Television Stations in Education

Over the weekend, I read an article about how some school districts are providing education to their students during this time of uncertainty.  There are areas in America where students do not have digital devices or access to internet so some districts are getting together with television stations to provide education.

In the past, online education for certain college classes meant you were up at 1:00 AM watching a prerecorded show on the local public broadcasting station.  When it was time to take a test, you might head into campus to actually take the test but all the learning was done by watching those shows.

That idea is being brought back by districts who want to make sure all their students receive an education.  It is felt that almost everyone has a television in their houses while not every house has internet, a computer, or digital device.

For some programs, teachers are creating actual videos at home to be broadcast later by the stations.  One example of this involves a preschool teacher who creates a 30 minute program at her house in Virginia but it will be broadcast to students in the DC area.

In Los Angeles, the local school district with its own television station has partnered with two more public broadcasting stations to provide educational programming to its students.  In addition to showing the programs, these stations will show how the material relates to standards and gives ideas to students on ways to look at the new material. It is called "At Home Learning" and 71 PBS stations have decided to run this enhanced material on their stations.

Since about 80 percent of its students live at or below the poverty level, this is a way to reach its students so they still get an education.  It is beleived that in the second week Los Angeles did this, they had at least 140,000 watching with an estimated 200,000 viewers.

Furthermore, not ever city using television to provide education is doing it equally.  In Boston, MA, the local PBS station and WGBH is providing programming for middle school and high school while the programming on the local PBS station in Bethlehem PA, provides mostly elementary grade material.

It is acknowledged that television does not allow the same interaction as zoom or google hangouts but for school districts with students who don't have the technology to connect,  this is what works.  It means students might not be able to ask questions at the same time but most districts have teachers talk to parents on a regular basis.

Special education people have expressed concern that many of their students will not be adequately serviced by the use of television, especially the blind and deaf. As we all know, this is something school districts have never had to face before and everyone is doing the best they can to meet the needs of students.

Personally, I think using the television is a good alternative in places that have television available.  It means that districts do not have to pass out devices and arrange for homes to get some sort of internet  in order to attend online classes.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If the normal cost of a ticket is $1300 to Italy and over night it jumped to $6900, what is the percent increase of the ticket?

Warm-up

One Airline just cut their daily flights by 70 percent.  If they'd had 1300 daily flights before the cut, how many do they have now?

Analyzing Friday The 13th Movie Profits.

It is a time when we have to come up with lessons for students that they can do while hoping we can continue the curriculum as written but the reality is we have to find lessons that will interest our students.

The other day, I stumbled across information on all twelve Friday the 13th movies that were made from 1980 to 2009.  The information includes the amount spent to produce the film, the amount brought in over opening weekend, the amount made domestically and the amount it made via world wide box office amounts.

At the bottom, it also includes average cost of production, opening weekend, domestic box-office and worldwide box office for one film and the totals for all twelve films.  The information is such that it would be easy to create a simple project students could do a home.

1.  Have students use a spread sheet to enter the information for each film for production costs, opening weekend take, domestic and worldwide box offices.  Remind students that the figures for opening weekend are usually included in the domestic box office figures so they might want to separate the two into opening weekend and the amount taken domestically after the opening weekend.

2.  Calculate the percent made for opening weekend, domestic and worldwide box offices as compared to the amount it cost to produce.

3.  Use the information to create graphs such as line graphs, double bar graphs, and even a pie chart.

4.  Ask students which film made the most profit and which the least and have them base it on the data.

5.  Ask students which of the movies in the franchise made at least as much as it cost to make the film during the opening weekend and which ones did not.  What about domestic box office or international box office?

6.  Ask the students to research why there haven't been any additional films made since 2009.  It has to do with Paramount Pictures who sold the rights to New Line Cinema after Part VIII didn't do well but the original director and writer got into a legal battle over who owned the rights.  The case is due to be settled sometime in 2020.

If they don't like Friday the 13th movies, maybe you could have students analyze Harry Potter, Star Wars, or The Avengers.  This site has the same information for lots of different movie franchises and you could let students choose the franchise they'd prefer to do. Then have them research why there haven't been any more done or why they might continue making additional movies.

No matter what movie franchises the students choose, they can do the same as suggested for the Friday the 13th movies earlier in this column.  Take advantage of student knowledge of films to assign this type of project.

