Math and the Police.

  Have you ever wondered how the police use math?  Most of what I know comes from personal experience or watching television shows like CSI.  I wondered about specific examples of how math is used by the police officers.

PBS has a great segment on how math is used in accident reconstruction. The unit begins with a 15 minute video in which a police officer talks about the ways he uses math in his job. The lesson comes with a worksheet so students can practice accident reconstruction.  It even includes the teacher guide. 

Plus Math has several articles on the topic.  One is a general introduction to various maths used by the police including information on inverse problems such as finding the shape of something based on the shadow, calculating speed based on length of a skid, clarifying blurry photos, and clearing up fingerprints.

The National Science Foundation has a great video on fighting crime.  It was made in conjunction with the Los Angeles Police Department and shows how math modeling is used to understand crime spikes.  The description offers a good summary of this topic and I would print this off to have students read after they watch the video.  Since my students are ELL, they don't always know what to write down when watching a video.  They do much better just being able to watch the video and then read about it.

This site has a lovely slide show which hows much of the material from above, combined to create a wonderful introduction to the question of "How do police use math?".

Last is something out of Texas which talks about a variety of ways math is used in police work.  It comes with the list, a work sheet to find information from the reading and short answer questions on the material.

Honestly, there are not that many decent units that discuss the math used in police work.  There is some material for elementary school but I teach high school and prefer finding units that allow my students to experience using the math.  Currently the best resource out there is the television show "Numb3rs" with all the associated worksheets that can be found on the internet.  I'd still prefer finding more units that show the geometry, trig, or other maths used by the different divisions of law enforcement.

NASCAR and Racing.

  Every school has that one or two kids who can tell you everything about a car engine from ratios to gaping.  You have the few who can tell you the stats of every football, baseball, soccer, game or race that has every happened.

Have you wondered how math is used in NASCAR and other major races?  Yes, we all know the rate x time = distance formula is the major math equation everyone thinks of but there is so much more math involved in racing.

NASCAR released a wonderful 16 page pdf file made for educators to help students learn more about the mathematics involved in racing.  Although the first couple pages refer to an IMAX movie, most of the activities do not need the movie to complete.  This guide has two sections, the first is for grades 4 to 6 while the second half is for grades 7 to 9.

The first section contains four activities that use skills such as finding the median, the average, pulling information out of the reading, predicting, and safety.  Each activity comes with the lesson plan, worksheets and suggested activities including having students create a small race car out of a home made play dough that they designed. The lesson plan includes answers to all questions.

The section section also has four activities that use skills such as calculating speed, velocity, and acceleration, calculating horse power, tires, angles, and friction, and air resistance.  Each lesson has everything needed to teach it from suggestions on introducing the topic, the worksheets, answers, and extensions. 

I think this is a well done set of activities because of the real world math applications and you could easily find a race on the internet to show students as a way of introducing the topic. 

Scholastic has a nice set of lessons that relate math to race cars. The three lessons cover drag, down force, and drafting.  Although this is more of a science unit, it would not take much to add a mathematical component so students learn to calculate drag, etc.  It comes with the teacher instructions, worksheets, car template, videos, and all the materials needed to complete this unit.

Math worksheet center has a great article discussing all the ways math is used in racing.  It would be simple to create a sheet filled with questions that students answer as they read it.  It is a good introduction to the topic.  The information is general but it gets the students started on how important math is.

Teach Engineering has a three to four day unit on designing cars to be efficient.  This has students design and build a race car to test.  Included in this activity is the cost of building the car.  Each group has a budget they have to stay within as they purchase supplies.  Even after they race their cars, students are required to graph the results so they can see visually.  This comes with everything needed to teach the unit.

Finally, from the Henry Ford organization is a 77 page educator digikit on car racing in America.  Although it is geared more to be used in a science class, there is still quite a bit of math involved.  Furthermore, it is a way to connect math to science to the real world.  Again, this has the lesson plans, the worksheets, answers and everything else needed to teach the unit.

I admit, I tend to look at all the material, pick and choose what I have time to teach in the class and which parts meet the standards best so I have a nice cohesive unit.  Check these out and enjoy.  You might even have one or two students do a project on this.  Enjoy.

Cartoon Corner

I love the "Mathematics teaching in the middle school" magazine put out by the National Council of Teachers of Mathematics.  In addition to all sorts of great articles, every month has a Cartoon Corner. 

The Cartoon Corner is an activity whose questions are based upon a mathematical cartoon.  For instance, the one for March 2015 involves a Fox Trot cartoon on Pi. 

The whole thing has 6 questions that all deal with the cartoon or the topic the cartoon covers.  The first question actually has students use four measurements to find the ratio of the circumference to the diameter (Perfect for my Geometry class as we just started that today.).  The second question deals with the area of a circle for each pumpkin from question one.

Question three asks students to justify the date and time people celebrate Pi day. The fourth question asks them about something one of the characters said and its relationship to pi.  The fifth question discusses which approximation is better and has students calculate relative error.  The last question asks them to find a fraction that gives a better approximation of pi than 22/7.

I really like this activity because it requires students to explain their thinking about various aspects of the problem.  In addition, most questions do require higher level thinking to find the answer. On the next page, the answers are provided.  This is followed by comments from people who helped field test the activity.

I've used a couple of these in the past with my high school English Language Learners and it worked really well.  I used one with Dagwood and his turkey sandwiches.  I enjoyed it because it made the students think about serving size.

I belong to NCTM so I can get access to all of the previous cartoon corners.  I love them and use them a lot in class.

Actuarial Math

I was watching an elementary basketball game and wondered if there was a place I could incorporate information on Actuarial Math.  Since I teach in a very small place with few job opportunities other than working at the store, for the city or for the school, I want them to see possible jobs. 

