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MAT 136 Exam 2 | Exam Actual Questions and Answers Latest Updated 2024/2025 (Graded A+, Exams of Mathematics

Northern Arizona University (NAU)Mathematics

Discovery approach for determining the value of pi - ✔✔1. cut out 3-5 cardboard circles of various sizes, with he center marked on each 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.) 3. for each circle, take the diameter and the circumference results and, on a calculator, divide the circumference by the diameter (c/d) 4. show that, no matter the size of the circle, the result will always be close to 3.14 state that we have a special name for this c/d relationship; we call it pi therefore the approximation for pi is 3.14 Discovery approach for determining the area of a parallelogram - ✔✔1. cut out a cardboard parallelogram in which each base is labeled b

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MAT 136 Exam 2 | Exam Actual Questions and Answers Latest Updated
2024/2025 (Graded A+)
Discovery approach for determining the value of pi - ✔✔1. cut out 3-5 cardboard circles of various sizes,
with he center marked on each
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.)
3. for each circle, take the diameter and the circumference results and, on a calculator, divide the
circumference by the diameter (c/d)
4. show that, no matter the size of the circle, the result will always be close to 3.14
state that we have a special name for this c/d relationship; we call it pi
therefore the approximation for pi is 3.14
Discovery approach for determining the area of a parallelogram - ✔✔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 - ✔✔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
pf3

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Download MAT 136 Exam 2 | Exam Actual Questions and Answers Latest Updated 2024/2025 (Graded A+ and more Exams Mathematics in PDF only on Docsity!

MAT 136 Exam 2 | Exam Actual Questions and Answers Latest Updated

2024/2025 (Graded A+)

Discovery approach for determining the value of pi - ✔✔1. cut out 3-5 cardboard circles of various sizes, with he center marked on each

  1. 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.)
  2. for each circle, take the diameter and the circumference results and, on a calculator, divide the circumference by the diameter (c/d)
  3. show that, no matter the size of the circle, the result will always be close to 3. state that we have a special name for this c/d relationship; we call it pi therefore the approximation for pi is 3. Discovery approach for determining the area of a parallelogram - ✔✔1. cut out a cardboard parallelogram in which each base is labeled b
  4. in the interior of the parallelogram, draw the height (labeled h) with one endpoint at a parallelogram vertex
  5. cut out this height
  6. show the children that you have cut off a triangle
  7. move the triangle tot he other end of the figure
  8. state that you have now formed a rectangle with length=b and width= h
  9. 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 - ✔✔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.
  10. cut out several small "square inches"- little squares, each with length of 1 inch and width of 1 inch
  11. cover the index card rectangle with 15 of these square inches
  12. 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
  1. 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
  2. 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.) - ✔✔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 x b x h. Also, when you know only the lengths of the triangle's 3 sides: Heron's Formula: A = √s(s-a)(s-b)(s-c) where s = (a+b+c) / 2 The "Discovery Approach" for determining the area of a trapezoid. (The children already have learned to find the area of a parallelogram.) - ✔✔a) Cut out two cardboard non-isosceles trapezoids. b) On one of the trapezoids, label the bases a and b, and the height h. c) Rotate the second trapezoid and place it beside the first one, forming a parallelogram. (Label the bases on this second trapezoid so that a and b correspond to the a and b lengths shown on the first trapezoid.) d) State that the base of the resulting parallelogram has length a + b. e) Explain that since the area of a parallelogram equals base x height, we know that in our parallelogram, A = (a + b) x h.