It is important to let them know that studios often look at information like this to determine if they will fund a sequel or pass on it.  If a film does not make enough money, studios do not want to invest in additional sequels as is the case concerning Friday the 13th films so they sold the rights but it doesn't always happen this way.

Let me know what you think, I'd love to hear.  Have a great day.

Two Population Apps

 Today, I'm looking at two more apps produced by the The Creative Learning Exchange in collaboration with BTN.  As with the previous two I reviewed in Monday's column, these two apps set up a scenario, discuss the factors in detail, show how the model is put together, and let students explore.T

The first is "Population Collapse" which explores population growth and natural resource usage.  It creates a small model to follow the population growth on a small island.  The model discusses birth rate, mortality rate, and uses some fairly real life based rates.

The model then goes on to set the use of the renewable resource in the form of trees and mentions tree capacity. The app goes into explaining how demand determines the amount of trees used each year and introduces the idea of stress which is defined as demand divided by tree capacity.


The model takes time to show the relations between the factors and explains why certain rates fall within certain limits.  It goes through each and every item on the drawing before showing students what happens and how long it takes for the population to collapse.

The app then goes through explaining how each factor effects the overall situation before introducing technology into the equation. It has students change certain factors to see how these change the final rates.

At the end, it suggests students make their own model to see how they can do on this.  This would be perfect to take some real life scenarios such as the deer population back in the 1920's where they killed all the predators and the population grew till they began starving.

The second app is Population Planner.

This app is only focused on the birth and death rates for a population.  The story is that you are a commander of a space colony and you are trying to get the population to grow at a certain rate so you have to play with the birth and death rates.


Each time you make a change, you run the model to see if you have made it.  If you don't, it tells you to try again but if you get close, it gives you encouraging messages.

I think, I'd have students do the population planner to let students learn about birth and death rates before adding in capacity, stress, and other factors.

I also think at the end of these two I'd have students create their own model for a population of animals and have them create it in the SPLASH! app. The app allows them to create simple models they can run and change values on.

Again, all three apps are free for android and apple devices.  They can be used at home during this time when students are expected to learn by distance.  Let me know what you think, I'd love to hear.  Have a great day.

Apps Allowing Exploration of The Exponential Function! Part 1.

Most of us are having to look at teaching via distance and most of us are not prepared for it.  I've spent my spring break exploring options for teaching classes this way but knowing my students, many of them won't worry about trying to keep up because they attend due to being under 16.  They see no reason for coming or doing the work.  So I've tried to find apps I can use to show these students that there are things they should know about including  I mentioned Creative Learning Exchange this past Friday but I want to spend more time on them because they have produced several  free apps which are well done and could easily be used in math classes.

 Retire Rich is an app that sets up a situation in which students are guided through the first two scenarios to determine which is better and in the process learn the program.

The story they provide is that Tara is thinking of putting away $1000 each year beginning at the age of 40 to 65.  She uses a fairly simple model and the app tells you the interest rate the account gets and it is basic.  When the program is run, she learns she won't get much more than $45,000 but if she does it from the age of 20 to 45, she'll end up with more than double what she would by waiting later.

After the second scenario, the student is encouraged to change the amount per year,  interest rate, or the ages of saving to see how these impact a person's final amount.

This means students can change variables to see how things change the overall picture.  How does interest rate change the final amount?  How does the amount saved change it?

What is even better is that students can double tap on each item for an explanation of part of it from interest to final amount.  The explanations include the basic mathematical information for each one.  In addition, there is a graph showing the growth of the retirement fund and a graph showing savings and interest.

This is a simplified model but it allows students to explore the concept of how to save the most amount within the shortest amount of time.  To make this more mathematically based, have students create a spread sheet with the same information to see if they agree with the figures produced by this app.  They can use the standard continuous interest or compound interest formulas to compare amounts.  This could  be turned into a project where students explore several scenarios and then create a prospectus for other students on planning for retirement.

The other app I want to look at today is Bacterial Sandwich.  This app looks at the growth of e coli in a sandwich.  The story is that someone packed a sandwich with 1500 bacteria in it at the beginning.  It looks at what happens to the bacterial when it is kept out in a room that is at 70 degrees.

