Friday, July 29, 2016

My Dream Bedroom

Building Plan, Floor Plan, Architectural  Over the period of several years, I would regularly assign a project to my Geometry class which took a while and required a variety of math skills and yet was a real world assignment.

The premise is simply that their parents won a million dollars so they've decided to build a new house.  So they get to design their dream bedroom exactly as they want. 

For the assignment, they must do the following.
1.  Create a floor plan of the room including the closet, bathroom, home theater or even their own basketball court.  The floor plan must be properly scaled.

2.  They must create drawings showing the four walls and the ceiling showing where all the doors, windows, movie screens, etc.

3.  They must calculate the cost of finishing the room with the flooring, walls, and ceiling.  They include lights, fridges, stoves, basketball hoops, etc.  When they calculate the amount of paint, they have to know what a quart or gallon covers so they can round up appropriately. I provide a nice sheet with every possible item I can think of from primer, to a matte finish, to gloss for the bathroom.  Now I send them to websites like Lowes to find what they are interested but I assign a percent to add to the cost to cover shipping out to the Bush

4.  They create a final write-up of the room itself and an estimate for finishing the room. 

Since I last did the project, iPads have arrived in the classroom.  I would change this assignment slightly by downloading a couple of apps such as one designed to create the floor plan of any house or use free web based software.  Some of the apps or software allow the user to create 3 dimensional views and populating the room with furniture, etc.

There are free apps out there designed to allow contractors, etc to create estimates for jobs that could be downloaded and used by the students as part of the project.  Tie all the parts together via a slide show, prezi or other program.

This is very real and uses lots of real life math.  This also provides students with the understanding of what is involved in creating a room to meet someone else's vision much like an architect or interior designer.  This could be varied to design a store, or any other building.


Thursday, July 28, 2016

The Math of Extreme Sports and Skateboarding

Biker, Motorcycle, Stunt, Man, Person  In two years, there will be another winter Olympic with snowboarding.  I got to watch it one year with a neighbor and I was impressed with all the twisting and turning they did.  I know we see things that are as impressive in other extreme sports but what is the math behind the sport?

Would it interest those one or two students who bring their skateboard to school?  What about the student who practices tricks with their bicycle?  How about the guy who heads up to the mountains to practice snowboarding?  Do they know the math they use every time they go off to practice their sport?

Skateboarder, Half-Pipe, SkateboardAfter researching the topic, it became clear that other than ads for certain books, there is very little out on the math behind extreme sports.  If you have a month available, check out this lesson plan for math that involves extreme sports.  It focuses mostly on slope, distance, midpoint, and functions.  It is requires that students create a presentation on one extreme sport of their choice and its associated math.  It integrates videos, math, technology, and the internet so students must research, create, synthesis, and create a final presentation.  It is very well written.

Otherwise you end up looking up the individual sports.  For instance, where is the math involved in skateboarding?  What about snowboarding or biking?  Let's start with skateboarding where there is math involved in both the creation of the board and with riding it although most of them math associated with riding it comes via physics. The Exploritorium has a great section which explains about the composition of a skateboard, the wheels, ect so everyone has a starting point.

CPalms has a great lesson on designing a skateboard ramp which requires the application of slope and similar slopes during the design process.  The lesson includes prior knowledge requirements, guiding questions, and the actual teaching lesson which includes a video, power point presentation, and all worksheets needed.  Although it is listed for 8th graders, it could easily be used in higher levels.

This site in the UK has a lovely article on designing skateboard parks in a general way but this interview from Bed Time Math that shows many of the mathematical topics a designer has to think about when creating a skateboard park.  It explains in detail why you might want a ramp with an angle of 20 degrees instead of 45.

This article at Scholastic impressed me with the various worksheets and lesson plan.  The worksheets incorporate graphing, math, and require students to justify their answers which is a great facet of the lesson.

We mustn't forget the math involved via the physics aspect of the sport!  This site has some wonderful explanations of certain jumps, the math, and lots of pictures showing where the forces are. The Exploritorium also has a unit on the forces involved in certain skateboarding tricks and includes detailed explanations with photos.  To finish off this section, this site has a list of wonderful links to videos, articles, etc to fill out the topic.

