Why Do Some Fractions Repeat as Decimals?
For a PDF of the following, click here. There’s a video of this material at the bottom of the page. If you’d like a PowerPoint that covers this material, email me at [email protected] Why some rational numbers repeat as fractions Why Some Rational Numbers are Non-Terminating Decimals I’d like to explore the relationship between non-terminating, … Read more
Exponents Part 2
two Exponents Part 2 Division In the previous section we learned that exponents are repeated multiplication, which on its own is not tricky. What makes exponents tricky is determining what is a base and what is not for a given exponent. It is imperative that you really understand the material from the previous section before … Read more
Exponents Part 1
exponents part 1 Exponents Part 1 Reading Math One of the biggest things to understand about math is how it is written. The spatial arrangement of characters is syntax. Syntax, in English, refers to the arrangements of words to convey meaning. Exponents are just a way of writing repeated multiplication. If we are multiplying a … Read more
The Purpose of Homework and My Response
The purpose of homework is to promote learning. That’s it. It’s not a way to earn a grade or something to keep kids busy. It’s also not something that just must be completed in order to stay out of trouble. Homework is a chance to try things independently, make mistakes and explore the nature of … Read more
Adding and Subtracting Algebraic Fractions
part 2 Introduction to Algebraic Fractions Part 2 In the last section we saw both how to reduce Algebraic Fractions, which if you recall, are also called Rational Expressions, but also how the math works. Because of the relationship between division and multiplication, and multiplication’s commutative property, we can reduce Algebraic Fractions like the one … Read more
The Smallest Things Can Cause Huge Problems for Students
preemptive Pre-Emptive Explanation It is often the case, for the mathematically-insecure, that the slightest point of confusion can completely undermine their determination. Consider a beginning Algebra student that is learning how to evaluate functions like: f( x )=3x− x 2 +1 f( 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGMb WaaeWaaeaacaWG4baacaGLOaGaayzkaaGaeyypa0JaaG4maiaadIha cqGHsislcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGymaa qaaiaadAgadaqadaqaaiaaikdaaiaawIcacaGLPaaaaaaa@43D9@ A confident … Read more
Combining Like Terms & The Order of Operations
Be fair-warned…this might seem pedantic, and I agree, it is. But, with good cause. The point of this discussion is to cause students to pause and think about something they’ve always done in math without any understanding. It’s true, you can combine like terms, but why? To that point, and I do not say this … Read more
Promoting Mathematical Literacy through Non-Procedural Questions
Math was okay until they threw the alphabet in it. I have heard, Math was okay until they threw the alphabet in it, so many times from so many adults, who I wish were trying to be witty, but are in fact completely serious. And these are reasonable, intelligent people. Why does the abstraction of … Read more
Why Teaching Properties of Real Numbers is Important
If you are going to do a fraction review, the lesson here might be of some help. I believe things are best reviewed in context, but this is a decent set of information that also introduces the real numbers and some other basics of math. The PDF icon to the left has a lesson outline … Read more
Algebraic Fractions Part 1
Algebraic Fractions Pt 1 Algebraic Fractions – MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbeqcLbCaqa aaaaaaaaWdbiaa=nbiaaa@3804@ Rational Expressions In this section we will learn how Algebraic Fractions can be multiplied, reduced and added or subtracted. This particular entry will cover reducing and how reducing uses the greatest common factor of all terms. It is often the … Read more
