Distances.

Last night, I realized that not every one uses standard tools to measure anything.  I am attending a series of lectures in costuming this weekend.  All aspects of making costumes both historical and fantastical.  This is interesting because everybody's body is different and most of us are not truly symmetrical. 

If you were to buy a pattern, on the back, there is a printed table telling how much material you need to buy to complete the pattern. Anyone who sews knows these are "guidelines" not set in stone because depending on the type of material, the pattern, contrasts,  etc you can often get away with less materials.

But what if you did not have the standard rulers, yardsticks and such? How do you measure things? Well in many native cultures, they insist on using thumbs, fingers, nose to fingertips, etc to measure anything.  The logic is that everyone is different and if you use your own body to measure things, then the outfit produced will fit your body in the correct proportions. 

Interesting idea!  Perhaps when teaching proportions, we can take time to discuss this idea to show how it works in a real life application that uses the idea without using all the numbers.  I need to give that some through.

Algebra Champ

The first year I used iPads in my classroom, I used Algebra Champ.  At that point, I was just learning how to use certain apps in class and most students who played with this would just rush trough it, guessing on the answer and then complaining that the app was "Boring!", so I removed it.  Now with a couple years of use, I have a better idea of how to integrate it into the classroom.

Algebra Champ is designed to practice solving one, two or multi-step equations.  This does not help them learn the basics of the process.  It does not give feedback.  It gives the problem and students can punch buttons until they get the correct answer.  They are not allowed to move on until they have selected the correct answers

On the the application.  Students get to choose an avatar and a name.  As you can see, I chose a female avatar who looks kind of feisty.  Once that is taken care of, they are ready to play.  Algebra Champ has four levels with problems ranging from solving one step equations in level one to requiring use of the distributive property to solve in level four.

As stated earlier, this is an app designed for students to practice solving multi-step equations.  So the good things about this app are
1. Every time a student goes through a level, there are new problems.
2. There are only 5 problems in each level.
3. They cannot move on until they select the correct answer.
4. Gives a percentage of correct.
5. Keeps a score board.


The things I do not like about the app:
1.  No real feedback - does not state wrong, just won't let you move on until you select the correct answer.
2. Does not show how the problem should have been done.
3.  No place to work the problem in the app (or at least as far as I could find.)

 Now the question is, will I use it next year?
Maybe.  In order for this app to be used, I have to do one of two things or even both.
1.  Set the percent level for 80 percent before the student can change levels.
2. Use an app like zoodle pad and have students use that to show their work.  They could either send the work to me via e-mail, dropbox etc. 

Personally, I think I would do both, especially if I noticed students just pushing buttons to get the right answer.  I want them to slow down and really work the problems, otherwise they will not improve.

Math Rings

Math Rings is a game but not the usual action game where you try to hit, kill, beat, shoot, or any other type of action, it is a logic game that can take a lot of thought to find the correct answer. 

The idea is that you move numbers and operations around so each spoke of the wheel is correct, totally correct.  The picture I have here shows that I got three spokes correct but the fourth is wrong.  That means there is a different way of arranging the numbers so it is correct.

I admit, it took me a few times through the directions to figure out how to play the game but once I got the hang of it, it isn't too hard.  You can move the numbers or you can move the operations and equal signs around so the spokes work.

So far the middle number has been one. You'd think that would make it easy but in reality, it isn't. It takes quite a bit of thought and some frustration to get everything aligned properly.  I would actually classify this as a logic puzzle rather than an actual game because it does require serious thought rather than using your reflexes.  I think this game could easily be used in any of my math classes for remediation, or scaffolding.

Over the summer, I've been toying with the idea of having some "games" available during class for the students who finish their work properly and need something to do for 5 minutes.  Of course my idea of a fun game is much different than theirs, so we'll see how they like this one.

