Lasting Ideas & Results:

Linear Patterns are solved using numeric (tabular) methods in this lesson as we strive to see purpose in developing an algebraic structure. This lesson investigates several linear situations that arise while planning a trip including distance, speed, fuel efficiency, and budgeting.

Essential Question(s):

How much money will Antonius need for gas to Denver and back again?

Can Antonius make it from Chicago, IL to Omaha, NE without stopping for gas?

How much money will Antonius save if he takes 3 friends instead of the 2 he originally planned?

What time will Antonius arrive in Denver?

Desired Learner Outcomes:

Students will be able to…Students will know…
solve a linear equation using a table
the difference between relevant and irrelevant information in a problem.
investigate problems by determining 1) what do I know, 2) what do I need to know, and 3) what comes next?how a bar graph and line graph are related and how they are different


NCTM Standards for Grades 6–8

Algebra Standard

  • identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations
  • model and solve contextualized problems using various representations, such as graphs, tables, and equations
  • use graphs to analyze the nature of changes in quantities in linear relationships
Geometry Standard

  • use geometric models to represent and explain numerical and algebraic relationships
Measurement Standard

  • understand relationships among units and convert from one unit to another within the same system;
Data Analysis and Probability Standard

  • use observations about differences between two or more samples to make conjectures about the populations from which the samples were take
Problem Solving Standard

  • build new mathematical knowledge through problem solving
  • solve problems that arise in mathematics and in other contexts
Communication Standard

  • communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Connections Standard

  • recognize and apply mathematics in contexts outside of mathematics


Summative Assessment(s):

Describe Performance TasksExplain &/or Reference Criteria
classroom/small group discussionanswers included in presentation
individual workanswers included in presentation
homework project - "What time will Antonius arrive in Denver?"answers included in next lesson


The presentation (keynote or powerpoint) includes detailed lecture notes with solutions to the problems.

Modifications, Adaptations, & Accommodations:

The homework assignment is open-ended, students may answer the problem using a table, spreadsheet, graph, or equation.

Required Attachments:



Non-profit Tax ID # 203478467