Creating Art Using Geometric Transformations

We expect a lot from students. In math, there is an emphasis on thinking, problem solving, communicating thoughts using mathematical language, trying, making mistakes, evaluating, trying again and re-evaluating. It is all part of the mathematical process, but, I often find that students get frustrated by the long bouts of concentration required of them.






I've begun to put more of an emphasis on art in my math classes. The art, of course, is directly related to the unit of study.





Recently, I had my class investigate Transformations through art. They had two objectives. The first was to use Rotations (Turns), Reflections (Flips) and Translations (Slides) to design a piece of art. The second was to explain their artwork using mathematical language during a student/teacher conference.







Before beginning, students investigated art from different cultures and found many examples of geometric art where the patterns relied on transformations of congruent shapes.

The examples shown are from Grade 6 students.

There is a great deal of math thinking that goes into well composed artwork. Shapes need to be spaced out evenly and centered. That involves measuring, planning, rough work, making
mistakes and trying again.








Students demonstrated a variety of examples of each translation. For example, some rotations involved centers of rotation within the shape, others had centres of rotation on a shape's vertex,  while  centres of rotation outside of the shape were also used.







This project took my class about three weeks to complete. They did not work on it from start to finish. Instead, it was something that they would return to over and over again.







Sometimes they used the project for down time - colouring with a friend - when they needed a break. Other times, an idea might pop into their head and they would put down what they were doing to incorporate their thinking before they forgot about it.




Spending a long amount of time on the project had many benefits. It allowed students to review ideas in their head after the instructional component of the Transformations Unit was over. As mentioned above, it gave students a chance for "productive down time" and an outlet for their creative spark. It also gave students an opportunity to really investigate what each other were doing. Ideas were talked about informally as students shared their artwork and their thinking when they wanted to.

Art and Math share a long history. The combination gives students opportunities for projects that really do connect to "the real world."

Puzzles in Middle School Math and Language Centres

I have begun using puzzles in my Math and Language centres. I have found that they can be used to demonstrate the need to plan and to assist in developing students' understanding of what planning looks like. I have used puzzles tio integrate cross-curricular ideas into math and language. I have also noticed that they offer some down time where students can socialize while coming together for a common goal.

PUZZLES USED TO PROMOTE PLANNING AND ORGANIZING

In my language classes, students learn to use the "Writing Process." Similarly, in my math classes, they use the "Four Step Problem Solving" method. Both require students to plan and organize. Puzzles teach this as well. While it might seem rudimentary, the BIG IDEA is that, to accomplish something complex, it is best to chunk it up into attainable bits. Furthermore, the chunking requires logical rationale. Most learn that the first thing that needs to be done is to separate puzzle pieces into groups; particularly edge pieces and pieces of the same colour or design. 

Organizing puzzles into edge pieces and pieces with similar colours and designs.

After the planning stage comes the application stage. This is where calculations are attempted, a rough draft is worked on or, in the case of a puzzle, the piles of pieces are connected. All three share a common point; that, despite the planning and organizing, putting it all together is not simple. It takes effort. Pieces that a student might think connect don't. Sometimes this is solved simply, by rotating a piece and trying again (do you see how I used that math word - integration). Sometimes, one must accept that the original plan wasn't quite right and that the piece needs to be re-categorized. After awhile, everyone comes to a point where a systematic approach is necessary - just picking up one piece at a time, trying it in every possible rotation and then putting it aside to try another piece, Genius is one percent inspiration and 99 percent perspiration (Thomas Edison).

After students complete a few puzzles, the lessons about planning, organizing and persistence become a symbolic point of reference that they all share.

While this has been as far as I have connected the planning process to puzzles thus far, I have considered manners of extending the learning. For instance, I have contemplated stopping students as they organize the class puzzle to ask them how many pieces they think make up the perimeter (estimation based on the proportional size of individual pieces) or to explain what percentage of edge pieces they think they have to locate first before they begin putting them together (demonstrating an understanding that being exactly correct isn't necessary in the planning stage).

PUZZLES TO INTEGRATE OTHER SUBJECT AREAS

Puzzles symbolically make a connection for students about the need to plan, organize and show resilience. While doing so, they allow students to think about the images in puzzles. Consider these puzzles about space and the ocean.

While studying the Biodiversity of Living Things students might work on a puzzle about living things. As they do so, they are likely to notice interesting features that would enable them to ask inquiry based questions. Why does a dolphin have a long, pointy nose? Is that thing a plant or an animal?

