Needs of the Subject Area

In the Algebra I curriculum it is important to include the topic of multiple representations.  This way of looking at the slope intercept form of a linear line helps students make connections to the different representations of a line.  Students learn how to translate their understanding of growth and starting point between a tile pattern where they can visually see the growth, an XàY table where they can see the growth in another way, a rule where they can see that the growth is changing X and the starting point as a constant value, and the graph which is a spatial representation of the line.  Multiple representations lead the students to learning about points of intersection and solving systems of equations.  Finding the point of intersection is a concept that students will need later in Algebra I and in other higher math classes.

Needs of the Student

Students are individuals with different needs to facilitate their learning.  Giving students multiple ways of understanding the concept of a line is important because it honors the fact that students are individuals that learn differently from each other.  Solving systems of equations brings the real world applications into a math class where the students can see that math isn’t something that teachers have them do just for the sake of “doing math”.  One example of a real world scenario is the Iditarod Trail Scatter Plot where the students used the information given on the graph to find the point where two people would meet during the course of the race.  Another example is a problem where two people were saving for a bike.  Although they were saving at different rates the students found the point of intersection: which week would each person have the same amount of money and how much money would they each have. 

Pre-Requisite Skills

State Content Standards:

• Use informal strategies (e.g. graphs or tables) to solve problems involving systems of linear equations in two variable form  y=mx+b

Sample Goals:

• Understanding graphs and tables
• Interpreting meaning from different representations of an equation

Sample Objectives:

• Students will apply and demonstrate their knowledge of “m” as growth factor and “b” as “constant” or starting value of a pattern to create graphs, tables, and expressions (rules)
• Students will be able to solve systems of equations using patterns, graphs, tables and expressions (rules)
• Students will be able to convert patterns ß à graphs ß à tables ß à expressions (rules) ß à patterns
• Given a real-world scenario, students will be able to create the pattern, table, graph, and expression (rule) that represents the information

Big Ideas:

• Interpreting data from graphs
• Interpreting meaning from different representations of an equation

Essential Questions:

• How should we effectively interpret the meaning of data from graphs and charts?
• How can we use charts and tables to effectively communicate information?