Today my students had a sub so we worked on a math worksheet that had to do with fractions. The students went through and did the worksheet on their own and then we went over the answers. The work is done individually but the students are allowed to ask for help. I used the work of a students prior to their corrections and it was a student who did no ask for any help on the assignment. There was no lesson taught before the worksheet it is all from prior knowledge of fractions.
The front side which was labeled Max and Min to me seemed the least effective. The students Sarah seemed to go through the exercise with easy but looking at it now, after I have seen the answers, I know it was not that easy. Problem 1. asks the students to tell whether the shaded part of the shape is ½ of it and then explain why. The second drawing, b), looks to almost everyone to represent ½ of the square but according to the answer key there is a missing part of the shaded top right square that makes it unshaded and therefore not entirely half. This question was a trick question, no student in the class realized this and neither did myself or the substitute teacher. The last drawing which was f), most students and myself saw as not ½, the parts do not look equal in anyway but the answer key said that they are technically half. I think that this question on the worksheet was horribly designed and should not be used. Sarah and many of her classmates understand the representation of ½ but now have to deal with these tricks of poor picture representation and feel tricked afterward.
The other side of the worksheet did a much better job of portraying portions of a shape.
Besides the horrible design Sarah did a great job, one of the problems I would like to point out are on the first side question 5. For question 5 Sarah was asked how many kittens were left after Jonathan sold 7, we learned in the previous problem that Jonathan sold 1/5 of his kittens and that 4/5 of the kittens were left. Sarah saw that 1/5 of the kittens was equal to 7 and that the total number of kittens was 5/5; 7 X 5 = 35. Sarah ended up writing that answer as 35 but the question did not ask for the total of kittens, it asked how many were left, 35 - 7 = 28. I think a way to help Sarah with this problem is first asking her to tell you what she did wrong, most of the time these students realize very quickly and can tell you they just forgot to subtract. I am thinking it could be possible that Sarah just assumed because she had to do the multiplication of 7 X 5 that she was all done and that she did not even think to look back at the question. If this is the case I think giving Sarah more problems like this one, story problems that have more than just one operation/step to them will help her to get more familiar with them and remind her to check what the question is actually answering. Knowing Sarah I predict she will see what she did wrong and when pointed out will remember to look back on questions, at least for a little while. I believe it would be best to help her through this stage, that I feel a lot of students go through, and getting her to check for the real question, look more into the question for what they are answering will get across on a deeper level if we give her more practice with the help of someone. Eventually she will catch onto this idea and it will stick with her forever.
These are actually great questions (on the worksheet) but they really resemble high level tasks more than simple answers that can be filled in on a worksheet. Hence, try to think about the structure of the lesson itself (this type of worksheet might not be conducive to independent practice, but would be conducive to a whole classroom discussion).
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