MAT 136 Exam 2 | Exam Actual Questions and Answers Latest
Updated 2026/2027 (Graded A+)
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Discovery approach for determining the value of pi
i. - ✔✔1. cut out 3-5 cardboard circles of various sizes, with he center marked on each
ii. 2. for each circle, measure the diameter and the circumference. (to measure the
circumference, roll the circle along a ruler or meter stick, or if the circle is cut from thick
cardboard or foam board, lay a string around the circumference and then pick up the string
and measure it by using the ruler or meter stick.)
iii. 3. for each circle, take the diameter and the circumference results and, on a calculator,
divide the circumference by the diameter (c/d)
iv. 4. show that, no matter the size of the circle, the result will always be close to 3.14
v. state that we have a special name for this c/d relationship; we call it pi
vi. therefore the approximation for pi is 3.14
•
Discovery approach for determining the area of a parallelogram
i. - ✔✔1. cut out a cardboard parallelogram in which each base is labeled b
ii. 2. in the interior of the parallelogram, draw the height (labeled h) with one endpoint at a
parallelogram vertex
iii. 3. cut out this height
iv. 4. show the children that you have cut off a triangle
v. 5. move the triangle tot he other end of the figure
vi. 6. state that you have now formed a rectangle with length=b and width= h
vii. 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
xh
•
discovery approach for determining the area of a rectangle
i. - ✔✔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.
ii. 2. cut out several small "square inches"- little squares, each with length of 1 inch and
width of 1 inch
iii. 3. cover the index card rectangle with 15 of these square inches
iv. 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
v. 6. state that we therefore can simply multiply length x width to obtain the area of a
rectangle. (A=LxW)
Updated 2026/2027 (Graded A+)
•
Discovery approach for determining the value of pi
i. - ✔✔1. cut out 3-5 cardboard circles of various sizes, with he center marked on each
ii. 2. for each circle, measure the diameter and the circumference. (to measure the
circumference, roll the circle along a ruler or meter stick, or if the circle is cut from thick
cardboard or foam board, lay a string around the circumference and then pick up the string
and measure it by using the ruler or meter stick.)
iii. 3. for each circle, take the diameter and the circumference results and, on a calculator,
divide the circumference by the diameter (c/d)
iv. 4. show that, no matter the size of the circle, the result will always be close to 3.14
v. state that we have a special name for this c/d relationship; we call it pi
vi. therefore the approximation for pi is 3.14
•
Discovery approach for determining the area of a parallelogram
i. - ✔✔1. cut out a cardboard parallelogram in which each base is labeled b
ii. 2. in the interior of the parallelogram, draw the height (labeled h) with one endpoint at a
parallelogram vertex
iii. 3. cut out this height
iv. 4. show the children that you have cut off a triangle
v. 5. move the triangle tot he other end of the figure
vi. 6. state that you have now formed a rectangle with length=b and width= h
vii. 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
xh
•
discovery approach for determining the area of a rectangle
i. - ✔✔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.
ii. 2. cut out several small "square inches"- little squares, each with length of 1 inch and
width of 1 inch
iii. 3. cover the index card rectangle with 15 of these square inches
iv. 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
v. 6. state that we therefore can simply multiply length x width to obtain the area of a
rectangle. (A=LxW)
