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Recognize the relationship between the apparent size of an object and its distance from the viewer.
View paper squares and use spatial reasoning skills to order the squares from smallest to largest.

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For each student:

Pen or pencil
Notebook or notepaper

For the whole group:

Scissors
Construction paper in a variety of colors
Marker
Tape

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Read and familiarize yourself with the activity.

Cut out about 20 squares from colored construction paper, each in a different size. Number the squares in random order. Write a large numeral on a small square and a small numeral on a large square.

Find a room for arranging the squares; this should not be the same room where students gather for the activity.

Arrange and tape the paper squares, so they are visible to a viewer along the back wall of the room, as are the numbers on the squares. Place some of the small squares close to viewers and some of the large squares farther. Also, place some squares at an angle to viewers and others flat against the floor, ceiling, or wall.

For background information, review the site linked below for information about spatial reasoning.

Spatial Reasoning: Why Math Talk Is About More Than Numbers

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Hold up two paper squares of different sizes, and ask students to identify the larger square. Then tell students that today they will observe a variety of squares and put them in order from smallest to largest. If students respond that this activity seems too simple or trivial, tell them to delay reaching a conclusion until they complete the activity.
Lead students to the back wall of the room where you have displayed the squares. Tell students to stay along the back wall.
Have students observe the squares and then list the numbers of the squares in order from smallest to largest. You or another leader may walk about the room and report the number of a square if students request it. Otherwise, provide no additional information about the squares.
When all students have completed their lists, collect the squares and then display them from smallest to greatest.
Have students compare the orders of the squares they recorded with the actual orders.
Ask students to explain why this activity was challenging. Lead students to recognize that distance and position both affect the apparent size of objects.
Next, assign each student a number. Have the students cut paper circles of various sizes and colors from construction paper, similar to the squares that you cut earlier. Then have them write the numbers you assigned them on the circles and tape the circles somewhere in the room.
Repeat steps 2-5 of the activity, using the paper circles.
Lead a whole-group discussion of the activity. Ask:
- What do you think is the lesson to be learned from today’s activity? (Objects can be difficult to compare when they are of different sizes and at different distances from the observer.)
- What real-life subjects or studies do the activity relate to? (They relate to astronomy because stars have different sizes, brightness, and distances from Earth; art and design because artwork might be observed from a variety of distances; and aviation because pilots use landmarks on the surface to help them land airplanes.)

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Circle Sort

Circle Sort

Circle Sort

Overview