When I was in college, I never thought about being an actuarial person.  I went for a straight math degree. 

I found this website Be an Actuary.  It talks about what it takes to become an Actuary, sample problems from previous exams, how its used in real life and a lot more information. 

The Actuarial Foundation has quite a few free activities for grades 4 to 12 that deal with actuarial math.  For instance, there is a lovely activity for ratios and unit rate for grades 6 to 8.  It deals with designing a water treatment plant.  It comes with the lesson plans, the interactive component where students apply ratios to scale designs of a baseball stadium, an amusement park, and an aquarium. In addition, it comes with the three worksheets for the unit.  It is a great unit on patterns and functions.

This section has lessons to cover algebra, combinatorics, data and statistics, financial literacy, fractions, decimals, and percents, geometry, graphics, and probability for grades 6 to 8 and other material for grades 9 to 12 including

 Science Buddies has some step projects that could easily be incorporated into the classroom.  These projects come with everything needed.  Some of the topics include, dice probabilities, estimation and population size, frequency of outcomes in a small number of trials, how do baseball stadium dimensions affect batting statistics, and several other topics that are worth investigating.

This is a nice way to show how mathematics is used in real life and using information from either of the first two sites, students can learn how the math they study prepares them for a career in this field.  People in this field can earn between $100,000 and $250,000 a year. 

Have fun.

Happy Easter To All

I Taught It Wrong.

I realized that I taught certain things in the wrong order in Geometry this year.  I usually teach 2 dimensional figures first, followed by volume and surface area of 3 dimensional figures and if I have time, I throw in circles.

After this year of teaching the material, I've come to the conclusion that I need to do 2 D figures such as triangles and rectangles first and include both circumference and area of circles.  This might make the transition into volume and surface area for 3 dimensional figures easier.

I hate to admit I made a mistake when I did not take into account the best order to teach this material.  Ohh well, now to look at how to help reteach the material.  I think I'm going to spend time introducing circles, the formula for area and circumference.

Picture 1 - square

I have this activity to introduce circles to my Geometry students.  I challenge them to create a circle from a piece of paper, scissors and a pen.  They may not use anything else, other than those three items.  A female elder from Dillingham shared it with a class I took. It is the method her mother taught her to make circles as they didn't have compasses to use.

First you cut the piece of paper into a square since a circle is x^2 + y^2 = r^2 and the r is the radius or the distance from the center of the square to the edge.  So you cut a piece of paper that is exactly the length from the center of the square to the edge after folding the square so there are four lines creased into it.  (Picture 1)

Picture 2 - With first set of cuts

Now take the short strip of paper and use it to mark a distance up the diagonals from the center to the vertex.  Mark the distance for each vertex.  Fold over the corners to form a small triangle with the base being perpendicular to the diagonal.  Cut the triangles off so you now have 8 vertex. (Picture 2).

Picture - 3 With second set of cuts

Repeat the process so you've made 8 smaller triangles that you cut off so now you have 16 smaller vertex and your square is starting to resemble a circle.  (Picture 3).  If you repeat the process a couple more times, you have something that looks almost like a circle and with a bit of trimming, you've got a circle. 

This is based on Archimedes theorem that if you have a polynomial with enough sides, you end up with a circle.  Out of all the years, I've done this, only one or two students figured it out.  Usually after 10 minutes of letting them struggle, I sit over at the side and slowly work through the process so students can wonder over and check things out. 

I love challenging them.  Give it a try.

Teaching Perseverance

Over the past two days, I've had students tell me they didn't want to try because it was too hard or they were afraid to fail.  I took the line that you have to practice to become good, just like in basketball.  Its fine to fail because each time you fail, you learn something and get better. Its almost like some of these students refuse to open themselves to the idea they can improve if they are willing to try.

I'm struggling to find ideas that might help these students move past their fear or mindset into being willing to try and try again.  I know there is a push for perseverance but in order for that to happen, there has to be a mind shift and I'm not sure how to accomplish that.

They are willing to spend hours upon hours practicing basketball but they are unwilling to expend the same energy on learning math.  I know there has to be a change in their mindset but I needed to find suggestions on the "How to change".

In the process of reading up on ways to change this mindset from "I can't" to "I can", using ways that are easy to implement, I came across a couple that sounded possible.

1.  The ADEPT method.  Each letter stands for a way of presenting the material.  A stands for Analogy or what is it like.  D is for Diagram or how do you visualize it.  E refers to example or experience it,  P is for plain English or what does it really mean, and last is the technical definition.  This appears to be a way to show students, help them understand it, and experience it.

I admit that sometimes I'm not sure how to create a way for visualizing a concept.  Its taken me a while to figure that out for some concepts but I still have others I'm working on.  I suspect this is important for many students.  This does have a lovely diagram for i and its cycle.  Its one I plan to keep for the next time I teach this material.

2.  This article provided 25 ways to change the mindset. One of the most interesting things in this list is to stop seeking approval because it slows down the learning.  This agrees with something I read from the teaching point of view that you need to praise the process not the person.  Many of my students who "can't" do it are the same ones who seek approval on every single problems.

I also liked the emphasizing growth over speed.  Learning fast does not always mean learning well.  In addition, one of the items says we should disassociate learning from failure.  The one thing I never do is allow a few minutes for reflection at the end of class.  Check out this list, it has some nice thoughts.

3. Mindsetkit has tons of real suggestions for helping change student mindset.  The suggestions come from many different sources including Khan academy, Jo Boaler, and others.  Some of the links are videos, some are ways of changing your teaching to help encourage students and others are designed to have students learn to analyze.

