9

Use a piece of paper as your whole. To teach $3/2 + 4/3$ do the following. Give each child/group of children 6 pieces of paper. One piece of paper should be left as a whole - the students can write 1 whole on the paper. Have the students fold 2 of the pieces in half lengthwise, label each half as $1/2$, and cut out the halves. Have the students fold 2 ...


8

The student who designed this problem wasn't thinking about the different wholes. IN your students problem, there are 3 different wholes. Anna's flowers - The whole is 5 flowers and $\frac{4}{5}$ are daffodils Beatrice's flowers The whole is 3 flowers and $\frac{2}{3}$ are daffodils The flowers of Anna and Beatrice combined. The whold is 8 flowers and $\...


7

Lots of different fractions all represent the same rational number. So if someone hands you two fractions, it can be difficult to tell if they represent the same number or not. For instance, you might need to do some work to determine if the fractions $\frac{18399}{30665}$ and $\frac{20991}{34985}$ represent the same number. However, all rational numbers ...


7

The word you are looking for is mediant. The mediant of two fractions $\frac{a}{c}$ and $\frac{b}{d}$ is $\frac{a+b}{c+d}$. According to Wikipedia, It is sometimes called the freshman sum, as it is a common mistake in the early stages of learning about addition of fractions. Teachers often do this in grading papers. For example, a test has two parts: the ...


5

...his argument is correct but I want to teach him that $300=1\times 200+100$ and reminder is $100$. But in previous solution its reminder is $1$ ($3=1\times 2+1$). How can I explain this without fooling or tricking him? If I understood it correctly, the question is how to explain the fact that equivalent fractions leave different remainders. Well, you could ...


4

Suggestion: Do not bother having students do calculations with two fractions until they can do a comparable operation with a fraction and a whole number. Example: Before teaching, say, $\frac{3}{2}-\frac{4}{3}=\_\_$, ensure they can answer something like $4 - \frac{1}{5}=\_\_$. Make sure all students can draw that on a number line and with area diagrams. ...


4

I like the cutting paper approach the best because it is cheap and easy, and it forces students to confront basic fractions by folding/cutting them out. But here’s another thought... For you to demonstrate: have several clear-plastic, cylindrical cups, each marked off in different fractions of a whole (maybe start with 1/2’s, 1/3’s, 1/4’s, 1/6’s, 1/8’s, 1/...


3

The student was conflating the sum $$\frac45+\frac23$$ and the weighted average (where the weights account for group-size differences) $$\left(\frac{\color{#00F}5}{\color{#180}{5+3}}\right)\frac45+\left(\frac{\color{#00F}3}{\color{#180}{5+3}}\right)\frac23\\=\frac{4+2}{5+3}$$ of the two given fractions/rates. Clearly, the sum of two positive fractions is ...


3

I don't know for sure. But I think a part of the problem comes from notation. I don't know how you've approached math education, but I find that students are often times confused by the distinction and overlap between the concept of division and the concept of fractions. I think the cause of this confusion is found in the notation we use and the order in ...


2

Admittedly, a fraction has twice as many components as (say) an integer, and these components greatly increase the numbers of ways they might interact, in a combinatorial fashion. Consider an arbitrary binary operation on integers: $a \odot b$. With only two components to the arguments, there is only a single relation that needs consideration: the one ...


2

What property of fractions or addition of fractions could they be misunderstanding, and how would you explain to the student where they have gone wrong so that they don't repeat this in the future? [Emphasis added.] Short Answer Fractions are numbers and they behave like numbers when we do operations on them. Many students never learn this. You (and the ...


1

Unless I'm misinterpreting the question, is this about division with remainders? I'd probably ask with "how many X are in Y?" and use composite numbers as my Y's to get lots of results For example, "How many 10's are in 60?", "how many 2's in 60?", "how many 15's in 60?" Then I'd ask, "how many 25's are in 60?&...


1

Use a language approach. This is not meant to be a snide remark; I came across a particular TED talk a while ago that illustrated how math is just another language and we must first learn the proper syntax. Of course, we know that adding fractions require the use of common denominators, so I would first introduce the topic of equivalent fractions. If the ...


1

Mathematically there really is no difference. The words "fraction" and "ratio" simply express the concept of dividing one number by another, and are used pretty much interchangeably in mathematics. They need not refer to comparing a part to a whole. The words "fraction" and "ratio" are also used with reference to ...


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