Magazine article Teaching Children Mathematics

Making Your Point

Magazine article Teaching Children Mathematics

Making Your Point

Article excerpt

Student Activity Goals

* Students will make and identify three- and four-sided figures on the geoboard or dot paper.

* Students will find areas of different triangles and quadrilaterals.

* Students will explore the relationships between triangles and quadrilaterals with the same areas.

Planning for Instruction

Each student will need a geoboard, rubber bands, and dot paper to record her or his discoveries. Students should share the shapes they have identified with other students, discussing how the shapes are similar and how they are different. As students identify shapes on their geoboards, they should record the shapes on the dot paper and begin to look for patterns. Students should be encouraged to explore, with directions, such tasks as the following:

* Identify several different triangular shapes on your geoboards.

* Make two different quadrilaterals with areas of 4 square units.

* Identify two different triangles with areas of 2 square units.

The dot paper in figure 1 resembles 5-peg-by-5-peg geoboards. Figure 2 gives figures with areas of 2, 3, and 4 square units. Teachers will need to show students what a square unit is on the geoboard. Prior to the following activities, students should practice counting squares and partial squares to find the areas for figures labeled on the geoboard.

Possible Discussion Questions

1. On your geoboard, make a triangle. Sketch your triangle on dot paper to share with your classmates.

a) What is the triangle of greatest area that will fit on your geoboard?

b) What is the triangle of least area that will fit on your board?

c) Can you have more than one "largest" triangle? "Smallest" triangle? Explain.

d) Did all triangles have the same shape?

e) Which triangles could be turned, slid, or "flipped" to look exactly like the other triangles?

2. …

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