Operations with Decimals and Fractions
This week we continued to explore several strategies outlined in our textbook Making Math Meaningful (Small, 2012). Specifically, strategies regarding operations with decimals and fractions, and understanding the relationship between the two.
It's easier, in my opinion, to start with fractions. There are several strategies for operations (multiplication, division, addition, subtraction) involving fractions that were presented in class. In terms, again, of classroom application I would begin with addition/subtraction since that would help develop an understanding of what fractions are before continuing onto multiplication/division. The most effective way, I thought, of explaining addition/subtraction of fractions was the visual representation we explored. It compares the fractions to a whole so students can estimate whether the result will be less than or greater than one. Using lego or strips of paper (which is what we did) you can add fractions with different denominators to get a sense of what they're worth. For multiplication and division of fractions students can break the question down into several smaller questions as demonstrated below:
We also looked at more advanced questions like the one below:
If the following image represents 1/4, what does the whole look like?
The answer to which is:
The above questions requires students to 'think outside the box' and apply their knowledge of fractions. This would be a good question for students who are accelerating faster at math than the rest of the class and are looking for more challenging questions and/or in higher grades as an application question.
Once students have a solid understanding of fractions, they will be better prepared to examine decimals. Decimals, in my opinion, are challenging; there's really no other way to put it. There are several tricks one can employ in order to faster solve the questions, but when showing them to students make sure they are aware why the 'trick' works. So, for example, if you wanted to solve the question 12x3.7 a student can 'pretend' the decimal isn't there which makes the question easier to solve, and then bring the decimal back into the answer; as demonstrated below (Small, 293):
The textbook, Making Math Meaningful, has other excellent strategies to help students grasp fractions, decimals, and the relationships between the two so I would highly recommend reviewing the text while making lesson plans for these concepts.
In terms of curriculum connections these concepts are part of number sense and numeration for grades 4-8 with increasingly more complicated fractions and longer decimals as students progress.
It's easier, in my opinion, to start with fractions. There are several strategies for operations (multiplication, division, addition, subtraction) involving fractions that were presented in class. In terms, again, of classroom application I would begin with addition/subtraction since that would help develop an understanding of what fractions are before continuing onto multiplication/division. The most effective way, I thought, of explaining addition/subtraction of fractions was the visual representation we explored. It compares the fractions to a whole so students can estimate whether the result will be less than or greater than one. Using lego or strips of paper (which is what we did) you can add fractions with different denominators to get a sense of what they're worth. For multiplication and division of fractions students can break the question down into several smaller questions as demonstrated below:
 |
| MacCuish, Megan (2015). [Image]. |
We also looked at more advanced questions like the one below:
If the following image represents 1/4, what does the whole look like?
 |
| MacCuish, Megan (2015). [Image] |
 |
| MacCuish, Megan (2015). [Image] |
 |
| MacCuish, Megan (2015). [Image] |
Once students have a solid understanding of fractions, they will be better prepared to examine decimals. Decimals, in my opinion, are challenging; there's really no other way to put it. There are several tricks one can employ in order to faster solve the questions, but when showing them to students make sure they are aware why the 'trick' works. So, for example, if you wanted to solve the question 12x3.7 a student can 'pretend' the decimal isn't there which makes the question easier to solve, and then bring the decimal back into the answer; as demonstrated below (Small, 293):
 |
| MacCuish, Megan (2015). [Image]. |
The textbook, Making Math Meaningful, has other excellent strategies to help students grasp fractions, decimals, and the relationships between the two so I would highly recommend reviewing the text while making lesson plans for these concepts.
In terms of curriculum connections these concepts are part of number sense and numeration for grades 4-8 with increasingly more complicated fractions and longer decimals as students progress.
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