I checked out several activities and I like them.  One I looked at has the teacher passing out a completed assignment and have the students to write feedback and suggestions to revise it.  This changes learning from the teacher to the students.  In addition they are seeing how the assignment should be done.

The "game" that caught my eye on this site is the one where students intentionally make mistakes and the others have to find them.  The mistakes can be ones they made or create.  I think I'm going to try this on Monday in my classes.

I associate changing student mindset with helping them develop perseverance.  I am going to try to find more suggestions for how to change mindset and share them.



NOTE:  My internet has been up and down recently.

Jeopardy Labs

  Today, I used Jeopardy Labs, a wonderful site filled with templates and already written games for the classroom.  I needed games for all my math classes and I found the games ready to go.  It was fantastic and I played them on my smart board.

The game came ready to go.  All I needed to do was input the number of teams and hit the start button.   Once the game came up, It was ready to go.  The page come up and its got the topics, amounts from 100 to 500 and the score appears at the bottom.  You as the teacher tap the + button if the students are correct and - if they are incorrect. 

In addition, when the students choose the topic and amount they want, they get a problem with a button underneath to show the correct answer or go back to the choices.  I ran it so if a team was wrong, I took the points off and allowed other people to try for the answer.

Most of the students in Pre-Algebra had a great time and worked so hard on the distributive property, combining like terms using addition, subtraction, or both, and simplifying expressions.   I have a couple who won't even try because they don't like trying it if they perceive it as too hard but the rest had a great time.

For Algebra I, I found one on solving multi-step equations that might require the distributive property, combining like terms, variables on both sides of the equal sign.  My students had a wonderful time and I discovered that one of my students who always took her time, actually can work a lot faster.

In Geometry, I had the students use one that required them to calculate volume, lateral area, or surface area for cylinders, prisms, cones, pyramids, or sphere. It was great because it helped students become more fluent in using the basic formulas and knowing which formula to use.

My students in Algebra II got to practice factoring quadratics both with a leading coefficient of 1 or other number, finding GCF's, factoring quadratics with GCF's and solving systems of equations.  It was great.  They all worked hard to be the first one but most of the time, the first one had the wrong answer.  This class set the lowest score at -2000 because of that.

In addition to having a large number of pre-made jeopardy games, it is also set up so you can create your own games for free.  You simply create a password and off you go.  The password is so you can go back in and edit the game.  If you decide to invest $20, you get more templates to work with, control over privacy and deleting the game, and you get a list of everything you have created.  Otherwise, it becomes public domain and available on Google.

I did not need to make any games at all.  I found everything I wanted but I found them by using the Google search engine.  The site has no search engine so its much harder and I do not want to go through over 300 games to find out exactly what I want. 

I plan to use this site again. Go check it out for yourself.

Shower Curtains and Math

  I had to replace the shower curtain in my bathroom.  It's about 10 years old, yellowed and it cracks every time it moves.  I replaced it but I really hate to throw things out so its been sitting on my bathroom floor while I figure out what to use it for.

Today, while helping a student, I wondered if a shower curtain could be used as a coordinate plane so students could move around while learning to use the coordinate plane.

In the Math equals love blog the teacher explained that she used duct tape and electrical tape to create the axis and the coordinate planes.  That answered my question on what can I use to make the lines.  This is cool.  So how can I use this once I'm done.

Use it to teach:
1. The coordinate plane, quadrants, and coordinates.

2. Midpoints and distance. Students can walk on it to physically notice what is going on.

3. Parallel lines and perpendicular lines.

4.  The four types of slopes.

5. Finding equations of lines including slope, the y-intercept, or from two points.

6.  Coordinate plane geometry

7.  Trigonometry such as trig ratios, positive and negative angles, standard position, co-terminal angles.

8. Coordinate plane battleship.

9.  Transformations.

10. Polynomials.

I can see so many different ways I could use this.  If I can secure a second one, I could easily create a unit circle to use in the classroom.  I think I need to pop buy the dollar store near my parents house this summer.

Connectivity

  I've been teaching math for a fairly long time and the way its presented has changed so much since I received my credentials.  Recently with the change of focus, I've realized that I should be teaching solving multiple step equations just before I teach slope and graphing.  Technically, if you put y = instead of a constant = you'd have a linear equation.

So I think next year, I'm going to teach solving one, two, and multi-step equations first then move to teaching linear equations as they are so closely related.  This year, I'm slowly realizing I need to connect with certain topics with other topics so students begin to see the relationships with in Math.

So the order I"m looking at for teaching this grouping is as follows.
1. Solving one step equations.
2. Introduce the idea of x and y values as coordinates and or points
3. Solving two step equations.
4. Introduce linear form, function, equations and connect with points
5 Solving multi-step equations with variables on each side.
6. Solving multi-step equations that require combining like terms or distributive property.
7. Identify m and b of  the linear equation.
8. Introduce graphing using m and b. 
9.  Show finding slope from graph using triangles and finding the b.
10. Finding the slope mathematically.

This is a big change for me because I'm so used to teaching solving one and two step equations in one unit.  Later on, I teach linear equations as if they are completely different and isolated.  I've been wondering if that is one reason my students have trouble transferring the knowledge.  Do they see these topics as completely unrelated and therefore must be treated as different topics?

I'm looking for ways to teach certain topics so they make more sense to my students.  So far my teaching factoring of quadratics is going well.
1. Factoring GCF out of the trinomial.
2. Teach the Diamond method of finding the factors.
3. Take those results to be used to factor the quadratic with a leading coefficient of 1.
4. Teach the Diamond method to find factors for a quadratic with a leading coefficient of a so a is not equal to 1.
5.  Have students use the factors to rewrite the trinomial into four terms.  They will practice taking it this far.
6. Complete the factoring from # 5.
7. Introduce the quadratic formula for equations that cannot easily be factored.

