Day 46: Fractions Quiz

6th Grade Math Standards: 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 . (In general, a/b + c/d = (ad + bc) /bd.)

The Learning Objective: Add and subtract fractions with like and unlike denominators

Quote of the Day: "One marker of a challenging personality is the tendency to describe oneself as a victim. The more people view themselves as victims, the easier it is for them to shirk personal responsibility for their circumstances.” – Ron Friedman

Question from Yesterday (as always from a student): "If the mistake of 2/7 + 2/7 = 4/14 is made it simplifies to 2/7. Will that always be the case if we fall for the wolf?"

Assessment: Checking the homework; circumventing the room; the weekly quiz; the quiz on fractions

Agenda:

1. Collect weekly quizzes
2. Check homework as students do various problems on their marker boards
3. Use decks of cards to play a game. The first card drawn is the numerator of the first fraction, the second card drawn is the denominator, the third is the next numerator, and the fourth card is the next denominator. Whether to add or subtract the fractions is determined by the color of the first card. If it is black, the students add and if it is red the students subtract. We used the marker boards to play this game. 
4. Pass out weekly quiz #8 

Glass-Half Full: There was a little debate about whether to push this quiz another day off or not. I am usually the one screaming to move forward and move faster. I felt with this particular quiz, that it was a fifth grade standard, and although some students still lacked consistency, all students to at least a small degree were demonstrating necessary skills and many students were at mastery. Sometimes we hit an iceberg. I feel as though that did not really happen today.

The two mistakes in the above picture to me are virtually correct. They were taken from two different quizzes and happened on several occasions. The students completed the wrong operation, but knew to keep the denominator the same, how to find a common denominator, and how to change the numerator. There is a red x, but I'm not concerned. On a side note, I wonder if I should be calling these problems correct. If these two problems were graded on a 4 point scale in stead of a black and white scale, they certainly would not earn 1's. To what degree in the real world are students being prepared better by having them go back and forth with addition and subtraction like this?

That said, there were still some mistakes that I have more concern over. This problem was something we spent considerable time on. Still some students came up with this answer, which is wrong on several levels. I'm going to continue to give feedback on this answer.

Regrets: The 8th question of the quiz (linked above) could have been worded better. The 7th question of the quiz was not covered well enough leading up to the quiz. We did work on finding a common denominator twice within a problem, but it was in a real-world context - this was just a mathematical context and students were forced to use order of operations which we have not covered to date.

The card game got a little confusing as I tried to implement mixed numbers with face cards. The trouble came when students got face cards twice or three times in a turn. They didn't know what fraction to use with what face card. They also were seeing face cards with improper fractions. Not that that was a problem for students that required a challenge, but for students that were struggling to reach the objective and not ready for such a challenge, it only dug them deeper into the hole. I think differentiating this game can be done if I were to use it again.

Link of the Day: I think this is interesting in terms of looking to spice up an exit ticket. I really like the idea of create a multiple choice question that will cause people to get the wrong answer (makes students think about potential mistakes in addition to finding the correct answer).