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Sowder et al - Reconceptualizing Mathematics 3/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 28 / 65

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10
2/3 9/9 2/3 –/3 –/3 3/3 –/5 4/5 4/11 4/20
Total
28/65 (43.1%)

  • Instructions

    Reconceptualizing Mathematics for Elementary School Teachers, 3rd Edition, by Judith Sowder, Larry Sowder, and Susan Nickerson, published by W.H. Freeman, is founded on many years' research and studies of learning processes and mathematics education. Reconceptualizing Mathematics is designed for use in classrooms in which students take an active part in learning mathematics. This team of esteemed authors has written the only textbook of its kind to both incorporate aspects of student-centered learning into lessons and model the teaching that will be expected of their students. To this end, the authors provide worthwhile tasks, activities, and support for facilitating discussions.

    Quantitative reasoning and problem solving are recurring themes in Reconceptualizing Mathematics. The authors approach problem solving in a way that teaches students to understand the elements present in the situation and how they relate to each other.

    Macmillan Learning and WebAssign have partnered to deliver a comprehensive and flexible suite of resources for your math for teachers course. Combining the most widely used online homework platform with authoritative textbook content, Reconceptualizing Mathematics extends and enhances the classroom experience for instructors and students.

    Question 1 includes multiple parts for representing a fraction, requiring students to plot a number on the number line using WebAssign's NumberLine tool, and reflecting on the differences between the representations.

    Question 2 illustrates geometric images for pattern blocks to find values of other geometric shapes.

    Question 3 has a student choose the appropriate number line from a selection of multiple choice graphs for displaying distance between fractions and mixed numbers.

    Question 4 features answers presented as a comma-separated list, emphasizing order from least to greatest, for fractions and mixed numbers.

    Question 5 highlights listing fractions close to certain values in a comma-separated list but not necessarily in order (as in question #4), and allows for a word answer such as “None”.

    Question 6 features entering any equivalent answer in fraction format.

    Question 7 requires the answer in simplified fraction form, including variables and scientific notation.

    Question 8 exhibits a pull-down for selecting inequality or equal signs for comparing fractions.

    Question 9 enforces fraction and simplified format and allows the word answer of “DNE”.

    Question 10 showcases students entering table values strictly in fraction format, decimal form, and/or percent form. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

    The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 2/3 points  |  Previous Answers SowRecMath3 6.1.003. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 0/1 1/1
1/100 2/100 1/100
Total
2/3
 
(a)
Mark this representation of 4 feet of a licorice whip to show
1
4
 of the licorice whip.
WebAssign Plot

(b)
Mark
1
4
 on the number line.
Click and drag each point to its appropriate position. Some points might be unused.
Created with Raphaël 2.1.001234
Created with Raphaël 2.1.0

NO SOLUTION

Help
(c)
Explain the difference in parts (a) and (b) by referring to the unit.

This answer has not been graded yet.

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2. 9/9 points  |  Previous Answers SowRecMath3 6.1.006. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9
1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1
1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100
Total
9/9
 
Using pattern blocks, get the yellow hexagon, the red trapezoid, the blue rhombus, and the green triangle.
(a)
Let the
hexagon = 1.
 Give the value for each of the other three pieces. (Note: The = sign means "represent.")
trapezoid Correct: Your answer is correct. seenKey

1/2

 rhombus Correct: Your answer is correct. seenKey

1/3

 triangle Correct: Your answer is correct. seenKey

1/6
(b)
Let the
trapezoid = 1.
 Give the value for each of the other three pieces.
hexagon Correct: Your answer is correct. seenKey

2

 rhombus Correct: Your answer is correct. seenKey

2/3

 triangle Correct: Your answer is correct. seenKey

1/3
(c)
Let a pile of four
hexagons = 1.
 Give the value for each of the other three pieces.
trapezoid Correct: Your answer is correct. seenKey

1/8

 rhombus Correct: Your answer is correct. seenKey

1/12

 triangle Correct: Your answer is correct. seenKey

1/24


Solution or Explanation
(a)
hexagon = 1; trapezoid = 
1
2
; blue rhombus = 
1
3
; triangle = 
1
6
(b)
hexagon = 2; trapezoid = 1; blue rhombus =
2
3
; triangle =
1
3
(c)
hexagon =
1
4
; trapezoid =
1
8
; blue rhombus =
1
12
; triangle =
1
24
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3. 2/3 points  |  Previous Answers SowRecMath3 6.1.023. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 0/1 1/1
1/100 1/100 1/100
Total
2/3
 
Given a number line and only the points for the indicated fractions, accurately locate and label the points for the given numbers.
WebAssign Plot
(a)
0

(b)
1
3
4

(c)
2
1
6

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4. –/3 points SowRecMath3 6.2.011. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
Place the following fractions in order from least to greatest, giving careful explanations for how you knew their size relative to one other and benchmark numbers. (Enter your answers as comma-separated lists.)
(a)
4
5
, 
4
6
, 
5
9
, 
2
5
(b)
11
13
, 
7
9
, 
22
33
, 
5
7
(c)
31
25
, 
27
24
, 1
1
5
, 
23
20
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5. –/3 points SowRecMath3 6.2.S.002. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/100 0/100 0/100
Total
–/3
 