Mathematics Assessment Project (MAP)

As part of my research for yesterday's column, I ended up at the Mathematics Assessment Project. The site was created and designed to be part of the Math Design Collaborative.  It has both formative and summative assessments for use in the classroom.  These assessments are designed for grades 6 to 12 and covers lessons, tasks, tests, professional development, and teaching for a robust understanding tool suite.
First of all, the lessons are classified as the formative assessments with 100 lessons covering a variety of topics.  Each lesson plan has everything you need to teach the lesson including the resources.  There is even a guide to be downloaded by teachers and administrators before starting.
Next is the summative assessment section they call tasks.  there are currently 94 tasks for middle school and high school.  I like that each lesson has the Mathematical Content Standard and is identified as to the level of task, such as apprentice or expert.  In addition, the task provides the rubric, an unscored student paper so you can practice along with a scored student paper so you can see how you did on the scoring. 

The test section is still in draft form but there are six each available for high school and for middle school.  The middle school tests are 80 min long but can be divided into two 40 min tests. In addition, each test comes with a rubric to use for scoring.  These are provided as examples of the types of tests students should be able to take and are based on the common core.

The professional development has 5 modules  in draft form to help learn more about using the formative assessments.  Each module comes with the session guide and handouts, sample lesson plans, and suggested lesson plans.  There is a video showing teachers trying the lesson and then discussing how it went.

Finally, there is the teaching for robust understanding (TRU) suite which is a framework and designed to help increase learning in the classroom.  It provides a series of downloads of material that could be used as self study or in a group. 

 This has a lot of great ready made materials that could easily be integrated into the classroom.  All this and its completely free without the need to sign in.

Mathematics Design Collaborative

While pursing a topic, I ended up at the Bill and Melissa Gates page for the Mathematics Design Collaborative.  The idea behind this site is to produce college ready students. 
When you first get to the page they have a list of topics and grades for material offered via the website.  Notice the list covers grades 6 to Algebra II course outlines you can download in PDF form.

For the fun of it, I clicked on evaluating statements about length and area under Algebra I.    It downloaded a two page PDF titled "

Professional Learning Module

Modeling the enactment of the Formative Assessment".  It has every step for carrying out this assessment and there is a web link at the top that sends you to corresponding page at the Mathematics Assessment Project.

 The explains every step in the unit along with the appropriate material to use at this point.  It assumes you will bring up the website associated with the material in the PDF.

 This last link leads you to the actual lesson complete with mathematical goals, introduction, materials required, time needed, mathematical practices, lesson type, mathematical content standards, and all resources that you can easily download.

So what you have is a nice formative assessment all ready to go with everything you need. 

I like having access to actual formative lesson plans because I do not always have time to  sit down and create these.  Tomorrow I"ll give more information on the Mathematical Assessment project which has so much to offer teachers.

The Teaching Channel

I love periodically checking in on The Teaching Channel.   I have found some great videos on general teaching, tools for teaching ELL's, math videos, etc.  It is devoted to helping all of us be better teachers and to get new ideas for ways to teach students.
I put transformations in the search engine to see what they have to offer.  There were four videos dealing with transformations that showed up on the top of the results.  They ranged between 4 minutes and 9 minutes long, so a nice length.
1. Deepening understanding of transformations.
2. Understanding transformations
3. Collaborative work with transformations.
4. Common issues with transformations.

I watched the first video on deepening understanding. The first thing I noticed was to the left, there was a learning objective, the length of the video and questions to consider while watching the video.  I like that so much.

The video cut between the classroom, the collaborative meeting and interviewing the teacher.  I liked seeing the whole process so that I can implement it at work with other math teachers.

The search also highlighted a blog entry on Formative Assessment that lead me to the blog entry on these four videos indicating that I should watch understanding transformations, common issues, collaborative work and finally deepening understanding.   This information tells me the four are together to form a fuller picture of teaching transformations in a better way. 

The Teaching Channel has 200 videos dedicated to teaching a variety of math topics for all grades.  Once I get back to school, I am going to find time in my schedule to watch the videos. My internet at home is not always that great and videos spend more time starting and stopping than playing.  It is frustrating but if there is a will, there is a way.