Tomorrow I'll look at the math of snowboarding and bike tricks.  Hope you enjoyed today's entry.




Wednesday, July 27, 2016

Coding and Math

Over the past two weeks or so, I've been working my way through the classes at Code.org.  I started with course 2 so I could get the full experience of working with it and I am in the middle of course 3.  As I've worked my way through each lesson, I've come to the realization that I need to know the basics in order to code effectively.  Even after starting this entry, I realized that there are two different types of coding and both involve math.


Penguin, Tux, Animal, Linux, CartoonThink about it.  You have the coding such as in hopscotch or scratch where you create a game using the visual blocks.  You might have the character dance, move around, or even make a few sounds but the other is actually using a language to create a routine that solves some mathematical equation.

 Because I started with Code.org, I thought of coding within the context of the first.  I thought the only math I needed was simply to decide how many steps my character took or how many repeats the subroutine needs to complete the design but this is only true if I stick with the small things.  If I want to create a more complex game or program, I defiantly needed math. It was once thought that you needed strong math skills to be a programmer but teachers are discovering that the programming may build math skills instead.

According to the Tynker blog, programming improves math skills and does it in a fun way at the same time.   Programming can help students visualize abstract concepts because they see the math in action.  I've seen it myself when I've goofed on an angle and the finished product wasn't correct.

Even when I created a design out of repeated shapes, I had to know the angles so I could instruct the pen to produce the basic shape and then another angle to offset it to produce the final picture.  There is a need to know measurement so the character can walk the correct distance, jump, or even dance.

Programming improves computational thinking such as logic, evaluating data, and breaking a problem down into more manageable pieces.  It helps students develop perseverance. In addition, they apply these skills to real world applications.  Programming also helps develop problem solving skills because you have to figure out where the mistake is and how to correct it.

 So if a student creates a game involving a projectile, he has to write in the proper mathematical equations otherwise the object will not follow the correct path.  There is also math involved in the object bouncing off of a wall or other solid item.  All these are examples of mathematical modeling that manifests itself visually in a game or app but what if students decide to program routines in a language such as Python which actually carry out some sort of mathematical calculations? 

This is where they need to have a solid basis in mathematics so they can write the program to complete the deed effectively.  If a student decides to create a program that factors a quadratic, they have to know how factoring is done even if they only use the quadratic equation.  In my opinion, they can look up the mathematics needed for any routine they wish to create by looking on the internet or in a textbook. They can learn what they need to know or become more solid in their understanding. 

So the next time someone asks, "When am I going to need this?" We can answer they will need it when they program!


Tuesday, July 26, 2016

Thoughtful Bell Ringers

While researching a topic on the internet, I stumbled across this really great site that is perfect for warm-ups or bell ringers or when you want to work on developing their ability to explain choices.  Its called Would You Rather?

This activity has pictures with an open ended question but which ever one, A or B, you choose you have to explain your answer.  Depending on the problem, you may be required to justify your answer with mathematics.

The problems  usually use a real world scenario such as pizza, chips, apples, or even sports teams.  Some of the problems include a link so you can add activities in or at least read up on the topic so you know more about it.  If it deals with sports, I usually have to look things up because I love Australian Rules but that is not a sport my students know about so I have to use theirs.  The author has 9 pages of these lovely thought provoking questions.

Another site I found that could also be used during bell ringers or warm ups is something called Visual Patterns.   This site has 220 patterns that show the first three iterations in the pattern and then asks you to find the number of objects if the pattern is repeated to level 43.  They also ask for the equation but they only provide the answers for the pattern to level 43.

These visual patterns are wonderful because they do offer some great thought but I would add that students need to show how they got their answer by showing their work in some manner.  This activity requires higher level thinking because you have to figure out the mathematical pattern or equation in order to find the answer to the question.

The final site if from Estimation 180 which is a site designed to help develop number sense.  There are about 220 pictures, each with a question requiring students to estimate the height of someone or something, estimate the number of things, etc.  All questions that help fine tune their number sense.  I looked at one that showed one cheetos cheese ball on a cookie sheet and asked students to estimate how many will it take to fill the tray.  He does not give one answer, he actually provides a video answer for the question.