I'm only up to step 3 but I had a student who looked at what we were doing and said "UnFOILing the equation."  First time, I've ever heard a student make a direct connection.  It was cool.  I'll get back to this when I'm finished with this part of the unit.

Yah Math

Today, I stumbled across a site called Yah Math. It offers videos, worksheets and quizzes for certain mathematical topics.  The site has materials for Algebra I, Geometry, Algebra II, Statistics, and Trigonometry.  Although their videos are on Youtube, you can still access them through the site successfully.

When you click on the class, you go to the page that shows you the topics and recommended order of presentation.  If you click on the individual topic, they give a suggestion of the order of material and a basic lesson plan.

The videos range in length from 10 to 40 min for each video.  There are 24 videos for Algebra I, around 30 for Algebra II, just over 45 Geometry videos, 3 for Trig and 12 for Statistics and a lone video on credit card interest.  Furthermore, all videos have a worksheet.  The worksheet has every example worked in the video so students can fill it out as they watch the video. followed by a quiz.

The quiz is a multiple choice quiz that requires a name and e-mail to take.  Once the quiz is finished, it is submitted and instantly graded telling which questions are correct and wrong.  In addition, the site even shows the correct answer.  I don't think there is a way for you as the teacher to access student responses but it is a good way to 

I  like this site because it could easily be used in a flipped or blended classroom so students take the worksheet home, watch the video, then take the quiz so they know what they still need to work on.  It would also work so if students miss a class they can watch the material and fill out the worksheet so they can catch up.

So many possibilities and just in time to use in several of my classes.  Go explore it and have fun.

Factoring Game.

  I just started on factoring with Algebra II.  I have been trying to think of something I can do towards the end of the unit to help review the idea of looking at the trinomial to determine which method to use.  Is it actually a perfect square?  Is it a difference of squares?  Is it a perfect cube.

First of all, the I love Math site has three nice games for students to practice factoring trinomials.  The first is a factoring puzzle.  The students cut the pieces out and then put the pieces together so the original problem and its factored forms lay next to each other.  With either problems or factored forms on all four sides of most pieces, the students will have to make sure everything is lined up.

Second is I have, you have a game sort of like fish where students are dealt either the "I have" (the problem) or the "you have" (the factored form).  So one person states I have this do you have the factored form ie (x-2)(x+2) for x^2 -4.

Third is Algebra Connect Factoring Game in which students roll  a pair of dice to determine which square on the playing board they have to factor.  The file comes with everything needed to play this game.

So, why not use a pair of dice to help set the coefficient for the second term and the constant of the trinomial.  This means students could end up with zero or negative numbers should you use colored dice.  For instance the red die might be negative and the blue positive or you could say in this round all numbers are negative or positive to add a chance for students to obtain different signs.

If students roll a pair of dice twice to get two numbers such as 24 and 11.  The problem they have to factor could be x^2 + 11 x + 24 which is (x + 3)(x + 8). On the other hand if they ended up with x^2 + 2x -10, they might not be able to easily factor it and would use the quadratic formula to solve it.

 I wanted a game that required the student to think about using the quadratic formula if it can't easily be factored.   I admit, I often use the quadratic formula myself because I find it easier with problems that have a leading coefficient.

So I got the idea of using dice to figure out the coefficients for the second term and the constant.  Start with a trinomial with a leading coefficent of 1.  The students roll two dice to determine what the coefficient of the middle term. They roll the two dice for the constant.  This gives them possibilities of 11 to 66 and a variety of numbers in between.

The nice thing is that using dice means the numbers change with a certain amount of randomness and the game can easily be replayed as needed.

Paper Inventions

  I just got a book by Kathy Ceceri called Make: Paper Inventions.  Yes I realize that this does not seem to fall under math but it turns out there is a wonderful chapter in the book called Paper Math.  After reading through the material, I realized this is the perfect thing for those days where you have something going on that is going to mess up part of the day.

The chapter starts off with paper fractals.  It goes a wonderful job of defining a fractal and then promptly has students creating a dragon curve fractal which when done resembles a fire breathing dragon.  The author even explains where this idea came from.

Next is the box pleat which is used to create the Action Origami Robot Worm.  There are tons of pictures showing each step of the process.  The photographs are so good, you actually see where all the folds are so its much easier to follow.  There is even a trouble shooting section on it.

Third is a lovely section called the Math of Cut Paper. This one is based on the idea that you can cut any two dimensional shape with straight sides from a sheet of paper using only a single cut.  I learned to cut a rhombus from a single sheet of paper when I took Math in a Cultural Context but this one shows how to cut a star using a single cut. 

This is followed by a very in depth section on creating a Mobius strip and possible variations to the single cut.  They suggest you add an extra twist. It even has a page later in the book you can check to see if you ended up with what you are supposed to.

The finally section is on making a Hexaflexagon is created out of a strip of paper, making a six sided figure. As you play with it, you end up looking at different sides facing up to the point, you can color in areas on the strip so you have multiple colors facing upward at different times.  This is so cool, I've got to try it myself this weekend.

The best thing of all is that there are links to websites on each and every one of these topics.  I want to check out the website to learn more about fold and one-cut patterns.  The side has printable patterns available for downloading to use in class.

Most of these topics are so easy to slip into a Geometry class so students have fun and enjoy making these creations.  I have a few days to play with some of these things before I can let my students play with these in my Geometry class on Monday.

The Distributive Property

  I'm in the beginning stages of teaching binomial multiplication with Algebra I and factoring in Algebra II so one of the first things I'm doing in both classes is to review the distributive property.

