# Let s think about how to multiply and divide fractions by fractions!

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3 fractions, and properties of multiplication and division that they learned previously. By examining several calculation methods that are presented, students can think about a method that can be applied any time. Students will confirm whether this method can work for calculations involving fractions that cannot be expressed as decimals and understand that it can be done. I wonder if we can change the calculation to fraction whole number? There are several ways to calculate but all of them can be transformed to a math sentence that multiplies by the inverse fraction of the divisor. I wonder if we can use the same method for fractions that cannot be expressed as decimals. Phase : Let summarize what we can do with numbers! 1 st lesson: Let s think about how to multiply a whole number by a fraction and divide a whole number by a fraction! (E) Students will think about how to calculate whole number x fraction and whole number fraction by going over what we know about multiplication and division calculations. (F) Students will feel a sense of accomplishment for being able to calculate all of the different the kinds of numbers they learned with the four operations. We have not learned how to multiply a whole number by a fraction and divide a whole number by a fraction, so let s think about those calculations! If we change the whole numbers into fractions we can do the calculation just like we did with fraction x fraction and fraction fraction. Now we can calculations involving the four operations with whole numbers, decimals, and fractions. 2 nd lesson: By reviewing our math textbooks from 1 st to 6 th grades, let s summarize what we can do with numbers! (G) Students will understand that when we use numbers, we can express quantities of objects, express order of objects, measure quantities, and calculate. We can count the number of objects. We can measure length, weight, etc. We can express ratio. We can calculate

5 20 5 = 4 = 4 (C) Using a property of division (when you multiply both the dividend and the divisor by the same number, the quotients will remain the same) change the division into whole number x whole number to pursue the calculation = 12 = 12 = 4 Present ideas about how to calculate and understand each others ideas. (B) and (C) above use the same property of division (A) might not work with different fractions. For example: Check to see if ideas from (A) to (C). Method (B) works well = = 15 8 can be solved using the Method (B) works well. If I write the calculation process clearly: 4 2 (! 5) (! 5) = 2 = 5 4 (4! 2) Method (C) works well = 15 8 = 15 8 Method (C) works well if I write the calculation process clearly: = (! 5) (2! 4) = (! 5) (2! 4) Method (A) works well, too. If we can find a multiple of the numerator and the 2 denominator 4 and 5 can do: 4 = 6 8 = (0 2) = 5 (40 5) it works. First we Then, do the We can write the calculation process of (A) more clearly: (! 2! 5) (4! 2! 5) 2 5 = (! 5) (4! 2) encourage them by saying What did we do when we did the calculation of fraction x fraction? By helping students recall this, you are helping them to think and come up with at least one idea that uses the property of division. Can students understand the solution methods presented by their peers? Can they see the similarities and differences in the ideas by comparing them to their own ideas? If the students never come up with an idea for exploring other fractions besides 20 5, ask them Do you think the methods we looked at today always work for any fraction fraction problem? Are they actively investigating whether the methods they find during this lesson can be used for other fraction fraction calculations? When a student presents method (B), if the student did not clearly explain the process of calculation by using a non-described number such as 15 of When we write the calculation process of (B), (C), and (A) clearly, all of the math 15 8, the teacher should ask a question such as Where does this 15 come from? and clarify that the 15 is x 5. Also, make sure to record it on the blackboard. Are students actively looking for a common calculation procedure by looking at mathematical expressions (A) to (C)? If students are having difficulty finding the common calculation procedure, the teacher will ask Are there similarities in the calculation procedures when we rewrote them more clearly? If students can t see the part about inverting the denominator and the numerator of the divisor and then multiplying the dividend, ask Where can you find the in the first math expression? to help them notice the idea. If the fractions involved in the second problem, such as 4 2 5, can be expressed as decimals ask the students, Can we divide fractions without changing them into decimals? 5

6 sentences involve multiplication by the inverse of 2 5. Journals writing I understand that if we can change the problem into a calculation that we learned before, we can solve it. I think that the properties of division are very important. I was surprised that we can do the problem using method (A). I felt happy that we found the calculation method for fraction fraction 6

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