In addition to these short activities, Estimation 180 also has lesson plans for grades 4 to 8 with a variety of topics such as expressions and equations, geometry etc.  I like that the lesson plans are actually more of a here is what I did, this is what my students responded, and this is where I got the material from.  

 I love these types of activity because these are a way of developing math literacy in the classroom.  I plan to use these as openers in my classroom so students have something to work on while I take roll and do the usual housekeeping during the first 5 min of class.  I'd like to thank US News and World Report for these websites.

Monday, July 25, 2016

Why Is It Important To Convert Measurements

Tape Measure, Tool, Measure, Meter, Tape I know a guy who if you ask the temperature will give it to you in Celsius which is great except if you live in a place where its all given in Fahrenheit.  He's the same guy who ended up being given a problem at work with mixed metric and standard that needed to be converted into the same units.  On the other hand, my mother operates only in miles per hour and when we drove from Alaska to Washington State via Canada, I had to translate km into miles.  Otherwise she would interpret the speed limit as being miles per hour rather than kilometers per hour.  One good reason to be able to convert from metric to standard and back again but what are other reasons for knowing conversions.

We all know its used in science class which means students are good at converting in science but the minute they pass through the door, they forget what they learned especially if it requires you to do it in real life.

One example is if you want to redo the carpet in your house, most rooms are measured using feet and inches, yet carpeting is sold by the square yard.  This is a type of conversion that they are likely to run into in real life.  What about ceiling tiles, paint, or even flooring.  These all require a type of conversions.

Certain jobs such as Pharmacy Technician need to be able to convert within the metric due to the medication prescriptions they fill.  Nurses and other medical personnel need to know that 1 CC is the same as 1 milliliter of fluid.  I once taught a basic math class for nurses at a small community college.  That was one measurement we made sure they knew because it is used in work.

If you participate in local races, many are in kilometers rather than miles and its nice to know how far you will be running if you participate in a 10 km race.  Its about 6.21 miles since 1 km = .621 of a mile.  What about if you buy a free cookbook from Amazon and it turns out the author provides measurements in metric, you have to convert so you can make the dish.  I have a few of those cookbooks myself.

Even if we don't want to know about conversions, we do need to know how to do them although most kids I know would tell me to go online and use a conversion calculator......LOL.  I'd like to know your thoughts on why its important to know how to convert measurements.


Friday, July 22, 2016

Three Suggestions For High School Math Teachers.

The U.S. News and World Report magazine has an interesting article containing three suggestions for high school math teachers to do this summer.  I always have such a list of things to do and usually get maybe two done but one of the things I do year round is the first thing on the list.

School, Lockers, Hallway, High SchoolThe magazine recommends that we connect with other math educators.  That can be difficult to do, especially if you are the math department in a small school in a small town that is a distance from anywhere with a larger school.  Thanks to the internet because it allows you to join groups so you can connect with others.  I love the google plus group Mathematics Education because it has so much that I am always finding good material.  I can post questions, receive responses and keep up on the latest.

In addition, I belong to the National Council of Teachers of Mathematics and I subscribe to two of their magazines.  Although I enjoyed the research one, I found the magazines for teaching high school and middle school math much more usable.  One feature I use regularly is the cartoon math.  I love it but my students sort of tolerate it because they hate word problems and this activity is heavy on word problems.

The second thing they recommend is to look for ways to make math more relevant including exposing students to some of the newer apps such as Desmos or GeoGebra which are both help visualize math.  Another suggestion is to assign students a performance task that is linked to a real world situation such as a disaster relief simulation.  If you read my blog regularly, you will notice I sometimes review apps or find real life applications of math on the internet.  I want to tell students they will use this when they do this.  It is important for students to see a connection.

The final recommendation is to look for inspiration by reading other educators blogs.  This is one reason I subscribe to several blogs, read the Mathematics Education group (Josh provides links to worthwhile blogs) and do web searches for new blogs.  I get ideas this way for my classroom.  I also check out sites like the NCTM or AMA (The American Mathematics Association) or other such group for ideas.

The one thing I consistently do year round is look for inspiration by reading blogs, talking to other math educators, or just putting out a holler for help.  Its a way to get past teaching students that if you are good at completing worksheets, you are good at math as noted by a teacher in the article.  So true!