Before having students run the actual model, the app goes through each factor in it and explains it clearly.

Then the app suggests the temperature be dropped to 68 degrees to see what the difference in growth is.  The student discovers the growth is significantly less under the second circumstance.

At the end, the student is again encouraged to  play with the different factors to see how it changes the final growth rate at the end.



This app even mentions that bacterial growth is exponential in nature.  So students are introduced to it in a safe way rather than being dropped into a problem in the chapter.

Instead of using a general problem giving the information, the problem appears in context with a real world situation.  In addition, students can play with this before they run the same numbers using the regular mathematical equations.

Once students are given the equation for bacterial growth, they can change the factors to see how these calculations match the answers from the app.

Both apps have a story setting up the context of situation and an explanation of the variables involved with the equations.  These are well done and easily understood by high school students of every level.

The nice thing about both of these apps is that they are both free and made to be used by both apple and android devices.  Wednesday, I'll review their two population apps to give you an idea of how they word.  Let me know what you think, I'd love to hear.

Warm-up

If a lemon tree produces 250 pounds of fruit this year and a lemon weighs 3.5 ounces, how many lemons did you harvest?

Warm-up

If one tree produces 45,000 flowers but only 1.25 % develop into fruit, How many fruit does the tree produce?

Mathematical Modeling and the Coronavirus.

 Although most of us are scared in regard to the Coronavirus, it is the perfect opportunity to study exponential growth.  In the past few days, there have been some great articles published on this topic and why not use them as part of a student assignment.

Since many of us will be setting up distance classes, this is the perfect time to introduce mathematical modeling.  There are tons of articles out there that can be used to help teach students more about this topic.

The CDC has released a simplified YouTube video on the Coronavirus following an exponential growth pattern.  It is a great introduction to the concept of exponential growth for a real situation.  I'd love to use it but not all my students have sufficient bandwidth to use it.  I might take screen shots to print off and make it available to them.

The New York Times is a great source for various articles dealing with the Coronavirus and its grown.  The link takes you to an article called the Exponential Power of Now that looks at two epidemiologists who noticed the numbers contained in a tweet and used excel to model the growth.  The article then goes into detail explaining everything.  In addition, there are links at the bottom of the article to other articles on the numbers (March 5), flattening the virus curve (March 11), worst case estimates (March 13), and mapping the social network (March 13).

The Washington Post has an article that explains why the Coronavirus spreads exponentially and ways people can flatten the curve.  This article has some wonderful animations designed to show things visually so students get a better idea of the changes as they occur.

The article found on Statnews gives links to at least one modeling program students can input numbers for their state or other states to see how fast people will be getting sick and how many hospital beds will be needed.  This article explains the model is actually made for hospitals so they can be better prepared for an influx of patients but it could easily be used by students to see how hospitals can use this model to plan.

This site gives better detailed information on mathematical modeling of the virus.  The article does mention how hard it is to create a mathematical model at the beginning of this because it is a new virus and no one knows anything about it so parameters are set using educated guesses.  As more is learned, the model can be adjusted. This article actually unpacks models used to predict the spread of infectious diseases and show how WHO and others are using these models to predict the future spread of the coronavirus.

This article has a simple explanation for mathematical modeling using a simple example to introduce the concept. This article is a great way of introducing the topic and building foundational knowledge for your students.  Most of my students have never thought about how mathematical modeling happens and this gives a great introduction.

As for actually doing simulations, check out the Creative Learning Exchange for their simplified infection game and free app.  They also have some nice mini lessons on energy drinks and zombies.  The other place to check is Stella software on the ISEE systems site.  They offer a free version which can be used from anywhere and if you check under models, you'll see a simulation is available to play with.

The simulator gives background information on the virus, provides model overview, the assumptions made for the model, policy and results which is the page where people can change numbers to see how it changes things, and a summary.  There are other models you can use from there so check it out.

There are lots of other articles out there but these are the most current.  I don't know what is going to happen next week but I'm prepared either way.  Let me know what you think, I'd love to hear.  Have a great day.

Return Of Worksheets and Packets?

 As we know, so many school districts have extended spring break or closed until further notice.  I hear the idea of moving classes from in person to online bandied about all over the place.  Yes, that is the ideal solution to closure and will allow teachers to continue teaching but there are some problems with that.

