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Using Technology to Implement the Common Core Standards July 26, 2013

Posted by Edward Deleon in : algebra, graphing calculators, math, media , add a comment

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As teachers look to implement the Common Core Math Standards, they are looking for resources to help them do this. In particular, they’re looking for technology-based resources.

Media4Math+ is launching a new series of technology-based activities that use the TI-Nspire to help implement the Common Core Standards. Our first activity focuses on this Common Core Standard:

 CCSS.Math.Content.8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1

We do so in the context of linear functions. Each TI-Nspire Activity comes with a TNS file and a Teacher’s Guide.

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In the linear functions activity, we start with a spreadsheet with x-y coordinates linked to a Graph Window. Students input additional values into Column A to see the corresponding outputs. The spreadsheets allows students to see clearly the idea that with a function for every input value there is a unique output value.

This naturally leads to the concept of the vertical line test, which students can see using the Graph Window. Finally, students are asked to graph the continuous linear function derived from formula in the spreadsheet.

Look for additional activities modeled on this first activity, which will focus on quadratic, exponential, and other functions.

Geometry Application: The Amazing Archer Fish July 24, 2013

Posted by Edward Deleon in : geometry, math, media , add a comment

Real-world applications of Geometric and Trigonometric concepts can sometimes dazzle with their mathematical elegance. One such example is the study of the amazing Archer Fish.

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On Media4Math+ we have just uploaded a teacher’s guide and activity. Here is a summary:

We first see a YouTube video describing how an Archer Fish hunts its prey:

[embedplusvideo height="300" width="450" editlink="http://bit.ly/1ajTVzO" standard="http://www.youtube.com/v/fhBZ40jIo4Q?fs=1" vars="ytid=fhBZ40jIo4Q&width=450&height=300&start=&stop=&rs=w&hd=0&autoplay=0&react=1&chapters=&notes=" id="ep1421" /]

 

The Archer Fish sprays water on insects perched on trees above the fish, knocks them down to the water, and then eats the helpless prey. The Archer Fish does this with deadly accuracy, while compensating for the effects of refraction.

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We first look at the scenario as an application of right triangle geometry. The water gun spray of the Archer Fish becomes the hypotenuse of a right triangle, while the vertical drop of the insect becomes one of the legs. We calculate how far the Archer Fish has to spray in order to hit the target.

Yet a complication arises, due to refraction. If you’ve ever seen a stick poking out of the water, it looks as if the stick is bent. This is due to refraction.

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Without compensating for the effects of refraction, the Archer Fish would miss the target. In this case we solve a trigonometric equation to see how much the fish has to adjust his aim in order to hit the target.

In short, Nature presents a mathematical problem and then goes about solving it.

Do You Use the TI-Nspire? July 15, 2013

Posted by Edward Deleon in : graphing calculators, math, media , add a comment
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Media4Math+ has a library of video tutorials for the TI-Nspire.

Media4Math+ has a large collection of video tutorials for using the TI-Nspire, whether it’s the original Clickpad, the Touchpad, or the new Nspire CX.

We’ve just made it easier to find these tutorials. While all of these tutorials are mapped to key concepts from Algebra and Geometry, we have also collected these videos by media type.

On the side bar, click on Browse By Type. You’ll see an expanded list. We just added “TI-Nspire Tutorials” as one of the clickable items.

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You’ll then see the full library.

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Coming soon: TI-Nspire Tutorials for the iPad app!

Overcoming the Limitations of Textbooks July 10, 2013

Posted by Edward Deleon in : algebra, geometry, graphing calculators, math, media , add a comment

While textbooks can provide a comprehensive overview of the curriculum, they sometimes do this at the expense of depth of coverage. Nowhere is this more obvious than in the number of worked-out examples in a textbook.

For many topics, a textbook will show 2, 3 or maybe 5 worked-out examples, but no more. The economics of textbooks requires a limitation on the number of worked-out examples. Digital resources have no such limitation.

Media4Math+ has a library of Tutorials that show a wealth of worked-out examples for key topics in Algebra and Geometry. Let’s look at a case study.