Thursday, July 21, 2016

Shanghai vs Singapore Math

Singapore River, Skyline, BuildingIt seems like every time I turn around, there is a new math method that is the perfect one to solve all the low scores, help students learn math, and is going to change everything. First it was Singapore Math, now its Shanghai Math.

 I have not used either Singapore or Shanghai methods but I know one home schooling mother who loved Singapore math because it helped her daughter learn math better.

So what does the media say about similarities and differences of these two programs since both are reputed to have helped their countries score higher.  One of the main similarities is the idea that all students can become good mathematicians and that all students progress at the same rate, covering the same lessons. They are all expected to meet high expectations so both programs set a higher bar than many other nations.

 In Singapore, students are expected to take higher level mathematics and be prepared to take higher level tests.  Further more, they all take the same math classes in the first few years of secondary school.

In Shanghai, math in both primary and secondary schools are taught by math specialists who teach one to three 35 min lessons daily while the rest of the day is spent in collaboration, correcting work, or going over exams.  In Singapore, math specialists teach math in the upper elementary and secondary classes but only 50% of the primary teachers have a university degree at all so the textbooks are designed to be taught by someone who is not a math expert.

Both systems have built in time to learn the specific concept before moving on.  They have a methodically prepared curriculum with carefully prepared lessons and resources.  Discussion is valued in both systems so teachers are always asking questions, students are demonstrating work but time is spent in every lesson to go deeply into that one concept.

Both programs use specific visual representations connecting the visual with the abstract.  Singapore regularly uses manipulatives such as unifix cubes to convey the concept so by secondary, students have a strongly developed number sense.

In both programs teachers base their teaching on the textbooks that all students use in the classroom.  The math books used in Singapore are written and taught in English even though for most teachers and students, English is their second language. This means that all concepts have to be well enough illustrated to be understood by all students.

On the other hand the math books in Shanghai are highly prescriptive even to the point of telling the exact method of teaching the math lesson and how students will learn the lesson.  Remember all students are expected to be on the same page and progress at exactly the same rate.

It was pointed out in Education Media Centre that country results for the PISA or TIMSS may be based more on how close the curriculum of the country matches the actual test questions on either of these two tests rather than the teaching style.  Another person pointed out that students who come from a home where education is prized and who are expected to do well, do better in school.  It also appears that the scores do not increase between the ages of 10 and 16 so it would appear that students need to develop a strong base in those early years.

We already know that if a student is not on level by the end of 3rd grade they have a significantly increased chance of not graduating and of dropping out.  After all the reading I've done, especially on the Shanghai method, I wonder how their teaching method compares to schools in other regions of China.  I also wonder if the PISA or TIMSS were given to students in say Beijing, or other places in China, would their scores be as high?  I'm also wondering how many students are enrolled in the Shanghai school system and how many of those students complete a full school from K to grade 12 or equivalent.

According to what I read, China only requires that students attend 9 years of school and if they go further, their families are required to pay a small fee.  I wonder how many students "drop out" at this point.  I also know that students still take regular exams and I read where 80 percent of students attend night and weekend cram lessons to ensure they pass their exams.  I wonder how many of these students who do well in Shanghai are taking these extra lessons to improve their grades?

I think it is wrong to adopt a system based on one test result that is limited and whose students may have had "extra" tutoring to pass.  From my experience teachers who are confident in Math and who know their math tend to have students who do better than those whose teachers are "scared" of math.  We need to find what works for our individual classes because one size does not fit all.







Wednesday, July 20, 2016

The Shanghai Method of Teaching Mathematics.

Mathematics, Formula, Physics, SchoolApparently, there is a sincere interest in the Shanghai method of teaching mathematics for both elementary and secondary school in Britain.  Since students from Shanghai score at the top of the PISA tests, the method used to teach the topic must be wonderful and if applied in the United Kingdom, should help those students improve their scores.

Before exploring the method, it should be noted that only the students in Shanghai and Hong Kong took the test so I don't know how this method compares to the rest of the country.

It appears that the premise of the Shanghai method is that the lesson is composed of a teacher led whole group instruction for about three-quarters of the time.  The book used is created and annually updated by the Shanghai Commission of Education so everyone is using the same textbook in class and using it regularly.

