Warm-up

 

Come up with an explanation to accompany the graph.  What would the x and y graphs represent and what would the steepness of the line tell you about the graph?

Reading And Interpreting Graphs

 

Over time, I've discovered that I do not spend enough time teaching students to read and interpret real life graphs.  They have trouble, reading what the X or Y axis means which makes it hard to interpret what is going on.  Graphs have to have a context so they can be interpreted. 

Line graphs should come with certain pieces of information.  It should have labels telling what the X and Y axis represents and the units such as per thousand or miles.   The horizontal axis usually represents a time element such as weeks, months, years while the vertical axis represent the quantity measurement such as 15,000 fish, or miles covered, or the amount a stock sold for. In addition, the graph's title should tell you exactly what the graph is about.

Next, check the scale on both the X and Y axis.  Is the scales by ones, 10s, 100s, 15000s for each axis or is one by 10's and the other by ones? It is important to know before one begins to interpret the data on the graph.  Then when you are ready to interpret the graph, know the question you need to answer.  When is the number of salmon being processed is at it's lowest or highest.  What is happening to the population in 1924?  

Finally to read the graph, one finds the point where the x axis value intersects the y axis. This is the answer to the question and students need to be able to explain the answer to others.  This requires several sentences such as "the processing plant was only able to do 15 fish per hour in May" or "After 15 hours of driving an average speed of 70 miles per hour they traveled 1050 miles.

On the other hand, most bar graphs compare two or more items.  These still have the X and Y axis but the x axis is often made up of items such as appliances or types of fish, and the y axis tells you what it is such as kilowatt hours used or number of fish caught.  These graphs should have a title and something to identify what is being compared such as weekend vs weeknight use or caught by subsistence or sportsmen. and they color that represents each. Again, you have to know the question in order to interpret the information on the graph and answers need to be given in complete sentences. 

TV411 has a really nice set of activities that require students to interpret data contained in a graph. The first set of questions go with a bar graph on the amount of electricity used by several appliances such as lights, heater, or refrigerator.  The two bars represent weekday use and weekend use and the site asks 10 different questions which require the student to really read the questions and the graph to find the answer.  At the end of each question, the student will submit the answer and they receive immediate feedback.  If the student gets the question correct, the program will tell them so and explain the answer in more detail while if they miss the question, the immediate feedback explains the answer in terms of the graph.  

The second activity asks eight questions on reading and interpreting a pie chart while the third activity provides two pie charts and a table for students to determine if there is enough information available to answer certain questions such as how many seniors voted for a certain candidate or if to tell if more senior citizens voted for a certain person.  I really liked the questions in all three activities because they require higher level thought to answer.  Let me know what you think, I'd love to hear.  Have a great day.

Using Current Events In Math

 

I've been reading up on using current events in your math class. It is a great way to show students connections between the math class and real world events so they can see real examples rather than situations that seem to have been designed to align perfectly with the material taught in the section.

When students use their math skills to understand and analyze current events, they find the math means more and it's relevant.  In addition, research indicates that students who study news and current events in school, tend to do better on standardized tests while improving in a variety of subjects and have higher reading levels and a better vocabulary.

A simple search on the internet will lead you to so many different sites with math news that can be utilized in class.  Or check your newsfeed for articles with graphs and data such as the latest data on Covid, or international countries that are open, or oil spills. One can also read the local newspaper for sales, discounts, tax increases, and so much more.  It's just a matter of looking around. 

Most news articles are set to be read by someone who is at a sixth grade level which means most high school students should be able to read the articles.  One way to use the article is to have students create a verbal summary of it via Flip grid or any other video program.  Another way is to create a page with a place for students to create a written summery and several math related questions on the rest of the page.  Students can do either individually or in small groups.

Another way of using the news is to teach students identify The Who, What, Where, When, and Why of the story before answering the following questions.  Can they identify where the math is in the article? How is the math used to help people understand the news? Finally, what questions or thoughts do students have about the math or story?  

Now if you want to take this a step farther, ask students if it is possible to make prediction based on the math contained in the story? Are there any other positions or points of view that can be supported by the math or data in the story? Can the students connect the news to anything else they've learned?

Furthermore, when you are teaching a new topic like piecewise functions, or box and whisker plots, look for authentic data.  Authentic data might include having students measure the length of their feet and their height before creating a scatter plot of the data and creating a line of best fit for the data.  An activity like this gets students fully involved.

Try having students find ads on certain things in the newspaper so they can compare and contrast certain items such as tablets, pens, clothing, etc. Or they can compare the raw data from the ads to the graphical representation to determine is the information in the ad is accurate or slanted.  Do a quick search for information on population growth or decline for your town, city, or state to see how it has changed over the past few years and then have students make a prediction on what will happen to the population in 10 or 20 years.  

