In math class, it is crucial that the first task of the lesson is accessible to all students, although it can serve different purposes for the lesson. Some anticipatory sets activate a pre-requisite skill needed for the lesson. Others can be used to promote a discussion of mathematical vocabulary by creating the need to define a mathematical pattern being noticed by the students. Others can be used to introduce the topic in a nontraditional way.
The lesson I am detailing comes from the functions unit of 8th grade math. The objective of the lesson was to introduce linear vs. nonlinear functions and to define the characteristics of each. Students have previously studied linear relationships and the definition of a function. In the anticipatory set for the lesson students are shown two visual patterns, one of which is modeling linear growth and one nonlinear, though they do not yet know this. The task asks the kids to determine how the pattern is growing and use a method of their choice to determine what a future step in each pattern would look like. The reason why this set is so effective is that is accessible to all and naturally differentiates based on the student. Students may visually notice how the patterns are growing and choose to draw the future steps to the patterns. Others may make data tables and use numerical patterns to find the future step in the pattern. Although not typically used at first by students, graphs and algebraic expressions can also be used to complete the task. Because of the various ways to approach the anticipatory set, it is then used as an anchor throughout the lesson to compare the tabular, algebraic and graphic representations of the patterns in addition to the visual. Once the graphic representations are shown, it is clear that one pattern is representing a linear function while the other is nonlinear. By then contrasting the other representations of the patterns, the characteristics of linear and nonlinear functions are defined across all representations. I have used this lesson successfully at the math 8 level, and I have created a version of this lesson that levels up to algebra and contrasts linear, exponential and quadratic growth. I appreciate how accessible the abstract concepts are made by using visual patterns and student intuition to do the initial exploration of the lesson objective.
The lesson I am detailing comes from the functions unit of 8th grade math. The objective of the lesson was to introduce linear vs. nonlinear functions and to define the characteristics of each. Students have previously studied linear relationships and the definition of a function. In the anticipatory set for the lesson students are shown two visual patterns, one of which is modeling linear growth and one nonlinear, though they do not yet know this. The task asks the kids to determine how the pattern is growing and use a method of their choice to determine what a future step in each pattern would look like. The reason why this set is so effective is that is accessible to all and naturally differentiates based on the student. Students may visually notice how the patterns are growing and choose to draw the future steps to the patterns. Others may make data tables and use numerical patterns to find the future step in the pattern. Although not typically used at first by students, graphs and algebraic expressions can also be used to complete the task. Because of the various ways to approach the anticipatory set, it is then used as an anchor throughout the lesson to compare the tabular, algebraic and graphic representations of the patterns in addition to the visual. Once the graphic representations are shown, it is clear that one pattern is representing a linear function while the other is nonlinear. By then contrasting the other representations of the patterns, the characteristics of linear and nonlinear functions are defined across all representations. I have used this lesson successfully at the math 8 level, and I have created a version of this lesson that levels up to algebra and contrasts linear, exponential and quadratic growth. I appreciate how accessible the abstract concepts are made by using visual patterns and student intuition to do the initial exploration of the lesson objective.