Following are three students' solutions to 9/16 of 48.
A) For each student, first evaluate the student's mathematical reasoning. Check whether the steps are mathematically correct or flawed, or indicate that you cannot tell.
B) Next, mark each student's work with "doesn't appear to understand," "may or may not understand," or "shows good understanding of" multiplication of fractions.
Jessica: 9/16 is 1/16 more than1/2. Half of 48 is 24, and 1/16 of 48 is 3, so 27.
A) Mathematical steps: choose one.
- Jessica's steps are mathematically correct.
- Jessica's steps are mathematically flawed.
- I cannot tell if Jessica's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one.
- Jessica doesn't appear to understand multiplication of fractions.
- Jessica may or may not understand multiplication of fractions.
- Jessica shows good understanding of multiplication of fractions.
C) If Jessica's steps are mathematically correct, use her way of thinking to solve 3/8 × 32. If they are not, explain how Jessica's reasoning is flawed.
Justin:

A) Mathematical steps: choose one.
- Justin's steps are mathematically correct.
- Justin's steps are mathematically flawed.
- I cannot tell if Justin's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one.
- Justin doesn't appear to understand multiplication of fractions.
- Justin may or may not understand multiplication of fractions.
- Justin shows good understanding of multiplication of fractions.

Stacy: 9/16 of 48? 9 × 16 = 144; 144 ÷ 48 = 3; and 9 × 3 = 27. So 9/16 of 48 is 27.
A) Mathematical steps: choose one. - Stacy's steps are mathematically correct. - Stacy's steps are mathematically flawed. - I cannot tell if Stacy's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one. - Stacy doesn't appear to understand multiplication of fractions. - Stacy may or may not understand multiplication of fractions. - Stacy shows good understanding of multiplication of fractions.

Question

Following are three students' solutions to 9/16 of 48.
A) For each student, first evaluate the student's mathematical reasoning. Check whether the steps are mathematically correct or flawed, or indicate that you cannot tell.
B) Next, mark each student's work with "doesn't appear to understand," "may or may not understand," or "shows good understanding of" multiplication of fractions.
Jessica: 9/16 is 1/16 more than1/2. Half of 48 is 24, and 1/16 of 48 is 3, so 27.
A) Mathematical steps: choose one.
- Jessica's steps are mathematically correct.
- Jessica's steps are mathematically flawed.
- I cannot tell if Jessica's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one.
- Jessica doesn't appear to understand multiplication of fractions.
- Jessica may or may not understand multiplication of fractions.
- Jessica shows good understanding of multiplication of fractions.
C) If Jessica's steps are mathematically correct, use her way of thinking to solve 3/8 × 32. If they are not, explain how Jessica's reasoning is flawed.
Justin:

A) Mathematical steps: choose one.
- Justin's steps are mathematically correct.
- Justin's steps are mathematically flawed.
- I cannot tell if Justin's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one.
- Justin doesn't appear to understand multiplication of fractions.
- Justin may or may not understand multiplication of fractions.
- Justin shows good understanding of multiplication of fractions.

Stacy: 9/16 of 48? 9 × 16 = 144; 144 ÷ 48 = 3; and 9 × 3 = 27. So 9/16 of 48 is 27.
A) Mathematical steps: choose one. - Stacy's steps are mathematically correct. - Stacy's steps are mathematically flawed. - I cannot tell if Stacy's steps are mathematically correct or flawed. 
B) Understanding multiplication of fractions: choose one. - Stacy doesn't appear to understand multiplication of fractions. - Stacy may or may not understand multiplication of fractions. - Stacy shows good understanding of multiplication of fractions.

Quizplus · Accepted Answer

The Answer of Following are three students' solutions to 9/16 of 48.
A) For each student, first evaluate the student's mathematical reasoning. Check whether the steps are mathematically correct or flawed, or indicate that you cannot tell.
B) Next, mark each student's work with "doesn't appear to understand," "may or may not understand," or "shows good understanding of" multiplication of fractions.
Jessica: 9/16 is 1/16 more than1/2. Half of 48 is 24, and 1/16 of 48 is 3, so 27.
A) Mathematical steps: choose one.
- Jessica's steps are mathematically correct.
- Jessica's steps are mathematically flawed.
- I cannot tell if Jessica's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one.
- Jessica doesn't appear to understand multiplication of fractions.
- Jessica may or may not understand multiplication of fractions.
- Jessica shows good understanding of multiplication of fractions.
C) If Jessica's steps are mathematically correct, use her way of thinking to solve 3/8 × 32. If they are not, explain how Jessica's reasoning is flawed.
Justin:

A) Mathematical steps: choose one.
- Justin's steps are mathematically correct.
- Justin's steps are mathematically flawed.
- I cannot tell if Justin's steps are mathematically correct or flawed.
B) Understanding multiplication of fractions: choose one.
- Justin doesn't appear to understand multiplication of fractions.
- Justin may or may not understand multiplication of fractions.
- Justin shows good understanding of multiplication of fractions.

Stacy: 9/16 of 48? 9 × 16 = 144; 144 ÷ 48 = 3; and 9 × 3 = 27. So 9/16 of 48 is 27.
A) Mathematical steps: choose one. - Stacy's steps are mathematically correct. - Stacy's steps are mathematically flawed. - I cannot tell if Stacy's steps are mathematically correct or flawed. 
B) Understanding multiplication of fractions: choose one. - Stacy doesn't appear to understand multiplication of fractions. - Stacy may or may not understand multiplication of fractions. - Stacy shows good understanding of multiplication of fractions.

Following Are Three Students' Solutions to 9/16 of 48