- Unit Goals
The goal is for students to understand graphing of linear functions. This means that students actually understand slope is a rate of change, and that in bare problems lines extend forever, in contextual problems the context restrict the domain and range, why y=mx+b is the slope intercept form of an equation, and how different forms of equations can be distilled down to y=mx+b.
- Relation of Goal to Curriculum
This is a unit that I am developing for the Idaho Falls High School Algebra 1 PLT (professional learning team). Our goal is to create a unit that covers the current Idaho state standards as well as the upcoming Common Core State Standards (however the standards covering linear graphing will be pushed down into 8th grade so the project will be given to the junior high school for implementation). To create the unit I will develop materials for myself, and borrow ideas from Glencoe Mathematics Algebra 1.
- Student Characterisitics
Algebra 1 is the most varied class that Idaho Falls has to offer. The class consists of students that are a year behind in math and this is their current grade level. The students may have taken half of the class (the junior high teaches algebra 1 in 2 years) but not the second half of the class. The class also is populated by people who failed one or more trimesters last year. Cognitively they can do the math, however the class is rife with behavioral and social issues that typically come with grouping kids in the same slow track for a lengthy amount of time.
- Student’s Current Level of Skill
The students do have the prerequisite algebra skills to do a unit on graphing, their technology skills are low. I have a class set of TI-84 plus calculators and many of them have difficulty trying to divide on the calculator. None of the students have used the graphing functions that the calculator possesses. In order to graph students need to be able to add, subtract, multiply and divide. They also have to have a sense of solution sets, and substitution of variables for numbers.
- Classroom Organization
The students are grouped in groups of 4, with the exception of the middle group that only has three in it. The desks do not face each other, they are all orientated so that all students can view the board. The students are encouraged to work in groups during the majority of the class time when I teach.
- Unit Introduction
I introduce graphing by talking about the relevance of graphing, how out of any topics in math graphing is the skill used most often because it is displaying data, and of any skill that they should walk away with math should teach them how to represent data in a visual way that quickly and easily shows information about a given subject. I then show them several examples of real world data such as graphs in the newspaper, the code for a CNC machine (which is 3-dimensional graphing), a utility bill, and other examples I can find. I also throw in that graphing will be done in every future math and science class. Then we usually discuss who has any previous experience with graphing what they remember, and what they might have liked to be different when learning the material (I use this to help keep the students that are repeating the class in a decent mood, it also allows me to do some ability grouping in case some students need to be paired with someone familiar with the material).
- Resources
Resource / Rationale
The Internet / Sites like NCTM’s Illuminations, and other sites that have graphing games and a source for contextual problems.
Math PLT / We will be sharing this unit once it is completed so I will be asking them for suggestions on things they wish they had and implementation ideas, as well as how to fix things during the revision process.
Glencoe Algebra 1 Textbook / I will use this mostly to steal problems from; however many of the problems are bare problems and I feel that contextual problems create a better understanding in mathematics.
Graphing Calculators / I will use these once students have a general sense of graphing so we can discuss the effects of changes in the slope intercept equation.
PowerPoint / I do use PowerPoint in my class due to my terrible handwriting; this is where I will incorporate many of the visuals.
Handouts / I like to give the students tools that scaffold their understanding, for example a paper with a circle in the center and then lines coming off of the circle creating 4 quadrants, in each quadrant students put a different representation of the equation in the center to help foster the concept that the table, graph, point-slope equation, and a verbal description are based off of the same equation
- Visuals
Name / Explanation / Design
Graphs with Context / A visual that shows many linear graphs each related to a fairly simple context on the side, this is to increase the students ability to read a scenario and see the graph that comes from the scenario. / A word problem with a high level of readability that also has a graph next to it representing the situation. There will be color coded words that will correspond with color coded parts of the graph emphasizing the link between the text and the graph.
Multiple Representation Handout / The multiple representation handout demonstrates how all of the different subtopics of graphing linear functions are related. / a paper with a circle in the center and then lines coming off of the circle creating 4 quadrants, in each quadrant students put a different representation of the equation in the center to help foster the concept that the table, graph, point-slope equation, and a verbal description are based off of the same equation
Understanding Slope / A visual for slope that links the equation for slope, how one plots using slope, and how one uses the concept of rate of change to understand the meaning of the slope in the problem. / The visual will have the slope equation, an indication of slope as rise over run, and a link to a contextual situation that shows the concept of rate of change.
Understanding Slope-Intercept Form / A visual that explains the variables in the y=mx+b equation, not only in terms of m is the slope and b is the y intercept, but in terms of what does the equation tell about a scenario, the concept of starting points and changes after that starting point. / Similar to the slope visual this visual will have the equation and an indication of what each variable means. There will be a link to a graph and a contextual problem.
Understanding Point-Slope Form / A visual that explains the point-slope equation and what the variables mean in that equation and how the equation can thought of as a rate of change starting from a value that was not zero. / Similar to the slope visual but with a different equations and an emphasis that the starting point doesn’t have to be on the y-axis.
How to Graph by Hand / A visual demonstrating how to graph slope intercept and point slope equations by hand, showing how to determine the starting point and then move the rise and run of the slope to create a second point to determine a line. / This will be step by step instructions that demonstrate how to graph equations starting at the intercept and the moving the rise amount and the run amount.
How to Use a Calculator / A visual on how to input equations into the graphing calculator, how to adjust the window, and how to create a table of values (since the class’ technology skill is severally limited in this department). / Step by step visual instructions with keystrokes that will result in correctly graphing an equation.
Independent vs. Dependent / A visual on how to determine the independent and dependent variable and how that changes the setup of the graph / This is a visual that will have some terms listed that clue students into the independent and dependent variable, where they go on a graph and an equation.
- Assessment
Formative assessment will be used daily as the teacher monitors group work during problems introduced during the instruction time, and during homework time.
Homework is graded on a 10 point scale for understanding each problem is looked at for misconception in understanding, if any are noted the teacher gives adequate feedback to students. Students have the ability to redo assignments that receive low scores due to lack of understanding.
Summative assessment will be completed in the form of a unit test.
- Assessments Relation to Goals
Formative assessment and questioning will assess for understanding of concepts of graphing linear functions. The summative assessment will also assess understanding and the ability to communicate ideas learned during the unit.
* Adapted from Unit Plan at