Material-less math and questions

Playing Piano

As a support person I often find myself with a class for a day, or a period, or even just a few minutes while the teacher is gone. I need something to keep the students occupied with something other than gossip. So when the question came up “Need games children can play without any material to improve mathematical skills for thousands of slum area’s children.” I paid attention.

The first suggestions were games of NIM, which is a game played with stones. Any sort of counter will do and they don’t have to be uniform. Basically the game is played by making a pile of stones then picking up a number of stones in turn eventually forcing your opponent to pick up the last stone. Rules can include putting the stones in various sized groups and picking from one group at a time. Having a minimum and maximum number of stones that can be picked up, or really anything you can think of.

The second suggestion was playing “20 questions”. The answer can be as simple as a number and increase in difficulty such as rules or functions, to equations of lines, or just about any sort of concept in math. Imagine guessing a number but not being allowed to ask if it is higher or lower.

When I teach 8th grade math I basically like to make sure my students can recognize each function from the graph, the equations, and the table. So this fits in nicely. Actually anything we define in terms of properties should, theoretically, be a good answer for a 20 questions game. The game can and should be a vehicle for teaching students how to think critically about the properties of an object.

The last suggestion was Bizz Buzz. I’ve played Buzz a lot, which is a simple game. The rules are: students line up or sit in a circle and count up saying Buzz when they reach the number or its multiple. Bizz Buzz is a variation using two numbers and their multiples. Too add even more difficulty try using numbers from different bases. After playing this in the classroom a few times I increased the difficulty one my time by asking students to say Bang when they reach a number that is a common multiple. Playing with factors and common factors should also work.

I might also recommend ideas such as http://www.mathinyourfeet.com/ which I think is a great method to learn math. Creating patterns of dance or stomps with your feet.

I was also talking to a music teacher a few weeks ago. He was trying to teach his students the relationship between fractions and notes using the old pizza method. I suggested he stay with what is natural and use the timing of the notes. Whole notes, half notes, quarter and eights are fractions of time not pizza. Sustained notes are simply adding fractions. Students would obviously practice with their instruments, but drums can be easily created. I would assume that difficulty could be increased with various time measures.

If you have any other suggestions please add them to the comments below.

 

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Algebra

Algebra Tiles
I think most people have heard of these, but not everyone knows what they are and how to use them.  I’m not really going to explain that here. I have however found a great power point that is very easy to explain. A direct link to the power point is here. The Alliance for the Improvement of Mathematics site is here http://www.delmar.edu/aims/
What I will do is explain how to make your own set of tiles.
Start with four different colors of paper. Card stock would probably be best. Red, blue and yellow green is suggested.  The x tiles will be red and blue and the y tiles will be yellow and green.  One color will be for positive and one color for negative. I would also laminate when done if you can.
When making the tiles the important part to remember is that the long side of the tile should be immeasurable.  This is easily enough to figure out by simple using any sort of diagonal on graphing paper. Make the short side 1cm in length. Make two different size tiles. This is important because the immeasurable length means that the tile is an unknown.  When introducing the tiles to the students for the first time let them measure all they want and eventually they should come to the determination that the length of one is x and the length of the other is y.
The next two tiles to make are squares that are x2 and y2. Finally you will want 1cm by 1cm squares of white. (You can substitute centimeter cubes for this) If you want you can also include 10cm long strips.
The tiles can be used for everything from adding and subtracting integers to multiplying and dividing polynomials.
Finally, I want to end with a great video from Dan Meyer. He is sharing his application video for Apple’s Distinguished Educator Program. It’s a fun watch and because he uses Vimeo it is visible on school computers.
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Algebra

Algebra Tiles
I think most people have heard of these, but not everyone knows what they are and how to use them.  I’m not really going to explain that here. I have however found a great power point that is very easy to explain. A direct link to the power point is here. The Alliance for the Improvement of Mathematics site is here http://www.delmar.edu/aims/
What I will do is explain how to make your own set of tiles.
Start with four different colors of paper. Card stock would probably be best. Red, blue and yellow green is suggested.  The x tiles will be red and blue and the y tiles will be yellow and green.  One color will be for positive and one color for negative. I would also laminate when done if you can.
When making the tiles the important part to remember is that the long side of the tile should be immeasurable.  This is easily enough to figure out by simple using any sort of diagonal on graphing paper. Make the short side 1cm in length. Make two different size tiles. This is important because the immeasurable length means that the tile is an unknown.  When introducing the tiles to the students for the first time let them measure all they want and eventually they should come to the determination that the length of one is x and the length of the other is y.
The next two tiles to make are squares that are x2 and y2. Finally you will want 1cm by 1cm squares of white. (You can substitute centimeter cubes for this) If you want you can also include 10cm long strips.
The tiles can be used for everything from adding and subtracting integers to multiplying and dividing polynomials.
Finally, I want to end with a great video from Dan Meyer. He is sharing his application video for Apple’s Distinguished Educator Program. It’s a fun watch and because he uses Vimeo it is visible on school computers.
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Snowmagedden

Did you see this cool activity created by our own Mr. Foster? Of course not I haven’t shown it to you yet.

A simple excel file Students are to label points on a number line. Then move numbers around to make the columns equal zero. Great for practice in adding integers, but also great for building the concept of finding zeros,
I’m also thinking it can help build the concept of equations, but putting the zero block in the center and asking students to add or subtract from the ends.

