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?