An integral part of the class is for teachers to continually ask and answer questions, have students work their solutions on the board and query students about their thinking.  An ongoing assessment to monitor student understanding.

There are four basic principals associated with this method of teaching math.  The first is that the teachers repeat mathematical vocabulary throughout the lesson and require that students use complete sentences to respond.  In addition, teachers have students repeat certain sentences in unison and often selected the more advanced students to model answering questions using complete sentences.

Second is that teachers focus on conceptual understanding and learning.  There is a heavy emphasis on pictorial or other manipulative so students gain understanding that allows them to transfer to the more abstract material.

Third is they have a clear goal they do not deviate from even when students ask questions about other aspects of the topic.  If the teacher is trying to teach one topic and a students gets a related topic, the teacher will not move on because the related topic is usually covered in another lesson.  The lesson is to only be on the planned material with no deviation.

Finally, the teacher has a good knowledge of the material and is aware of potential misunderstandings of the topic so they are prepared.  They know their topic but these teachers general teach only two classes a day at most not the usually 5 to 6 a day most of us handle.

According to a question and answer section of the Daily Mail newspaper in the United Kingdom, primary teachers are trained in math and only teach maths, not a variety of subjects.  In addition, the students are all on the same page in the textbook at the same time but the students who are quicker do not move ahead, instead they help demonstrate the materials.

Apparently one student answers the questions and the others repeat the answer.  It is a highly regimented and repetitive teaching method with the idea that all students will learn the material and none will be left behind.  The arrangement of the classroom is one where students are in rows so students can focus fully on the teacher and the material being presented.

There are indications that these students are tested on a frequent basis so they are monitored  more than our students.  I'm going to guess that by taking the actual program and moving it to the United Kingdom, their students may not do as well as they hope because the program was developed for a specific cultural group.  The mindsets of the Chinese tend to be quite different to those in Britain and this math program is geared for that mindset.

I think the program has some excellent elements but I'm not sure it is wise to simply apply the whole program as written without taking into account British society.  Will it work?  I don't know but what I do know is that I've seen districts develop programs that worked well for their students but the same program did not work for other districts because it the student population was not taken into account.

Honestly, this sounds more of the chasing the rainbow looking for the one program that will elevate scores and get the students where they are "supposed" to be.  Unfortunately, people will be disappointed if results are not astounding within the first year or two.  The reality is that any new program can take 5 to 7 years before favorable results are actually being seen.  Only time will tell how well this works.


Tuesday, July 19, 2016

Numbler App

Numbler blank board
Numbler is a wonderful app that resembles a numerical scrabble but instead of words or sums, you have to create a full equation where two sides are equal to each other.  This app is put out by Braining camp who have put out other great apps.

This is the free version which only allows you to play against the computer.  If you want to play against other people, you have to get the full version.

The idea is that you use some or all of the tiles at the bottom to create an equation that is true.  You can combine the tiles for larger numbers and you can only use the operation tiles once.

I started with the 0,2,6,7,3,0 tiles.  I came up with 60/2 =30 which is a true equation.  The computer added =6 x 5 to the right of the 30.  At the end of the round, I had 11 points while the computer had 22.


The idea is that you keep playing until you run out of tiles or you can't play any more. It sounds easy but it becomes progressively more difficult as more and more equations appear on the board.

Anyone who plays this is going to have to move beyond simple equations such as 4 = 4 or 4 + 5 = 5 + 4.  It is possible to add a 45 = 9x5 = 45 = 40 + 5 = 49 - 4 and it covers a whole roll.

Every time you add a bit more to the original equation you add to the basic point value so sums can increase.  As you note, some square are triple value, others double, others just add 5 or 10 to the sum but these do not count the second time through.

Each time you play, the app automatically counts up the value and adds it to the score sheet.  I found it seems to count quite accurately.

This is a challenging game that could easily be integrated into even a high school math class because it requires a lot of thought.  I've had to stop and really think about the numbers I have and how to work around things when the board is more filled.

I admit for myself, I ended up resigning from the game before it was completely over because I couldn't find a place to play anything so I'm not fully sure when the game is over. 