In most places in rural Alaska, internet is not unlimited.  I've paid about $115 for 25 Gb which when streaming movies does not last very long at all.  Some of the major cities like Anchorage and Fairbanks have access to unlimited internet but that is extremely limited.

Furthermore, many students rely on their local school for access to videos and other online activities but if the school is closed, they can't do it.  Few places other than the large cities have a public library.  Most villages rely on the school library for access to books, or computers.  In addition, the internet outside of the major cities is not very reliable at all and sometimes comes in limited amounts each day.

I know we are not the only ones who have students in this predicament.  It is something so many teachers have to face ass school after school suddenly has to make the switch.  I suspect my school is going to put together packets filled with examples and worksheets to send home to students so they don't fall behind.  This makes it harder for some students to learn because they need the in person interactions so they can ask questions, interact, and figure things out with the help of a teacher.  I don't think either online or worksheets will meet the needs of certain students who need more specialized instruction.

I plan to approach the whole subject with the question of "Will this meet the needs of my students"?  If the answer is yes, I can use it but if it is no, I'll throw it out.  Honestly, until we meet next Monday, I don't really know how the district sees things.  I'll continue reading posts in two groups I belong to on Facebook that deal with this topic and if I see things I can use, I'm putting them in a file I keep.

Even though the whole topic of the Coronavirus is scary especially since we don't really know what is happening from day to day, hour to hour, and minute to minute.  This virus does provide a wonderful opportunity to discuss mathematical modeling and how it is being used by various groups to predict what will happen in various countries, in the world.

I might just make a packet on mathematical modeling to give students a better idea of the topic and how it is being used by the government to predict the spread of the Coronavirus.  My algebra I class is studying exponents and we are getting ready to study exponential growth.  Since the spread of the Coronavirus is exponential in form, it meshes nicely.

On Friday, I'll provide links for information on the Coronavirus and mathematical modeling.  These links can be used to put together packets for students so they can learn more about how people predict the spread of disease.  Let me know what you think, I'd love to hear.  Have a great day.

Even Alaskan Schools Are Moving To Online

As most of you know by now, I live and work in a part of Alaska which is not on the road system.  I am out near Nome, the end of the Iditarod race.  Late Friday afternoon, I received a notice from my superintendent letting us know that school for students is cancelled till March 30th while teachers have to report on March 23rd to figure out how to deliver online versions of our classes.

For me, it is not a hard thing because I keep up to date on technology and I still figure out how to use it should I need it.  Well, now the time has arrived.

Many companies are waving fees to make their programs available during this time of crisis but it's hard to keep tract of everyone of these offers so Paul Solarz assembled as many of these as he could in one place.   Paul is author of "Learn Like a Pirate" opened the Amazing Educational Resources page which assembles all that information and it will be evolving as more is added.

This lists companies in alphabetical order, a link, a short description of what is offered, and the free service offered.  The list is by no means complete but I understand it is growing daily as people add to the list.  I know that it has places I've never heard of so I'll have fun exploring the sites.  In addition, this site has a facebook group of the same name so I joined that to keep up on top of things.

Furthermore, I'm keeping an eye on the Desmos people because they always have great things.  I've asked to join their facebook group because it is focused right now on distance learning.  They have several webinars (I missed the first one but caught the repeat) but the topics include Distance Learning with Desmos and several others that I plan to attend over the week.

Matt over at Ditch That Textbook is offering information and help on setting up elearning for your classes.  The link leads directly to the 50 e-learning activities, templets, and tutorials.  I guarantee this is one site I"ll be exploring in detail as I figure out ways to keep my students interested and engaged.

Shake up Learning has some great tips and suggestions for people who suddenly find themselves preparing for online classes in the middle of the semester. This is another site I'll be referring to as I prepare lessons for online.

Even ISTE has made 10 suggestions designed to help make going to online classes smoother including the idea that students should sign in a couple times a day rather than planning to spend the whole school day on line.  In addition, they recognize that many families may only have one device at home that has to be shared by everyone.

One site, NewsELA recommends that all digital material should be cell phone friendly because that is the device many students will be using.  In addition, they also recommend people create one to two weeks of printed material because not everyone has access to the internet and may normally use the library but if the library is closed, they may not have access at all.

