Saturday, October 31, 2015

The Time Change and Math

Alarm Clock, Clock, Time, Wake Up   This is the perfect time for using infographics and statistics.  Every November and March, we change clocks either forward one hour or back one hour.  We've been doing it for a while.  Supposedly, this move helps save energy in the summer by giving us more daylight but I'm wondering if it really does.

This would make a great research project that would culminate in a presentation, an infographic, a poster or even a comic strip.  I did some reading myself and found these facts.

1. It reduces annual energy use by 0.03% and could even increase energy consumption.

2.  Although it can lead to increased exercise among kids, it can also lead to a 10% increase in heart attacks due to the spring adjustment.

3. There is an 8% increase in traffic accidents the first Monday after the spring change due to lack of sleep.

4. Robbery rates at the spring change drop 7%.  Maybe robbers are sleeping in?
The above came from CNN news.

The Statistic Brain has some lovely stats on Daylight Savings Time in regard to electrical use.

The Better Sleep group has stats on sleep deprivation.

Even the National Geographic has information on it.

If you want an official study, check this paper out from the National Bureau of Economic Research.

Friday, October 30, 2015

Desmos and teachers

Parabola, Parable, Mathematical Function  Thank you to Josh Fisher for this lead.  I have used the Desmos app in the classroom for graphing because it does not require students to rewrite every equation before graphing.  It means my students who struggle can complete the graphing assignment before they get frustrated and give up.

Due to an entry in the Mathematics Education google plus group, I learned that they have a teachers section with already created activities for use in the classroom.  The teacher gets a code the students use to sign in and as the teacher you get a list of who signs in. 

They have a pairs game to learn more about parabolas. I saw a parking game where students create the parking space using algebra.  if they spaces are not the correct size, the cars can't park.  They have one where students create the graph that controls the amusement rides.  I saw 8 to 10 activities that will easily fit into lessons without a problem. 

I tried the car parking one and it required placing dividers equally so the cars could park in the slots.  There are 13 different parking scenarios to do.  It was challenging to use my eye to make the lines equidistant but once I had the cars try to park, it was easy to readjust the lines.

In addition, there are the components to build your own activity so you can create an activity geared for the specific standard you are teaching.  You can put in a series of screens that include instructions like "Explain your thinking" or any questions you need answered on a graph.  It looks quite easy to design the activity.

I know this can be done on the computer but I'm not sure it works on iPads.  When I tried it on the iPads, the browsers shut down and the iPad turned off. I'll check with the company to see what is going on.  I think I"ll be using these activities in the classroom. 

Thursday, October 29, 2015

An Ah Ha Moment

 Today while teaching my Algebra I class about the slope intercept line I had a breakthrough in my own teaching.  I realized we teach the standard linear equation as Ax + By = C and the slope intercept as y = mx + b. 

In the past I have never shown a connection between the two equations.  Today, I suddenly realized that we assume the students can make the jump from -A/B to m without the connection.

So today I wrote the notes to the left for the students so I showed the connection rather than assuming they would make the jump.  Do you know that many books do not show the jump either?  If you work with students who are a not as good with their math skills, they can easily miss that jump without the additional clarification.  I had my students put this in their notebooks. 

Too often we teach the material in the same way we learned it and with the same gaps.  We assume all our students will make the jump without having that one missing piece.  I remember in one class I took at college, the professor always hit a point in the problem, drew an arrow, stated it was intuitively obvious and then wrote the answer.  I hated that because the arrow was always in the spot I needed to see to connect the dots.  It always made me mad so I understand that missing link.

Perhaps we can look back in our own histories and remember the times that our brains did not make that jump everyone else made when we teach things like this.

Wednesday, October 28, 2015

A look back in time.

Slide Rule, Slider, Scale  I got to thinking about how much our ability to do calculations have changed.  I think my friends grandfather used slide rules to find answers to the higher level problems.  I don't think I've even seen a slide rule but my friends grandfather speaks of them fondly. 

I also remember others who speak fondly about tables they used for logs and natural lns so they could do calculations.  I had some one explain how to do that and I thought it was cool.

A friends father showed me his first calculator.  I think he said it cost something like $400 back then and was a TI something or other.  I couldn't believe he paid so much for a calculator.  The new ones you get at the dollar store do almost the same things for $1.00.  Of course, the calculators I used were TI's like the TI-74's which did so much and cost maybe $100 but now you can get an app for your phone that does as much and is free!  Wow.

