3.+Linear

=Linear Relationships=

A Collection of Tasks for Learning or Assessment LR
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**A Lesson Series Possibility**

 * Developing Understanding** (slope, reading graphs, 4 ways to tell a story) Access lessons from http://t4.jordan.k12.ut.us/teacher_resources/MathSite/impact.alg.htm
 * 1) Match the graph using CBRs See Alg 4.1a part II--the last page with 6 graphs. (Specifically focus o how to give directions to the person mathching the graph, that is how fast to walk forward or backward--you can get to the rate of thange. If you want to do two days with CBRs, then do Alg 4.1a part II--the pages with graphs and tables.
 * 2) Stories from Graphs 4.1a first page, or Beginning Rates of Change Alg 5.0
 * 3) Four ways to tell linear change stories (Tables, Graphs, Stories, Equations) Alg 5.1b
 * 4) Slopes of Stairs Alg 5.1a Builds understanding of rise and run of real stairs.
 * Solidify Understanding** (slope, different story contexts—beyond time and distance, function rules to equations)
 * 1) Model linear change using manipulatives. Trains and Staircases Pre 6.1
 * 2) Slopes from a Table and Rates of Change Alg 5.1c
 * 3) Rules from Tables and Graphs Alg 4.2
 * 4) Families of Equations, Pattern and Function Families Alg 4.4a and b
 * 5) Stories from Graphs Alg 4.1b parts 3 and 4 and Graphs Tell Stories Alg 4.1c
 * 6) Zooming in on a Linear Equation Alg 5.2 and 5.2b
 * 7) Proving Equation Rules Alg 4.2b
 * Practice, extension and application** (Slope-intercept and standard forms of equations, line of best fit, data collection and analysis)
 * 1) Linear Change--Story Contexts Alg 5.3 to 5.8
 * 2) Parallel and Perpendicular Alg 6.2
 * 3) Detective Work using different Equation Forms Alg 6.2
 * 4) Line of Best Fit Alg 4.6 or 4.7
 * 5) Predictions from Data and Graphs Alg 4.

Patterns and Rules
In this lesson, students complete input-output tables to graph functions. They then look at the tables and graphs and note any patterns they see. In the second part of this lesson, students examine tables and come up with the equations that match the data.

Students examine sequences, find the next few terms, and come up with rules for the sequences.

Students use geometric concepts (perimeter, volume, surface area) to complete data tables. Then, they come up with rules that match the tables and patterns.

Slope, Rate of Change, X- and Y-intercepts, and Stories from Graphs
Students complete input-ouput tables for various functions. Then they calculate the slope, discovering that the slope is constant in the table and that the slope is the coefficient of x in the equation.

Students use CBRs to create distance/time graphs.

Students analyze distance/time graphs and create stories.

Students analyze distance-time graphs to create stories that match the graphs. Then, they create graphs to match a given story.

Students analyze a graph of Jack and Jill heading up the hill and answer questions about the graph as well as the rate Jack and Jill are traveling.

Students match a story to a graph and then write stories to match the remaining graphs.

Students analyze graphs of real world situations and interpret what the slope and intercepts mean in the real world situation.

Students graph real world situations and then determine what the x- and y-intercepts mean in the real world situation.

Slope-Intercept Form
In these two lessons (variations of each other), students discover slope-intercept form of an equation. They also examine the effects on a graph of changing m and b.

Students examine patterns to find the 10th term, the 0th term, and the slope (rate of change). They use this information to write a formula that matches the pattern.

Quick draws are a great! Using the attached template, give students points to graph, equations to graph, x- and y-intercepts, etc. Once they have graphed the equations, ask questions about slopes, x- and y-intercepts, etc. Use this as a daily warm-up.

Linear vs. NonLinear
In this lesson, students examine tables, equations, and graphs for linear and quadratic functions to determine the differences.

In this lesson, students examine the graphs of several different types of functions.

Assessment
In this project, students create constellations. Then they find the equation for each line of their constellation.

Two variations of the same performance assessment. Students analyze the graphs of participants in a race. They commentate the race from start to finish, demonstrating their ability to read graphs and provide information about rates.