
  • Apply mathematics in unfamiliar situations by translating between different representations (equations and graphs).
• Criterion B: Investigating Patterns
  • Formulate hypotheses based on systematic investigation of graphs and algebraic forms (e.g., how parameter 'a' affects graph shape/direction).
  • Use appropriate technology to explore and confirm mathematical patterns (Desmos exploration).

IB Concepts & Approaches:

• Conceptual Understanding: Functions and their representations
• Approaches to Learning (ATL) skills developed include Communication, Critical Thinking, and Use of Technology

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Learning Objectives

By the end of this lesson, students will be able to:

1. Recognize quadratic functions in standard form: ( y = ax^2 + bx + c ).
2. Identify parameters (a), (b), and (c), and explain their roles in shaping the graph.
3. Predict the shape and direction of the parabola based on the value of (a).
4. Use Desmos to graph quadratic functions and interpret the effects of changing (a).
5. Connect quadratic graphs to real-world contexts (e.g., projectile motion).
6. Communicate understanding clearly through collaborative and individual activities.

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Materials Needed

• Whiteboard and markers
• Projector and computer to display Desmos online graphing calculator
• Student devices or computers with Desmos access
• Printed Desmos-ready Worksheet (see provided script)
• Timer or clock
• Notebook and pencils

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Lesson Breakdown

Time	Activity	Details & Teacher Talk	IB Focus & Notes
5 min	Bell Ringer & Engagement	Say: "Y’all noticed some equations had (x^2) instead of just (x). Those are called quadratic functions. Today, we’ll explore what makes these functions special."	Activating prior knowledge, clear communication
10 min	Introduce Quadratic Function Equation	Write on board: ( y = ax^2 + bx + c ) Say: "This is the standard form of a quadratic function. Let's explore what the letters mean."	Criterion A: Knowing and Understanding the form and terminology
15 min	Identify Parameters (a), (b), and (c)	Explain: - a controls the shape & direction - b affects the middle of the graph (axis of symmetry) - c is the y-intercept Example on board: (y = 2x^2 + 3x + 1) Ask: "What is (a)? (b)? (c)?" Write answers together.	Conceptual understanding plus formative questioning to check student grasp
15 min	Link Equation to Graph Shape	Say: "Quadratic functions make a U-shape called a parabola." - If (a) is positive → opens up - If (a) is negative → opens down Draw two sample parabolas on board for visual.	Visual representation supports understanding of function behaviors, linking algebra and geometry
20 min	Desmos Graphing Demo (Teacher-led)	Direct students: 1. Open Desmos graphing calculator 2. Enter, one at time, each equation: - (y = x^2) - (y = -x^2) - (y = 2x^2) - (y = -3x^2) Ask: "What do you notice about the shapes? Which open up or down? How does (a) affect the width/narrowness?"	Integrate technology (ATL Skill) to explore graphical properties, fostering critical thinking/testing hypotheses
20 min	Student Worksheet (Desmos Activity)	Students work individually/pairs to: - Identify (a,b,c) for given functions - Predict parabola direction before graphing - Graph functions in Desmos - Match graphs to equations - Reflect on real-life parabola connection (basketball curve) Teacher circulates to assist and prompt mathematical thinking.	IB ATL communication, collaboration, and reflection; real-world application fosters inquiry
10 min	Class Discussion & Sharing	Prompt students to share: "How does parameter (a) affect the graph?" "What examples from real life can you find for quadratic graphs?" "Why is understanding graph direction important?" Use student responses to reinforce conceptual clarity and connect to Criterion A & B.	Consolidate knowledge, metacognitive reflection, promoting learner agency
5 min	Closing Statement & Preview	Use strong closing: "So today we learned that just one number — a — completely changes how a graph looks. Tomorrow we’re going to go deeper and predict graphs without even drawing them.”	Set expectations and motivate curiosity aligned to IB inquiry culture

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Differentiation Opportunities

• For Diverse Learners: Provide step-by-step scaffolded examples on the worksheet.
• Advanced Learners: Challenge to analyze the effects of varying (b) and (c) on the vertex and intercepts (preparing for vertex form).
• Visual Learners: Emphasize graph sketches and technology use.
• Kinesthetic Learners: Use physical graph cards or graph plotting on coordinate boards if available.

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Assessment

Formative Assessments During Lesson:

• Q&A during explanation to check understanding of parameters
• Student worksheet responses, reviewing completed sections to monitor comprehension
• Observation of Desmos activity engagement and ability to interpret graphs

Summative Assessment (Next Lesson): Anticipate a quiz on graph identification, drawing from standard form to parabola shape prediction without graphing tools.

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Teacher Reflection Points

• Did students connect the algebraic parameters to graphical features?
• How effectively did Desmos facilitate understanding?
• Were students able to predict graph behavior without technology after practice?
• What adjustments could support deeper inquiry next lesson?

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Desmos-Ready Student Worksheet (March 23, 2026)

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Name: ___________________

Part 1: Identify the Parts

For each quadratic equation, write the values of (a), (b), and (c):

1. (y = 2x^2 + 5x + 1)
2. (y = -x^2 + 4x - 3)
3. (y = 3x^2 - 2x + 6)

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Part 2: Predict BEFORE Graphing

Circle your prediction and explain why:

Equation	Opens Up or Down?	Why?
(y = x^2)	Opens Up / Down
(y = -x^2)	Opens Up / Down
(y = 4x^2)	Opens Up / Down
(y = -2x^2)	Opens Up / Down

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Part 3: Desmos Graphing

Graph the following equations on Desmos:

1. (y = x^2)
2. (y = -x^2)
3. (y = 4x^2)
4. (y = -2x^2)

Answer:

1. Which graphs open upward? ______________
2. Which graphs open downward? ______________
3. What controls the direction? ______________

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Part 4: Match the Graph To Equation

A. Opens up wide parabola
B. Opens down narrow parabola

Match each:

• (y = 4x^2) → _______________
• (y = -x^2) → _______________

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Part 5: Real-Life Connection

A basketball is thrown into the air. Why does the path look like a curve instead of a straight line?

Answer in 1–2 sentences:

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Teacher Quick Answer Guide

Part 1:

1. (a=2, b=5, c=1)
2. (a=-1, b=4, c=-3)
3. (a=3, b=-2, c=6)

Part 2:
Positive (a) → opens up
Negative (a) → opens down

Part 3:

• Opens upward: (y = x^2, y = 4x^2)
• Opens downward: (y = -x^2, y = -2x^2)
• Direction controlled by (a)

Part 4:

• (y = 4x^2) → A (opens up wide)
• (y = -x^2) → B (opens down narrow)

Part 5:
Because the basketball’s path is influenced by gravity, its height changes with time following a quadratic function, creating a parabolic curve instead of a straight line.

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Additional Support for Technology Integration

• Prepare a class account or shared link (if school policy allows) for saving Desmos graphs.
• Use Desmos Activity Builder if teacher wants next-level integration with real-time student response dashboards.

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Final Note

Feel free to request:

✅ Fully integrated Desmos Activity Builder with automatic feedback
✅ Printable worksheet with graph illustrations included
✅ PowerPoint or Canvas slides with animated graphs and stepwise reveals
✅ Differentiated worksheets for diverse learners (low, medium, advanced)

Ms. Graves, with this plan and worksheet, your students will gain strong, inquiry-driven engagement that links algebra computation, graphical intuition, and real-world relevance — all firmly grounded in IB philosophy. This hands-on technology usage supports critical understanding and prepares learners well for future explorations into quadratic functions and beyond! 💛