SMART Adventures Mission Math 1: Sabotage at the Space Station

This is a paid app that I stumbled across one day when it was  offered for free.  SMART Adventures is a game that gives students a chance to practice their math skills in a fun game.  The idea behind the game is that you are a junior agent and you're assigned to help find out why things are going crazy at the space station.  This app is geared towards females and the only choice for your character is a female one so boys might not be excited about using this one.

Once the student has set the skin, hair, eyes, and clothing, your agent is ready to go.  This app has an introduction to set up the mission and a leader who gives orders.  The junior agent has others to help her as she goes through the space station solving math problems.  The space station has 5 levels with one to two labs per level.  Each lab is different and requires a different math skill to complete.

This photo shows the two labs on level 1.  To open the lab, you tap on the door and they slide open so your character can go in.  Once in a lab, someone comes on and states the problem along with information on how to do the work.

 Each lab has a problem based on the type of lab it is. This lab is the computer lab and the premise is that the computer language got messed up and its your job to solve the simple problems and find the answer in Mandarin Chinese.  If a student works through all the labs, they will have practiced basic arithmetic, fractions, decimals, bar graphs, place value, measurements of volume and mass, factors, multiples, angles, polygons and spatial rotation.
Students see applications for space travel, chemistry, mechanical and electrical engineering, computer science, and other topics.

One of the best things, is the student can pause the game and pick it up exactly where they left off.  This app is geared for middle to upper elementary but it could easily be used in middle school or high school for students who need remediation or scaffolding for basic skills.  I admit, I had a great time playing it myself and like it. 

Nextlesson

I was checking my account in Schoology when I discovered they have a list of apps for their website.  I choose Nextlesson which has both free and paid lessons.  They allow a free sign up or you can use your google signin for this site.

Once you've checked in, you get a page with the following information.  You have an option of checking your lessons, checking out new features or explore the lessons by standard or topic.  When I chose subject, I was taken to a page with a

 search engine at the top.  Under it, there were lessons listed under editors choice, free lessons, performance based tasks, activities, rank and reason, 21st century, projects and PBL's, and finally essentials.

The lessons are for grades K to 12 in Math, ELA, Social Studies and Science.  It is easy to check out a free lesson, make adjustments and download it to your lessons

This is a lesson on Ebola and Math.  There is a one click download button, shows you the standards the lesson meets, grades and gives you an idea on what its about.  Once you download it into your lessons,  you get a lesson plan and all the sheets you need to teach the unit.

This is awesome.  I downloaded the app associated with Nextlesson to my schoology account, I am going to go through the free lessons and choose the ones I want and finally, I'll figure out how to put the lessons in the apps so I can assign them to my students.  Cooool.

More on Writing in Math.

I found this book called "Write on! Math" by Rovert Gerver.  It is subtitled "Taking Better Notes in Math Class"  I am always on the lookout for ways to increase literacy in my math classroom so when I stumbled across this on Amazon, I ordered it.  I managed to get it for way less than the listed price.

The book comes in at around 90 pages with four chapters focused on the topic of taking better notes in math class.  The first chapter discusses communication in general, using pictures etc.  The second chapter focuses on the notes students take in class.

It is the third chapter that really catches my interest as it is titled "Writing Techniques.  It has three dozen strategies to use in the class for writing mathematics.  Imagine, three dozen writing strategies!  The final chapter is on writing research papers in Math.  That is such an awesome idea and it would scaffold skills learned in the English class.

One tip I like is simply that all figures must have a figure number and a descriptive, one sentence caption, just like you find in a regular text book.  The example he gives is the Eiffel Tower and he even gives three examples for effective captions because he says identifying it as the Eiffel Tower is not enough.

I will post information over the next school year as I work my way through the tips to let you know how the tips work in my classroom.

What do you do?

Due to budget cuts, many teachers end up having to double up and teach two different classes in the same period.  I'm having to do it.  I asked to put my Pre-calc class with my Pre-algebra class because I figure the older students will be a bit more independent.

