Self-assessment/Reflection Questions
These questions are for your own use to assess and reflect on your own understanding of some central ideas of this unit. After determining your own answers, click "Show Solution" to read more information about the question and the alternative responses. You may also find it valuable to discuss these questions with your colleagues.
Item 1
Mr. Hamid asked his students to draw and shade the whole after he presented the following shaded region as 2/3:
Which of the following student drawings and reasoning should he accept as correct?
A. Because the denominator is 3, I divided the rectangle into thirds. Then I shaded 2 parts because the numerator is 2.
B. The rectangle is a third, so I need three of it to make a whole.
C. The rectangle is 2/3. I divided it into halves so that each half is 1/3, and I just need three of the 1/3's to make a whole.
D. I divided the shape into 3rds. Since the shape was 2/3, I added one more 3rd to make the whole.
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Item 2
Ms. Yoon presented her students the following shaded region as 3/2, and asked them to draw one whole:
One of her students, Arman, drew the following and said, "I divided the rectangle into two halves, so each is one-half. The numerator is 3, so I needed three of those halves."
Which of the following statement should Ms. Yoon accept as true about Arman's drawing and reasoning?
A. Arman correctly identified the unit fraction 1/2 and copied it (iterated it) three times to get the whole
B. Arman correctly identified the unit fraction 1/2 , but he should have iterated two times to get the whole.
C. Arman was incorrect. He should have divided the rectangle into three equal parts, because the rectangle is three one-halves, and then iterate the one-half by two to get the whole.
D. There is no way for Arman to find the whole because 3/2 is more than a whole.
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Item 3
Ms. Anita asked her students to locate the approximate position of the fraction 5/6 on a number line shown below:
Her students came up with different answers. Which of the following students' responses should she accept as correct?
A. Audrey: It should be after 4/4 because 5 is greater than 4 and 6 is greater than 4.
B. Binsar: It is between 2/4 and 3/4 because it is more than half.
C. Celia: You cannot find it in this number line because there are only fourths and the fraction is in sixths
D. Diego: It is between 3/4 and 4/4 because 5/6 is almost a whole and closer to a whole than 3/4 is.
Show Solution
Item 1
Mr. Hamid asked his students to draw and shade the whole after he presented the following shaded region as 2/3:
Which of the following student drawings and reasoning should he accept as correct?
A. Because the denominator is 3, I divided the rectangle into thirds. Then I shaded 2 parts because the numerator is 2.
B. The rectangle is a third, so I need three of it to make a whole.
C. The rectangle is 2/3. I divided it into halves so that each half is 1/3, and I just need three of the 1/3's to make a whole.
D. I divided the shape into 3rds. Since the shape was 2/3, I added one more 3rd to make the whole.
Show Solution
Item 2
Ms. Yoon presented her students the following shaded region as 3/2, and asked them to draw one whole:
One of her students, Arman, drew the following and said, "I divided the rectangle into two halves, so each is one-half. The numerator is 3, so I needed three of those halves."
Which of the following statement should Ms. Yoon accept as true about Arman's drawing and reasoning?
A. Arman correctly identified the unit fraction 1/2 and copied it (iterated it) three times to get the whole
B. Arman correctly identified the unit fraction 1/2 , but he should have iterated two times to get the whole.
C. Arman was incorrect. He should have divided the rectangle into three equal parts, because the rectangle is three one-halves, and then iterate the one-half by two to get the whole.
D. There is no way for Arman to find the whole because 3/2 is more than a whole.
Show Solution
Item 3
Ms. Anita asked her students to locate the approximate position of the fraction 5/6 on a number line shown below:
Her students came up with different answers. Which of the following students' responses should she accept as correct?
A. Audrey: It should be after 4/4 because 5 is greater than 4 and 6 is greater than 4.
B. Binsar: It is between 2/4 and 3/4 because it is more than half.
C. Celia: You cannot find it in this number line because there are only fourths and the fraction is in sixths
D. Diego: It is between 3/4 and 4/4 because 5/6 is almost a whole and closer to a whole than 3/4 is.
Show Solution