Making Sense of Equivalent Equations and Expressions

 Posted by  Algebra
Jun 142013
 
Making Sense of Equivalent Equations and Expressions

Here are some questions your students have been wanting to ask you in your algebra class. Daniel Chazan and Michal Yerushalmy in their article On Appreciating the Cognitive Complexity of School Algebra posed these questions about equivalence of equations , solving equations, and equivalence of expressions for us teachers to ponder upon.  How often do we give students the  opportunities to think about these questions? Questions: If one can add x to both sides of an equation in one variable—and if [...]

Why PEMDAS is ‘morally’ wrong

 Posted by  Math videos, Number Sense
May 292013
 

Here’s a video that explains why you need to memorise PEMDAS order of operation and why you don’t need to. Minute Physics who made this video made a mistake in assuming that PEMDAS is taught in schools without emphasising that multiplication and division should be done whichever comes first from left to right. But he does explain the ‘why’ behind the rule plus the importance of knowing fundamental ideas such as the distributive property and the associative property. This is [...]

What is an algebraic function?

 Posted by  Algebra
May 272013
 
What is an algebraic function?

An algebraic function is a function created by applying the operation of addition, subtraction, multiplication, division, and extracting the nth root. Let me give an example. Suppose you have the function f and g where f is a linear function and g is a constant function.  Let f(x)=x and g(x) = -3. We can create another linear function h by multiplying f and g that is h(x) = -3x. We can also create another linear function l where l = f – [...]

What is algebra?

 Posted by  Algebra
May 222013
 
What is algebra?

Didn’t we say in our algebra class that in the grades they study about numbers and so now they will be studying letters instead? Didn’t we say that in algebra we now use x instead of box (in 3 + ___ = 15, we now write 3 + x = 15)? And isn’t it that since this announcement our algebra class activity has been about finding that 24th letter? Well, we reap what we sow. Just a friendly reminder to [...]

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