- #1

jing2178

- 41

- 2

So in this case 12/25 and 18/30 is 30/55

So should we be surprised when students say 2/5 + 3/4 is 5/9 ?

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In summary, students may be told that they got 12 out of 25 in their first maths test and 18 out of 30 in their second maths test, giving a total of 30 out of 55. However, this does not mean that 12/25 and 18/30 can be added together to equal 30/55. These fractions represent different wholes and cannot be combined in this way. Using an analogy of cutting a cake and a pie in half, the two tests have different maximum points and 1 point is worth more in one test than in the other. Therefore, the average of the two tests is 54%, not 30/55. It is the teacher's responsibility to properly explain this concept

- #1

jing2178

- 41

- 2

So in this case 12/25 and 18/30 is 30/55

So should we be surprised when students say 2/5 + 3/4 is 5/9 ?

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- #2

lendav_rott

- 232

- 10

Err, 12/25 can't be added to 18/30 just like that :D

Fractions are part of a whole. The two tests are 2 different wholes.

I was taught this as a kid - they said "what would I get if I cut a cake and a pie in half and added the halves together?" I said, you would get a half of the pie and a half of the cake.

In your example, the two tests have different maximum points, so 1 point is worth more in 1 test than in the other - that's why you use fractions -> 12/25 < half, 18/30 > half. On average the tests have 54/100 correct results or 54%. I don't know man, the most obvious stuff in maths, is the most difficult to explain :/

Fractions are part of a whole. The two tests are 2 different wholes.

I was taught this as a kid - they said "what would I get if I cut a cake and a pie in half and added the halves together?" I said, you would get a half of the pie and a half of the cake.

In your example, the two tests have different maximum points, so 1 point is worth more in 1 test than in the other - that's why you use fractions -> 12/25 < half, 18/30 > half. On average the tests have 54/100 correct results or 54%. I don't know man, the most obvious stuff in maths, is the most difficult to explain :/

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- #3

- #4

llstanfield

- 27

- 0

jing2178 said:We all know that 12/25 + 18/30 is not 30/55 yet students are happily told that they got 12 out of 25 in their first maths test and 18 out of 30 in their second maths test giving a total of 30 out of 55

Well in my opinion, this indicates either a tremendous misunderstanding, or miscommunication between the teacher and the student. If the students were properly taught, they would understand that the two fractions (or ratios) could not be added in that manner. Even the most contemporary teachers introduce the 'method' of utilizing the LCD in order to add the fractions.

However, as a teacher, you'd have to explain that adding these two fractions is equivalent to adding for instance: 1/4 to 1/3. Both fractions are basically division equations. So you would start by explaining that (after going through the process of division), .25 =/= .33, in the same way .48=/=.60. Because of this, you cannot simply add the numerator across, as well as the denominator! So similar to your students' claim, 1 slice out of 2 slices of an orange plus 2 slices out of 8 slices of an orange equals 3 slices out of 10 slices of an orange is completely incorrect! You can even picture this pictorially.

Because a fraction is another way of explaining an equation of division, you cannot possibly add the two fractions provided the top in that way. The point that I'm making, is that it's the teachers' responsibility to point this crucial aspect out.

- #5

CellCoree

- 1,490

- 0

I would like to address the confusion surrounding fractions in education. Fractions are a fundamental concept in mathematics, and it is important for students to have a clear understanding of their operations and relationships. However, the example provided highlights a common issue in teaching fractions - the focus on memorization rather than understanding. Simply memorizing rules and procedures without understanding the underlying concepts can lead to confusion and mistakes, as seen in the given example.

As educators, it is our responsibility to ensure that students not only memorize procedures but also understand the reasoning and logic behind them. This will enable them to apply their knowledge in various situations and avoid confusion. Additionally, it is crucial to use real-life examples and hands-on activities to make fractions more tangible and relatable for students.

Furthermore, it is important to address misconceptions and clarify any misunderstandings that students may have. In the given example, it is essential to explain that adding fractions with different denominators requires finding a common denominator, and the resulting fraction may not always be simplified.

In conclusion, we must strive to teach fractions in a way that promotes understanding and critical thinking rather than just memorization. This will not only help students avoid confusion but also build a strong foundation for their future math studies.

A fraction is a mathematical expression that represents a part of a whole. It is written in the form of a numerator over a denominator, such as ⅔, where 2 is the numerator and 3 is the denominator. Fractions can also represent ratios and proportions.

Many students struggle with fractions because they have a hard time understanding the concept of a part of a whole. Fractions are also more abstract than whole numbers and require a deeper understanding of mathematical concepts such as division and equivalent fractions.

There are several strategies that can help students understand fractions. One approach is to use visual aids, such as fraction bars or circles, to help students visualize fractions. Another strategy is to relate fractions to real-life situations, such as dividing a pizza into equal slices. It is also important to review and practice fraction concepts regularly to reinforce understanding.

Some common mistakes students make with fractions include mixing up the numerator and denominator, not simplifying fractions, and not understanding the concept of equivalent fractions. Students may also struggle with adding, subtracting, multiplying, and dividing fractions if they do not have a strong foundation in basic fraction concepts.

To assess students' understanding of fractions, you can give them written or oral quizzes, have them complete fraction worksheets, or observe their problem-solving skills with fraction problems. You can also use real-life scenarios and ask students to apply their fraction knowledge to solve problems. Additionally, providing feedback and addressing any misconceptions can help you gauge students' understanding of fractions.

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