59
Final test and working on mistakes
Textbook: pp. 154–155
GoalDo the year-end test and learn to work on mistakes.
New words
final test · yakuniy nazoratmistake · xatoanalysis · tahlilchecking · tekshirish
Explanation
In the final test solve the problems by the four stages: read everything first, begin with easy problems, draw the diagram accurately. When done, check the answers: do the angles sum to 180° and do the sides satisfy the triangle inequality. After you get the result, work on mistakes: write each one down and find its cause (arithmetic slip, theorem misused, unclear diagram). Then solve the problem correctly and solve a similar one again. Making mistakes is part of learning.
Worked examples
A wrong solution: an isosceles triangle has apex 50° and the student wrote the base angle as 50° too. Cause: in an isosceles triangle the base angles are equal, not the apex. Correct: (180° − 50°) : 2 = 65°.
A gap in a proof: a student wrote “the triangles are equal because their three angles are equal”. That is not a criterion. The correct approach is to show one of SSS, SAS or ASA.
Class activity
For the mistakes of the final test make a three-column table in your notebook: “mistake”, “cause”, “correct solution”.
Practice
1
A triangle is written with angles 50°, 60° and 80°. What is the sum?
190
2
Two angles of a triangle are 50° and 60°. How many degrees is the third?
70
3
What should you do first when you find a mistake in the final test?
Write it down and find its cause.
4
Why is it useful to solve a problem again by another method?
Because if the answers agree the result is reliable, and a mistake shows up.