On the other hand,  my mother talks about working at a place that had a computer that took up the whole floor and had maybe 8 kb of memory and used punch cards.  She was so impressed with that.  Someone once told me, they used to wet down the punch cards, iron them and then stick them back in someone's stack.  Apparently the cards would shrink just enough to clog up the readers. 

Now I'm working on a computer that is so much smaller,  faster, and more powerful than what my mom worked with.  As a matter of fact, I think my cell phone will do as much as this computer.  I can actually do all my math on the calculators I put on my mobile devices. 

Think of how much life has changed over the past few decades. In fact, so much more can be done in the math class with just the mobile devices than our grandparents did.

Tuesday, October 27, 2015

Inside Mathematics

Fractal, Splash, Liquid, Abstract  Today while looking for performance tasks, I came across a group I've never heard of.  Inside Mathematics!  They have sections for educatiors, tools, videos, resources, problem of the month, and performance assessment tasks.

What is nice is that the performance assessment tasks cover from grade 2 all the way up to high school tasks which are divide into the stands.  Each task come with the tasks, the rubric and suggested answers so you have a guideline.

I looked at the performance task on quadrilaterals.  The packet is 20 pages long and starts with the task and the rubric, then has multiple examples of answers and how each was graded according to the rubric.  I love that because it helps me see how this was done.

Many of the videos are designed to help teachers improve their teaching rather than show how to do it.  I saw one on ratios that I hope to check out.  Admittedly, it appears most of the videos are geared for elementary but I'm sure I can use some of the material since many of my students are ELL.

I look forward to watching several of the videos when I get a spare minute or two.

Monday, October 26, 2015


Hotmath is a lovely website with four games that focus on Algebraic skills.  As they appear to be flash based, I don't think they will work on the iPads.  That said, they do work on computers so they can be used in class. 

Frog, Amphibian, Animal, GreenThe first game is Catch the Fly in which you give the frog the x and y coordinates so he can catch a fly.  You see the fly moving around. Once it lands and is still, you type in the points and hit the button.  The frog moves up on the fly, shoots a tongue out and grabs it.It is a great way for the student to become familiar with reading the coordinate plane. 

I enjoyed the Algebra vs the Cockroaches game where you put in the value for y =     to show the line with a zero slope and shoot your weapon to kill the cockroaches.  I chose the rocket!  If you wait a bit, you get more cockroaches running along the line.

Then there is Number Cop which is a challenge, even at normal speed.  The idea is you choose a number and then click on the multiples that race towards you as you are the speeding cop car.  This was quite fast and many of my students could easily get frustrated.  I wish there was an easy level so a person can develop the skills to use the game.

The last one is Factoris which is a take off on Tetris and I could not figure out how to do it.  I suspect its because I've never played Tetris so I had no idea how to play.  I think if I took time, I would learn it.  It looked like a multiplication game using factors to create a product.

For my classroom, I would assign Catch the Fly and Algebra vs the Cockroaches as part of the lesson but I'd use Number Cop and Factoris as free time games so they can play it if  they choose too.

Sunday, October 25, 2015

Survivor Algebra

Mathematics, Algebra, Homework, School  While researching games, I came across this series on something called Survivor Algebra on cool math.  It is several pages long and is more of a teaching method rather than an actual game.  It is gamification of the algebra class based on the Survivor game complete with tribe names and directions on running it.  Although this is for college, the author includes information on working with middle school and high school students.

This article includes the rules, the set-up of the class and how to teach based on research, types of exams, and ways to decrease anxiety.  It is cool because there is information on putting students in tribes, explains the best materials to help students pre-learn the material (flipped classroom), how to cut down on socialization time when they should be doing math, motivating students, gaining and keeping their trust,

Cool Math is a really awesome website to integrate into the classroom.  It has some very student friendly explanations which can be used inside and outside of class for a variety of math levels.  I use this website in class so students can be exposed to the material from sources other than myself and the textbook.    While writing this, I found a nice explanation of Pythagorean Identities for my Pre-Calculus class on Monday.  It also has a nice section on fractions for the pre-algebra class.  So guess where most of my kids will be on Monday?

Saturday, October 24, 2015

More math activities

Digital Camera, Cam, Gadget, has some really nice math activities for all grades, especially for high school students.  Although there are only 13 activities, I already found one that would make a fine geometry activity and could be used in several places in the geometry class.

The original suggestion is for a geometry scavenger hunt.  The idea is that you prepare a list of geometry terms for the participants.  Make sure they all understand the terms and then send them out to take photo's of objects representing the terms.  It is suggested the pictures be downloaded and shown so everyone can agree if the photos do contain the terms.

