Graphical Transformations Activities for Middle School

Instructor: Heather Jenkins

Heather has a bachelor's degree in elementary education and a master's degree in special education. She was a public school teacher and administrator for 11 years.

As students study graphing, have them explore the many different ways graphs can be transformed on a coordinate grid. Use these multi-sensory activities to help students understand graphical transformations.

Graphical Transformations

Up, down, left, right, in, out. These aren't just dance moves, but ways that students can manipulate graphs of functions. When students understand graphical transformations, they can connect the mathematical changes to an equation that translate into the movement of a graph. Use these activities to help students learn about graphical transformations.

Moveable Human Graph

Students will create graphs of functions using their bodies and then move to show vertical and horizontal graphical transformations.

Materials

  • Masking tape
  • Markers
  • Dry-erase boards
  • Dry-erase markers

Teacher Directions

Preparation

  • Prior to the activity, create a coordinate grid on the floor of your classroom or other area.
  • Use masking tape to create the x and y axes as well as the grid lines.
  • Use a marker to label the measurements on the x and y axes.

Activity

  • Demonstrate how to create vertical (up, down) and horizontal (left, right) transformations on a graph using a simple function such as x2.
  • Divide the class into small groups and provide each one with dry-erase boards and dry-erase markers.
  • Ask one group to come out to the coordinate grid you created.
  • Have the students in the group use their bodies as points to demonstrate the graph of a function. The students who are not participating in making the graph can calculate the x,y coordinates that each student needs to stand on.
  • Provide students with a function that will shift the original graph up, down, left, or right, such as x2 + 4 or (x - 5)2.
  • Have the students who are not creating the graph with their bodies calculate the coordinates for the different points on the transformed graph and direct their classmates to move to the correct positions.
  • Conduct a class discussion on how the graph moved on the coordinate grid.
  • Repeat the same process until each group has had the chance to create a graph with their bodies.

Discussion Questions

  • How do you create a vertical shift in a graph? How do you create a horizontal shift in a graph?
  • Why is understanding the use of parentheses when transforming a graph important?

Match the Transformations

Students will match graphs to their type of graphical transformation.

Materials

  • Graph paper
  • Red colored pencils
  • Blue colored pencils
  • Signs (vertical shift, horizontal shift, reflection over x-axis, reflection over y-axis)
  • Masking tape

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