I am researching this topic because I am one of the tech people at my school and I think I need to be prepared to help any teacher who has a question on using online resources via distance.  I assume that many of you are in the same boat I am and need these resources.  As I develop lessons and ideas, I will share them here.

I hope this helps.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

One orange tree produces on average 275 oranges each year but a good farmer can get a tree to produce 500 oranges per year.  What percent increase is that between an average tree and one coddled by a farmer?

Warm - up

There are 70 Friday the 13ths between 2010 and 2050.  How many on average are there every year?  Would a decimal answer be reasonable? Explain your answer.

The Entrants Cost for the Iditarod in 2020

 It is the time of year when the Iditarod has already started.  The racers are on their way to Nome and one racer had to drop out but her husband stepped in to finish the race.  Today I'm only going to talk about the cost to the entrant to participate in this world renown race.  This does not cover the cost of the entity that puts it on, only the racers.

The racers have to spend around $22,000 dollars to enter the race and this cost does not include the cost of the dog team.  The racers are not entering for the prize monies.  They enter for the challenge because the first place winner is only expected to win about $50,000.

Now to the costs.

1.  The entry fee is $4000 per musher.

2.  The mushers have to pay a fee of $1500 to pay to have their dogs flown from Nome back to Anchorage along with the musher, their gear, and a handler.

3.  The have to pay $350 for the pre race vet check and they have to place a deposit incase the dog needs special care during the race.

4. Mushers plan allot another $1500 for expenses such as food and lodging both before and after the race, and the sky kennels used to transport dogs when they fly home.

5.  The handler runs another $500 on average but it depends on several factors such as where their home base is.

6.  Mushers will spend around $1800 for dog booties which are used to protect the dogs feet during the long trip.  The total cost depends on the number of dogs the team has.

7.  Dog Food can run upwards of $2400 for bags of food set all along the trail.  The race officials require that each musher have at least 60 pounds of food at every checkpoint.  Furthermore, nothing is returned so what ever they do not use, becomes waste.  Most mushers will send out between 1200 and 1800 pounds of food at about $1.00 per pound and it costs at least $1.00 per pound to ship the food out to the various checkpoints.

8. People spend at least $1000 on plastic sled runners and spare parts to be used during the race.  This also includes sending spare sleds out to later checkpoints just in case but it does not include the cost of the sleds themselves.

9. The mushers spend at least $250 to send their own food out to various checkpoints so they won't starve.

10.  Mushers also spend another $500 for personal supplies such as socks, batteries, toiletries, hand and foot warmers, and other important items.

11.  Competitors then budget another $8000 to cover things like harnesses, at least two sleds, sled covers, vaccines, medicines, axes, proper clothing, and everything else needed for the dog.  They are going to be outside for a couple of weeks so they need to have enough to survive extremely cold weather.

Now this does not include the cost of the dog sled. Some competitors lease dog teams that they train with the kennel owners while others buy and train their own teams.  It is estimated that leasing a dog team can run between $15,000 to $20,000 and another $2000 per dog per year to cover the cost of shelter, vet bills, and food.

Just to let you know, the cost for 2020 is estimated to run about $3.5 million to organize and run the roughly 1000 mile race.  The Iditarod cannot exist without corporate sponsorship because the $4000 entry fee is not enough to cover all expenses.  As stated earlier, most mushers are not in this race for the money but for the challenge because if they win the first prize, it will barely cover the cost of the dogs and running the race.

I covered the cost of entering this race because many students have heard of it but are unaware of how much it costs to enter.  Have students turn this information into an infographic to share with others.  Let me know what you think, I'd love to hear.  Have a great day.

Ways to Use Tangrams in Math

I have used Tangrams in my geometry classes before.  I have a worksheet where they are told to make a certain shape using specific pieces.  One of the shapes is a triangle using all seven pieces while another is a concave tangram.

I know there are other ways to use them but have never taken the time to figure that out.  I've looked for apps to use but only found ones that had pictures that students needed to recreate.  Tonight I found one called Hands-on Math Tangrams on the apple store but it costs $2.99 and I don't know if it would work for high school students.  It says it helps students develop understanding of shapes and properties, visual problem solving, basic fractions, classifying angles, symmetry, rotations and translations.  I have not tried it yet because I prefer to try light versions before I invest in a full version that costs.