Enter each of the fractions into the appropriate answer blank. (Enter your answers as comma-separated lists. If any answer blanks are empty, enter NONE.)
5
7
 
27
52
 
12
36
 
32
30
 
11
24
 
2
3
 
3
8
 
40
45
close to 0
close to
1
2
close to 1
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6. 3/3 points  |  Previous Answers SowRecMath3 6.3.003. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 1/100
Total
3/3
 
Find one equivalent but non-identical fraction for each of the following fractions and verify on a number line that the two fractions are equivalent.
(a)
4
5
810​
Correct: Your answer is correct. webMathematica generated answer key
(b)
3
4
68​
Correct: Your answer is correct. webMathematica generated answer key
(c)
0
9
07​
Correct: Your answer is correct. webMathematica generated answer key


Solution or Explanation
Part (b) is shown for
3
4
 = 
6
8
.
 The fractions are equal if the distance is the same on both number lines; in this case, they have the same location on the number line. Both parts (a) and (c) would be similarly drawn (i.e., partition the interval into equal pieces).
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7. –/5 points SowRecMath3 6.3.005. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
Write each fraction in lowest terms. For efficiency's sake, try to find the greatest common factor of the numerator and denominator.
(a)
450
630
(b)
28 · 55 · 13
64 · 14 · 13
(c)
175
112
(d)
x2y5z9
xy6z5
(e)
(3.5 ✕ 107) ✕ (2.1 ✕ 108)
4.9 ✕ 104
✕ 1011
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8. 4/5 points  |  Previous Answers SowRecMath3 6.3.006. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 1/1 1/1 0/1 1/1
1/100 1/100 1/100 1/100 1/100
Total
4/5
 
For the following pairs, place <, >, or = between the two fractions. Use your knowledge of fraction size to complete this exercise.
(a)
2
4
  Correct: Your answer is correct. seenKey

>

  
2
5
(b)
103
102
  Correct: Your answer is correct. seenKey

>

  
77
78
(c)
8
9
  Correct: Your answer is correct. seenKey

=

  
32
36
(d)
8
9
  Incorrect: Your answer is incorrect. seenKey

<

  
9
10
(e)
11
14
  Correct: Your answer is correct. seenKey

>

  
31
64


Solution or Explanation
(a)
2
4
 > 
2
5
,
 because fourths are larger than fifths
(b)
103
102
 > 
77
78
,
 because
103
102
 > 1
 and
77
78
 < 1
(c)
8
9
 = 
32
36
,
 because
8
9
 = 
8 ✕ 4
9 ✕ 4
(d)
8
9
 < 
9
10
,
 because
8
9
 is 
1
9
 away from 1, but
9
10
 is 
1
10
 away from 1
(e)
11
14
 > 
31
64
,
 because
11
14
 > 
7
14
 = 
1
2
,
 but
31
64
 < 
32
64
 = 
1
2
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9. 4/11 points  |  Previous Answers SowRecMath3 6.4.002. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11
–/1 1/1 0/1 1/1 0/1 0/1 1/1 0/1 –/1 –/1 1/1
0/100 1/100 1/100 1/100 1/100 1/100 1/100 1/100 0/100 0/100 1/100
Total
4/11
 
Write the following decimals as fractions, if possible. Change to simplest form or lowest terms. (If not possible, enter DNE.)
(a)
0.875 =
(b)
0.43 = Correct: Your answer is correct. seenKey

43/100
(c)
91.333   = Incorrect: Your answer is incorrect. seenKey

274/3
(d)
1.3 = Correct: Your answer is correct. seenKey

13/10
(e)
0.9 = Incorrect: Your answer is incorrect. seenKey

1
(f)
0.93 = Incorrect: Your answer is incorrect. seenKey

14/15
(g)
0.53 = Correct: Your answer is correct. seenKey

53/99
(h)
0.053 = Incorrect: Your answer is incorrect. seenKey

53/990
(i)
4.76 =
(j)
8.094 =
(k)
0.1213141516171819110111112113114115   = Correct: Your answer is correct. seenKey

DNE
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10. 4/20 points  |  Previous Answers SowRecMath3 6.4.013. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1/1 1/1 1/1 0/1 1/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
1/100 1/100 1/100 1/100 1/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
4/20
 
Go to http://illuminations.nctm.org/, then search the Number and Operations Interactives for Fraction Models. Use this applet to complete the following table.
Fractions Decimal Percent
Correct: Your answer is correct. seenKey

1/4

 		0.25 Correct: Your answer is correct. seenKey

25

 %
11
10
 		Correct: Your answer is correct. seenKey

1.1

 		Incorrect: Your answer is incorrect. seenKey

110

 %
Correct: Your answer is correct. seenKey

33/10

 		3.3 %
19
20
 		%
250%
21
4
 		%
1.4 %
14
5
 		%
3.4 %
90%
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