A Math Forum Web Unit
Suzanne Alejandre's

Understanding Factoring through Geometry

Main Activity

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Materials:

  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 - 3 sheets per pair of students
  3. 1 ruler per pair of students
  4. Overhead transparency of similar grid paper.

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Main Activity:

  1. Each pair of students should have:
      1 bag of tiles
      3 sheets of grid paper
      1 ruler

  2. Using the overhead to model, direct the students to set one piece of grid paper between them with the tiles ready to use.

  3. Direct the students to make a rectangle (using the tiles to represent 1 square unit) that represents "6".

  4. Model at the overhead. If you have an odd number of students,
      the extra student can be your partner at the overhead, or
      you might have one pair of students stationed at the overhead, or
      you might have pairs of students rotate.

  5. Show all possibilities for "6" in tiles.

  6. If necessary, model another number, asking for a suggestion from the class. If someone gives you a number that is too large, ask the students whether they have enough tiles - determine the maximum for the number of tiles provided.

Classwork

    Form all the rectangles possible to show:

    Using one sheet of grid paper, record your (or your and your partner's) findings. Draw each of the rectangles found for each numeral.

Processing Activity:

  1. Put a chart on the whiteboard or chalkboard or poster board.

  2. Pairs of students fill in the chart with what they have found during the activity. [If appropriate, extend the chart to ......]

  3. Ask the students to label their classwork so that each rectangle is also represented numerically.

    Example:

  4. Questions to talk to your partner about:

    What numbers only have two rectangles that can represent them?

      These are prime numbers

    What numbers can be represented by more than two rectangles?

      These are composite numbers.

    List the lengths and widths of the rectangles that represent "10".

      These are factors of "10"

Process the responses with the class.

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