https://padlet.com/cricellis/brrzxpdo7ha5 Fractions en-us 2019-01-29 16:35:02 UTC 2025-11-29 18:41:51 UTC hello@padlet.com cricellis https://padlet.com/cricellis/brrzxpdo7ha5/wish/325480951 This article shows why we invert and multiply when dividing by fractions. The problem is that to understand the reason for the inversion, students must have a substantial background knowledge of multiplying fractions. Students in the middle school level can struggle to grasp this understanding.]]> 2019-01-29 16:42:44 UTC https://padlet.com/cricellis/brrzxpdo7ha5/wish/325480951 cricellis https://padlet.com/cricellis/brrzxpdo7ha5/wish/325894946 I feel that the main reason that we should not teach students to invert and multiply when dividing fractions is because it is so procedural. Many teachers use the invert and multiply concept, myself included sometimes, to bypass the actual meaning of dividing fractions and give students a simple procedure that will lead them to the correct answer. The problem is that students do not actually understand what it means to invert and multiply or why we do it in the first place. Barlow (2008) mentions an activity where students were asked to create a word problem for the expression 6 divided by 1/2. This proved to be very difficult for the students because they don't understand what it means to divide by 1/2. Many students created scenarios that actually described the expression 6/2. I believe students need to understand division by fractions in order to be successful in this activity, but if we keep teaching through procedure, "invert then multiply", students will not truly understand. Clarke (2012) mentions that we need to "give a greater emphasis to the meaning of fractions than on procedures for manipulating them" (p.374). This further extends my assertion that we need to avoid teaching procedures while teaching students the four operations involving fractions. "The ultimate goal should be to develop students who can reason proportionally" (Clarke, 2012, p.374).]]> 2019-01-30 15:58:36 UTC https://padlet.com/cricellis/brrzxpdo7ha5/wish/325894946 cricellis https://padlet.com/cricellis/brrzxpdo7ha5/wish/325908621 One concept that can be difficult for students to understand is how to compare the size of fractions with different denominators. Below is an activity that gives students the opportunity to compare fractions by lining them up on a number line. I have also included two fractions that are actually equivalent to see if students recognize that they should be in the same place on the number line. 

Prompt: Place the following fractions on the number line in order from smallest to largest. 

3/4, 1/2, 1/8, 2/8, 11/12, 9/12, 3/2, 1/16]]> 2019-01-30 16:22:02 UTC https://padlet.com/cricellis/brrzxpdo7ha5/wish/325908621 cricellis https://padlet.com/cricellis/brrzxpdo7ha5/wish/325917183 One concept that I have also found is difficult for students to understand is the concept of being more or less than 1. Sometimes when students see fractions, they immediately think that it must be less that one. At the high school level, this is especially clear when students are trying to identify vertical shrinks and stretches to functions. Typically students understand that if a function is being multiplied by 3 it will stretch and become bigger. Likewise, if you show them that a function is being multiplied by 1/3, they understand that the graph will shrink. The problem is when you ask them what happens if you multiply a function by something like 5/3. Many students will see the function being multiplied by a fraction and immediately think it will shrink. This shows that students do not understand what it means for a fraction to be bigger or smaller than 1. The link below shows multiple fraction activities that are great. In particular the activity labeled "More or less than one" will help students to develop this number sense. ]]> 2019-01-30 16:36:05 UTC https://padlet.com/cricellis/brrzxpdo7ha5/wish/325917183 cricellis https://padlet.com/cricellis/brrzxpdo7ha5/wish/325922290 It is very important to show students how the four operations of fractions can be applied to the real world. One aspect of real like where fractions play a huge role is in cooking. Below is an activity that gets students thinking about when to use addition, subtraction, multiplication and division of fractions as well as providing them with opportunities to connect their understanding to the real world. 

Activity:
In problems 1-4 explain whether you need addition, subtraction, multiplication or division to solve the problem. 
1. Sarah needs 1/3 cup of flour to make 1 apple pie. If she makes 9 apple pies, how many cups of flour would Sarah need?

2. A soup kitchen had 6 1/2 gallons of soup at the start of the day. They had 2 1/10 gallons of soup left by the end of the day. How many gallons of soup did they use during the day?

3. A smoothie calls for 4/6 of a peach, 1/2 of a banana, and 2/6 of a kiwi. how much fruit will be in the smoothie?

4. Ryan has 8 apples and cut them all in thirds. How many apple pieces does Ryan have?

Now it is your turn! Develop a word problem for each operation of fractions (addition, subtraction, multiplication, and division).]]> 2019-01-30 16:45:42 UTC https://padlet.com/cricellis/brrzxpdo7ha5/wish/325922290