For 3/21 - Response to Let's Be Rational Math Background
Comment on a section of the LBR Math Background that was helpful to you. Describe the content and format of the section. Explain how it would be helpful in preparing you to teach the concept to students.
Reading the Developing a Multiplication Algorithm, the Number line Model seemd most useful for me. When multiplying fractions, one could draw a line and partition it by the first fraction amount. In order to break it into (or mulitply) by another fraction, one could break or repartitiion the already existing partitioned line into the second fraction amounts. The product of the numerator gives the numerator of the product and the product of the denominator gives the denominator of the product. This section would be helpful in visualizing even large numerators and denonmorators. As a teacher I would use this model often because of it's simplicity. Students can create number lines out of anything or anywhere. Breaking down a line is an easy visual for students to see equal parts within a set of other parts.
ReplyDeleteI agree that using a number line is a versatile tool in teaching students about breaking down numbers. I think this activity would also coincide with comparing and ordering decimal fractions. There are several misconceptions that students often struggle with when learning about ragged decimals. For instance, using a number line to have student put decimals in order and support their answer (like in activity 17.9).
DeleteI found this very helpful as well, Katherine. It is hard for me to work with fractions, but as I am learning this and seeing how to teach it, it is making more sense. What has really helped me from this section you wrote about is the focus on thinking about what the question is asking (whether grouping or sharing), and then making a diagram of the problem. The visuals suggested/provided have helped me enormously in thinking about fraction and decimal problems! It is much easier to see what is meant by partitioning a fraction when I can see the rectangle all divided up and shaded in with all the parts labeled. Also, it is so true that the way the question is asked is a key to how to solve it, so we need to be very clear when we pose a problem to students.
ReplyDeleteI found that the explanation/examples for division as a grouping situation (p. 24 and more on p. 25) helped me think about what dividing by a fraction actually means. The example given...9 divided by 1/3 can be rephrased as how many 1/3's are there in 9. Start with 3 1/3's equals 1; you have nine of these, so 3 x 9 is the answer. I liked too how this reasoning could then be extended to 2/3, 3/3, and 4/3 (p. 26).
ReplyDeleteI agree that the visuals, the language, and the explanations in this section are really helpful in explaining how division works with fractions. The diagrams shown are a great representation of what students may think and how we should help them think! It is also a good reminder to myself to be mindful of the language and framework of the questions I am asking of my students.
ReplyDeleteI found the reading very relevant to what has been being taught and retaught in the sixth grade. We have been using a lot of number lines on p 16, the area models on p 18, and breaking numbers into more workable numbers to multiply as on p 20. I have found the questions being asked to lead students and being patient to allow students to have time to think or have to experience persistence is important. I would like to learn more about instructing students to have better table discussions with their math. Students are very good at trying to get me to help before they fully think and I am finding that students are continuing to think that math is just about answers or calculations and not more fully understanding the math. This article is very important for new teachers to see examples of explanations that are not simply a Kahn video of the algorithm!
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