If you make a mistake, the app crosses out the whole set and via a dialog box, it says this is not a true equation and you must try again.

I like the game mostly because I enjoy this type of challenge.  I want to try it with my students to help them build perseverance and develop their critical thinking skills.  I've read that students learn using games so I've been exploring games that students might enjoy and may help them develop their skills.  This is one that does it.

Check it out, give it a try, and let me know what you think.

Monday, July 18, 2016

Math Bash Free

 Math Bash comes in two different versions, the free and the paid.  The free has some of the topics while the paid allows access to all topics.  I am only looking at the free version.

The app offers select practice question sets, quick start random questions, advanced question selection and matching pairs.

The matching pairs is my favorite because its like concentration where you have to match the equation with its solution.  You have a choice of identifying 2D and 3D shapes or Brackets but you can also select a topic from a fuller list so that you have more choices.  It is timed but only for how long it takes to solve.


 Select Practice Question set has you select a topic which in this case are fractions, decimals, percentages, mental calculations, algebraic expressions and mixed algebra questions.

The mixed algebraic questions offered questions on factoring, identifying the equation of a graphed line, or number patterns.  Since it is a quiz, it is timed.  You do have the option of selecting from a different list.

The list they refer to is the list you get when you click on the advanced question selection so you can work on a specific topic.  Not all the topics are accessible but enough are to give the kids a chance to really practice the skill.  Only the ones without the asterisks are available but for $1.99 you can get the full version. 

The last choice is the start random questions which is exactly as it sounds.  You start taking the quiz as soon as you click on it.  If you miss a question, it lets you know, shows the correct answer, and moves on without giving you a point. 

It is geared for the 11 to 14 crowd but if you teach high school, this could be used to scaffold skills that students are weak in when they arrive in High School.  There are four different versions of the paid app because its wants to provide support to the UK, the US, and two other programs such as the International Baccalaureate Program.  There is an paid elementary version set up along the same lines.  Give it a try and let me know what you think.

Friday, July 15, 2016

Gambling, Casinos, and Math!

Whenever I pass through Vegas, I think about something some friends told me in regard to gambling.  They lived there at the time and always said that if you want to use slot machines, use the ones at the grocery stores because the odds are better.  I never thought about that until I stumbled across a website that explains odds at casinos in detail.

Play, Card Game, Poker, Poker ChipsIts actually a non-technical discussion on the basic math associated with casinos and how they make their money.  Its really quite fascinating and give insight into the whole topic.  Furthermore, the examples are quite detailed and easy to follow.


 The author explains why math is so important in the gaming industry, discusses house edge, explores odds vs probability, clarifies win rate, goes into volatility, risk, player value, and complementaries.  I like that the paper even tackles casino pricing and mistakes along with gaming regulations and mathematics.  At the end are tables that show the house advantage for the most popular games and for major casino wagers.  Please note there is a comment at the end about this being the authors intellectual property and it cannot be used without permission.

You might wonder why we'd look at casino math in a math class.  Aside from seeing people card counting in certain television episodes and watching those poker games on certain channels, it might be good to know how casinos actually work.

I know a guy who used to earn a fair bit money by gambling but most people who go do not win much money.  In the long run, people are lucky to break even and its nice to know what the house edge is vs your actual chances of winning.


This slide share show specifically at the mathematics of casinos. It is very technical but once you get about half way through, you hit the formulas showing the mathematics that apply to gambling itself.  The equations are clear and its a nice presentation.

On the other hand, the Mathematics of Gambling out of the UK goes into specific games to look at the gambling mathematics for Roulette, Craps, Blackjack, Poker, Bingo, Keno, and Slots but its all based on the theory of probability.  I checked the section on Poker and the author determined the number of ways of each hand such as a Royal Flush occur.  I found it quite interesting.

There is the nice site with a PDF on an Introduction to Gaming Mathematics that explains the math and gives lots of nice examples.  Its a well written 37 page paper that has lots of great information on this topic.  I think this is the paper I'd read before attempting this unit because I don't really gamble.  The last time I went to a casino, I took a grabbed the nickles and dimes from my purse and used those for the slot machines......LOL.

Enjoy exploring this topic.  Yes this is a good topic for a math class because it is applied probability and people need to know why you are more likely to loose in the long run. 

