Foraging for Real World Math
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# Foraging for Real World Math

useful articles to incorporate math in the real world in the classroom!
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## Usain Bolt vs. The Cheetah: Olympians of the Animal Kingdom

Find out how your favorite Olympians might fare against the wilder side of the animal kingdom.

This article compares some of the world's fastest and strongest Olympians to animals in the wild. As athletic as we humans think we are, we stand no chance against the animal kingdom. For example, the cheetah is twice as fast as Usain Bolt and the sailfish can outswim 22-time Olympic medalist Michael Phelps. We were both fascinated by these numbers and comparisons. We feel that secondary students would be just as intrigued, drawing upon their interest in sports competition and wild animals.
This engages the mathematical ideas involving comparisons, ratios, intervals, rates, percentages, and conversions. Students have to analyze relationships between the numbers, distances, speeds, and weights in order to draw conclusions, and they then must interpret these results in the context of the problem. This supports several of the Common Core's Standards for Mathematical Practice, including "make sense of problems and perservere in solving them" and "model with mathematics." Even though the mathematics is not explicitly stated in the article, there are many ways to engage the students in mathematical discourse and activities. The following are several ideas for how this article could be used in the mathematics classroom.
- Students can calculate the ratios between the athletes and animals.
- Students can calculate the conversion rates between different units of measure that are not stated in the article.
- Students can calculate speeds given the distance traveled and the amount of time it took to travel that distance.
- Students can create and interpret graphs of the races and include information such as speed and acceleration.
It would be interesting to see where the data is coming from, and determine whether they are racing the best humans and the best animals or the average ones, and see if there is more variance for one group or another. It would also be interesting to have the students think about what would happen if the racing conditions were to change, would the cheetah do just as well over long distances?
To build on the article in the classroom, the students could set up their own races, perhaps either among the animals or pitting themselves against an animal. They could extrapolate from the data to perhaps race the animal, or even the athletes, against other moving things, like cars or trains. This could involve the students investigating to collect more data to simulate these races and perhaps translating these to graphs as well. The article easily allows for the incorporation of multiple representations and promotion of graph literacy, as the students can create graphs of the races or even be given graphs and have to name the mammals being raced based on the data.
In order to engage with this article productively, students would need to be familiar with the Olympics and the level of athleticism that these people possess. There are also a lot of animal names in the article, so it would be beneficial to provide the students with a little information about the animals and a picture so that they can visualize the racers. There are also some higher level vocabulary words in the article that could be addressed to help students understand the article.

-Bella and Shelby-

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## Teens and Their Mobile Phones / Flowtown (@flowtown)

Have you ever wondered what teens were really using their mobile phones for?

The article captured our attention primarily because the majority of teenagers will be able to relate to a technology/cell phone theme applied to real issues they experience in life. We think this will be engaging for students because it is a topic that is so close to them in a way that allows for the analysis of a number of visual displays that they can pick apart and mess around with, thinking throughout about how they would fit into the data. To engage with the graphs, the students have to have some understanding of what a cell phone is and can do. There are also some math symbols and phrases that they have to understand, such as percentages, 3 in 1, and average, and they need some graph sense and number sense.
Overall, the students have to interpret the different types of representations presented and really engage with the graphs to understand what they are saying, as there are many charts dealing with different texting factors. The students will have to become data detectives and develop their comprehension, graph literacy, and statistical literacy. The students will develop their number sense, ability to interpret graphs, data collection, recognition of important features/relationships on graphs, and hypothesize about the arguments and make inferences about the purpose of the graphs. The article introduces the idea of selection of a representation and creation to display the data. Since there are no solid arguments, the students have to pay attention to the relationships presented and think about what the arguments could be and what the author was trying to use statistics to do in this case. They can make observations and speculations based on their graph literacy and can even predict how the future generations look. The students have to engage with proportional reasoning to judge magnitudes and to recognize the proportions, numbers and percents to identify variables and what they translate to. There is also an average that is introduced and probability also lies within the graph with the driving portion. They could expand from here in many ways to explore the probability that a driver chosen at random will text and drive in their school community, or even translate the percentages to probabilities and work from here. The students have to use strategic competence to choose what to look for in the graphs and pick out the principle relationships and analyze why certain measures/graphs were chosen. This can lead to a development of critical literacy, as the students will have some questions about the decisions the author made. The students overall develop their statistical literacy in analyzing and interpreting the graphical representations and then formulating their own opinions and arguments about teens and their cell phones.
A great way to expand on this article for the classroom would be to make the students come up with these arguments and construct their own representations about them to show their point in the best way, perhaps collecting data from the classroom community. They would have to determine how to collect the data, how to represent it, and then what argument to make about it and whether it supports the argument on the given graph. This can also introduce the issue of sample size and experiment techniques.

