Standard 8.1.3
Concept (Big Idea): Properties
How (or) do they determine different representations?
How can properties be used to write linear equations?
Why are they important?
How are properties used to transfer information from one representation to another? (Example: from a table to a graph, equations to a graph, graph to an equation, one form of an equation to another).
Concept (Big Idea): Proportional Relationships
What is the relationship?
What can proportional relationships tell us about representing linear equations in multiple forms?
Why is this helpful to understand?
How can we use proportional relationships to represent concepts in everyday life?
Standard 8.1.4
Concept (Big Idea): Predictions and Inferences
What properties allow inferences to be made?
Can we make these types of predictions without linear functions?
What do these predictions allow us to do?
Why are predictions and inferences important?
Concept (Big Idea): Problem solving using linear functions and equations
How can we relate mathematical solutions to real world situations?
Why might it be helpful to solve problems using mathematical equations?
What steps do we need to follow to solve problems using linear functions and equations?
The study of linear equations is essential to mathematics. Before students can move on to deeper applications (such as calculus, etc.), students must understand linear functions. This includes how to graph linear functions and how to transfer between equations, charts, and graphs. Learning how to use linear equations aligns with the Oregon core standards 8.1.3 and 8.1.4, and also with the NCTM standards for sixth through eighth grade algebra. According to these standards students should know how to identify, interpret, define, and solve a variety of equations and linear functions as well as identify their corresponding graphs and tables. The concepts of Algebra that are used in linear equations will carry students on through all other courses of mathematics. Concepts such as finding slope will be built upon for years to come. For these reasons, linear equations and functions have been listed by the state and national standards as an essential part of the eighth grade math curriculum.
The above rationale provides reasoning as to why using linear equations is essential, but it is a useful skill because it teaches students how to interpret equations and transform them into tables and graphs. Students are inherently learning how to interpret other things in the world around them if they are able to recognize the same mathematical relationship in multiple forms. One example of this would be writing a paragraph about a painting. The words are essentially describing what is going on in the painting much like an equation describes what is occurring in a graph. Linear relationships can show how something changes over time. This is a concept that students will use in conducting science experiments, looking at population changes in major cities, or even tracking their own improvement in school, sports, or other activities.
Many careers in today’s society use linear equations or reference them in some way. Health care professionals, scientists, economists, financial planners, and many other all use linear equations in their respective fields. Jobs that involve the use of linear equations are what keep our economy going, and knowledge of how to use them will allow students to succeed in a competitive job market.
List of Pre-Requisite Skills for Using Linear Equations:
-Plotting (x,y) coordinate pairs
-Using the slope formula
-Graphing from an x,y table
-Knowledge of start value and rate of change
-Basic algebra skills
I will be teaching part of block 3: Using Linear Equations in Oregon Focus on Linear Equations: Stage 3.This block consists of graphing using slope intercept form, writing linear equations from graphs, writing linear equations from key information, and different forms of linear equations. The textbook aligns this block with two Oregon core standards as shown below:
Oregon Core Standard:
8.1.3 Identify and interpret the properties (i.e. slope, intercepts, continuity, and discreteness) of linear relationships as they are shown in the different representations and recognize proportional relationships ( y/x = k or y = kx ) as a special case.
Oregon Core Standard:
8.1.4 Use linear functions and equations to represent, analyze and solve problems, and to make predictions and inferences.
These are the overall goals for my 10 lesson unit.
1.) Students will understand the process of identifying linear relationships in multiple forms.
2.)Students will understand how to use problem-solving strategies involving linear functions and equations.
3.) Students will be able to identify linear equations/relationships in multiple forms.
These are my overall objectives for my 10 lesson unit:
-Students will be able to draw a graph from a linear equation on graph paper.(Cognitive, Applying)
-Students will be able to translate an equation in writing from standard form to slope intercept form. (Cognitive, Understanding)
-Students will be able to write a linear equation from key information (slope, y-intercept, etc.) (Cognitive, Applying)
-Students will be able to solve for a missing part of a linear equation using key information. (Cognitive, Applying)
-Students will be able to write their own linear equations to solve problems based on real world scenarios. (Cognitive, Creating)
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