Thursday, July 14, 2016

Hot Air Balloon Maths

Hot Air Balloons, Hot-Air Ballooning  I adore watching those colorful balloons sail across the clear blue sky.  Some people live in areas where they never get a chance to see the beauty of these creatures as they follow the wind while others live in a place that has celebrations where so many fill the sky like stars scattered in the night.

So what maths are used in reference to hot air balloons?  If you saw my weekend posters, you've seen two math facts so far, but what other math do hot air balloons use.


Using this site you can find out the measurements and weight for a standard balloon which can then be used in this activity.  Although this rubric is actually for student made balloons but with a small adjustment this could be turned into an exercise using the information from the article.  It has students find circumference, diameter, volume in inches to feet, weight, and lift potential. There is also enough information to calculate surface area.

For this next one, you will probably end up having to create a worksheet to accompany it but the material in it is great. Overflite has information for calculating the weight of the air and modeling hot air balloon lift. It is full of step by step examples and clear explanations.  Its areal life activity and could easily be integrated into a project.

On the other hand, I found a balloon simulator that requires students to take off, fly over to a place where they drop something from the balloon, fly back to the starting point and land.  As pointed out by the blog with the information, this is a form of mathematical modeling.  It is not just a  game because they have to control the burner, watch the altitude, speed, vertical speed, etc just like any pilot.  The simulator does require flash to run so it has to be used on a computer or through a site that provides the flash if using an iPad or a android based device.


Even Khan Academy has an eight minute video with a balloon example for the calculus class.  So if you are teaching calculus you can slide this in under derivatives.  Finally, an upper level example.  There is also this 88 page PDF from University of Texas At Austin which looks at hot air balloons, linear functions and linear systems.  The first eight or nine pages covers this topic, provides the questions, scaffolding questions and answers so you can easily integrate it into your classroom.

The final link is to the CTE online which has a nice lesson on hot air vs helium balloons.  I read this and immediately thought of the mythbusters episode where they used helium balloons tied to a chair to see if they could get the chair to fly with someone in it.  That would be a great introduction to this activity. 

In this activity, students are going to calculate how much hot air they will need for their balloons and they use a linear equation to help find out how much air they need to lift an object.  They calculate the amount of air for a toaster and then extend it to a house.  The lesson has everything you need to conduct the lesson from opening to extension to grading rubric.  It sounds like fun.  One thing is that you might need to join the site to access the lesson but its free and allows you to access all the lessons.


I would like to thank Adam Liss for today's topic.  It was a comment he made that inspired this entry because where I live, I never, ever see a balloon in the air.




Wednesday, July 13, 2016

The Olympics and Math Part 2.

Tower Bridge, London, London Olympics  On to more ideas and lesson plans that use the Olympics to teach math.  I really enjoy watching the Winter Olympics because some of the sports, especially the ice dancing, are so graceful that the athletes just flow and make it seem so easy.

Right now, we have the summer Olympics coming up and many of the stations will be devoting hours and hours of time to broadcasting these events.

nrich has a lovely card game with events and results that are mixed up so it is the job of the student to cut the cards apart and match them correctly.  This would make a great introduction along with a clip from the early Olympics.  In addition, nrich also has a logic exercise to determine the medal table based on the information given.  Furthermore, nrich has a page of possible activities dealing with the 2012 Summer Olympics that could be the focus of the whole unit.

From the United Kingdom is a lovely page on the 2012 Olympics that were held in London.  This site has a large selection of activities and suggested activities including an interactive graph that looks at number of medals won and the country for all the Olympics from 1896 on.  Many of the activities are from nrich and some are disconnected but others are actually are divided according to grade level.

Again from 2012 is the Olympic blog with lots of interesting problems that deal with math all the way from tennis rackets to field hockey to the bobsled.  Many of the problems here could be used as bell ringers or warm-ups.  I like the variation in the problems and many require some thought.

Education world has a nice lesson plan on graphing Olympic results past and present in times, medals, or points.  The directions are clear and it offers a variety of sources to find the information.  This is from the 2006 and 2008 Olympics but it can easily be used.  Most of the links are still up and running.