Why not send the students out to take photos as a homework assignment, download or share the photos to a program which would allow them to annotate so they identify the part of the photo that meets the term by circling the object and writing an explanation of why it meets the definition of a term.  In other words, defend their choice through writing.  This shows a more indepth understanding of the term.

Hut, Ruin, Ireland, House By The SeaAnother application of this same scavenger hunt idea is to send students out to take pictures of whatever interests them. When they come back they download the photos to their annotation program and they can identify the slope of each parts of the item.  For instance, the picture to the left has all four slopes in it.  By identifying the slopes, I make more of a connection.

I could also look for examples of shapes such as rectangles, triangles, etc.  I could even look specifically for triangles and then classify them by side or by angle or by both and turn it into a presentation. 

Then there is the activity to find the best priced pizza in town using price and diameter.  Even if you don't have a pizza place near you, this can still be used in class.  I live in a place where the closest pizza place is about 140 miles away but we can buy frozen pizzas in town.  So I send students working in pairs out with their mobile devices and a ruler so they can find out the diameter of the frozen pizza's at the two small stores in town.  They can actually just snap a photo of the pizza with the ruler showing the radius or diameter.  Once they get back, I can have students use this activity to figure out which pizza is the best buy.

The last activity I looked at would be appropriate at this time of year or anytime you have a bag of miniatures.  Students record the name of the candy, the weight and the calories in a data chart for the different types of candies in the bag.  Once done, they create a bar graph based on calories for each type of candy.  I would have students add a written report discussing if the candies all weighed the same and if they didn't was this comparison reasonable. I might even  have them calculate the weight per gram.

Friday, October 23, 2015

Fun Maths

Retro, Pen Paper, Math, Calculations  Today, I stumbled across the Fun Maths website which advertises itself as a website for High School Math.  It has both a teacher and a student section.

The teacher section offers printable worksheets, math projects, and games and puzzles while the student section offers games and tutorials.  The worksheet are nice and many approach the topic in a slightly different way so it can be used to provide additional practice.

The site provides workshops in numeracy, algebra, geometry, measurement, trig, and statistics.  All the subjects a teacher is likely to need.  The math projects covers tessellations, Valentines math and circle math.  Finally the games section sends you to the student cool games site with 14 games.

For students, there are many tutorials for different math topics.  The tutorials tend to be short explanations with examples but the games section has some really nice games like Ratio Blaster where I had to blast invading spaceships with the correct ratio that corresponds to the ratio on the gun.  At the end, it gave me stats and told me which ones I'd missed.    Then there was the Alien Angles game where I was given an angle and I had to move the arrow to that angle using only my eye to gauge it.  I checked and if I was close enough I got the points, if not, it let me know but in either case, a protractor appeared so I could check it.

Do these games work on the iPad?  I don't know as I didn't get a chance to check but my suspicion is that these games are probably flash based but it can be used for worksheets and tutorials without a problem. 

Thursday, October 22, 2015

Online Algebra Games

Some days I look for online Algebra games for my students.  I found a nice site with several games that will only work on a computer or a tablet with flash.  This means it will not work on the iPad. 

Math-Play has some really nice Algebra games.  The first one, one step equations, is really quite nice.  Students are given a multiple question and each time they determine the correct answer, they are given a chance at a 3 point throw.  However, if you miss the question, you automatically miss the shot.  Every time you get the correct answer, you get a chance to attempt a 3 point throw by deciding where to aim.

The equation games uses a concentration format where two square are flipped to see if they have the same answer.  If you are wrong, the two squares flip back and you try again until you start matching them.  The absolute value equation games is in the format of who wants to be a millionaire so more money is earned with each correct answer.

There are 18 different Algebra games offered including a game for solving systems of equations, one on the coordinate plane, one on slope intercept, one for finding square roots and so many other games that students should find challenging and interesting.

In addition, this site offers 14 Geometry games in an assortment of formats,  11 Interactive games for elementary and middle school students, 14 classroom games plus more games for elementary and middle school students.

It turns out you can use some of these games on your smart board and the team or student who gets the correct answer can go up to the board to make the shot or do the activity.  This means I can incorporate this game into my daily lessons using my smart board.  Cool!  Another resource.

Wednesday, October 21, 2015

Geoboard part 3

I've found that students often have difficulty translating the counting of squares on the graph to using the slope formula.  To most of my students, these are two totally different concepts.

So I've started having students find two points on the geoboard like in the picture to the left.  They turn the line into a triangle so they can see the rise and the run or the difference in Y values and the difference in X values.

They use the pen to draw lines showing the two y values and write down the difference and repeat the process for the x values as shown in the picture.  This provides students with a visual.  The next step is to calculate the slope using the standard formula to verify the visual. 