Teaching about functions and their inverses is tricky. One of the keys to understanding function inverses is to show that the graph of an inverse (if an inverse exists) is a reflection of the graph of the function across the graph of
y = x.

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The graph of a function and its inverse.

But the notion of a graph reflected across y = x is not an easy concept to get across. This is best shown through a multitude of examples. For the topic of Functions and Their Inverses Media4Math+ provides 18 worked-out examples (including linear and non-linear functions). Analyzing these 18 graphs allows a student to finally comprehend what this idea of something being reflected across the graph of y = x means.

The collection of 18 worked-out examples is shown in this Slideshare PowerPoint presentation.

Media4Math+ has a large and growing collection of Tutorials that show many worked-out examples, allowing students to see patterns in the solution and better understand the concept. This is one of the many ways we allow math educators to overcome the limitations of textbooks.

Math in the News: Plane Crash in San Francisco July 9, 2013

Posted by Edward Deleon in : algebra, geometry, math, media , add a comment

This PowerPoint Presentation has just been added to the Math in the News archive on Media4Math+:

Making Math Relevant with Current Events July 8, 2013

Posted by Edward Deleon in : algebra, geometry, math, media , add a comment
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Making Math Relevant with “Math in the News.”

Students often come to class with knowledge of current events and will discuss them in Science and Social Studies classes, but rarely in Math, since there are so few opportunities to do so. However, there is a wealth of opportunities to connect their growing knowledge of Algebraic and Geometric concepts with their relevance in the real world.

The summer and early fall provides ample opportunities, in particular during hurricane season. In a recent issue of Math in the News, we showed how to use a spreadsheet to simulate the random motion of a hurricane. This activity allows students to explore the concept of a random number in the context of the random path of a hurricane.

Start by introducing the concept of a “random walk.” Using Excel, we create a “random walk” simulation of a hurricane path.

The key idea is that a truly random walk simulation would not produce anything like a hurricane’s path. A controlled randomness is what is required and this allows us to introduce the notion of managing the random variables.

In order to end up with a path that goes in a northwesterly direction, the random number generator must favor moving up and to the left, rather than down and to the right. The latter are not, of course, excluded, but the preponderance of the movement is in the preferred direction. Furthermore, students can tweak the random variables to create a hurricane path that goes toward the Gulf of Mexico or, like Hurricane Irene, along the Eastern Seaboard.

Try this activity as a back-to-school introduction to (or refresher on) random number generation.

Here is the PowerPoint presentation from SlideShare. You can also see our complete collection of Math in the News PowerPoints on Media4Math+.

Multimedia Lesson for Algebra July 3, 2013

Posted by Edward Deleon in : algebra, math, media , 1 comment so far

Digital Resources for Algebra

Incorporating Digital Resources into your math instruction is now simpler with online resources. Media4Math+ has a library of digital media that allow you to add multimedia components to your lesson planning. Let’s look at an example.

A Lesson on Slope

 Suppose you are preparing a lesson on the topic of slope.  The Common Core Standard you are trying to address is this.

 CCSS.Math.Content.8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph.

You want to create a PowerPoint presentation.

Media4Math+ provides easy access to all the resources, by allowing you to Browse by Topic.

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You’ll see a number of digital resources available in support of the topic.

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Of the resources available, you see a number of Tutorials on using the Slope Formula.

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Slope Formula Tutorial: Example 1

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Slope Formula Tutorial: Example 2

You decide to download these examples and add them to your Presentation.

Next, we have a Math Solver for calculating the Slope.

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Math Solver: Slope Formula

You can input different coordinates and the Solver shows the steps in finding the slope of the line connecting those points. You include a link to this page on your PowerPoint.

 Finally, we look for an Application of Slope and find a video clip that calculates the slopes of hills in Tuscany, Italy, for people cycling.

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Applications of Slope: Video on Calculating Slope for Cyclists

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Applications of Slope: Video on Calculating Slope for Cyclists

You download the video and incorporate it into your PowerPoint presentation.

Media4Math+ provides you the Digital Resources to put together lesson presentations quickly and easily. Here is a Slideshare version of this presentation.

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