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## The facts about smoking [Infographic] - Webctor.com

This artifact captured our attention because smoking is such a pertinent issue throughout the world. Students are likely aware of the need to instill change and to combat the fact that so many young people are smoking, and they may benefit from learning about the numerous negative effects that smoking has on our health and society. This article also offers a lot of different ways in which students can access mathematical ideas, such as percents, numbers, probabilities, averages, and graphs, all through interesting visual representations.
The students first see how many people smoke worldwide, a number that is then translated to a probability: 1 in 5 people. They could be pressed to think about what this means for their school community: How many of our peers will be smokers? There is then a percent of high schoolers that are smokers, a number they can relate back to the total to see how many high schoolers make up all the smokers and then determine the probability that a high schooler will be a smoker. Next is a pie chart of the racial distribution of smokers in the United States, engaging with the students’ graphical literacy in reading the percentages and seeing the relation to the visual, perhaps sparking students to question if there are different representations to better display this information. There is then a section about deaths caused by smoking, which students could use to translate to a probability or again relate it to their local community using additional data. Next is a graphical representation of the amount of money available for controlling tobacco juxtaposed with the amount actually spent by states. This makes a strong argument that the students can read and critique by engaging with the pie chart. This also may bring students to question the social injustices involved with how our government is spending our tax dollars. There is then a graphic that states that only 5 out of 100 people who try to quit are successful. Students can again apply that statistic to a different population while also thinking about how that statistic was formed. Lastly, there is a graphic displaying the average life expectancy of smokers and nonsmokers. Here the students can think about what average means and how this average life expectancy was formed from the data, and what that data might look like based on the given average. They have to think about the numbers and what they mean, where the numbers came from, how they translate to the representations, and what argument they are making. This article engages students’ number sense and mathematical language skills, as well as providing representations and visuals to engage with.
Because of the many arguments made in this article, students have the opportunity to take a critical stance and question these claims. For example, how did the researchers define a smoker? Is it someone who smokes every day or is it anyone who has ever tried smoking? Are they only accounting for cigarette smoking, or does it include other forms of smoking as well? Students can question where this data came from, and was it from a representative sample. If not, can we really trust the claims they are making? Are the authors biased? Lastly, students can consider the many different representations of data, from pie charts and percentages to more pictorial displays. What does each of these show and hide? How do they draw on the reader’s emotions to convince them of a particular argument?
The visual and numeric representations greatly reduce the language demands needed to engage with this article. Students are likely familiar with cigarette smoking and some of its negative effects, but they made need additional context in order to make sense of some of the information, such as tobacco control programs and carcinogens. Teachers need to also be cognizant of the fact that some of these students' family members may be smokers, or even the students themselves, so it is important to be sensitive to student responses and reactions.

