Mathematics for Elementary Teachers with Activities, Loose-Leaf Version Plus MyLab Math -- Access Card Package (5th Edition)
5th Edition
ISBN: 9780134800196
Author: Sybilla Beckmann
Publisher: PEARSON
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Chapter 4.5, Problem 8P
AThe exchanges that follow are taken from Developing Children ‘s Understanding of the Rational Numbers: A New Model and an Experimental Curriculum by Joan Moss and Robbie Case [53, p. 135]. “Experimental Si” and “Experimental S3” are two of the fourth-grade students who participated in an experimental curriculum described in the article.*
*From Journal for Research in Mathematics Education, Vol. 30, No. 2, 122—147 by Robbie Case and Joan Moss. Copyright© 1999 by National Council for Teachers of Mathematics (NCTM). Used by permission of National Council for Teachers of Mathematics (NCTM).
Experimenter: What is 65% of 160?
Experimental S1: Fifty percent (of 160) is 80. I figure 10%, which would be 16. Then I divided by 2, which is 8 (5%) then 16 plus 8 um.. . 24. Then I do 80 plus 24, which would be 104.
For each of the two students’ responses, write strings of equations that correspond to the student’s method for calculating 65% of 160. State which properties of arithmetic were used and where. (Be specific.)
Write your string of equations in the following form:
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☐
Part 1:
A linear electrical load draws 1₁ A at a 0.72 lagging power factor. See the table to find ½ for your
student ID. When a capacitor is connected, the line current dropped to 122 A and the power factor
improved to 0.98 lagging. Supply frequency is 50 Hz.
a. Let the current drawn from the source before and after introduction of the capacitor be 1₁ and I₂
respectively. Take the source voltage as the reference and express 11 and 12 as vector
quantities in polar form.
b. Obtain the capacitor current, Ic = 12 − I₁, graphically as well as using complex number
manipulation. Compare the results.
c. Express the waveforms of the source current before (į (t)) and after (i2(t)) introduction of the
capacitor in the form Im sin(2лft + 0). Hand sketch them on the same graph. Clearly label your
plots.
d. Analytically solve i̟2(t) − i₁ (t) using the theories of trigonometry to obtain the capacitor current
in the form, ic(t) = Icm sin(2πft + 0c). Compare the result with the result in Part b.
= x³, y = 8, x = 0.
Let R be the region bounded by the curves y = x³
1. Sketch the region and find the area. Write your answer in simplest fractional form.
2. Sketch the solid you obtain by rotating the region R about the x-axis.
3. Find the volume of the solid obtained by rotating the region R about the x-axis
using the disk/washer method. Write the formula you are using. Write your answer
in terms of π. Draw the approximating rectangle that you rotate.
4. Find the volume of the solid obtained by rotating the region R about the x-axis
using the shell method. Write the formula you are using. Write your answer in
terms of π. Draw the approximating rectangle that you rotate.
5. Which method did you find easier and why? [There is no wrong answer for what
you find easier, but explain.]
6. Sketch the solid you obtain by rotating the region R about the y-axis.
7. Find the volume of the solid obtained by rotating the region R about the y-axis
using the disk/washer method. Write the formula…
Chapter 4 Solutions
Mathematics for Elementary Teachers with Activities, Loose-Leaf Version Plus MyLab Math -- Access Card Package (5th Edition)
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