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Understanding the Equation “y = mx + b”

Overview: Middle or high school students develop and exhibit their understanding of the relationship among the parts of the linear equation y = mx + b through multiple means–table, line graph, equation, computer model, and word problem.

Lesson Objectives

Curriculum Context

Concepts

Students will be able to: 

  • identify slope and y-intercept in an equation, graph, and table of values generated by the equation y = mx + b.

  • construct STELLA® models of linear equations that produce graphs of increasing, decreasing, andhorizontal lines.

  • discover and define horizontal and parallel lines using STELLA®.

  • identify and define positive, negative, and zero slopes of lines on graphs.

  • create a booklet of linear equation problems.

distinguish between events, patterns, and structures of mathematical equations, given an understanding of the iceberg graphic. (per Extension 1 – accompanying document, “Extensions”)

Math benchmarks:

  • Compare a given prediction with the results of an investigation.  

  • Produce the rule (function) that explains the relationship (pattern) between the numbers when a change in the first variable affects the second variable (T-chart, two-row table, or input/output machine). 

  • Demonstrate understanding of rate and unit rate. 

  • Describe and use variables in a contextual situation. 

  • Match an equation with a fitted line. 

  • Write a rule to extend patterns.

  • Solve linear (first degree) equations using models/manipulatives, symbols, and or graphing in a one-step equation.

  • Recognize the relationship among tables, graphs, and verbal descriptions.

 

Integration with writing through the use of the 6-Traits of Writing model to assess the final project

  • Change over time

  • patterns and trends

  • accumulations

  • interdependencies

  • structure generates behavior

  • temporal and spatial boundaries

 

Materials

Time

Systems Tools

  • Math single-tile manipulatives (optional)

  • Computer projection device

  • STELLA® software

  • Student computers

  • Iceberg visual

  • Accompanying materials for printing

Ten or more one-hour long periods 

 

  • Computer modeling

  • Iceberg visual

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