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## Philip H. Howard | Soft Drink Industry Structure

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## Vitamin D

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## Creative Review - New York magazine: data done right

The best in visual communication...
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## The 892 unique ways to partition a 3 x 4 grid

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## Is The HPV Vaccine Safe? v 2.0

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## The Value Of College, In 2 Graphs : NPR

In terms of both unemployment and earnings, the gap between high school and college grads keeps getting wider. But people keep questioning the value of college.
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## HIV Infections Rise Among Young Black Men In U.S. : NPR

The number of new HIV infections in the U.S. is relatively stable at about 50,000 people a year. But HIV is on the rise in people under 25, federal data show. The upswing is driven largely by infections among young black men.
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## What Americans Earn : NPR

Half of all Americans made less than \$50,000, and half made more. Here's one way American income breaks down, including state-by-state results.
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## How The Poor, The Middle Class And The Rich Spend Their Money : NPR

The poor spend more of their money on essentials like groceries and utilities. The rich spend more on education.
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## Immigrants Working In America, In Two Graphics : NPR

The U.S. is still a nation of immigrants: One in six U.S. workers was born somewhere else. Here's where America's immigrants come from, and what they do for work.
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## Are Football Players Really Living Longer Than Baseball Players? Why Grantland's Study Is Wrong

In this article, Greg Matthews argues that Bill Barwell’s article “Mere Mortals” makes a false claim by stating that professional football players live longer than baseball players. Barnwell’s argument is based on data collection of the ages of former professional sports players and a statistical test that proves that the mortality rate between the two groups is statistically significant. Matthews sets out to disprove this claim by collecting his own data and performing a statistical analysis that controls for the ages of the players. He finds that when age is accounted for, there is no statistically significant difference between the mortality rates of football and baseball players, and all Barnwell proved was that “the old die more often than the young.”
This article caught our attention because of its highly mathematical language, especially for a nonacademic article. We thought this would be great in an upper level statistics course to show how statistical testing is used in the real world, even in sports. It is also a great example of critiquing an argument one hears and then testing for oneself whether it is actually true. This type of mathematical thinking is necessary when reading math in the real world, and students must learn to take a critical stance and mathematics can give them the tools they need to dissect and test the validity of these claims.
We could see this article being used in the classroom to introduce a number of statistical concepts and show their usefulness outside of the classroom, such as statistical testing, confounding variables, confidence intervals, p-value, Fisher’s exact test, logistic regression, and density estimators. It could also be used as a more extensive project where students read the original article “Mere Mortals” and attempt to improve upon it as Matthews did. This article can also be used more generally to show the usefulness of statistics for making interesting arguments and using it to answer questions in all different fields.

This article would engage secondary students because of its focus on a context most students are familiar with: sports. However, there may be some students who would need additional background knowledge in order to appreciate and understand the article. Additionally, this article uses advanced academic language and students would likely need assistance to unpack all of the information it contains.

Via Shelby Crandall
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## What America Spends On Groceries : NPR

Food is much cheaper than it was 30 years ago. We're spending more of our grocery money on processed foods. And other insights.

The dietary habits and increasing obesity of our country are often spoken about in popular media, and this article provides data on how grocery spending habits have changed over the past three decades and how this might be affecting our health. We now spend more on processed foods and less on meat and dairy products. Students will be able to relate to most of the information in this article, as grocery shopping is a commonality among all students and their families. They can discuss this information with their families and see if their buying habits fit this trend. Students are also probably aware of the health concerns facing our country and the need to eat healthier foods.
In the classroom, the students could push even further by talking to their parents and coming up with their own spending on groceries that they have to construct into a representation, making the decision of what to choose as variables and how to represent the data to make an argument about their families’ grocery spending habits. They could compare their representations as a class to the other students. They could also look more into the idea of percent changes, coming up with a formula from the data set and seeing how the columns in the graphs relate to each other. For example, they could be given two of the tree columns in the last graph and have to recreate the third.
In regards to contextual information needed to engage with the artifact, the students would have to understand the basic food groups and have some background knowledge of these groups, including processed foods. The language of the article includes terms such as "much bigger" and the students could have to justify whether this is misleading or accurate, as well as how the author uses language to support his argument.