Likewise, while studying Space, students might also work on a puzzle about space. Questions are inevitable. Did the Space Shuttle really get close to the moon? What are those objects that aren't stars and planets? If the sun is so bright, why is space dark?

I particularly like puzzles that are maps. As students organize a map puzzle, they must think about what they know. 

The lakes all go together in Ontario. Oh wait, this long, big lake is actually in Manitoba. The state of Montana has to go beneath Alberta and Saskatchewan.  I wonder if Montana trades a lot with those provinces?

The more they think, the deeper their learning.

At some point during a unit, students can be asked carefully chosen questions about the puzzle meant to lead into thinking and learning activities.

Why were the images in the puzzle chosen? Is the overall  image realistic or unrealistic? Would you take out an image or add an image to make the puzzle match what we are learning in class more closely? Design your own puzzle to illustrate an important idea that we are learning about.

SOCIALIZING AND COMING TOGETHER TO ACHIEVE A COMMON GOAL

Something that I have become aware of as a teacher and a parent is that students cannot be thinking all day long. They need some downtime to recharge and even to socialize in positive ways. Puzzles offer an opportunity for this while also bringing the class together to achieve a common goal. As I have tried to point out, puzzles promote active learning (planning and organizing) and incidental learning (noticing small details). Students sitting down together to socialize sometimes find themselves learning without really knowing it. They find themselves talking about a subject area in unexpected ways; this coral reef is beautiful, remember how we were studying that global warming is destroying them, and, they help each other out; here, I think this piece might fit. 

Puzzles can be difficult endeavors that take a lot of time. Completing them gives a class a goal and a sense of shared success. As students work together, they begin to see hidden talents in each other. Sometimes, the best puzzle-ers are those who don't always get praise.  Kids who might have a difficult time focusing sometimes find themselves focusing on a puzzle for long periods of time. Kids who might not get noticed for being the most industrious might be the best at finding the hard to find pieces.

Of course, there are some downsides to puzzles in the classroom. They can be expensive. Pieces go missing or get bent and dog eared over time. They require space to complete and they take up that space for extended periods of time. However, I have found that the positives outweigh the negatives. I hope that you do to.

On Line Book Talks in Middle School

Using Social Media in the Language Classroom

Reading for Homework

When I taught younger elementary students, creating an "At Home" reading program was simple. A newsletter was sent home explaining to parents and caregivers how important it is to read with their children and how important it is for children to read every day. The newsletter was accompanied by a reading log for students to fill out and for their parents to sign.

In Middle School, this does not work so well. Students read longer books, so reading out loud with a parent or caregiver is no longer a viable option. Reading Logs may be used to monitor student progress, but many students learn that their is no way for adults to truly know whether they actually read what they said they read or not.

Too many times, I noticed that Reading Logs filled out by students followed a formula. A long chapter book was picked and each entry listed a new chapter. The exact same pen was used to fill out each entry. The entries were scrawled messily in barely legible handwriting, while the log itself was crisp and clean, as if it had never seen the light of day - an odd dichotomy to say the least. Before collecting the Reading Logs, I would watch students madly writing on a form that they were vainly trying to keep hidden from my field of view.

What I felt was that the students who were avid readers were following the spirit of the Reading Log while those students who most needed to read every day had learned to "game" the system.

On-line Book Talks

My solution is for students to read a book and then review it on-line as a Book Talk. Other students read the review and then ask questions. The reviewer responds to the questions and then continues the conversation.

Start With a Short Book Review

The format of the book review is simple. Students state basic information about the book (e.g., title, author, genre, number of pages), they summarize the plot, they describe their favorite part and they give a recommendation. I point out to students that one way to show how smart they are is to write concise reviews. I have students read some examples of book reviews from past years. We discuss how long reviews are difficult to read and I provide some mini-lessons on how to write concisely (e.g., by not repeating a thought, by staying on topic etc.).

Set Up the Proper Environment

Setting up the proper environment for good on-line Book Talks takes an equal amount of effort.

First, I set up "Small Groups" and determine which students will be a part of them. For Book Talks, I place students into Homogeneous groups.

Then, I create a framework for how the "Small Groups" will be used. My class and I co-create agreements to promote healthy on-line interactions. Agreements always include ideas like "No Put Downs," and the use of "Appreciations Statements." Students often include other ideas to ensure that their Book Talks run smoothly. For instance, a group might decide that all posts need to have actual content (a question or an answer to a question) to keep the thread uncluttered and easy to follow.

