Evaluating Our Definitions: Equations and Functions

After reviewing several of my classmates’ definitions and seeing how they defined “equations” and “functions,” I feel that I could change some of the wording in mine.  One of the things teaching middle school students has taught me is the importance of using “student-friendly” vocabulary.  If students can’t understand the words that are used to [...]

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6-B-1: The Magic of Proportions

Proportion Example #1
As a teacher, I hate taking sick days. Unfortunately, working with middle school students does not present a very sanitary environment so I’m always looking for ways to stay healthy. Drinking water is something simple I can do to help me accomplish this goal. We’ve always been told that we [...]

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6-D-2: Applets

Algebra Balance Scales from the National Library of Virtual Manipulatives
http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html

This uses a seesaw to represent an equation. The student is given an equation and begins solving it by placing the appropriate terms on right and left sides of the seesaw. For instance, for the equation -3x + 2 = -8 the student would [...]

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6-A-3: My Definition of Equations and Functions

In this post, I will provide my own definitions for the terms “equation” and “function.” These terms are not research based and are derived from my own experiences in mathematics. I’ll post a revision later.
Equation – An equation is a statement of equality between two mathematical expressions. These statements may or may [...]

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Non-Linear Pattern Webquest

For my webquest, I chose to explore the Fibonacci sequence and fractals. Both of these concepts provide great examples of observable mathematical patterns in nature. The following post will provide a brief description of both concepts, some interesting points and pictures from each, and ideas for how this webquest could be modified for [...]

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My Reflection on Math Myths

Here are two common myths that I have encountered as a student and a teacher and my reflections on each.
There is a “math mind” – some people have it and some don’t.
One argument that people make when they encounter difficulties in math is that they just don’t have a mind for math. People reference [...]

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Pascal’s Triangle

Pascal’s Triangle is a great example of a non-linear pattern that has applications in the world of algebra and equations. The numbers from each row can be used when factoring polynomials. The triangle is formed in the following way.

The outside edges of the triangle are made up of ones that form an isosceles [...]

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Working with the Definition of Linear Patterns

Non-Traditional Patterns (Official Definition): any pattern that does not follow a repetitive or symmetrical pattern.

Linear Patterns (in 7th grade language): a group of numbers or shapes that look like they repeat in the same order.

Linear Pattern (Official Definition): any pattern that appears to contain repeating sequences of shapes or numbers.
(from: http://www.wgquirk.com/NCEEES.html )
These two [...]

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Reviewing the PUMAS Website

PUMAS (Practical Uses of Math and Science) is a website that provides lesson plans for activities that are rooted in real-world scenarios. I took some time to review some of these activities and found one that would be somewhat useful to me during one of my spring units.

Every year without fail, my students struggle [...]

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Multiplicative Property

Word definition: The multiplicative property states that any number multiplied by its reciprocal (one over the number as a fraction) yields a product of one.

Numeric Form: 1/7 x 7 = 1
Algebraic Form: m x 1/m = 1
Proof: m x 1/m = m/1 x 1/m = m/m = 1
Example:
You are making cookies.  The recipe calls for [...]

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