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Why do some students struggle so much with fractions?

Because it is actually very complicated. I myself never really understood fractions till I learned of it's construction through natural numbers. The idea of fractions as a formal expression of ...
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What is the MOST efficient paper/mental multiplication algorithm for integers?

I would say that you need to understand that you are dealing with primary education. This means that, after that, you have secondary education and maybe after that you might have higher education. The ...
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How do I teach the difference between Linear Equations and Equation of a Line

Etymology/Grammar "Line" is the root word, a noun whereas "linear" is a derived word, an adjective. So, apart from the grammar distinction, one could call "line" and &...
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What is the MOST efficient paper/mental multiplication algorithm for integers?

Instead of a comment, I go try an answer, extending the good comments already there... If it comes to computers and runtime, I know the Karatsuba algorithm as an example of a very fast algorithm. If ...
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6 votes

How do I teach the difference between Linear Equations and Equation of a Line

I suspect that two issues may be partly underlying your intuition: First, the equation $y = mx + c$ gives $y$ as an explicit function of $x$, whereas $ax + by + c = 0$ only gives a relation between $...
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2 votes

How do I teach the difference between Linear Equations and Equation of a Line

Your intuition is fundamentally not correct. These are all equations of a line, and your textbook is correct to include them in the same chapter. The term "Linear Equation" is used because ...
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2 votes

How do I teach the difference between Linear Equations and Equation of a Line

They aren't very much different from some perspectives. If what you care about is the question "Is this point on the line or not?" then you can simply plug your $(x,y)$ values into either of ...
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How do I teach the difference between Linear Equations and Equation of a Line

The only "real" difference (except for maybe some analogies that work differently as in your house/street example) is that the linear equations are a proper superset of the equations of ...
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-1 votes

Why do some students struggle so much with fractions?

Some students struggle with fractions because some teachers taught them fractions in a way they can not see the relation between fractions and daily life. In this Spanish-language video, a lady ...
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