Some groups like to include posts just to offer Appreciation Statements.
Other groups find that this creates too many replies and makes following a conversation more difficult.
They prefer embedded Appreciation Statements.

Introduce Students into How to Ask a Question

When I introduce Book Talks, I provide examples of Book Talk questions for the students to use. I found this on-line source that I developed my questions from:

http://theliterarylink.com/bloom_questions.html

Later, I have my class investigate a Q-Chart so that they can formulate their own thinking questions.

Here is an example of a short conversation between students.

In the beginning, students use questions that I create for them.
Later, they create their own using a Q-Chart.

The real thinking occurs when students answer
the questions and then continue the conversations.

Getting Involved

As a teacher, I take a small role in the Book Talks. Sometimes I schedule the talks; but I have found that students are quite competent at scheduling their groups independently. I monitor posts to ensure that comments are on topic and positive; however, I have also found that students monitor each other very well. I check that everyone completes a Book Talk and offer feedback. I have found that when students know that I am interested in their ideas, they put more thought into their responses.

Offering feedback lets students know that you're interested in their ideas.

Final Thoughts

I have been running on-line Book Talks for three years. I organize them as homework. Instead of just "reading for 30 minutes" each night, students know that they have to read to prepare for their Book Talk.

I have found that students are sometimes able to hold each other accountable more effectively than teachers can. For the Book Talks to work, everyone must participate and the students will call each other out for not doing so. Unlike oral book talks, I can see who is participating and who is not. Students running a Book Talk also know that if their group is not participating, their Book Talk will not look very good. So they motivate each other.

Many students look forward to presenting their ideas on-line and look forward to their Book Talk much more than if they had to write a more traditional book review. They get enjoyment out of the responses that they receive from their fellow students.

Lastly, you might have noted that the students' responses that I have provided do not always demonstrate good grammar. I am not too concerned about that. If a point is not made clearly, students ask each other for clarification or point out that their question was not responded to properly. In reality, it gives the students a real life understanding of the need for good grammar.

Try on-line Book Talks for yourself and let me know how yours worked out. I always check my blog for responses.

For today's blog, I how I'm using "Edmodo" in my Language Class, but everything I point out can also be accomplished on "Google Classroom."

Maker Class - Building Gliders

This post will describe how to build simple and inexpensive model gliders while teaching concepts of flight. To assist in organizing your classroom, I have also attached some files that I use to keep students to schedule and to assess them. I designed these gliders as part of an investigative inquiry for Grade 6 students. As such, the instructions that I give here are basic. The end product of this tutorial isn't a very good model glider, and that is done on purpose.

Students build their first model with my help. Then, they investigate how real gliders are built. Next, they experiment with the design of their own gliders; they move the wings a little forwards or backwards, they build new wings that are longer or thinner, they find ways of improving the aerodynamics of their model, they create their own building techniques so that their glider is stronger, they add weight to balance the force of lift, they play with the rudder and ailerons to get their gliders to roll and bank and ect. and ect. Because the materials are inexpensive and the techniques are simple, students are free to explore and learn from their mistakes.

The total building time for students in the classrooms that I've taught is about 40 minutes.

Material List
scissors
tape
straws
construction paper
a few coins

I find straws to be a very useful building tool for students in the classroom. They are light and fairly strong for their weight. Furthermore, they can be connected together to increase their length quite easily. 

Pinch the end of the straw...

The pinched end of a straw.

...and then push the pinched end into the end of a second straw.





The fuselage of the glider is made from four sets of straws that have been connected to add to their length. 

The straws are taped at their junction for strength.

Bundle four sets of straws are together. Tape them near the front and near the middle. Make the bundle as "square" as possible.

After that, connect another two straws together to increase their length. Push them through the fuselage.

This will create a "t" shape. After that, cut a piece of construction paper the length of the wing. Notice the small hole in the middle. Slide the front of the fuselage through the hole.

Tape the straws to the inside of the wing. This will keep them from wiggling and sliding awkwardly.

Then, tape the back edge of the wing close and trim off any extra length of straw.

Once this is done, use the same technique to add a horizontal stabilizer to the rear of the plane.  

Almost done!

Now comes the tough part. Add a vertical stabilizer. Students have a difficult time making a vertical stabilizer that is sturdy. Their's tend to flop over. But that is part of the process. 

