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New Video Resources for Measures of Central Tendency April 3, 2020

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Media4Math has just posted eight new videos on the topic of Measures of Central Tendency. These videos cover topics ranging from mean, median, mode, sample mean, mean of a probability distribution and can be used with any unit on data analysis. Here is a list of the videos, along with links.

Video Tutorial: Measures of Central Tendency: Finding the Mean of a Data Set I
Video Tutorial: Measures of Central Tendency: Finding the Mean of a Data Set II
Video Tutorial: Measures of Central Tendency: Finding the Median of a Data Set
Video Tutorial: Measures of Central Tendency: Weighted Mean
Video Tutorial: Measures of Central Tendency: Finding the Mode of a Data Set
Video Tutorial: Measures of Central Tendency: The Mean and Normally Distributed Data
Video Tutorial: Measures of Central Tendency: Sample Mean
Video Tutorial: Measures of Central Tendency: Mean of a Probability Distribution

New Resources on Place Value April 1, 2020

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We recently published seven video tutorials on place value, useful for students in upper elementary. Here is a summary of these videos:

  1. Comparing and Ordering Whole Numbers Using Place Value
  2. Comparing and Ordering Decimals Using Place Value
  3. Organizing Data Using Place Value
  4. Reading and Writing Whole Numbers in Expanded Form
  5. Reading and Writing Decimals in Expanded Form
  6. Rounding Whole Numbers
  7. Rounding Decimals

Each video is about 4 to 5 minutes in length and includes several real-world examples each concept. Each video also includes a transcript, which, for subscribers, is a downloadable PDF.

Math Resources for Studying the Corona Virus March 31, 2020

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In the current issue of Math in the News, Media4Math investigates the Corona Virus from a math perspective.

The dramatic growth in cases of the Corona Virus is a real-world opportunity to explore exponential functions. In this issue of Math in the News, students explore exponential growth and exponential functions.

This issue uses real-world data sets, along with graphing calculator activities for analyzing this data.

Media4Math Resources Are Standards Aligned March 31, 2020

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We have added a Standards Alignment page to Media4Math: https://media4math.com/CCSS-Alignment. Here you will find how resources in our vast digital library align to the Common Core State Standards. This becomes a quick way of identifying digital resources for lesson planning.

When Doing Math, Reach for the Stars January 6, 2019

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screen shot 2019-01-06 at 12.47.17 pmThe students at the Weiss School in Florida were part of an incredible launch of a new satellite. Can you think of a better way to motivate students to embrace STEM in general and math particular?

The satellite will be used to measure the impact of extreme temperatures on bacteria.

To learn more about this project, go to this link.

Also, the Weiss School itself has a page on their Web site dedicated to updates on the project. Click this link. In particular, here is the link to the live satellite data. Click this link.

Share this with your students. with the goal of encouraging a mathematical mindset. Here are some key ideas to highlight:

  • There are no limits to what you can do in math and science.
  • You are never too young to learn or too old to learn.
  • Math can be a team endeavor.

Finally, as a way of connecting specific math concepts to this project, share with the students the following ideas:

  • Launching a rocket into space involves working with algebraic functions. Show them the graph of a parabola to show what the part of a rocket would look like.
  • Bacteria reproduce at such a rate that it can be modeled with an exponential function. Show the power of doubling through a numerical sequence  or with a graph.
  • The force of gravity is what makes objects fall. Gravity is an inverse-squared function, which has its own unique properties. Show a graph of a rational function to show how gravity is a strong force at relatively small distances but becomes much weaker at greater distances.

Why Are Castles So Tall? January 2, 2019

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Encouraging a Mathematical Mindset

Ask your math students this question: Why are castles so tall? Students of all ages and grades can provide an answer, and while the goal isn’t to get a mathematical answer from your students, it provides an opportunity to frame a mathematical question.

All children are familiar with castles from fairy tales, as well as from myths and legends. Cultures around the world have different types of castles. Show your students pictures of castles from different parts of the world. Here are some examples.