The same type of predictions could be applied to world records at the Olympics especially since this year the Olympics are being held over the summer, or weather patterns.  Weather patterns are good because much of the west has been experiencing a significant drought for the past 20 years.  Students could make predictions on the water level in Lake Mead and other lakes whose levels have dropped significantly.  They could predict when the water levels drop to being totally unusable.

Anytime there is an election, especially one for the president, have students look at the maps showing which states went republican and which went democratic so they can see how the states voted.  They should then compare these results with a map showing population densities and the distribution of electoral votes so students can see that having the most number of states does not mean you will win the presidency.  It depends on which states you get.

Lots of real math in the newspapers.  Let me know what you think, I'd love to hear.  Have a great day.

First Day Activity

 

I have an activity I love doing the first day of class before I pass out the textbooks, composition book, expectations, and the syllabus. It is one that doesn't require a ton of preparation, and only really needs a pen or pencil and paper.  

It is an activity that doesn't require students to remember actual mathematics after a long summer, nor does have them take notes.  It does help them ease back into school and it is fun.  Furthermore, the activity only takes 15 to 20 minutes to complete.

First thing that is needed is a regular sheet of paper that is divided into 16 squares.  Each box has a letter or set of letters so they are distributed as Box 1 is A & B, Box 2 is C & D, Box 3 is E & F, Box 4 is G & H, Box 5 is I & J, Box 6 is K & L, Box 7 is M, Box 8 is N, Box 9 is O & P, Box 10 Q & R, Box 11 is S, Box 12 is T, Box 13 is U & V, Box 14 is W & X, Box 15 is Y and Box 16 is Z.

Every student will get a copy of the paper.  They are given 10 minutes to try to think of at least one word for every letter of the alphabet. but take time to let them know if you will or will not accept variables as an answer.  In other words, if they can't come up with a word beginning with Z, can they use the variable Z?  I do not allow that.  They have to use regular words.

At the end of the time, have students stand up and leave their answers on their desk.  Give students 5 minutes to walk around the room, checking out everyone else's solutions for suggestions  but they cannot rush back to their papers to fill out words for the letters they haven't done yet.

At the end of 5 minutes, students go back to their desks and they are given another 5 minutes to fill out missing letters.  Once they've done this, you have two choices.  You can collect the papers and continue with your normal routine or you can go around the classroom writing all the answers for each letters.  What you'll find is that students will struggle with finding math words for certain letters such as Z, J, or W.  

I usually list all the words the whole class has come up for each letter.  If no one found a word for a certain letter such as J, I do not give it to them, I make them look it up online.  When they look up a word online, they also have to explain what it is if it's an unusual word.  They might find zero for the letter Z and that doesn't need an explanation but if they use jump for the letter J, they might have to explain that one.

I have done this so many times and each time the students do it, they have been involved and most students liked it a lot.  Let me know what you think, I'd love to hear.  Have a great day.

Warm up

If one coconut yields 425 ml of coconut milk, how many will you need to make 3.5 gallons of coconut milk?

Warm-up

If one coconut produces .75 cup of coconut water, how many coconuts will it take to produce 32 ounces?

Power Grids

 

It's that time of year again.  Between the hot temperatures and the out of control fires, the power grids are under a lot of stress.  Consequently, there is a lot of math involved in the production and distribution of power.  Power companies have to predict when there are decreased demands on the system to keep them running.  

The math involved includes differential equations, linear algebra, and graph theory which are used in grid simulations designed for operators to both monitor the systems and calculate the requirements of the system.

Power grids are actually complex systems that cover huge geographical areas and are composed of multiple devices.  In addition, the power system is made up of multiple generating sources connected by a network for transmission.  If any part of this stutters, the results are a rolling blackout or a blackout. The system has a weakness when power input changes from one minute to another when electricity is generated by wind power while it's pretty stable when generated from a coal-fired power plant.  So the mathematical models must include these because many systems combine wind, coal-fired, nuclear, and solar systems.

Unfortunately, writing mathematical models must incorporate a lot of different equations that govern every aspect of power, it's transportation, type of current, and so many other factors. The system is constantly solving all these different equations in real time so operators know exactly to correct any instabilities of the power flow. 

Another aspect of this situation is that communication and battery backups have to be factored into the situation because if the power goes out, how long will your cell phone work if the towers go down, or if they manage to stay up, how long can you be without power before your batteries die?  In addition, most power companies rely on cell phones now to communicate with their workers.

So some of the equations deal with the idea of setting repairs so that they are prioritized based on how long certain backup batteries at places such as hospitals or cell phone towers. In addition, they have to factor in where certain breakers lie in the subsystems and which ones have backup batteries.  

Thus the modeling programs used must take into account of so many factors and elements to provide everyone with the best information possible to keep the system working through all of the extra demands.  Math is responsible for the modeling used by power companies to be as efficient as possible. Let me know what you think, I'd love to hear.  Have a great day.