I've used Hippocampus in the past but I quit using it because it didn't work well on the iPads which is all I have easy access too.   I just revisited it and it now works much better on the iPad.  Too see how it now works, I selected a developmental math and clicked on adding integers.  It showed a short 4 to 5 min video for the students to watch.

I was thinking that I could easily have students begin the new topic the day before and have them watch it just before class ends so they have an introduction.  The video component allows students to watch the material as many times as needed.

If you look at the bottom half of the page, there is a blog that provides the lesson plan for the material. It includes the assessment, learning objectives, assignment and even a rubric for grading.  In addition there is a link for the actual reading itself.


The material is like any textbook with a reading, practice problems, vocabulary and examples.  The only issue is that some of the java based applets do not work on the Mac but there are other ways to provide those applets.  One way would be to download the applet so it works off line and show it via the teacher's computer.

There are even practice problems which will allow the student to check their answer.  What I like about the practice problem is that there is an explanation for each answer and why it is right or wrong.  This is immediate feedback so students know what is going on.

So with this in mind, I think I'm going to follow the suggestion of a math teacher from Honolulu I met.  She taught two different classes in one period and arranged it so she taught one class while the other worked on the assignment, switched the next day and on Friday's the students would get a quiz and time to get caught up.

One other thing about this site is that I can sign in and customize the material for the students so I can pick and choose what to use.

Last year, I was trying to do a combined Pre-Algebra and Algebra I.  I tried to teach a lesson each day to both groups but it was hard to manage since I felt like I wasn't doing a good job.  This new idea sounds like it will work much better and if I have students watch and rewatch the videos on days that I am teaching the other class.  I hope to have one to two helpers to work with the Pre-Algebra class.

I don't know if it will work but I think I have a better plan this year than I had last year. Yeah!!!

Connections

I read an article on three ideas for math teachers to do this summer.  I think it should have had four ideas.  Yes technology, relevancy, and inspiration are all important but we forget connectivity.  We need to connect the topics in math so students no longer see each section as independent of each other.

For instance:
1. The distributive property. 

 This diagram can be used to show students something like 16 x 14.  The large square represents the 10 x 10 or 100 units.  The small rectangles are 10 x 10 or 100 units and the smallest squares represent ones or  24.  So the total is 100 + 100 + 24 or 224.  If you calculate 16 x 14, it does equal 224.  This is a good visual way of showing the distributive property.

It can also be used for multiplication of binomials such as (x + 6)(x + 4).  the largest square represents X times X = x^2.  Each rectangle represents 1X so you have 10X and each small square represent 1 x 1 or 24 total units.  If you look at everything, you end up with x^2 + 10X + 24.  You can use the same drawing but use blue for positive and red for negative and you can show (x - 6)(x + 4) in a visual manner so students see what is happening.  This is a nice way to show a connection between the two.

2.  Right angle triangles.

A.  Show the triangle on a coordinate grid to show students the idea that the legs are actually x and y values.   This sets things up to jump over to the unit circle, to basic trig values.

B.  The triangle on the grid sets students up to see the Pythagorean theorem.
      1. Use the grid with obtuse and acute triangles and the variations of the Pythagorean theorem formula to show why a triangle is right, acute or obtuse. 

3.  Unit circle and trig graphs.
A.  Show the correlation between the values on the unit circle and the sin or cos waves.
B.  Show the correlation between the sin waves and the oscilloscope.

These are just a few ideas for showing connections between topics and ideas in math.  Too many of my students see each idea or topic in math as isolated and unrelated to anything else.  I need a way to show them the relationships.  I think this might help their ability to transfer knowledge among situations.  I plan to try it this coming year and we'll see how it works.

CK-12 foundation

Over the summer, during a class, I learned about the CK-12 foundation. This is a great website filled with a variety of resources for both teachers and students. 

 Yes, it is web based but the foundation also has textbooks that can be downloaded from Amazon for sure for free.  The nice thing about the foundation is that they offer materials for Math, Science and several other subjects so if you need textbooks, videos, assessments, etc they are available.

