Graphs and Functions

Overview

This 25-minute lesson is designed for a small group of 3 seventh-grade students, integrating elements from the International Baccalaureate (IB) Middle Years Programme (MYP) mathematics framework aligned with the Masterbooks General Science 1 curriculum. Students will explore the concept of functions through graph interpretation and simple creation, connecting mathematical thinking to scientific inquiry (a key interdisciplinary approach encouraged by the IB).

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Learning Objectives

• MYP Mathematics Criterion A: Knowing and Understanding
  Demonstrate knowledge and understanding of functions and their representations through graphs.
• MYP Mathematics Criterion B: Investigating Patterns
  Model situations using functions, interpreting and constructing graphs to describe relationships.
• MYP Science- Mathematics Connection (Interdisciplinary objective)
  Apply mathematical graphing skills to analyze scientific data from experiments or real-life phenomena.

Students will be able to:

1. Identify and interpret the characteristics of linear and simple nonlinear functions.
2. Plot basic functions on a graph using given data points.
3. Connect graphical information to practical scientific questions/models.

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Materials Needed

• Whiteboard with markers
• Graph paper for each student
• Rulers
• A printed data set related to a simple science experiment (e.g., temperature vs. time during water heating) adapted from Masterbooks General Science 1
• Colored pencils or markers
• Stopwatch or timer (to simulate data collection intervals)

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Lesson Breakdown

1. Introduction & Activation (5 minutes)

• Engage: Begin by showing students a printed graph of temperature change over time as water is heated (simplified curve from Masterbooks General Science 1). Ask: "What do you notice about the shape of this graph? What might the x- and y-axes represent?"
• Link to IB Framework: Emphasize that in IB, math helps us understand and describe the natural world, linking tightly with science.
• Objective sharing: "Today, we’ll learn how to read and create graphs called functions — an important tool in both math and science!"

2. Exploration and Practice (15 minutes)

• Activity A – Graph Interpretation (7 minutes):

  • Give students copies of the temperature vs. time graph.
  • Ask them to identify intervals where the temperature changes steadily and where it does not — relate this to linear vs nonlinear functions.
  • Discuss characteristics such as slope, intercepts, and curve shape.

• Activity B – Graph Creation (8 minutes):

  • Provide a simplified data set showing time vs temperature at 5 equal intervals.
  • Each student plots points on graph paper with assistance.
  • Use rulers to connect points and observe if the function looks linear or nonlinear.
  • Encourage students to describe what the graph tells them about the temperature changes over time.

3. Reflection and Assessment (5 minutes)

• Discussion:
  • Prompt students to explain how the graph can help predict future temperature changes or understand cooling/heating patterns, linking back to the science context.
• Formative Assessment:
  • Students verbally explain one key insight gained from the graph.
  • Teacher observes the correct use of function vocabulary (e.g., slope, intercept, linear, nonlinear).

4. Extension/Possible Homework

• Challenge students to collect their own data at home (e.g., measuring shadows every 10 minutes) and plot their own function graph. This promotes inquiry and real-world mathematical application, core IB values.

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IB Learner Profile & Approaches to Learning

• Inquirers: Develop curiosity through data observation and questioning.
• Thinkers: Apply critical thinking to interpret graph characteristics.
• Communicators: Share explanations clearly during reflection.
• Approaches to Learning Skills: Focus on communication, self-management (time during plotting), and thinking skills (analysis of data).

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Teacher Notes

• Facilitate rather than lecture, allowing students space to discover the graphical relationships.
• Encourage making links between math and scientific concepts in Masterbooks General Science 1 for authentic interdisciplinary learning.
• Keep explanations concise given time and small student number to allow hands-on participation.

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By blending meaningful graph activities from mathematical and scientific perspectives, this IB-aligned micro-lesson scaffolds a deeper conceptual understanding essential for young learners stepping into more abstract math topics.