8.6 Analysis of Student Work This section contains a problem situation posed to middle school students involving their u

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8.6 Analysis of Student Work This section contains a problem situation posed to middle school students involving their understanding For this problem and its corresponding set of student solutions, complete the following of comparison fractions and decimals, and a set of student solutions to the problem. (a) Take 5 minutes to attempt to solve the problem yourself (without appealing to sources such as s textbook, or looking at the student solutions). (b) Examine each of the student solutions to the problem. In writing, indicate ways in which cach student was "on-track." Identify errors, misconceptions, or incorrect assumptions revealed in ca student's written work. (c) Determine whether each student's answer to the problem is correct. (d) Rate each student solution to the problem as high, medium, or low. (e) Compare and discuss with a classmate or in a small group the rating you gave each student solution (1) Now give each student solution a numerical score. First, determine the total number of points th and the criteria you used in deciding whether a solution was rated high, medium, or low you would assign to this problem, and then determine the number of points you would give for each student solution (for example, 5 out of 8 points). (g) Compare and discuss your numerical scores with a classmate or in a small group. (h) Construct at least two ideal solutions to the problem that employ different solution strategies PROBLEM SITUATION. One way to compare fractions is to convert them into decimals. For instanc comparing 3/8 and 2/5 can be done by first converting 3/8 to 0.375 and 2/5 to 0.4 and then comparing the decimals, Suppose that Mary is attempting to compare the fractions 9443/9444 and 9444/9445 using this method. When she converts each of these fractions to its decimal form, the number 0.9998941 is displayed on her calculator. Therefore, she concludes that the two fractions are equal. (a) Is Mary's conclusion correct? (b) If Mary's conclusion is correct, explain why it is correct. If Mary's conclusion is not correct, explain why it is incorrect, identify which fraction is larger, and explain why. Student Solution 1: (a) No, Many's conclusion is not correct. (b) It is incorrect because the two fractions. cannot be equal. 9443/9444 is larger becaus the pieces of the practions are larger. Student Solution 2: (a) yes.
? 3 correct because in both fractions you are using the number 44144, the Other number only changes by One & the place of qui change from denominator to numerator allowing the fraction to be equal yes Student Solution 3: (a) (b) Student Solution 4: (a) (b) because only Missing the arrest is in both instances. Their munchers mays be berger but in terms of what they measure Sups are the No, just because the calculator stakes they are, may noinnean they w the calculator may not have enough numbers 4444/94445 because it thas beggen denince 271
Student Solution 5: (a) (b) not exactly the calculator can only display so Places If the decimals many number were extended, one would be lazer than the other. 9443 9444 is the larger fraction b/c both denominators numerater are Smuller #t's than the other fraction.. out of 4 + 1/3, 4 is larger. 80 out of 9443 9444 9445 9443 Sy is larger 06. The denominators each tell the number of picces by which the whole is divided. The laugh the denominator, the smaller the prices. Because of this, &Y/9444 is bigger than yours, so Yams leaves a Smaller gap than ¼/qual4. So 94441/1445 is qatl quater than 944% 4444. eft's kind of like: 3/3 vs 3/4. 3/4 is greater yes Student Solution 6: (a) (b) Student Solution 7: (a) +
If many gris the same answer for each fraction then they are equal. If you compare each that fraction it shows the numerator is only one less than the denoming for for both fractions NO There are more pails to the whole in 9444 9443 is smaller by one part, 9445 9444 although they are very close in comparison when converting to decimals, 9444 is one larger 9445 and a bigger whote. No, her calculator is rounding the number of 9443/9444 is larger because ¼/4 is bigger than 1/5 no- This probably was not enough display digit on the calculator for the recto that would probably show the difference between the two. 9447/ 9445 is larger because there are more pieces filled in than 444. Student Solution 8: (0) Student Solution 9: (4) Student Solution 10: (₂)