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Himeji Castle, Japan

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Neuschwanstein Castle, Germany

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Château de Pierrefonds, France

The castle shown at the top of this blog is Edinburgh Castle in Scotland. Ask your students what all the castles shown have in common. Don’t immediately go to height as a common characteristic, or you may miss some interesting observations from your students.

You can also show them this Google Earth tree view from the top of Edinburgh Castle in Scotland (view in Chrome): Click here.

Media4Math Classroom has a lesson module on this that explores castle height from the standpoint of indirect measurement. In particular, a castle’s defenses would have required as much advance notice of an approaching army and a tall castle provides a line of sight that reveals longer distances. This module uses trig ratios as a means of calculating distances.

But the topic of castle height isn’t restricted to the province of trig. Here are some ideas that you can use to incorporate this topic of castle height into your math instruction.

Low Floor-High Ceiling Ideas: Castle Height

  • Create a castle tower using Lego blocks. Count the number of blocks needed to build the tower. Math question: How many Lego blocks would it take to build a tower ten times taller?
  • Create a castle tower from available classroom materials. Measure the angle the tower makes with the floor.

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Math questions:

— How does the angle change as the tower increases in height? 

— What would you need to do to maintain the angle measure for a taller tower?

  • Look at the triangle formed by the height of the tower, its distance from an observer, and the top of the tower.

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— Math question: What kind of triangle is this? 

  • This is the view from the top of Neueschwanstein Castle. The castle is 213 feet tall and  provides a panoramic view.

Math investigation: Estimate how far into the distance you can see from the top of the castle.

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Encouraging a Mathematical Mindset January 1, 2019

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Before we can expect a student to answer a mathematical question, shouldn’t we want them to ask a mathematical question? Were you born answering questions? No, you were born to learn, to ask, and a child’s early years are a seemingly endless trail of question marks.

Moreover, isn’t our job as math educators to get students to recognize when some of their questions are, in fact, mathematical in nature? Many a child would be intimidated to solve a math problem, but wouldn’t they be delighted to know what they just asked is an interesting math question?

Math doesn’t start with algorithms, but rather ends with them. Math starts with questions, and sometimes those questions don’t even sound mathematical at all. We can use curiosity as the entry point to mathematical investigation.

Here is an interesting question that doesn’t sound mathematical at all:

Why do elephants have wrinkled skin?

This is a question you can ask a child with no fear of math anxiety. Their answers, whether mathematical or not, should be illuminating. Yet, it is completely a mathematical question.

Elephant

Media4Math Classroom has an entire module dedicated to answering this question, and although the target math concepts involve rational functions, the goal is to get students thinking about the question, rather than insist on an immediate answer. Yet the question about elephants can be asked of any child at any grade level.

Imagine, by contrast, telling students, “The ratio of surface area to volume reveals how efficiently an animal retains or releases heat energy.” This is not engaging. This is intimidating. It provokes the kind of math anxiety we want to eliminate from our classrooms. Also, this approach focuses on algorithmic solutions instead of the underlying question.

Asking Mathematical Questions

Getting a child to recognize that he or she just asked a mathematical question is a way of empowering the child’s math sensibilities, and creating a math mindset. For example, show them a picture of a group of balloons.

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Encourage them to ask questions based on the picture. While the point isn’t to specifically ask mathematical questions, the goal is to highlight when they have asked such questions. Any questions that include these interrogatives can be reframed as mathematical questions.

How many…?     This can involve counting, estimating, measuring, adding, or even multiplying.

How much?     This can involve measurements with money.

What colors…?   This can involve sorting, ratios, or even percentages.

Since our goal is to encourage a mathematical mindset, let the questions guide the math. Here’s an example. Suppose that as a class, you decide this is the most interesting mathematical question:

How can we make sure that most of the party balloons are red?

This is a mathematical question that has a variety of different solutions. The math skills used could involve sorting, counting, calculating ratios, fractions, and percentages. If you divide the class into small groups and have the groups discuss how they would solve this problem, you are encouraging a mathematical mindset where the mathematical investigation drives the mathematical solution.