I took time today to explain to the Algebra I class that the distributive property was used in one method for multiplying binomials.  This is the first time I used the connection between the property and a second topic so they understand it is used in more than just that one time when properties are reviewed.

When I tried to find ways to connect the use of the distributive property in math such as connecting it with factoring, I could not find anything.  I found a few ways to introduce the topic and lots of ways to teach it but no connections.  So I looked for a couple of different ways to introduce  or teach the distributive property in nontraditional ways.

In Math Equals Love she introduces the distributive property using combinations of food just like you might see at McDonalds or Burger King.  I think this could easily be extended to combinations of candy, soda, or any other food.  I think this is a cool way to introduce or remind students of it.

Although More Time to Teach has material more geared to 3rd grade, her Distributive Doctors idea is easy to adjust to middle school, high school and due to the way things are cut apart, it might make it easier for students to visualize what is happening with the variables and constants.

Math Geek Mama starts with a word problem that she lets students work on before introducing the distributive property.  By going over the word problem, she shows it is a distributive property and it doesn't matter when you double the total.

Now for my take on when we should talk about it in the Math class. When we talk about it while teaching properties, it might be good to show how it applies to multiplication in general, multiplying polynomials by a monomial, factoring in general and in terms of polynomials.  We can also show how it is used all the time when we shop, go out to the restaurant, or figure out candy in a bag.

I think too often we teach the math processes individually without showing how it is going to be used later in the class.  This is one thing, I"m trying to do as I teach my math classes.

Pi Day!

  Welcome to Pi Day, the day designated to celebrate the beauty of the most famous irrational number in the world.  The day celebrating a ratio of circumference to diameter.  The day people joke about with "Pie are not square, they are round!"  A day with its own organization.

Imagine, Pi has been calculated to the one trillionth digit!  A length that is so mind boggling that we just accept it rather than think about it.  I love Pi but my students fight me when using it.  They want to use 3.14 while I'm trying to have them use the Pi symbol because its more accurate.

Have you ever had a Pi scavenger hunt in your room?  Put up QR codes with information and facts on PI?  Then have them write down the trivia such as information on the RAF unit who has Pi as its symbol?

Did you know?
1.  NASA created a Stellar math challenge to show people how they use Pi in their work?  Image being able to show students a real life use of Pi other than for calculating the area of a circle or volume of a cone, sphere, or cylinder?

2.  There is all sorts of compositions out there based on the digits in Pi.  This activity explains how to compose a piece of music based on Pi so your more musical students could easily craft their own compositions on garage band or other app.

3.  What about an assortment of numerical puzzles involving Pi?  The New York Times Blog has a lovely list of puzzles your students can try.

4.  Check out Teach Pi for over 50 ideas and activities to help out on Pi Day.  Activities cover everything from crafts to events, projects, lessons, and songs.  The lessons cover everything from historical ways to calculate pi to figuring out the best price of a pizza or how much pizza each student gets based on the number of pizza's and students present.

5. To finish off the list of resources, the Exploratorium has a wonderful list of suggested activities and links to make celebrations even more fun.

If you want other ideas, just do a quick internet search for ideas.

Finally, Happy Birthday to Albert Einstein who was born on March 14th many years ago and who had a profound influence on the world.

How Much Does It Cost?

  Did you ever wonder how much it costs every time we change clocks for Daylight Saving Time?  We all know the personal cost the next morning when we drag ourselves out of bed, feel lethargic all day long and spend the first week feeling just out of sink with the world.

It turns out it costs this country between 350 and 450 million dollars.  In addition, there are three areas where the cost is most prevalent.
1. Increase in heart attacks immediately after the change.
2. Increase in injuries in certain professions.
3. Loss of productivity.

So what type of activities can we provide students with just to see the real life implications of the change rather than just thinking of it as getting one more hour of sleep or losing an hour of sleep.

1.  Figure out the per capita cost of the change for adults 18 and over.  Although $400 million sounds like a lot, how much is it actually per person.

2.  Prepare an infographic on the cost of the increased number of heart attacks, the medical cost of the increased injuries, etc.

3.  Create an interactive map on google.  Huffington Post has a great graphic which shows that the economic costs are higher in the east vs the west.  Students could research why that happens.

4. The New York Times has a wonderful article that gives more specific details on the number of injuries in certain professions. For instance injuries increased by 6 percent when clocks moved forward but in terms of work day losses, it is more like 67%.  Imagine researching the normal number, adding the 6% and creating a graph. 

5.  ZD net published a great article on the cost involved in IT (Informational Technology) resulting from the time change.  Its actually higher than I could have predicted.  This information could be used in an infographic, a presentation, or a chart. 

6.  In the same article,  they published the alleged energy savings from California and per the Federal Government but do these savings out weight other costs?  That topic alone would make a great topic for a project.  Perhaps it would be possible to work with the English department to set up a debate "Should we eliminate daylight saving time?" while the students in math find the data to support both sides.

One thing I did read explains why the number of injuries increase on Mondays.  Apparently people put off doing anything till Sunday night/Monday morning to readjust their bodies so they lose on average 40 minutes of nightly sleep.

Teaching Volume vs Surface Area

  I've been teaching area and volume in my Geometry class.  I gave a quiz recently that showed me they still struggled with some of the language involved.  For instance, I've been teaching the formulas for volume using both lwh and Bh so they might see the connection that volume is the area of something (base) times its height.  The results of the quiz indicated that students saw base as a one dimensional concept and having no relation to area.

So I'm going to reteach some of the material while moving forward in the hopes that students will see the connection between area, volume, and surface volume.  I prepared a four column graphic organizer for student notes.