One way is to fold a piece of construction paper in half and then cut it about 5 cm along the bottom of the fold. 

Then, fold tabs to the right and left.

This is what it should look like from the top when the back side has been taped together.

Tape this to the horizontal stabilizer. Adding a straw can add more stability.

At this point, the model glider should look something like this.

All that is left now is to cut ailerons and a rudder...

...and then add some weight to the nose.

As I stated at the beginning. This first attempt will not work very well. The wings are too wide and the vertical and horizontal stabilizers require some modifying. At the end of 40 minutes, the versions that most grade 6s build is pretty flimsy. They need to spend time working on making their model more aerodynamic and stronger. But, it is a start.

I usually give students two or three more periods to research, build, experiment and then go back to the drawing board to start all over. 

I also put my class into teams. Every member of a team builds their own glider, but all the gliders in a team must be built for a different purpose; fly for a long distance, carry a load (e.g., a bolt), do a roll over, bank to the right and left ect. and ect. 

I hope my instructions work well for you. Happy building. 

Attached are PDFs of different forms that I use in class to keep the students on schedule and assess them. I wish I could attach them as documents, but I haven't figured out how to do that as of yet. As with anything on my sight, please feel free to use it at will or change it to your needs. If you do something amazing, let me know so that I can improve my craft as well. If you appreciate what I'm doing, just mention me somewhere. 

My Assessment Tracking Sheet (Ontario Curriculum)
https://drive.google.com/file/d/0B-2_v6_EOf_UMnZZdUp5dFB3aVU/view?usp=sharing


Student Project Worksheet
https://drive.google.com/file/d/0B-2_v6_EOf_UQU9xSDVHd2pXNXc/view?usp=sharing

Project Schedule with Rubric https://drive.google.com/file/d/0B-2_v6_EOf_UUG9IVWIyMjFPNlU/view?usp=sharing

Chess as a Math Centre

Search "chess improves math" on an internet search engine and a plethora of sites show up. I stopped investigating them at the fifteenth page of results.

A good paper that summarizes the general academic research on the affect that teaching chess has on student's math abilities can be found through this link -

http://sgo.sagepub.com/content/5/3/2158244015596050

In its conclusion, it states that:

"...the game of chess is a powerful tool to build children’s problem-solving competence in the mathematical domain, even with brief courses..."

The American Chess Foundation found that "chess improves visual memory, attention span,
spatial reasoning skills, capacity to predict and anticipate consequences and an ability to use criteria to drive decision making and evaluate alternatives."

Chess is a natural component of Math class and Math Centres. I'll add some extra reasons why.

In an earlier blog post, I pointed out that people naturally connect with reading on an intimate level because we read for enjoyment. Unfortunately, this same connection is not easily made to Math. As I suggested, many people think math is a tedious means to an end, a task, a tool. We use math to do our taxes, not for enjoyment.

However, we can connect with games. Games are entertaining. They are fun. And Chess is a game that incorporates Mathematical Thinking.

When teaching Problem Solving in math, we promote a method that usually chunks the process into steps. Students show that they understand the problem. Then they make a plan. Next, they carry out their calculations. Finally, they check to see if their plan worked or if there might be a better way.

This IS chess.

Chess is a game of problems. "What opening will allow me to control the middle of the board? How can I defend against an attack? What should I do now that my opponent has figured out my plan? How can I checkmate my opponent in the fewest possible moves?" Each problem has a wide variety of possible solutions. Opponents are constantly planning, predicting responses and altering their plans accordingly. Geometry and the rules of the pieces are the method of calculations. Teachers talk about direct, honest and timely feedback when assessing students. In chess, the feedback for every move meets those three criteria.

Reflection is also an important stage of learning. In chess, reflection is made more powerful with the use of Chess Notation. Players can use symbols and an understanding of the grid pattern of the chess board to notate each move (there's a lot of math going on there).

Here is a link to one of many websites that teach chess notation. I like this site mainly because of the title to their tutorial - "How to Read and Write Algebraic Chess Notation."

http://www.chesshouse.com/how_to_read_and_write_chess_notation_a/166.htm

Here is a link to a free computer chess game that can be played by students on-line (Flash is required). It can be found at the aptly named website "Math if Fun."

https://www.mathsisfun.com/games/chess.html

And for those that might not know how to play, much less teach chess, here is a link that should solve your problems.

https://www.chesskid.com/learn-how-to-play-chess.html

I've been using chess in classrooms for about 8 years now. I find that many students absolutely love the game. However, it does tend to attract boys more than girls (my chess team this year has 17 boys and 1 girl) and those who like competition more than those who don't. I have gone out of my way to promote girls to play chess and to get those who shy away from competition to play as well. What I have found works best in both cases is to allow for partners to play each other. It gives students the chance to talk about their moves before making them (communication in math!). This added social element usually solves both groups of reluctant players.

