Title: Heads Up!
The lesson is a hands-on project. Students will work in pairs to gather various measurements, organizing the data into a provided chart. The measurements will be used to review, reinforce, and introduce skills such as measures of central tendency, coordinate graphing, and various ways of representing data (i.e., stem-and-leaf plots, box-and-whisker plots, frequency tables, etc.).
Standard(s): [MA2015] (8) 15: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8-F5]
Title: What is the slope of the stairs in front of the school?
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Standard(s): [MA2015] GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Title: Scale Drawings
During this lesson students practice measuring and converting to scaled measurements. Students measure various places on campus, such as a classroom or the gym. They place their findings on a spreadsheet. After converting these measurements to a scaled version, students draw a scaled model.
Standard(s): [MA2015] ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)
Title: Rise-Run Triangles
This lesson offers students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.
Standard(s): [MA2015] (8) 8: 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-EE6]
Title: How Did I Move?
In this Illuminations lesson, students are provided with a method for understanding that for y = mx + b, m is a rate of change and b is the value when x = 0. This kinesthetic activity allows students to form a physical interpretation of slope and y-intercept by running across a football field. Students will be able to verbalize the meaning of the equation to reinforce understanding and discover that slope (or rate of movement) is the same for all sets of points given a set of data with a linear relationship.
Standard(s): [MA2015] AL1 (9-12) 46: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [S-ID7]
Title: On Fire
This unit of five lessons, from Illuminations, introduces the components of a fire-safe and fire-wise environment. Students create a fire-wise location through calculations and measurement of percent slope, defensible space distance and various vegetation separation distances. The unit plan culminates with students designing a fire-wise property and testing their fire-wise IQ.
Standard(s): [MA2015] (8) 27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [8-SP3]