I want the students to fill this out as I review the formulas, definitions and other details of the two dimensional figures.  Once they've filled the first column, the second will carry the notes that the base uses the area formula for the three dimensional figures.

I downloaded several nets of three dimensional figures from senteacher to use for having students  write down the individual shapes that make up the 3D figure. I have a second organizer for students that will have them write down the number of each shape that makes the 3D figure, the formulas for surface area, and the measurements so they can calculate both the volume and surface area of the figure.

This site has interactive materials so they can see the 3D shape as it turns around so students can see the whole figure.  You can change the rotation and speed of the figure  To one side is the net for the figure which folds up and unfolds and can be paused as needed.  It does require flash so may not work on the iPads.

To end, both Math Geek Mama and Great Math Teaching Ideas both have packets of nets ready to do and all you need to do is download them.

Don't forget to change your clocks tonight as its time to spring forward.

Designing a House.

  Did you ever wonder what it takes to design a house to your specifications?  What it takes to plan the budget for the house?  How math is involved?  I'm at a point in my life that I want to design and build my own house. So this got me to wondering about the math involved in designing and building a house.

So according to a lesson in Hot Chalk Lesson Plans, it involves a budget, area, and financing.  The lesson is set for middle school but it could easily be adjusted.  The nice thing about financing is that a small difference in the percent rate can make a huge difference in the final amount paid for the house.  In addition, it uses the I = PRT or I = e^(prt) depending on the level of mathematics needed.

This site requires students to plan a house using geometric shapes. It requires students to keep track of the money they spend for building supplies so they stay within the given budget.  You might need to adjust the budget depending on the part of the country you live in.

Math-kitecture has a lovely set of lesson plans available for the classroom.  One of the activities on the page requires students to create a floor plan of their classroom using an online software.  They end up using estimation, measuring skills, proportion, and ratios to create the floor plan. They include a huge list of resources to help teach this unit and they include apps for the ipad that work.

Another site with great lesson plans is the Dream House page.  The page included the important information on the cost of land, the price of building, etc.  It shows the standards and requires a write up.  Its got a lot of great information.

This site looks at mathematics of financing a house.  It shows several different ways of calculating the mortgage and figuring the monthly payment. 

Any of these activities could be set up to include students using a computer program to show the house.  This free site, Home Styler, allows people to create a floor plan on the computer. The program can provide a 2D or 3D view, shopping list, or have the measurements in feet or meters. In addition, after creating the floor plan, you can add furnishings, decorate the rooms and finish off with landscaping.

Students can easily use the computer to create a spread sheet for the costs, a brochure to sell the house, create a report for a perspective buyer of financing options and other such activities. 

Integrating Math with Maps

  Today while guarding a door for an event, I started wondering about the ways I could use maps in a math class.  I'm not talking about MAPS testing, I'm talking about the old fashioned road maps mom would try to read in the car while dad was driving and the kids were crying "I'm bored" and "When do we get there?".

I know there are wonderful directions you can get off the internet but I usually get with the one set of directions with one wrong turn and I end up in the wrong place (even with a GPS).

I found some great sites that offer cross-curricular activities that allows math classes to use geography.

1.  This Teacher Vision site has Popular Geography Activities for the Math Classroom page. It has a list of 24 activities for a variety of grades but some of those geared for the elementary school can be adjusted for older students.

There is a lovely unit on longitude, latitude, and reptiles in which students find a country using longitude and latitude.  They also learn a bit about certain reptiles.  Add in Google Earth to find out the distance from one country to another and apply the rate times time formula based on the standard air speed of a standard jet to determine how long it might travel from one place to another.

This also opens the possibility to having the students due a bit of research on the animals, range of weights, and other data so they can calculate variations of weight, height, etc.

Some of the activities cost money, some don't.

2.  Scholastic has a nice activity called Math with Maps and Globes.  Although this states it works for K to 8, I think a couple of the activities could easily be used in the high school with a small variation.  The first activity has students use straws but I think I could have the students measure distance using a tape measure so as to use the key to determine the actual length.  Again using Google Earth, students can find the distance and compare their calculations with Google.  This leads to being able to calculate the percent error and a discussion of error.

3.  Finally is a nice activity from Rice University on the Mathematics of Cartography.  It discusses maps in general, talks about the math used in cartography and has some practice problems, some of which are actually more like games but it makes them use longitude and latitude.

Stay tuned for another installment in ways to use math in other subjects.

Cool Video Site.

I love finding sites with fun activities or videos.  The ones that make the students laugh while they pay attention and they learn something.  Well I found a really cool site.  It's Math Antics.

Math Antics has several strands of free videos covering arithmetic, fractions, geometry, percents, and Algebra basics.  In addition, each strand has at between 7 and 18 topics.

This site offers the introduction, exercises, examples (video), worksheets and the answers for each topic.  Only the first two or three topics in each strand are free, the site only  charges $20 per year for total access to everything.

The way each lesson or topic is set up is as follows:
1.  The topic has an introductory video students watch to learn more about the topic.  The man who does it, has really good explanations that show relationships between things and is very detailed without being too wordy.  There is humor, good language usage and its fun.  I showed a video on solving two step equations that had my students laughing over the material.

2. There is an examples  video to go with the exercises worksheet.  So Rob the instructor is showing how to do the exercises on the example video step by step so students can fill out their  sheets as Rob fills his out.

3.  The third step is to assign the worksheets designed to help students practice certain aspects of the lessons and there is an answer key available should it be needed.

I showed this site to the middle school math teacher who finds it just as good as I do and I know he plans to use it.  I suspect both of us will pay the $20, so we can  use the site to help teach our students.  I know my students pay more attention if its a video than my talks.  I suspect they might learn more when I start using this.

