Rotations - O & M Meets Math

By Susan LoFranco on Apr 24, 2017

  • The student will recognize the rotation of shapes. 
  • Find objects in the environment that are rotations.
  • Orientation clockwise and counter clockwise
  • Understanding the concept of movement in space 90, 180, 270, 360 degrees - both clockwise and counter clockwise


spice bottles

  • Masking Tape 
  • 4 Quadrant Graph Paper - either bold or raise lined
  • Markers, dots, tape to connect points on graph
  • 4 or 5 spice bottles


Vocabulary: counterclockwise, clockwise, rotation, 

Depending on the time the teacher has with the student, Parts 1, 2 and 3 can be done in separate sessions. 

Part 1: 

To prep for this part of the lesson, using the masking tape, mark the floor with a large + sign which will represent the four quadrants of the graph paper.  This exercise will ask the student to replicate with their body what will later be done on graph paper. Initially the student will move to a stated quadrant and then turn the degrees related to that quadrant.  At the most abstract the student should be able to move into a stated quadrant and know the direction to orient their body before moving first. 

  • Before beginning exercise on the grid you have made on the floor review with the student turning 90, 180, 270 and 360 degrees while standing in place.  
  • Whatever direction the student is turning in (clockwise or counterclockwise) the student should describe the degree of rotation in the opposite direction needed to get to the same point.  
  • After reviewing the rotations in place move to the grid on the floor.
  • Review the quadrants reinforcing how quadrants are numbered in counter clockwise order beginning with the top right quadrant (1). 
  • Have the student move clockwise then counterclockwise  90, 180, 270 and 360 degrees into each of the quadrants made by the grid on the floor.  
  • While the student is rotating, at each turn ask the student how many degrees they are turning in the opposite direction. 90 degrees on way is 270 degrees in the opposite direction.  
  • Once the student is confident, continue on to Part 2.  

Part 2:  Rotation worksheet

Student will be using The Rotation Worksheet to rotate a figure around the x,y axis.   

Click here to open the answer sheet.

  • With the student, review the quadrants on the graph paper moving clockwise and counterclockwise.  
  • With the student, turn the graph paper clockwise then counterclockwise 90, 180, 270, and 360 degrees.
  • Before beginning the rotation, student should identify the points on the grid which will be rotated.
  • Record the points (using the student's media of choice) for use when rotating.
  • When beginning the rotation the student should turn the paper (clockwise/counterclockwise) the appropriate number of degrees in order to draw the figure in each of the quadrants.  
  • With the student, draw the first rotation (90 degrees clockwise) using the coordinates identifed earlier to plot the points on the grid. 
  • With the student, connect the points to complete the figure. 
  • With the student, identify how many degrees counterclockwise the figure is. 
  • If the student is confident, have them continue rotating the figure around the axis, identifying the counterclockwise position at each rotation. 

Part 3 - Assessment 

Student will use their understanding of rotations to move the spice jars to another quadrant on the graph paper. The teacher will need to place the spice jars in one quadrant as in image above or however they might fit into one quadrant.

Question to Student:  Imagine that you are in your kitchen.  You are moving your spices from one cabinet to another.  If you want the spices in the same order and the cabinet you are moving the spices to is 270 degrees clockwise on the grid from where the spice jars already sit what will be the new formation of the spice jars?



Rotations collage


Rotation Rules You Tube video


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