 I clicked on Algebra and the page listed all the topics covered in the class from real numbers to matrices and quadratics.  I find this really nice because I can look for a specific topic.  Once I clicked on graphs in the coordinate plane, I got a page that showed all the activities associated with the topic.

There are readings, videos,  activities, study aids, assessments, weblinks, and real world situations.  Everything you need to help students learn the material.  The best thing is once you decide which of these you want, you can add them to a flexbook and download that to use. 

You also have the choice of adding it to a library, sharing things, download (in PDF, mobi, or epub formats)  or customization.  It is free to join and I plan to use this website for a class I have to teach.  Due to the way the schedule ended up, I have to combine two classes and I can use this website to prepare materials for the older students so they can be more independent learners so I can work with the younger students. 

I see so many ways I can use the materials in all my classes.  Yeah!

Radiation

Yesterday, I posted an activity on Marie Curie.  In the google plus group, one of the folks posted a video on the most radioactive places on earth.  The video includes information on Madame Curie's home but it also includes some places I would never have guessed were even radioactive.  Watching the video lead me to see there is another real life math lesson.
1.  Students watch the video.
2.  Students re-watch the video and fill out a data sheet on the material covered in the video.
3.  Students use a spread sheet to put in data to create bar graphs, pi charts, etc.
4.  Students write up a conclusion to go with the graphs.

Idea 2.
1.  Students watch the video and fill out a data sheet.
2.  Students go on the internet to do research on the narrator's claims.
3.  Check to see if the claims of radiation output match commonly accepted radiation outputs.
4.  On a spreadsheet, input the data and create two sets of spread sheets to compare the claims in the video with the ones found by the student.
5.  Students write up a conclusion on how correct the claims are.
Extention.
Students research the rates for human exposure per year and figure out how much of each item the person needs to be exposed to before they reach the legal limit in the United States.

Marie Curie

Thanks to an article on the Makers google plus group, I got the idea for this math exercise.  This article on Marie Curie's possessions and what people must go through to access her radioactive papers.  It explains what she thought of some of the elements she studied and how casual her attitude was towards various radioactive elements.

Of course at this time, very little was known about radioactivity so when Marie and her husband worked with it, they used regular lab coats and even kept small amounts in their pockets.  So I bet you are wondering where I'm going with this. Think about it.  Radiation uses  the half life formula, so using the internet and a spread sheet programs,  students can:

1. Read the article and list the various radioactive  elements Marie Curie and her husband studied.
2.  Research the half life of each element listed in the article.
3.  Find out the "safe" levels for each element.
4.  Using a spread sheet, calculate how long it will take for the radioactive item to become safe.
5.  Research exposure rates for each element.
6.  Use spread sheet to calculate the exposure rates needed for people to become sick and die.
7.  Create graphs to present the data.
8.  Create a write up on the information.

Nice real life mathematics calculations.  In addition they get some science about radiation and they learn more about Madame Curie who was one of my hero's growing up.

National Library of Virtual Manipulatives

I love the Virtual Manipulatives web site out of Las Vegas, NV.  Unfortunately, their website is Java based which means I cannot use it on the ipads in my classroom. Since I lasted visited the website, the Virtual Manipulative folks have gotten together with a company to produce an app for computers so students can still use the manipulatives while off line. 

The app is made by Matti Math and is designed to be installed on a computer so students can work either on a Windows or Mac off line.  It means there is no need for an internet connection, no need for Java, but it is only designed for the computer, not for tablets yet. 

Unfortunately, I do not have easy access to computers because there are like 3 carts of computers for the middle school/high school and that means you have to sign up in advance.  You could use the computer room but that is often in use by the elementary school students.

I know that I can get certain individual apps through the itunes store but there are times I do not want to download a bunch of single apps that do the same thing, the one web site does.  It takes less memory that way.   On the other hand, this is a nice website if your students are using computers with a decent internet connection. 