Feel free to play with it.
We were also talking about setting up a way for students to access these files and turn them in on their own. We are thinking a separate google doc for each student. You can access the document here. When you share the link (a setting in google docs) your students don’t need an account to view the page.
There is also a company Zoho.com with many of the same features as google docs. I uploaded the document there also. I think the formatting looks a lot better than it did in google docs. In Zoho you can share the document with other Zoho users (free plan even) but you can’t share outside of Zoho unless you buy the premium plan. They also have an option of sharing to a group.
One idea we did have is to differentiate the lessons and give some students more challenging spreadsheets. This of course would mean sending each one to individual students negating the advantage of a group.
One final thought is that sharing the documents will mean a link somewhere. Either a hyperlink in a class blog (try to find a blog that isn’t blocked). The other option I can think of is a URL shortener.
A service like tinyurl.com will shorten the URL (the address of the web page) to something such as http://tinyurl.com/4amf5cc It is even possible to customize the last part of the link. Perhaps something like a name and a date. Then you can assign each student a different spreadsheet and they can remember the URL easily.
Enjoy your snowday, and share some of your favorite lessons.

Snowmagedden

Did you see this cool activity created by our own Mr. Foster? Of course not I haven’t shown it to you yet.

A simple excel file Students are to label points on a number line. Then move numbers around to make the columns equal zero. Great for practice in adding integers, but also great for building the concept of finding zeros,
I’m also thinking it can help build the concept of equations, but putting the zero block in the center and asking students to add or subtract from the ends.

Feel free to play with it.
We were also talking about setting up a way for students to access these files and turn them in on their own. We are thinking a separate google doc for each student. You can access the document here. When you share the link (a setting in google docs) your students don’t need an account to view the page.
There is also a company Zoho.com with many of the same features as google docs. I uploaded the document there also. I think the formatting looks a lot better than it did in google docs. In Zoho you can share the document with other Zoho users (free plan even) but you can’t share outside of Zoho unless you buy the premium plan. They also have an option of sharing to a group.
One idea we did have is to differentiate the lessons and give some students more challenging spreadsheets. This of course would mean sending each one to individual students negating the advantage of a group.
One final thought is that sharing the documents will mean a link somewhere. Either a hyperlink in a class blog (try to find a blog that isn’t blocked). The other option I can think of is a URL shortener.
A service like tinyurl.com will shorten the URL (the address of the web page) to something such as http://tinyurl.com/4amf5cc It is even possible to customize the last part of the link. Perhaps something like a name and a date. Then you can assign each student a different spreadsheet and they can remember the URL easily.
Enjoy your snowday, and share some of your favorite lessons.

The Poster Session

I’m already planning for my big summer presentation. How it is possible to use web 2.0 technologies, specifically a wiki, to help teachers and administrators across schools to collaborate on math curriculum.

As some of you may know I am currently taking a graduate certificate course through Johns Hopkins University and the International Society for Technology in Education.

One of the requirements for this program is to present at the annual ISTE conference (Formally the NECC conference). 18,000 people are expected to attend this conference.

I hope to present the best of Waukegan Public Schools. I will appreciate any and all help given. Actually, the entire project is about how administration and teachers can work together to get this done.

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The Poster Session

I’m already planning for my big summer presentation. How it is possible to use web 2.0 technologies, specifically a wiki, to help teachers and administrators across schools to collaborate on math curriculum.

As some of you may know I am currently taking a graduate certificate course through Johns Hopkins University and the International Society for Technology in Education.

One of the requirements for this program is to present at the annual ISTE conference (Formally the NECC conference). 18,000 people are expected to attend this conference.

I hope to present the best of Waukegan Public Schools. I will appreciate any and all help given. Actually, the entire project is about how administration and teachers can work together to get this done.

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Mathmusicians

Pythagoras, depicted on a 3rd-century coinImage via WikipediaOk so a couple of videos have been floating through my PLN this week.  I followed them to their youtube home and found one mathmusician.  Oddly enough I remember one musician spending hours , or what seemed like hours, telling me how chords in music aren’t random but based on mathematical principals.

So I’ve always known there was some sort of connection between math and music, I’m just not really sure of the connection.  You won’t either after this blog post, but I hope someone figures it out and explains it to me.
Anyway, the videos she creates are pretty cool and do a great job of connecting real world mathematics to doodling.  After watching the videos I thought it would be great time filler for those half days when you can’t really teach anything and the students just don’t want to learn anyway.
Show them the video and turn them loose to be creative. Just be sure to ask them to explain what they can of the math before you hang them on the wall.

If you don’t have the time or ability to get a youtube video into the classroom here is a link to a cool Pythagoras Tree applet.  Students can draw those pretty easily.

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Mathmusicians

Pythagoras, depicted on a 3rd-century coinImage via WikipediaOk so a couple of videos have been floating through my PLN this week.  I followed them to their youtube home and found one mathmusician.  Oddly enough I remember one musician spending hours , or what seemed like hours, telling me how chords in music aren’t random but based on mathematical principals.

So I’ve always known there was some sort of connection between math and music, I’m just not really sure of the connection.  You won’t either after this blog post, but I hope someone figures it out and explains it to me.
Anyway, the videos she creates are pretty cool and do a great job of connecting real world mathematics to doodling.  After watching the videos I thought it would be great time filler for those half days when you can’t really teach anything and the students just don’t want to learn anyway.
Show them the video and turn them loose to be creative. Just be sure to ask them to explain what they can of the math before you hang them on the wall.

If you don’t have the time or ability to get a youtube video into the classroom here is a link to a cool Pythagoras Tree applet.  Students can draw those pretty easily.

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What is Important in Math

This is a great Ted Talk http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html

The basic question is should we teach students how to do stuff by hand or is it better to teach concepts?

This isn’t to say calculators should be introduced in kindergarten, but honestly let’s question what is important when teaching math.