MAT 136 CERTIFICATION EXAM 2026
QUESTIONS WITH SOLUTIONS GRADED A+
◉ Discovery approach for determining the area of a parallelogram.
Answer: 1. cut out a cardboard parallelogram in which each base is
labeled b
2. in the interior of the parallelogram, draw the height (labeled h) with
one endpoint at a parallelogram vertex
3. cut out this height
4. show the children that you have cut off a triangle
5. move the triangle tot he other end of the figure
6. state that you have now formed a rectangle with length=b and width=
h
7. say that since the rectangle's area is length (b in the model) x width (h
in the model) and the rectangle was formed from the parallelogram, then
the area of the parallelogram is b x h
◉ discovery approach for determining the area of a rectangle. Answer:
1. cut out a cardboard rectangle with length 5 inches and width 3 inches.
note that these exact dimensions do not have to be used.
2. cut out several small "square inches"- little squares, each with length
of 1 inch and width of 1 inch
3. cover the index card rectangle with 15 of these square inches
, 4. discuss that, since area refers to the number of square inches that it
takes to completely cover a geometric shape, the area of this 3 x 5
rectangle is 15 square inches
5. say that instead of actually covering our rectangle with squares, and
then counting the number of squares, we could have multiplied 5 times 3
to obtain 15 square inches
6. state that we therefore can simply multiply length x width to obtain
the area of a rectangle. (A=LxW)
◉ The "Discovery Approach" for determining the area of a triangle.
(The children
already have learned to find the area of a parallelogram.). Answer: a)
Cut out a cardboard parallelogram in which each base is labeled b. b) In
the interior of the parallelogram, draw the height (labeled h) with one
endpoint at
a parallelogram vertex. c) In the interior of the parallelogram, draw the
diagonal that does not intersect the
height already drawn.
d) Cut on this diagonal. e) Rotate one resulting triangle and place it
exactly on top of the other triangle to
show the children that you now have formed 2 identical (congruent)
triangles.
f) Say that since the area of the parallelogram was b x h, and the
triangle's area is one-half the area of the parallelogram, then the area of
the triangle is
QUESTIONS WITH SOLUTIONS GRADED A+
◉ Discovery approach for determining the area of a parallelogram.
Answer: 1. cut out a cardboard parallelogram in which each base is
labeled b
2. in the interior of the parallelogram, draw the height (labeled h) with
one endpoint at a parallelogram vertex
3. cut out this height
4. show the children that you have cut off a triangle
5. move the triangle tot he other end of the figure
6. state that you have now formed a rectangle with length=b and width=
h
7. say that since the rectangle's area is length (b in the model) x width (h
in the model) and the rectangle was formed from the parallelogram, then
the area of the parallelogram is b x h
◉ discovery approach for determining the area of a rectangle. Answer:
1. cut out a cardboard rectangle with length 5 inches and width 3 inches.
note that these exact dimensions do not have to be used.
2. cut out several small "square inches"- little squares, each with length
of 1 inch and width of 1 inch
3. cover the index card rectangle with 15 of these square inches
, 4. discuss that, since area refers to the number of square inches that it
takes to completely cover a geometric shape, the area of this 3 x 5
rectangle is 15 square inches
5. say that instead of actually covering our rectangle with squares, and
then counting the number of squares, we could have multiplied 5 times 3
to obtain 15 square inches
6. state that we therefore can simply multiply length x width to obtain
the area of a rectangle. (A=LxW)
◉ The "Discovery Approach" for determining the area of a triangle.
(The children
already have learned to find the area of a parallelogram.). Answer: a)
Cut out a cardboard parallelogram in which each base is labeled b. b) In
the interior of the parallelogram, draw the height (labeled h) with one
endpoint at
a parallelogram vertex. c) In the interior of the parallelogram, draw the
diagonal that does not intersect the
height already drawn.
d) Cut on this diagonal. e) Rotate one resulting triangle and place it
exactly on top of the other triangle to
show the children that you now have formed 2 identical (congruent)
triangles.
f) Say that since the area of the parallelogram was b x h, and the
triangle's area is one-half the area of the parallelogram, then the area of
the triangle is