Check it out, see what you think and have fun playing with it.

A+ Click Math App

 A + Click Math is a series of apps from Igor Kokcharov for grades K to 12.  I happened across the one designed for 12th graders at the iTunes store the other day and downloaded it.

First I'll say that this app and the other apps are free and advertised to be based on the Common Core.  This app has over 350 questions in 6 strands that a student can work through or can focus on a single strand.  

If a student wants to work on a specific strand, they click on the drop down menu to select the strand and those question classified as being part of the strand remain while the others disappear. It turns out the strands are in order so the first 20 are Arithmetic, the second 40 might be Algebra, etc.

 Each question comes with a picture and four possible answers so the student gets practice with multiple choice questions.


The student selects the answer and they get immediate feedback on the correctness of their answer. If their choice is correct, a green stripe appears on their answer, if its wrong, they see a red stripe. In addition, the app provides a solution even if the student gets the answer correct.  The solution includes an explanation of the math behind the problem.

The best thing about this app is that you do not need an internet connection to use it but the questions never change so its easy to memorize the answer and do well.  On the other hand, some of these questions are quite challenging and most students will not be able to rush through the app.

They also have a web site students can use rather than downloading the app on the iPad.  It has the same material as the apps with the same questions and formats. 

Angry Birds and Math

  Angry birds is a popular game played on a mobile device.  As you probably know, the premise is simply to launch the birds so you destroy the pigs and the blocks.  If your first shot doesn't work right, you readjust until you succeed.

Perfect for the math class because it forces the player to use vectors and parabolas as noted in yesterday's entry but are there  other ways to use Angry Birds in the classroom?  Yes.

In this blog entry "Angry Birds Teach Math" the author explains 4 different ways to use the game in the math classroom and includes all the materials necessary.  The first activity looks at the red bird and quadratics, the second focuses on the yellow bird and flying tangent to a curve so you can use both linear equations, tangent lines, derivatives and piece wise functions.  The third is based on the Star Wars version of Angry Birds. We look at Hans Solo shots using either a linear or a parabolic function.  The last one looks at shots that bounce off of things using reflections and perpendicular lines.

The Math Techniques and Strategies blog has a lovely list of 5 math lessons using Angry Birds including links to reach the lesson itself.  I love that one of the lessons ties conic sections, especially the parabola with the game while another helps students identify equations of the parabola, zeros, apex and requires the use of systems of equations.  This really is just what it says, a list of math lessons.

Math Movement discusses the movement based on an article that appeared in Wired magazine in which a physicist talks about the physics of Angry Birds.  The physics that it uses is math.  The flight of the red bird is friction-less so the only thing needed is for a person to plan the initial angle of launch.  This article includes the algebraic quadratic equations for 3 different launching angles. It is quite interesting.

Finally from Greenapples wiki space,  one can get some worksheets and other materials to use in the classroom from practicing their multiplication to calculating destructive parabolas from nine different places.  In addition, one of the links is to live binders which has quite a few resources of its own.

So Angry birds becomes the hook to pull students into math. Add in a You Tube video and you are set.

Orienteering, Etc and Vectors

  I wanted to find more hands on activities for my students so when I teach vectors they don't have to only use the book or worksheets.  I want them to experience a chance to experience vectors personally.  So as a continuation to yesterdays blog, I've found a few more activities that sound fun.

1.  Orienteering with vectors.  This is a lovely exercise where students orienteer around the school, keeping track of distance and direction, so they can create a scale model of their path.  This activity helps teach resultant vector.  The lesson plan gives enough information so you can set up such a course in your school.

2. Navigational Vectors is a site with 8 piloting lessons based on vectors.  These are called piloting lessons designed to help students navigate the skies.  The first lesson introduces vectors by having the student calculate the distance between their town and the state capital.  It covers displacement, reading maps, determining vectors and scalars in real situations.  Each lesson teaches more about vectors including taking into account wind and finding the arrival time.  At the end, a student can take the "Pilot Test Flight" which has the students use all their knowledge to complete this activity.

Although the lessons are just directions, they are clear and each lesson has students completing an activity that practices the application of what they are learning.  In addition, the starting point is the student's home state and it assumes there is an airport in the town so the student can do the work.  Every thing is clear and laid out in steps.

3. As a way to introduce vector addition, Mythbusters has two different videos that show a great introduction to vectors.  In addition, this video shows a truck speeding down the road with a ball being fired out the back to show vector addition.   Either of these would provide a great introduction to the topic.

4.  What about using vectors to create a dance?  At Teach Mathematics, there is a very short description talking about using vectors to show the choreography of a dance.  Imagine giving your students (the more artistic ones) a chance to use vectors to create a dance that could be performed by a small group of people as a the product for a project? 

5. Finally what about relating vectors to the game "Angry Birds"?
a. This  video that introduces vectors and scalars using angry birds before beginning the lecture.  Its short but great.
b. This PDF of an article at Mathematic Shed relates parabolas and vectors to angry birds in a fun way with precise examples. 


The last example could also be used when teaching parabolas.  I'm getting ready to teach factoring to Algebra II and  I think I'll sneak this material in there, just before I begin vectors so that I'll have a nice topic to use to tie the two topics together.

Vectors, Vectors, and More Vectors.

  Around the time I teach matrices, I also teach vectors to another class.  I'm always on the lookout for ways to teach vectors that show students they mean something other than the dry material found in the textbook.

This activity is a great way to introduce the use of vectors though a treasure hunt.  It is a seven page PDF showing how vectors are used to find the treasure using a program from the Concordia Consortium.  The material is older but it could easily be adjusted to use google earth for the map.  You could also use the original island map with annotation tools.

