# Polygons and Fraction Circles

Age: 4 & up

Prerequisites: Fraction circle application, polygon application.

Screen objects: Ten red outlines of fraction circles down left side of screen, with red radii drawn to indicate the sectors. First circle is undivided, second circle is divided into two equal halves, third circle is divided into three equal thirds, etc. At bottom of screen are eight outlines of polygons placed in random order. All of these outlines are colored blue to match the geometric insets.

Presentation: (Individual or small group)

1. Invite the child(ren).
2. Announce that you are going to launch the polygons and fraction circles.
3. Launch the polygons and fraction circles application.
4. Start with the fraction circle with three sectors. Click on each sector in turn. Count the sectors as you click: "One, two, three. Three sides". The sectors will darken when pressed like sticky buttons.
5. Ask the child(ren) to find a polygon with three sides. After it is found, ask "What else do we call a polygon with three sides"?
6. Drag the blue triangle to the red fraction circle with three sectors. When the triangle is in place, large purple dots will appear at the points where fraction circle radii and points of the triangle touch the circle.
7. Try dragging the pentagon to the fraction circle with the four sectors. It will stay in place, but the purple points won't appear. Say, "Hmm... No purple points. Let's try this fraction circle." As you say this, drag the pentagon over the next fraction circle, the one with five sectors. The purple points will appear. Say, "Purple points. One, two three, four, five purple points."
8. Continue with the rest of the regular polygons.
9. When finished, notice that there are no polygons matching the fraction circles with one and two sectors. Ask why there are no matching polygons for these fraction circles. Discuss.
10. Say to yourself "I can quit the application, or I can do it again." Depending on the interest shown by the child(ren), quit the application or push the "Try Again" button and repeat the presentation.
11. Be sure to quit the application and return to the launcher when finished.
12. Offer the child(ren) the opportunity to perform the exercise.

Variations: Matching fraction circles and polygons side by side.

Extensions: Design work with fraction circles and polygons.

Points of Interest: Purple points appear when match is made. Highlighted points are sticky buttons which child may count. There are no one-sided or two-sided polygons.

Control of Error: System responds by highlighting points where inscribed polygon and radii of fraction circle touch the circle. If a match is not made, no highlighting occurs.

Direct Aims: To relate fraction circles and polygons by means of points on circle touched by inscribed polygon and radii of fraction circles.

Indirect Aims: Preparation for exercises in recognition of external angles of regular polygons.

Software Affordance: Easy to manipulate, transparent figures and control of error to support the child's autonomy.

Software Constraints: Unlike the polygons in the geometric cabinet, the polygons cannot be rotated. Unlike the polygons made of geometry sticks, the sides of the polygons are rigid and cannot be added or removed. The sectors of the fraction circles cannot be removed from the circles. The sectors and circles cannot be rotated.