Students with visual impairments may face challenges when working on the Mathematics standards in the Common Core State Standards (CCSS). As a response to this, Perkins School for the Blind convened a panel of experts to identify specific standards that would be a potential challenge to students who are blind or visually impaired, and then proposed ideas for materials, foundational skills, tips and strategies, and lesson ideas to help to address these challenges.
This post is part of a series about different parts of the Mathematical standards.
A function is a set of inputs and a set of permissible outputs where one output is directly related to one input. It is often compared to a machine where one thing goes in is directly related to what comes out. Students may start by learning a function table in early grades but will use this knowledge through high school.
This skill leads to the understanding of linear relationships. Practice with tactile drawing of input tables and graphs (single and four quadrant) is essential.
Nemeth: superscript indicator, baseline indicator, fraction indicators, radical, index of radical, termination indicator, and parentheses
Understand how to graph points, independent vs. dependent variable
Know how to set up a table of values
Know how to read tables and graphs
Understand a Vertical Line Test
Calculate slope/rate of change of a line graphically
Understand the layout of an equation and how to read tables and graphs
Distinguish between linear and nonlinear functions
understand independent vs. dependent variable, the idea that functions can be modeled in a variety of ways, and how to read tables and graphs
Calculate and interpret constant rate of change/slope from a graph
Calculate and interpret initial value (y-intercept) from a graph
Represent linear relationships graphically
Understand resources available to draw a graph and what works best for that student so he/she can draw the model easiest based on his/her fine motor skills and knowledge of what would make a graph rise or fall
Distinguish rate of change within an interval of a function
Interpret directionality and steepness of the graph of a function
Sketch a graph given algebraic context or a scenario (slope and initial value)
Create a plausible story given a graph
Use the concept of function to solve problems
Understand how to read tables and graphs
Understand what types of numbers would be used in different situations
Understand how a fraction can represent a rate of change
Understand how to use a symbolic representation to make a table of values and graph points
Understand how to manipulate equations into equivalent forms and solving equations
Understand the properties of exponents and percent
Understand the relationships between functions algebraically, graphically, verbally, or in tables
Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions).
Have students make a table consisting of the number of items in the independent variable column and the total cost of x items in the dependent variable column
Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions).
Have students make a table consisting of the number of items in the independent variable column and the total cost of x items in the dependent variable column
Determine the values or rule of a function using a graph or a table.
Make the graph or table relevant to real world problems
The student will need to be explicitly taught how to read the graph or table
Describe how a graph represents a relationship between two quantities.
Use meaningful examples
Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions).
Have students make a table consisting of the number of items in the independent variable column and the total cost of x items in the dependent variable column
Determine the values or rule of a function using a graph or a table.
Make the graph or table relevant to real world problems
The student will need to be explicitly taught how to read the graph or table
Choose problems that relate to a student’s interests.
Number of animals mapped to number of legs, etc.
Use the concept of function to solve problems.
Construct graphs that represent linear functions with different rates of change and interpret which is faster/slower, higher/lower, etc.
Identify spots on a graph that are at zero, at a high point, at a low point, growing, or falling.