One last thought on the math.  Give a homework assignment where students watch one or two different races, mark down the times for the half way point and the end so they can figure out if the person was slower or faster during the second half, or create a graph on the speed of the athlete.

And to finish things off, have the students play this math Olympics game to practice word problems.  There are 20 questions and if you miss any, you must start again.  The problems are not that hard but they do require some thought and would be good for a review for all ages.

I've noticed that there are tons of things out there for elementary students, all designed to improve math skills but far fewer activities for middle school or high school.   Most of us do not have time to create lessons from scratch so we look but its hard when we find material for the younger ones but not the older students.


Tuesday, July 12, 2016

Math and The Olympics Part 1.

Hands, Protection, Olympic Rings  This year, the Olympics is being held in Rio de Janeiro, Brazil from August 5 to 21.  This is the first time that any place in South America has hosted any Olympics.  The Olympics offers a wonderful opportunity to integrate this topic into the math classroom.  I do not know when your school year begins but my students begin around the middle of this time.

It seems like a great way to review some basics even for my upper level classes.  The most obvious ways to use the math with the Olympics  are:

1.  Finding the rate traveled by the runners in various track and swimming events. Calculations could include a per sec, per min, per hour rate. 

2  Keeping a percentage going of medals won by each country.

3. Graphing the results per event and overall.

4. Calculating results based on the number of team members and medals acquired and then graph the results.

5.  Population of countries versus number of representatives or population of countries versus the number of medals won.

All of this information will be accessible via the internet.     No longer do you have to wait for the results to hit the newspaper.  They are now almost instantaneously available to all.  So what are some other ways to use math in regard to the Olympics?

1.  By using the results from this website, students can select one sport and one event to find the results over the years.  Once they have the information, they can calculate rate of improvement over the years by various countries.  For instance in looking at men's basketball, 1904 the first time it was played in the Olympics and the United States won.  So by going through all the results from 1904 to 2012, they can find out how many times the United States won the gold, silver, or bronze medals and then make a graph showing the results.

2. If students look at the times for say the 100 meter race, they can find out how the wining times have improved over time.  For instance the winner of the 1896 race ran it in 12 seconds while the winner in 2012 ran it in 9.63 seconds.  That is about 2.5 seconds faster.  These figure can be used to calculate percent increase in the race.  They can also do a comparison between the Olympic and World records.

So more tomorrow on Math and the Olympics.

Monday, July 11, 2016

Smart Graphs App

Smart Graphs is a great free app put out by the Concord Consortium that meets common core standards.  This app uses graphs to help teach very specific topics from Algebra I and II.  It has 19 graph related activities spread out over four topics

Smart Graphs covers linear equations, quadratic equations, transformations of functions and exponential expressions.

Each section is broken down into subtopics.  For instance the transformation of function is broken down into translations, dilations, reflections, all of them and inverses so students get practice with each topic.

Linear equations have both linear and systems so students can do both.  One of the sections under linear equations is called points, intercepts, and slopes, Oh my and it looks at the x and y intercepts.

The quadratic equations section focuses on graphic quadratics, quadratic word problems and quadratic functions in vertex form which is something my students do not get enough practice in.  The exponential function covers graphing, growth and decay.

Once the student selects a subtopic, the first screen has a short review of the material as a reminder before the student gets the questions.

The material in the review is quite specific with good definitions.

Once done with the review, the app moves on to the questions with two possible answer forms.  The  first is a multiple choice answer.



If the student selects the incorrect answer, it tells them it is incorrect but it will not give the correct answer.  The student must go back and try again. Once they have selected the correct answer, it provides and explanation.

The other type of answer is the one where the student finishes the graph.  The way that one is corrected is by comparing their answer with the one given by the app.

I've noticed that it can sometimes be difficult to get the curve you desire but as far as I'm concerned if you get pretty close, that is great and is fine.  it gives students a chance to learn to compare graphs.

Now for the extras offered at the website associated with the app.  If you go to the developers website, you will find lesson plans for every subtopic in the app.  Each lesson plan is divided into three parts so you know the essential questions and standards, the assessment and the learning stage itself in nice detail.  In addition, there is also a ready to go assessment sheet which asks students to practice what they learned.

These extras are available for all subsections on the app.  Check it out.