K-4 MATHEMATICS STANDARDS

    GEOMETRY AND SPATIAL SENSE ACTIVITY

    Standard's bullets addressed by activity

    • describe, model, draw, and classify shapes
    • investigate and predict the results of combining, subdividing, and changing shapes
    • develop spatial sense

    Materials needed

    • Square tiles or square pieces of paper

    Description of Activity

  • Group or classroom management practices

      • Groups of two to four students.

    Using two of the squares, ask students how many different ways the squares can be put together to form a new shape. As they form new shapes, the sides of the squares must match up. They cannot be put together, for example, only at the corners. Have the class agree that if the shape can be rotated or flipped to form a shape congruent to one already given, then it is not a different shape.

    (Students will find only one way to put the squares together.) When they agree on the number of new shapes, now ask them, "What if you started with three squares? How many shapes could you make?" (Students should be able to find two ways to put the squares together.)

    Now have students start with four squares. How many new shapes can they find? (Students should find five new shapes.) If you have organized the information on a chart, students may detect a pattern.

    Using their observations from the previous trials, ask them to predict, without trying any first, how many new shapes they can find if they start with five squares. Have them write their predictions on their paper. Then, ask them to work in groups to find all of the shapes. Draw the shapes they find on the board or overhead. (Students should find 12 new shapes.)

    Once they have found all 12 of the new shapes, now ask them to find the ones that can be folded into an open-top box. Some students may want or need to use large grid paper. The shapes can be drawn on the grid paper, cut out and folded to test for an open box.

  • Extensions

    • Ask students to predict the number of new shapes they could create if they started with six squares. After they write their prediction, they should draw all possible shapes. Using their observations from those that could be folded into open-top boxes, students should predict the number of their figures that can be folded into cubes. Now find them. What patterns do they notice? What if there were seven boxes?