How can we use math to model and understand real-world situations through proportional and linear relationships?
Critical Thinking: Students analyze and apply proportional and linear relationships to solve real-world problems.
Communication: Effectively articulate the concepts of proportional and linear relationships through various representations.
Global Citizenship: Understand the impact of mathematical models on solving global issues and making informed decisions.
How do equations, graphs, and tables of linear relationships help us understand where something starts and how fast it is changing?
Students will model real-world situations using tables, graphs, and equations to demonstrate understanding of linear relationships.
Skills Demonstrated
Students will be able to…
Recognize proportional relationships as linear functions through the origin.
Understand and apply slope as a measure of constant rate of change.
Write, interpret, and graph linear equations to model real-world and mathematical situations.
Communicate reasoning using key vocabulary: slope, y-intercept, constant of proportionality, linear function, proportional relationship, rate of change.
Describe how one quantity changes in relation to another by analyzing the graph’s shape and slope.
Identify intervals where the function increases, decreases, or remains constant.
Explain the meaning of linearity and rate of change in real-world terms.
8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.B.6: Use similar triangles to explain why the slope (m) is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.F.A.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
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