Posted in Algebra, Geogebra, High school mathematics

Embedding the idea of functions in geometry lessons

GeoGebra is a great tool to promote a way of thinking and reasoning about shapes. It provides an environment where students can observe and describe the relationships within and among geometric shapes, analyze what changes and what stays the same when shapes are transformed, and make generalizations.

When shapes or objects are transformed or moved, their properties such as location, length, angles, perimeters, and area changes. These properties are quantifiable and may vary with each other. It is therefore possible to design a lesson with GeoGebra which can be used to teach geometry concepts and the concepts of variables and functions. Noticing varying quantities is a pre-requisite skill towards understanding function and using it to model real life situations. Noticing varying quantities is as important as pattern recognition. Below is an example of such activity. I created this worksheet to model the movement of the structure of a collapsible chair which I describe in this Collapsible  chair model.

Show angle CFB then move C. Express angle CFB in terms of ?, the measure of FCB. Show the next angle EFB then move C. Express EFB in terms of ?. Do the same for angle FBG.
[iframe https://math4teaching.com/wp-content/uploads/2011/07/locus_and_function.html 700 400]
Because CFB depends on FCB, the measure of CFB is a function of ?. That is f(?) = 180-2?. Note that the triangle formed is isosceles. Likewise, the measure of angle EFB is a function of ?. We can write this as g(?) = 2?. Let h be the function that defines the relationship between FCB and FBG. So, h(?)=180-?. Of course you would want the students to graph the function. Don’t forget to talk about domain and range. You may also ask students to find a function that relates f and g.

For the geometry use of this worksheet, read the post Problems about Perpendicular Segments. Note that you can also use this to help the students learn about exterior angle theorem.

Posted in Algebra, Geometry, Math blogs

Math and Multimedia Carnival #7

Welcome to the 7th edition of Math and Multimedia blog carnival.

Before we begin Carnival 7, let’s look at some of the trivias about the number seven:

Now, lets start with posts that involve mathematics sans technology.

Guillermo P. Bautista Jr., the organizer of Mathematics and Multimedia Carnival, presents Generating Pythagorean Triples posted at Mathematics and Multimedia, saying, “A simple strategy in generating Pythagorean Triples.”

Mike Dimond presents Squares ending in 5 – Two Digit Numbers posted at Education For All, saying, “Learn how to quickly calculate the square for two digit numbers ending in five. The post goes over how to quickly calculate 75 * 75.”

I also grab the post Numbers and Variables, the first in the series of post on teaching algebra to students in their first year of High School from the blog Learning and Teaching Math.

John Golden presents Math Hombre: Variable and a Problem posted at Math Hombre, saying, “This post tries to give a couple of contexts for middle school or Algebra I development of the concept of variable.”

Let me include on this list my latest post titled  Counting Smileys which shows several solutions to counting problems that are used to introduce variables and algebraic expressions.

click link to view source

Now, for mathematics with technology:

David Wees presents Is Interactivity in Mathematics Important posted at Professional blog | 21st Century Educator, saying, “This blog post is a discussion of the importance of using interactive tools when teaching mathematics.” This is one way indeed to involve students in the learning.

Alexander Bogomolny presents Fascination with Tessellations posted at CTK Insights. The post presents several Java applets that illustrate various hinged tessellations and ways of inserting hinges into an existing tessellation.

Terrance Banks presents Treasure Hunt Activity posted at So I Teach Math and Coach?, saying, “Review Activity – Treasure Hunt for Algebra”

Gianluigi Filippelli presents Gravity vs height posted at Science Backstage, saying, “The dependance of gravity by height plotted with Scilab”

Tamarah Buckley presents Instant Feedback posted at Infinitely Many Solutions, saying, “My blog focuses on using iPads in a secondary math classroom.”

Pat Ballew presents Microsoft Mathematics is FREE! posted at Pat’sBlog, saying, “Software for every kid, at just the right price…”

Finally, let me share my post on Squares and Square Roots which presents a series of activities for teaching these concepts meaningfully using the free software, GeoGebra.

That concludes this edition. Submit your blog article to the next edition of mathematics and multimedia blog carnival using our carnival submission form. Past posts and future hosts can be found on our blog carnival index page

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