However, there are ways to use regular tangrams made by students.  I had one activity that had students make their own tangram square using nothing more than written instructions with measurements.  Once they finished the square, they were asked to color in the pieces before cutting them out.  This activity is good because it makes them read rulers and that is one of the standards.

On the other hand, one can use this which has students create their own tangram using a coordinate plane and geometric line segments.  Furthermore, it helps students practice using geometric terms to create something so it reinforces vocabulary.

Tangrams can be used to help students work on estimation and percents.  Let students work in small groups.  Each person in the group creates a shape using 3 to 7 tangram pieces on a piece of graph paper.  When done, the paper is passed to the person on the drawers right.  Each person will estimate how much of the grid is covered by the shape as both a fraction and a percent.  Then they could the number of squares associated with the shape and  total number of squares so they can calculate the actual fraction and percentage.  This provides a visual way for students to see the relationship.

Another activity is to let students determine the fractional amount each piece is of the whole.  For instance, the largest triangles represent 1/4th each, the medium triangle, the square, and the parallelogram are all 1/8th and the smallest triangles represent 1/16th of the whole.  Students then create concave shapes that represent say 1/2 of the total area of the 7 pieces..  Once they figure out one shape, they try another shape made up of different pieces covering the same amount of area. Have them repeat the activity for 1/8th, 3/4th or 7/16th.  This activity is good for helping students understand equivalent fractions and area.

Let students explore how many convex polygons can be made from the all seven tangram pieces..  The question was first posed in 1930 and two Japanese mathematicians came up with 13 convex polygons are possible.  This paper addresses the question and shows the 13 convex polygons with enough lines to recreate them.

There are other activities but I'll save those for another day.  Have fun exploring these.  Let me know what you think, I'd love to hear.  Have a good day.

Card Games To Use In Math.

 I am looking at card based games because used poker decks are so easy to get and it is good to use something other than technology on occasion in class.  Furthermore, cards are more kinesthetic than digital devices.  I don't think middle school or high school math students are too old to enjoy card games.

Card games provide a break from the usual worksheets or textbook while still focusing on specific skills.  In addition, cards provide something students can move around, hold, and touch while working on concepts.  These games also provide additional practice for students who might need it.

How about Multiplication war to help strengthen student multiplication or to help those who struggle with it become more proficient with their facts.  Each set of students will have a deck of playing cards.  Black cards represent positive numbers while the red cards represent negative numbers.  The Ace is worth 11, the Jack is worth 12, the Queen is worth 13, and the King is worth 14.  Deal out the cards so the deck is split, so each player has 26 cards.

To start the game, each player flips over the top two cards and carries out the multiplication.  The person with the higher product, gets all four of the cards. The two players then flip two more cards over.  If the cards are all the same which would produce a tie since the products are equal, so these are put off to the side and the players turn over the next two cards in each stack.  The one with the higher product wins all the cards including the ones set to the side.  The players keep going through their stack of cards until one person has all the cards and they are the winner.  If you time the game, then the person with the larger number of cards is declared the winner.

There is also exponent war which is played  almost the same as multiplication war except for a couple of things.  The first card drawn is the base while the second card is the exponent. The one with the higher result is the winner just as in multiplication war.  If this is played by middle school students, all numbers are positive but if it is played by high school students who are taking higher math classes, you can keep the black cards representing positive numbers while the red cards mean negative values.

Students could also play hit the target using order of operations to acquire a specific number.  This game is played with 2 to 5 players and one deck of cards.  Again the ace represents 1 or 11, the Jack is 12, the Queen is 13, and the King is 14.    The group decides on the target number together which could range from 1 to 30 at the beginning and expand as they become better at it.  One person turns over the top 5 cards.  Everyone in the group works to get an answer that results in the target number but if they haven't managed it within a couple of minutes, flip over another card to see if that helps.  The first person to find a correct answer gets the cards, selects the target number and turns over the next 5 cards.  Continue until the deck of cards is used and the person with the most cards at the end is the winner.  If there is a student who struggles with this type of thing, you can let them solve for the target number using only four cards as a way of differentiating.

If you want more ideas, check out the 50 plus page pdf here.  Although, it is geared for K to 6, there are games that can easily be modified for older students.  The thing is, many students need to practice working with fractions or decimals even in middle school or high school so many of these games will work.  Furthermore, just do the black cards are positive and red cards are negative to make the games a bit more challenging for older students.

Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If the number of accidents increases by about 6% the day after Daylight Saving Time starts and there are 28 more accidents, how many accidents are there before the time change?

It Changes Tonight

Clocks Change Tonight for Daylight Saving Time.

8 Possible Dice Games to Practice Specific Math Skills in High School

 Most students love to play games because it makes things more fun.  The nice thing about dice based games is that one can use regular dice or digital dice.  Regular dice have a nice kinesthetic feel while one cannot loose the digital dice.

I've discovered a few games that are based on dice but can be played by high school students.

1.  The Area Game.  Students split into groups of two.  Each group is given two dice, a colored pen each, and a piece of graph paper.  The idea is that one student will roll the two dice and create a rectangle with length and width of the two dice before coloring the shape in.  The other student does this to find the measurements for their rectangles.  The two students continue till they run out of room to add anymore rectangles or squares.  They count the total area for each player and the player with the most area covered is the winner.

2.  Binomial Multiplication.  This can be done in groups of two or more.  Roll two dice to find the numbers used for the binomial terms.  For instance I roll a red 2 and a black 5 so I have to multiply (x - 2) (x + 5) to find out what trinomial it forms.

3.  Trinomial Factoring.  Roll three dice to provide the coefficients of the trinomial and let students factor it if they can using any method they know.  So if you roll a black 2, red 3,  and red 4, you'd give the students the trinomial 2x^2 - 3x - 4 to factor.

4.  Polynomials and roots.  In this you roll the number of dice to match the degree problem you want so you have the coefficients of the polynomial terms.  Then roll a single dice for the root and let the students practice using either polynomial or synthetic division to find out if it is a root and or what f(c) equals.

5.  Transformation games - roll two dice three times to find the vertices of a triangle.  Students will draw the triangle on a coordinate grid.  Then roll one more pair of dice to provide the translation of the original triangle.  Once the triangle has been translated, roll the two dice to find the dilation factor to apply to the new triangle.  This can be repeated with quadrilaterals, pentagons, or other sizes.

6.  Battleship using two dice and a coordinate grid.  The dice have to be at least 12 sided to work well.  Each student will color in the location of their battle ships on a coordinate grid before beginning.  They will have a screen made out of manila folders or on their tablet.  I bet one could even set it up using Desmos for this.  Once both players have their ships in place, they begin rolling the dice to find the x and y values.  The student reads out the coordinate result and the other student lets them know if they scored a hit.  If they did, they can roll the dice again but if they missed, the other student will roll and read out the coordinate of their roll.

7.  Order of operations. Roll 5 dice and write the numbers on the board.  Students can use any operations to find a goal number.

8.  Mean, median, mode, and range.  Roll 10 twenty sided dice and let the students use those numbers to practice finding the mean, median, mode, and range for theses numbers.

These are just a few games one can use in the math classroom using dice.  Let me know what you think, I'd love to hear.  Have a great day.

The Economics of Producing a Concert.

 If you live in a city or close to a city, you know there is some sort of concert happening on a regular basis.  It might be Lady Gaga who hit town or it might be the local symphony orchestra. Either way, it costs something to put it on.

We are always trying to build student interest in math so let's look at some practical applications such as the cost of putting on a concert.

So the figures here are based on a musical concert done by a big name group.  The cost of the ticket rose from $84.63 in 2017 to $94.31 in 2018.  This is up from the $30 to $40 tickets back in the 1990's.  Unfortunately, groups are no longer making money by selling their music, they make it on the concert circuit.

Furthermore, concerts need to be more interactive to attract people and make them want to attend.  When a promoter sets the price of the ticket, they have to take into account the expected revenue versus the expected costs.  Some of the costs include the artist.  If the artist is the only one, they get the fee but if it is a band, the band will have to split the fee.  Add to that the cost of band's crew who also have to be paid.  The promoter might also hire someone to be an opening act for the big name.  The opening act warms up the audience and makes the concert last longer.

