Linear Functions

By (date), (name) will construct a function when given a data set for two linearly related quantities, table... of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.
  • By (date), given a glossary of formulas for finding slope and a linear relationship (e.g. slope is m= (y2-y1)/(x2-x1), and the equation of line is y = mx + b with b being the initial value, a.k.a. the y-intercept), (name) will be able to accurately construct a function when given a data set for two linearly related quantities, table of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.
  • By (date), given a graphing calculator to interpret the data and a step-by-step tutorial (e.g. Writing Equation of Line) on how to use the graphing calculator, (name) will construct a function when given a data set for two linearly-related quantities, table of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.
  • By (date), when given a table of values for two linearly related quantities, using online graphing software (i.e. Geogebra - Introduction to linear equations, (name) will construct a linear function correctly for (4 out of 5) problems.

UDL Strategies About UDL

  • UDL I 3.1 Activate or supply background knowledge
    Instead of students spending time agonizing over the exact formulas for the task, teachers can provide students with a formula chart to activate their knowledge. Providing a formula chart (i.e. a list of the formulas need for the task such as formula of a line y = mx + b in which m = slope and b = y-intercept) will still allow the student to construct the function and represent their understanding of linear functions on a coordinate plane. The use of formula charts is also beneficial because it teaches students to be resourceful, and that they can still complete a task even if they have difficulty memorizing all of the related formulas.
  • UDL II 5.2 Use multiple tools for construction and composition
    Instead of expecting students to complete all the calculations in their mind, students who might not be comfortable with calculation skills but can conceptually understand linear functions, should be given a graphing calculator as a tool to help them create functions from a table values, coordinate points, or a graph. Students are to interpret how to create functions, and they might need a calculator with graphing components to facilitate that understanding.
  • Foster collaboration and communication
    Instead of having students work independently on the task, teachers could allow the students to work in groups (e.g. jigsaw method where students are assigned roles and then teach each other the work from their role) so that students can learn from their peers and work together to find a solution. The group work activity teaches students to have ownership over their work and to be accountable for providing their group with the correct solution and problem solving steps.

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Common Core Standards

8.F.4 Use functions to model relationships between quantities
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Standard Staircase

Linear Functions Current Goal

By (date), (name) will construct a function when given a data set for two linearly related quantities, table of values, or a graph representing the linear function for (4 out of 5) problems on a teacher-created worksheet.

Referenced Strategies

  • Calculator

    A calculator is a mathematical tool that can perform basic to complex mathematical operations. A simple calculator usually has functions for...

  • Math Dictionary

    A math dictionary is a type of dictionary that contains mathematical terms, definitions and visual representations. The math dictionary may ...

  • Reference Materials

    Reference materials are resources that a student can use when completing academic or social and emotional learning tasks. These materials pr...