Students will be able to calculate the area of isosceles triangles without directly measuring the height.
Setup Time: 5 minutes
Mini-Lesson Time: 25 minutes
Time: 50 – 60 minutes
Instruction: Whole class, groups and individuals
1. Teachers should construct a model of an isosceles triangle. Two sides of this triangle should be built using two 24” Toobeez tubes. The third side should consist of two 16” Toobeez tubes with a sphere in the center connecting to the other two tubes in a triangular arrangement.
1. The class should be led in a discussion to determine the unique qualities of the model. Teacher Note: Students should realize that two sides of the triangle are equal in length.
2. After the class arrives at the appropriate observations, teachers should present the definition of an isosceles triangle on the board. Students should copy this definition in their notebooks.
3. Ask the class to recall any math strategies used in studying triangles. Teacher Note: The desired answer is the Pythagorean theorem. If this has not previously been studied, precede this lesson with Activity #2 “Pythagorean Puzzler,” which offers an excellent introduction.
4. After the class recalls the Pythagorean theorem, ask the class whether that theorem can be directly applied to the model of the isosceles triangle.
Teacher Note: Students should realize the model is not a right triangle and the Pythagorean theorem does not apply.
5. Teachers should introduce the area equation for triangles:
Area = ³ base x height
6. Ask the class the strategy for determining the base length.
7. After students realize the base can be directly measured, have a volunteer measure the model’s base length with a meter stick and report the result to the class.
8. Ask the class: “Can any side of this model be measured to determine the height of the triangle?” Allow a discussion so ideas can be introduced.
9. Once it is agreed upon that no side can be directly measured to determine height, the teacher should insert a 16” Toobeez tube extending from the center sphere of the base to the sphere at the apex of the triangle.
Here are available Training Options!
1. Divide the students into groups.
2. Read aloud the following Activity Challenge Box to the group.
Challenge: Students will be able to calculate the area of isosceles triangles without directly measuring the height.
3. Teachers should instruct students that the same area value arrived at in the setup can be attained without measuring the height.
4. As an introductory y clue, groups should be instructed to try and use the Pythagorean equation to solve their problem. Allow the groups ample time to arrive at a solution.
5. In the event that no group offers a solution, present the strategy on the board by slowly introducing individual steps and providing time between each step for the groups to brainstorm.
6. The solution:
To close the lesson, end with a group discussion about what was learned during the activity. Circle up the group and work through the following questions. If possible, record the group’s responses on flip chart paper so all comments are displayed.
Here are some additional topics for discussion:
1. Additional qualities.
Have the students draw various isosceles triangles and measure the angles. Ask them to determine additional qualities ofthe isosceles triangle.
2. Extension/Follow up.
Provide students with the height and base length of an isosceles triangle. Have the students solve for the length of the two additional sides of the triangle.