The National Library of Virtual manipulatives cover grades preK to 12 in Numbers and Operations, Algebra, Geometry, Measurement and Data Analysis.  Many of the apps within the library cover several grades and can be used for different classes.  I know that using the apps on my Mac, I get the message that I need to activate the Java and then I'm told its out of date, do I want to update it. 

I'll be checking a couple other websites to see if they can be used on the ipads.  Its a wish of mine but who knows if it will actually happen.

Simplify

Simplify is a calculator that can help simplify radicals and give both the exact answer or a decimal approximation.  It does square, cube and fourth roots for any number inputted.

If you put in a number such as the sqrt85, it shows that 85 cannot be broken down any further and that is the answer.  It also gives the decimal approximation.

On the other hand if you ask for the sqrt120, it shows the break down of what times what is 120 and then the answer with both a root and with a decimal approximation.

You can also find the cubed root of 120 and the fourth root.  Each time it will show the breakdown if possible along with the final answers.

This is a calculator so it could only be used to check answers. It does not have any explanations or lessons to help learn the actual process.  The only real way I see using this app is to have students do the work and then have them check their practice work using this during a guided practice.

Engineering Math App

I don't remember what I was searching for but I came across Engineering Math 101 by WagMob.  No I don't teach engineering at all but the free version has two lovely chapters on complex numbers.  The material is in nice small chunks and make a great reference so students do no have to go through the book to find everything.

The first chapter covers complex numbers, imaginary numbers, Argand diagram, complex conjugates, adding and subtracting complex numbers, multipyling complex numbers, dividing complex numbers and the complex plane.  Each has an explanation with either a diagram, examples or both.  If you click on a topic, the app takes you down the page to the proper part.


The second chapter covers the polar form of complex numbers, Euler's Formula, De Moivre's Theorem and Powers of Complex Numbers. 


Chapter 1 and 2 are in the learn portion of the app.  There is also a review part of the app which has 7 flash cards to review 5 basic terms and 2 formulas. 


The full app is $1.99.  Unfortunately, this appears to be a reference app because it does not have a way for students to practice problems but on the other hand, I can send students to this app when they ask "Where in the book is this stuff?"

Traveling by Air

I sit here once more in the local airport getting ready to travel.  I watch all the people who scurry from here to there, line up at Starbucks for their morning caffeine, or  stop through one of those numerous food places for a meal.  I wondered how many people are transported every day if the planes are full.

You know, students could use the Internet to look up specific airline and their schedules between two cities and the type of plane used on that route.  A bit more research and students can find out how many people the plane can carry and the fare being charged that day.

So now the student has the information needed to calculate the amount of revenue each flight makes. As for expenses, a quick letter should get that information.  On the other hand, the student should be able to get a figure for cost of the route on the Internet or at least an addy to send the request to.

Hmmm, there is also the concept of maximum weight an airplane can handle so students could divide maximum weight by number of people the airplane holds to figure out the amount of luggage each person is allowed.

   I fly on some very small airplanes.  When you check in they ask you for your weight and you are allowed 100 lbs of luggage including your carry on.  Anything over that and you pay extra.  I have taken some of my friend's stuff because I was under and they were over.  Think what would happen if all airlines did that?

Tweeting in Math

My students love to text.  They love to text to each other during class if they can sneak it in, between classes, after school or any other time they can manage.  I'm thinking of using Twitter in the classroom but I don't use a cell phone at school since as an adult I am trying to set a good example. The other thing is that my cell phone does not work at the school due to a different provider being the carrier there. 

Honestly, the school frowns upon using cell phones in school but I can take the premise of Twitter and use it in my classroom.  I like the 140 character length because you have to be concise.  Now with that in mind and the fact that my students would rather cut and paste material,  maybe I could apply the 140 character length to summaries,  to writing a problem based on a picture, or describing what is wrong with a problem.

I hope to increase student writing in the math class and most students hate to write so by using the 140 character limit, it might make them willing to write if they know they have to write a bit.

Of course, this is where their being concise comes in.  They won't be able to use fluff to fill it out and it might improve their over all writing.   We'll see how it works when school starts.