A Math Forum Web Unit
Suzanne Alejandre's

Understanding Factoring through Geometry

Sponge Activity

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  1. Set of squares for each pair of students: square pattern blocks, or square cut-out pieces of paper, or tiles
  2. Grid paper that matches the squares - 1/2 sheet per student
  3. 1 ruler per pair of students
  4. Overhead transparency of similar grid paper.

Sponge Activity:

    As students walk into class, hand them a half-sheet of graph paper. The overhead projector should be on showing the following directions:

      Please follow the directions as best you can!

      1. Draw 5.
      2. Draw a rectangle that shows 5.
      3. Draw a square that shows 5.
      4. Record your results on the graph paper.

    Your mindset should be that there is no one right answer. Your interest is in having the students respond, and you hope to get a variety of responses.


Select 4 students to go to the board and draw a shape that shows 5. (If, as you have walked around, you have not found 4 students with different drawings, after the students have put their representations of 5 on the board ask if there are other ways.)

Select another 4 students to go to the board and

  1. Draw a rectangle that shows 5.
    Ask the students: (a) What is a rectangle? (b) What is a square?

  2. Draw a square that shows 5.
    If a student is able to draw a square that shows 5, discuss the length of the side. Is it a whole number?

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