Planning

Justify Your Answer

My Dream Bedroom

  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.

The Math of Extreme Sports and Skateboarding

  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?

After 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.

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.


Think 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!

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.

Why Is It Important To Convert Measurements

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.