Then there is the cost of the venue which can range from several thousand dollars for a smaller one to over $50,000 for the big ones.  In addition the promoter may have pay for lights, a sound system, staging, and a production crew if the venue does not include those in the rental fee.  They might also have to pay for security, parking attendants, and a clean up crew if it is not provided by the venue as part of the rental cost.  Depending on the venue and it's location, the promoter might need to purchase special permits or licenses.

The promoter also needs to provide marketing and advertising for the concert.  The cost of this depends on the the type of advertising the promoter does.  It costs more if they use radio, television, and print ads in addition to social media.  The more the concert is advertised, the more tickets they sell and the more the expenses are.

Furthermore, most groups sell merchandise to raise more money. It is said that merchandise accounts for about 6 percent of any bands income.  When bands sell merchandise, they build their brand and their followers will buy things to show their pride in being a follower of the band.

The final part of the equation is the price of ticket sales.  The price of the ticket includes all of the above and one more thing.  The ticket price has to include the cost of using the ticketing platform that the promoter has linked the website to.  The particular platform might let the promoter keep the booking fee but charge him an initial set up fee and a monthly charge while others might just charge a per ticket fee or a monthly charge.  It depends on the company.  The bottom line on ticket sales is that the easier they make it for people to purchase the tickets, the more they will sell.

This article gives some solid numbers on the cost of a month long tour done by the band Pomplamoose back in 2014.  They played 24 concerts in 23 cities over a 28 day period and wrote about the experiences.  The whole tour cost them almost $148,000 to produce but they only managed to bring in almost $136,000 so they took a loss of $12,000 on that tour.

Furthermore, this article gives the general costs of everything involved in setting up a concert from the basic to medium, to premium costs so students get a better idea of how much each part costs.  They can use the material in this to calculate the cost of setting up a concert as if they were a promoter.

Let me know what you think, I'd love to hear.  Have a great day.

Cost of Elections

  We have an major election coming up in November.  The country will be choosing a new president and it involves primaries and the actual election. What type of costs are involved in holding an election.

The costs will vary depending on the location of the county and the type of election itself.  It is estimated there are over 10,000 jurisdictions who are in charge of running elections.  This does not include subdivisions in each jurisdiction such as school boards, municipalities, fire districts, and a variety of other elections.

Over the past 50 years, new laws have moved the responsibility for the cost of elections from the municipalities to the state.  Consequently the way states help pay for the cost of elections varies from state to state.  This includes the voting equipment, people to run the elections, the space used for elections, and so much more.

This website has a list of approximate costs for select counties in certain states.  The data is from 2012 or 2013.  According to the list, it costs around $209,000 to hold a local election to repeal a specific bill in Mojave County Arizona.  In Riverside county in California, it cost around $113,500 to hold an election on allowing a Walmart Super Center to be built in the area.  The costs given on this site are per local question and if taken together can add up to a huge amount.  The nice thing about this information is one can create graphs or infographics on the information.

This site has great information on the total cost of elections from 1998 to 2018 with a break down on presidential years to show congressional and presidential elections while showing only the congressional elections in the years that did not have a presidential election.  The site also has a great double bar graph showing the same information as in the written format.  It is possible to use this information to calculate the percent increases on electoral costs every two years.

This site looks at the cost of both the republican and democratic candidates who ran for president from 1980 to 2016 and a projected cost for 2020.   The costs include the biggest spender and the total party cost so students can determine the percent ratio of the biggest spender to the total amount spent.  There is also enough information for students to create their own double bar graphs out of the available information.  In addition, it lists the top 5 most expensive presidential campaigns of all time and the top 5 candidates who spent the most money.

It wouldn't take much to find out how many people voted in each election and how many people voted for the republican or democratic candidates so it is possible to calculate the per voter cost.  Then it is possible to calculate the increase or decrease percent for the same 40 years.  So many possibilities.

As far as finding out the cost of actually setting up the physical polling places for a regular election, I couldn't find out the information.  I can find general information but no solid figures.  The only solid figures I could find were in terms of the people who ran and how much they spent,  It was only for the first site, I was able to find more specific information but it is still difficult to find.

The information of running for congress or president is enough for students to create graphs or infographics discussing the over all cost to be president and comparing and contrast if the one who spent the most won every election.  Let me know what you think, I'd love to hear.  Have a great day.

Warm-up

If there are four cups of pepper corns in a pound and 267 pepper corns in one cup, how much does one pepper corn weigh?