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## What Americans Actually Do All Day Long, In 2 Graphics : NPR

Working, sleeping, cooking, watching TV. Here's what the average American does on a typical day, down to the second.

This graph caught our attention because the context is accessible to everyone, as every student will be able to relate to dividing their time each day among different activities. It is also interesting to see what people are doing all day, where the majority of their time falls, and what activities the “average” American engages in. By using this relevant and engaging article, students will hopefully find the mathematical content more interesting and ultimately gain a deeper understanding.
In this artifact, there can first be a conversation about what the “average American” and “typical workday” mean, as well as how the author collected this data into an overall average. The first graphic is very intriguing, as the sizes of the bubbles show the proportions of the activities in regards to the amount of time spent engaging with each activity. The students here can really engage with their graphical literacy in the interpretation of the graph, seeing the times in hours, minutes, and seconds and then how that translates to a proportion. They could investigate why this particular representation was chosen for the activities, thinking about how the author came up with the proportions and with what purpose. They can consider if the amount of time is represented as the area of the circles or possibly just the radius, and what would be the implications of each of these representations. Also, what does the graph offer by arranging the circles in this way, and what does it hide? In the second graph, there is a further breakdown of two of the activities from the previous graph, displayed still using proportions but in a type of bar graph that builds on itself. They can again ask why this particular representation was chosen to display this data, and why the author chose not to continue with the circle representaiton. Does it have a purpose and make a stronger argument than the previous representation? This graph also has a y-axis to display the amount of time spent on each activity. Where is this information in the first graph?
To push on these graphs in class, the students could be challenged to come up with the percents and ratios of the activities (perhaps even extending to probability) and from there see how these are represented in the given graphs. They could make an argument for a better representation if they believe one exists and then display the data in a different way of their choosing. There could also be an activity in which the students collect their own data in small groups, discuss what activities they do on a typical day, and then create an interesting visual representation. The class could then compare and contrast their representations and also compare them back to the original graphs, determining how they fit into the life of the “average” American.
Students may need some contextual background knowledge to understand some of the vocabulary, such as leisure and commuting. They may also be confused about how the data is averaged and why it is broken down into seconds. For example, there were probably no respondents that answered that they spend exactly 33 minutes and 36 seconds shopping each day, but on average, most people spend this amount of time each day. This could open up a discussion about what an average is and how the data might look based on the given averages.

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## In Deeper Water

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HOW to show the value of freedom—specifically, its costs? The Spanish region of Catalonia goes to the polls on November 25th for an election that is seen as an...
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## How Much CO2 Is Created Byâ�¦

Every action, every event, every person, everything emits a certain amount of carbon. This interactive visualization examines some of those scenarios.
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## The Sunscreen Smokescreen

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## Album Sales Hit Record Lows. Again. : NPR

Digital music sales are growing, but can they grow fast enough to save the struggling industry?
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## A Nation Of Meat Eaters: See How It All Adds Up : NPR

Americans eat more meat than almost anyone else in the world, but habits are starting to change. This may be in part because of health and environmental concerns. We explore some of the meat trends and changes in graphs and charts.
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## Evidence Mounts Linking Head Hits To Permanent Brain Injury : NPR

With growing controversy over the risk of permanent brain injury in contact sports, researchers find an association between repetitive head trauma and brain disease in samples taken from deceased athletes.
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## The U.S. Economy, Sliced And Diced In Two Graphics : NPR

Economic growth slowed in the second quarter. We look at just how the U.S. economy breaks down into goods and services.
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## 50 Years Of Government Spending, In 1 Graph : NPR

Of each dollar the federal government spends, how much goes to health care? How much goes to defense? How much goes to other programs? And how has spending changed over time?
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## Income For Young, Middle-Aged And Elderly Americans, In Two Graphs : NPR

There's a huge variation in earnings across the lifespan. Here's how it breaks down, in two big graphics.
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