Good Luck and Happy Chess

Technology in the Classroom

This post is connected to my series of posts on Math Centres.

Technology in the classroom is promoted as one of the ways, if not the way of being a 21st Century Teacher. There are a lot of reasons for this opinion. Young people are engaged with their technology and educators want them to be similarly engaged with their learning. Technology allows students to access a world of information in a wide variety of formats. It is also a way of replacing a lot of expensive school purchases - from textbooks to manipulatives. This point is especially true if students bring in their own devices to schools.

Now, I am of the generation that pioneered computer technology in the classroom. When I was in grade 7, my middle school purchased a dozen PET computers, made by Commodore.

This picture is courtesy of "Science and Society Picture Library Prints" http://www.ssplprints.com/image/94110/commodore-pet-personal-computer-c-1980

 

 

I remember the excitement of using BASIC to get my name to scroll down a monitor in blocky letters. By high school, I was creating simple "choose your own adventure" type role playing games. I spent countless hours learning how to organize my ideas and debugging them when they didn't work But, the truth is, my school never taught me any of this. They opened the door by showing me the "scroll your name down the monitor" code. I pretty much taught myself the rest. As I grew older, I taught myself all manner of software out of interest and sometimes even necessity. After I graduated from university, I got a couple of jobs just because I said I could use software which, in truth, I had never seen before. But, each time, I dove in and, over a weekend or two, became an "expert." Of course, by "expert," I mean that I knew just a little bit more than anyone else in the office. Now, enough about me. I only write this down to be transparent about my ersatz credentials.

 

When I think about technology in the classroom, I have a few rules.

 

First, I like it to be free. Private business looks to public education and sees billions of dollars to be made. There is a reason that <insert name of immensely profitable corporation here> wants elementary children to use their devices or apps. They want a customer for life. They are maximizing their profits. At its heart, these companies have business models that are little different from soft drink companies that put vending machines in schools. They offer a deal in order to get the kids hooked. The use of devices has become as addictive as sugar. There is an argument that the deals that tech companies are offering are altruistic - apps and devices do have some benefits to learners. However, bottled water (mostly sold by soft drink manufacturers) in vending machines also has its benefits.

 

 

 

Secondly, I like what technology has to offer to be advertisement free. It wasn't that long ago that this was an important condition demanded by educators. It is now mostly forgotten, replaced by lessons in media studies. To continue my earlier analogy, it is very similar to how sugary treats are now in every lunch sack. Social mores regarding the health of children have been replaced by "freedom of choice" arguments from junk food manufacturers and health lessons teaching children about "sometimes" foods and suggesting that families limit trans fats (as opposed to avoiding them completely). Listen, advertisements work. The most profitable companies in the world wouldn't spend billions of dollars advertising if they didn't. They work especially well on young people. Schools completely lack the resources to balance the onslaught of advertisements children witness with education, and putting them in the background of leaning experiences implies that they really are okay.

 

This picture is courtesy of "Science and Society Picture Library Prints" http://www.ssplprints.com/image/130806/richardson-claire-polaroid-sx70-model-i-land-camera-c-1973

 

Thirdly, I like the technology to do something that is actually better than what it is replacing. Does a device take a better picture than a Polaroid Camera with a flash? Can the device record a conversation better than a cassette recorder? Can a student use their finger to draw and print on the touch screen better than they can with some markers and a piece of paper? Is the information on a website better researched and more clearly written than what can be found in a children's encyclopedia (which never have advertisements in them)? If the technology isn't better, then, it is really just a gimmick.

 

Next, I like the technology to make learning more engaging for students. The key word here is learning. Some educational video games and apps offer far too much playing time for the amount of learning that goes on in them. Especially when the learning comes in the format of multiple choice questions or questions that students learn to "game" (i.e., get points for without learning or knowing what it is that they answered). As a parent, I am shocked when choosing a movie on my family's once-a-week family movie night is made overly difficult because my elementary school aged children have already watched a litany of movies at school. Using social media in the classroom needs to be more than having one student post a thoughtful comment which is followed by a host of cliché replies.

