The first strategy that I used was division. As a middle school math teacher, I teach basic operations with word problems. Division is a very fast and simple approach to this problem. The second strategy uses manipulatives to make groups of 8. This represents 1 pencil per student. Each student would get 3 pencils since there are 3 groups of 8. I feel that this strategy could be useful in elementary school to introduce basic operations and for the visual learners. The third strategy uses a double number line. I personally do not like this strategy but it is in the 7th grade curriculum. I have also seen it used in elementary school. The double number line is intended to introduce equivalent fractions and unit rates. The double number line begins with your starting information which in this case is 24 pencils and 8 students. It does not matter which unit goes on top. From there I continued to divide the number of pencils and the number of students by 2 until I reached the solution. All 3 strategies successfully led to the same solution.
I agree with your approach. When ever possible I also think word problems should be broken down into basic operations. I like your second strategy. That strategy would allow students to know how and why they have to divide to get the answer and would appeal to students who are more visual learners as you mentioned. I had not heard of the third strategy until I read it in your blog post. I do like the strategy. I also feel that it is not necessary since the other two strategies are so strong, however I admit I am still knew to it and I wouldn't want to limit myself in any way. If that strategy is useful even just one of my students than it is worth me learning that strategy.
ReplyDeleteI also like the idea of using manipulatives. For my science classes, I have bins of junk (I call them "makerspace boxes") on my tables - they include play doh, pipe cleaners, etc that students can use if they are more visual learners. We also use them for set activities - like doubling mass and looking at the center of mass between two celestial play doh bodies and creating stick figures to put on fault block diagrams to find the hanging and foot wall. Perhaps "makerspace boxes" of basic manipulatives could be useful in math so for those students who are more visual or kinesthetic they have the option of using the tools that help them. I also had to look up a double number line and it seems rather confusing to me - I could see them being useful for students to understand percents of percents which is a thing I see high schoolers struggle with. Do you think it would be useful in that situation?
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