Teach Engineering has a lovely activity that combines history, vectors,  and geography together in an activity designed to show students how dead reckoning relates to vectors.  The lesson explains that vectors are used to show fluid movement in many branches of engineering before explaining dead reckoning to the students.

Although the lesson itself is paper based, it would be easy to scan into the computer to upload so students could use a program or app that allows them to draw or easily erase mistakes.  It has everything needed except for colored pencils.  Just download and go.

 Jen Silver's Math Bloghas a lovely activity for creating a vector maze.  The activity comes with an example to show how its done.  Then students are expected to try it themselves.  The idea is the student creates the smallest sum of lengths wins.  There are rules they have to follow about setting up the vectors but it requires thought and lots of planning.  I looked at it and immediately wanted to try it myself.

In addition, she provides a free downloadable PDF file with 8 different templates for students to use.  The starting and finishing point may be different or the walls within the maze may change so this activity can provide lots of challenges for your students.

This site has a lovely video on Vectors in Climbing which talks about how vectors are used in climbing.  It introduces using vectors in a real life situation while introducing the topic, talking about adding vectors using two different methods, decomposition of vectors, and vectors and angles.

In addition, there is a paper from a lady in Norway who made the video and refers to it in the paper.  Its a well written paper with some very good information.  It relates body geometry to vectors and climbing academically.

More tomorrow on orienteering and other activities that help students learn vectors.

Vectors and Matrices

  I teach these as separate subjects but I've often wondered if there is a connection of any sort.  It appears that vectors are classified as matrix but matrix are not vectors.

I discovered this cool website which talks about using both vectors and matrices in real life with great examples and which math class it applies to.

So under Geometry, there are 10 different topics covered that use either vectors, matrix or both.  For instance, in animation, it shows how vectors are used to determine how the light is shown on the figure composed of triangles.  How to create 3 dimensional figures out of flat two dimensional painting.  Or even bathroom tiled floors and getting it right.

Then there is physics and biology with a lovely exercise on modeling the climate change and melting of ice in the arctic.  What about using vectors to model turbulence?  That's included in 6 topics in this section.

What about game theory and computer science?  Under this group, you can find game theory and soccer, or simple computer models to recreate the world.  This talks about modeling gas molecules, flocks of birds, or even bats! 

At the very end are 10 activities from the NRICH site to learn more about matrix and vectors.  One activity has students figure out the shortest air route between London and Cape Town.  Another students calculate the actual speed and bearing of an aircraft that is flying with a wind.

I especially love the piece on maths in computer modeling because  it provides some very indepth information on this topic.  It connects vectors to computer games and shows how it works.  In addition, it has exercises for the student to play with.  This article even gets down to explaining why triangles are used to form 3 dimensional objects and the job vectors do within simulations and other types of games.  The information in this activity could easily be used for a full week in class.

Finally, there is a short article on what computers cannot do.  There are limits that most of us don't worry about but the limits came out of code-breaking in World War II and the enigma machine.  I think this would be a cool way to connect history with math so students see that each is not an isolated subject but interrelated.

Have fun exploring this site.

Back to Technology

  I'm due to teach matrices later this semester in late April, early may.  I wanted a slight different way to teach the topic instead of just using a lecture and lots of written work.

I discovered you can do matrices using the Excel spread sheet.  I didn't know that because when I did matrices, students still were required to do them by hand rather than use the calculator.   I think that it took a while to enter data and you could do it as fast or faster by hand.

I was thrilled to find a lovely power point presentation from Nuffield College in the UK that I was able to download and its perfect to use as an introduction for using Excel to solve matrices.  It actually gives the commands you need to work the math in Excel.   In addition, it takes you through the steps to create the matrix, do addition, subtraction, scalar multiplication, transpose, multiplication, find the inverse and the determinant.  If you do a web search, look for Matrix Commands in Excel and Nuffield College.  It should pop up.

This pdf file has wonderful step by step directions with illustrations for using Excel 2007 to do matrices.  It covers everything the previous power point covers but  goes one step further.  It gives instructions on using inverse matrices to solve systems of linear equations.  This file could easily be printed out and given to students so they can work their way through each topic.  I love the way it has illustrations so a student can compare their work with the pictures to see if they are doing it correctly.

Once the students have mastered working with matrices in Excel, they are ready to actually do some problems.  I think I would assign work throughout the process of learning Excel so it correlated to the matrix material being taught. I think that would help them learn the process better. 

So know I have an idea of how I'll teach this topic later in the year.

Polynomial Use In Everyday Life - 11 Ways.

We know polynomials are used in roller coaster design but where else are they used?  How are they used?  Who uses them?  I hate trying to snatch an answer out of thin air so I've been researching this so when I'm asked I can respond sensibly.

1  Polynomials are used in industries that deal with physical phenomena or modeling situations dealing with the future.

2. Polynomials are used in financial planning to predict how much money you will have in so many years, perhaps for when you retire.

3. Polynomials are often used in construction to plan how much material to order for a project.

4. Polynomials are used to plan how long it will take to earn the money needed for the future, including expenses.

5.  Polynomials are used in gravitational acceleration.

6. Polynomials are used in modeling situations such as predicting which way the stock market might go or how selling at various prices will effect the total amount sold.

7. Polynomials are used in physics in a variety of situations.

8.  Polynomials can be used in both electronics and chemistry.

9. Polynomials are used to determine the concentration of a drug in the blood system.

10. Polynomials can be used to determine the weight of a sick person.

11. Polynomial regression in used in stats.

I can see dividing the class into small groups to research one topic and report back to the class.  I didn't realize it was used in this many different areas in life. I love learning.