Use this methodology to encourage students to develop a mathematical mindset. Engage a student’s curiosity and problem solving. This then puts students in a frame of mind to better understand the procedural and algorithmic side of math. They’ll begin to see that algorithms are tools of math, but that the real mathematics is in the mindset.

 

Why Media4Math Classroom? December 2, 2018

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Have you noticed how the “real world” applications in math textbooks are never all that compelling, interesting, or for that matter realistic? In fact, many “real world applications” in math textbooks are contrived.

There’s a reason for this.

Textbooks are very formulaic in their delivery. Editors have a limited number of pages to convey key math concepts, so anything out of the ordinary, like a rich real-world example of a math problem, has the potential to take up a lot of book real estate.

But as math educators we know that rich math problems can’t be shoehorned into a half-page textbook feature. In fact, real-world math problems have these characteristics:

  • They cover multiple math topics clustered around the central real-world applications.
  • They don’t have a single solution, but offer a rich variety of solutions.
  • They require thoughtful approaches and creative problem solving.
  • They are challenging and can even be fun.
  • They are not the stuff of textbooks.

To convey the richness of math, you often have to take it upon yourself to create these rich math experiences. This is where Media4Math Classroom can help you.

“Real” Real World Math Problems

Media4Math Classroom is a growing collection of instructional modules that don’t shy away from real world applications of math. We do what textbooks stay away from.

Here’s an example from one of our modules, “What Is Function Notation?

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We use the scenario of a cheetah chasing a gazelle to explore and apply functions. The underlying problem that we explore is based on the following premise:

  • Cheetahs can quickly accelerate to catch gazelles, but they can only maintain this speed for a short while.
  • Gazelles, while not as fast as cheetahs, have adapted to dart away from the cheetah long enough to tire out the cheetah.
  • How can we model this behavior mathematically to see when a cheetah successfully catches the gazelle, and when the gazelle gets away?

The goal of this module isn’t to apply math to some contrived problem. Instead, the goal is to fully investigate a phenomenon and bring to bear the relevant math to better understand it. So, this module explores this scenario and in the process the following math concepts are used:

  • Exploring a speed vs. time graph so that students can see the powerful acceleration of the cheetah. This Desmos-based graphing calculator activity has students do curve-fitting, explore quadratics, but mostly to see the raw power of the cheetah mathematically.

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  • Explore the domain and range of the piecewise function that defines the cheetah’s motion.

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  • Analyze the distance-vs-time graphs for the cheetah-vs-gazelle to see that the cheetah has more than enough time to catch the gazelle. This is also a Desmos graphing calculator activity.

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  • From this, students can see that everything is stacked against the poor gazelle, and yet it finds ways of escaping the cheetah. This is explored mathematically through this displacements-vs-time graph, which maps the distance between the cheetah and gazelle.

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Throughout this module students pursue the story of the cheetah and gazelle not to solve a specific (textbook) math problem but to understand a natural phenomenon mathematically. This is the approach we take in Media4Math Classroom.

Tell us what you think. Write to us at admin@media4math.com.

 

 

 

Halloween-Themed Math Resources October 15, 2016

Posted by Media4Math in algebra, geometry, math.
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HalloweenMathActivities

 

Media4Math has created a collection of math resources that are Halloween themed. This collection includes games, interactives, presentations, and more. To see the complete collection, go here.

Start with our Pumpkin π activity: http://www.media4mathplus.com/SlideShow/231/Pumpkin-Pi. In this multi-grade activity students measure the diameter and circumference of different sized pumpkins, create a scatterplot, estimate the line of best fit, and determine the slope of the line. This hands-on activity is a great way to explore the concept of π, while weaving in other concepts.

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Or try our whack-a-mole games. This suite of games test divisibility rules. Depending on the game, students are either “whacking” pumpkins or bats with numbers on them. Students gain points when they identify the correct divisibility rules, but they lose two points when they choose the wrong number.

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Check out the full collection!

 

 

Why OER Resources Matter May 23, 2016

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