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Constant Dimensions

Students will measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, regardless of the units. For many middle school students, this discovery is surprising. This activity involves the applicaton of several skills such as, plotting points, creating a table, measuring, ordered pairs, and coordinate plane.

Weblink address (URL): 
Constant Dimensions

Standards & Objectives

Learning objectives: 

Learning Objectives:

Students will:

  • Critique various units of measure based on their appropriateness for this particular activity.
  • Use a linear graph to model, analyze and make predictions.
  • Draw conclusions about the relationship of two dimensions based on collected data.
Essential and guiding questions: 

Questions for Students 

  • Although more pennies were used than M&M’s when measuring the width, did the size of the width actually change?
  • Take a look at your six points. Do they appear randomly or does there appear to be a pattern?
  • If someone used gumballs to measure the length and width, and their ordered pair were placed at (22, 10), would we suspect that they made a good measurement? What if the ordered pair had the coordinates (16, 10.5)? What is your reasoning?
  • What unit of measure could be used that would have produced a point very close to the origin? Why?
  • What remained constant even when the units of measurement changed?
  • What algebraic rule is associated with the ordered pairs? Write an equation that shows how the two dimensions are related for this rectangle. Can this rule be written in the form length : width = __ : __ ?
  • If the length of the rectangle is 13 wooches, determine the width of the rectangle in wooches using (1) your line of best fit and (2) your algebraic rule.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

Extensions:

  • Using the data that students collected for their rectangle, graphing calculators can be used to perform a linear regression and determine the line of best fit.
  • You can provide other rectangles and ask students if the ratio is the same for every rectangle. Though it’s not the same for every rectangle, students should see that rectangles with the same ratio have the same "shape," leading to the concept of similarity.

Helpful Hints

Materials:

  • Rectangle Measure Activity Sheet
  • Rulers (both inches and centimeters)
  • Alternate units of measure (pennies, paper clips, M&M’s, beads, width of index finger, width of pencil)
  • Graphing calculator (optional)

References

Contributors: 
Roxann Johnson
Originator: 
Ayers Institute for Learning & Innovation