These last few classes we have dived in to the hated world of fractions. As a student I went to Kumon. After hundreds of multiplying and dividing fractions I just learned the algorithm for simplifying when multiplying fractions and never really understood the core ideas of fractions.
For me, the fractions kit was the most useful activity we have done since September. Not only do we create something ourselves that we can bring in every classroom we go to, we learned how it can be applied in the classroom. With most other subjects we learn one or the other. In class we learned multiple types of questions that we could use the fraction kits to help solve. We also learned how to modify it for the different grades (figure one) and how complicated the fractions are. We discussed what fractions students need to know for different grades. This helps teachers not overwhelm students and having them do more cutting than they need to. It helps kinesthetic and visual learners stay engaged. I was also excited when we got to use them in class the next week. It was something I made and I understood which made it more exciting to use.
For me, the fractions kit was the most useful activity we have done since September. Not only do we create something ourselves that we can bring in every classroom we go to, we learned how it can be applied in the classroom. With most other subjects we learn one or the other. In class we learned multiple types of questions that we could use the fraction kits to help solve. We also learned how to modify it for the different grades (figure one) and how complicated the fractions are. We discussed what fractions students need to know for different grades. This helps teachers not overwhelm students and having them do more cutting than they need to. It helps kinesthetic and visual learners stay engaged. I was also excited when we got to use them in class the next week. It was something I made and I understood which made it more exciting to use.
The other useful part of the fraction kits if how our professor made a large class set with magnets to put on the board (figure two). She made her out of foam which I prefer over the construction paper. For a child that has ADD or ADHD the foam ones might be better for fidgeting and are less likely to rip.
I have been tutoring multiple students for the math competency exam. Fractions are something that most people don’t get. There is one type of question that gives students ¾ of the students and they have to find out what the ¼ is. This is a question type that most of my students struggle with. I have tried many ways of explaining this question to students and they really haven’t had a deep understanding of the question. During one of my tutoring sessions I thought about bringing the fraction kit and seeing if using manipulates would assist my student. By breaking the parts of the questions up using the pieces of the fraction chart, it helped the student visualize the problem and hold the pieces. Allowing the student to rearrange the pieces the way they were visualizing it in the head allowed them to see where they were making a mistake. They could learn to visualize it in a different way and understand the question and answer.
I have been tutoring multiple students for the math competency exam. Fractions are something that most people don’t get. There is one type of question that gives students ¾ of the students and they have to find out what the ¼ is. This is a question type that most of my students struggle with. I have tried many ways of explaining this question to students and they really haven’t had a deep understanding of the question. During one of my tutoring sessions I thought about bringing the fraction kit and seeing if using manipulates would assist my student. By breaking the parts of the questions up using the pieces of the fraction chart, it helped the student visualize the problem and hold the pieces. Allowing the student to rearrange the pieces the way they were visualizing it in the head allowed them to see where they were making a mistake. They could learn to visualize it in a different way and understand the question and answer.
We used our fraction kits to solve problems or various types. It took me a second to figure out how to show the question using the fraction kits. I knew the answer immediately, because I was so used to doing these kinds of questions in my head. It was great to really break these kinds of questions down into simple steps. This way I knew how to teach them and explain them to my future students.
When we brought our fraction kits back for the next class we used number lines to order fractions from least to greatest and demonstrate how you know that. We started out by drawing out the number lines and placing all of the numbers with marker. We then used our fraction kits to make each fraction using the pieces. It started out easy, but as we put more and more fractions down we traded different pieces of fractions. We were using our understanding of equivalent fractions. Originally, we were switching equivalent fractions because we wanted to keep all of the colours the same or we wanted to condense a fraction to make room for other fractions. For me, it did not register that we were using equivalent fractions, we measured the size of the pieces that we were switching to see if they were equivalent (figure three). I think that would be an interesting way to each equivalent fractions to students. We didn’t realize what we were doing and I discovered this after the fact. This can help with addition and subtraction of fractions. Having students do this to rather than multiplying and teaching students about making the denominators similar might make more sense to students.
When we brought our fraction kits back for the next class we used number lines to order fractions from least to greatest and demonstrate how you know that. We started out by drawing out the number lines and placing all of the numbers with marker. We then used our fraction kits to make each fraction using the pieces. It started out easy, but as we put more and more fractions down we traded different pieces of fractions. We were using our understanding of equivalent fractions. Originally, we were switching equivalent fractions because we wanted to keep all of the colours the same or we wanted to condense a fraction to make room for other fractions. For me, it did not register that we were using equivalent fractions, we measured the size of the pieces that we were switching to see if they were equivalent (figure three). I think that would be an interesting way to each equivalent fractions to students. We didn’t realize what we were doing and I discovered this after the fact. This can help with addition and subtraction of fractions. Having students do this to rather than multiplying and teaching students about making the denominators similar might make more sense to students.
In our textbooks it says “The rectangular pizza pieces allow students to develop images of the sizes of different pieces (fractions) as well as the relationship between pieces”. This was something I did not realize. By starting with a whole for each of the fractions and then cutting them up might help the students understand the parts of a whole. Students might also understand a little better how all of the fractions relate to each other. By folding 1/3 first and then folding 1/6 and understanding the if you divide it in half you get the later fraction.
Below is a link on how to make fraction kits with your own class. They are extremely useful!
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