This is the first time I've done this activity and so far, it is proving to help students understand the process better.  By drawing the lines, it helps students understand its a difference or distance between the two values of Y or X.    I have been looking for something like this and I finally found it.  Yeah!

Geoboard app part 2

Today, one of my students figured out how to streamline the transformation activity on Geoboard.  I'm used to physically adding new bands as  needed  to show movement but one of my students played with it to figure out how to create a copy that could be moved around to do the translation.

First off, he created a rectangle on a coordinate plane using the larger board.  Under the left end of the blue bands, there is a small symbol composed of a square, triangle and what looks like a drop of water.  He touched this so the rectangle filled in and the corners became visible. This is the 9th icon from the left. 

Then he clicked on the two squares under the right side of the red bands.  This made a duplicate of the original square.  It is the 7th icon from the left.  It is great because you can rotate the whole shape clockwise or counter-clockwise.  The shape was moved about 5 units then rotated to its current position.

Then tap outside the shape and all the markers disappear.  If desired the student can calculate area through the use of a calculator which types the numbers on the geoboard.  They can also create hand written notes on the face of it.

 Now the finished product can have a screen shot taken of it and then sent off to the teacher.  This was fun for me learning something new.

Tomorrow I plan to  talk about how to use geoboards to help transition from finding the slope using a graph to the equation for finding slope.

Tuesday, October 20, 2015

Geoboard app.

Cubes, Hundred, Maths  Last night as I pondered a way to help my students translate the written directions for transformations, I realized I have the Geoboard app on the iPads.  Geoboards are the perfect vehicle for this so later today when I teach Geometry,  I will have the students use the Geoboards to help them see the movement.

They can create the coordinate plane using one color of rubber band for the x and y axis.  Then they put the original shape so they have the starting point.  As they read the directions to move the shape, they can use the rubber bands to make the new shape.

I think by following this step by step, they can physically do the transformation and check their answers.  Due to cultural learning's, they want to know if each and every problem is "right".  I want to give them ways to check their work  without having to tell them it is right. 

Since they didn't talk about manipulatives for high school teachers when I got my teaching credentials, I've had to learn by trial and error.  I did a quick search on the internet and found this lovely pdf from Math Forums on using geoboards in the classroom.  The 37 page document starts with the Pythagorean Theorem and Area followed by 6 complete lessons.  Yes its dated 1995 but the information is as applicable today as it was in the past.

This short article from NRICH which includes a few games that can be played with the geoboads.  Although this article is geared for elementary teachers, the information can easily be applied to secondary. 

Finally, check out Dr. Nicki's Guided Math Blog for some awesome links on using geoboards for guided math activities.  It is well organized and awesome ideas.  Please check it out if you need ideas.  These resources are going to make geometry more dynamic this year.  Yeah!!!!!!

Monday, October 19, 2015

Calculation Nation

Calculation Nation is a website maintained by the National Council of Teachers of Mathematics that is filled with various educational, mathematical games.  These games are flash based so are only able to be used on computers or devices that are flash enabled.  They do not work on my iPad.

The reason I found this site is I was looking for a game or two that would help my students become more fluent in determining transformations so I did a web search.  The search took me to this location for the flip slide game.  The student enters the transformations using a series of arrows to show direction and numbers to show how many squares the triangles should be moved so the green triangle is where the blue triangle is.

It takes some thought and it is rather fun.  In addition to this game, there are 12 more games designed to help the student acquire mathematical skills.  The nice thing about this website is that you may go in as a guest so you end up playing the computer but if you sign up, you can play other people. 

I enjoyed exploring EQ of Attack or a mathematical version of battleship where you calculate the line of firing so you hit as many things as you can with the bombs trajectory.  It came with all the noise one would expect from a sea battle.  Then I tried slam ball which is a game where you bounce balls off the side of the enclosure and try to go through point balls to gain points.  It takes a little while to get the hang of it but it requires thought to determine if you want to shoot up or down.

Dig it has students choose a fraction and then show on a number line where the location is.  There is a shovel that will dig for gems at the location you designate on the number line.  If you are right, then the shovel digs, if not you loose a turn.  The final game I played was Ker-splash where balls drop down this toy and the terms it hits end up on that player's side  While the other player is rolling, you combine like terms in the combination area so you free space for more balls. It is a bit faster paced than the other games but I enjoyed it because of that.  It gives great practice on combining terms. 

I wish it would work on my iPads. There are some downloadable apps for tablets but I need to check them out.  In the meantime, have fun with Calculation Nation.