 

Saying all of this, I have witnessed social media work very well. Recently, I had students post book reviews on-line. I was impressed by the thoughtfulness of most of the reviews and by the back and forth commentary with their peers.

 

This picture is courtesy of "Wikimedia Commons"

https://commons.wikimedia.org/wiki/File:Think..._will_it_save_production_time%5E_Plant_efficiency_starts_with_your_ability._-_NARA_-_535136.tif?uselang=en-ca

 

Lastly, I like technology to make my job as an educator more efficient. I can write anecdotal notes quite quickly. I have coding systems that allow me to get a lot of data into my pencil and paper checklists. And if I drop my assessment duotang on the floor, it never breaks. When I write report cards, I can place two or three sheets of notes beside each other and scan from one to the other easily. I have tried using a variety of apps for assessment, but none has been able to replace what I already do. I'm a touch typer and I am adept at spreadsheets. I've yet to find an app that can do more, faster, than what these two abilities allow me to do.

 

I have made it part of my practice to use the device provided to me by my school to photograph examples of student work. I currently have a huge number of photos in my files with labels like "DSC098763.JPG" that I don't have the time to rename. As a result, finding a particular student's work entails that I view photo files as large icons, thus slowing down my search. Videos increase my workload even more. When I go home, I am loathe to assess a student's work by watching a video that takes 30 seconds of viewing just to get to the point that I want to assess. That time adds up in a class of 25 or more students.

 

Technology does offer me the ability to save a learning experience to use it again. This saves me time, as long as I can use it again. Changes in curriculum and expectations don't always make this possible. Technology also makes it possible to create extremely interesting and interactive activities for my students. However, my rule of thumb is that the time that goes into the creation of an activity should be at least close to the amount of time that it will actually be used by students. In other words, efficiency dictates that I shouldn't spend an hour creating a learning experience that my students will only use for 15 minutes. Of course, as I type these words I find myself looking up to the ceiling and exclaiming to the bumpy white finish, "so why do I keep doing it then !?!"

 

This post ended up being quite long winded. That wasn't my intention. I really do like technology. In fact, I plan on writing a post (hopefully soon) that will point out how I use technology and what websites, apps and software I have come across that meets the standards that I have stated in this post. This site is "The Handy Teacher" after all, and its purpose is to offer handy and useful ideas, not just rants.

Admitting that you are poor at math vs Admiting that you are poor at Literacy

This post is the second of a series that I am writing about Math Centres. The topic of this post is an idea that I discussed with other educators at a recent workshop that I went to #PeelMathCentres.


I have been at a few other workshops recently where the following analogy was made.


"People seem to easily admit that they are not good at math. For example, when it is time to tip a waiter, no one would bat an eye if someone at a dinner party passed the job off of figuring out15% of the total bill. On the other hand, it would create quite the stir if someone at the same dinner party said that they couldn't read the menu. Very few will admit that they are not good at literacy."

When the analogy has been made, I have looked around the room to see lots of heads nodding in agreement. But it doesn't ring true for me.


First of all, amongst my group of friends, no one would admit that they couldn't figure out 15% of a bill. If someone did, they would be ridiculed. It would be like admitting that one couldn't use a hammer. So, the analogy is made based on an opinion that isn't true for everyone.


Herein lies the problem with the analogy. Math can be used to solve problems. So can reading. But when we think of reading, we don't automatically think about reading something like an operations manual or a government form. If people did, many would probably say that they didn't like reading much either.


When we think of reading, we think of the connections that we make to reading - reading text messages, a novel, a Twitter post, a favourite magazine. When we think of math, we think of a task that we must do. Often times, that task has a consequence for not doing it correctly (tip that waiter too little, and service won't be so good the next time we visit that restaurant).


Math, as traditionally taught in school and understood by many, is a chore. We read before we go to sleep; that's not the time when anyone who wants to get some sleep would do their taxes.


However, math can be engaging. Playing many card games requires strong mental math skills, completing puzzles requires an understanding of geometry as well as planning skills and playing chess requires logical reasoning.


Using Math Centres gives teachers the opportunity to work in small groups or one-on-one with students while the rest of the class independently consolidates what they have learnt in math. To promote their independence, activities need to be engaging. It is an opportunity to illustrate to students that they can connect with math just as they are able to connect with reading.