Divide and Conquer


I like to find different ways for students to understand the invert and multiply algorithm and this summer I have seen some good ideas for representing division of fractions.

First I will direct you to Graham Fletcher’s blog, GFletchy. Earlier this year he wrote about his method which I like for daily use in the classroom. His strategy is to have students find ways to turn the denominator into one whole.  In his post he also directs you to two other sources for this topic. One source is Fawn Nguyen who wrote about a rectangular model, an interesting model for conceptual understanding. The other source is Christopher Daniel’s blog, Overthinking My Teaching. He discusses a model I had never heard of before, using common numerators to divide fractions.

I also want to share an online widget that I found years ago called the DIM Calculator. This widget allows students to enter any two fractions then follow the instructions to learn why invert and multiply works.

I have used the DIM Calculator in the past, but I will definitely be introducing these other ideas to my students in the future.

Posted by Ilana Cyna in Math, 0 comments

Apparently Life is Expensive….

My favourite math task of all time is a financial planning assignment. I have blogged about this previously, but I think it is worth mentioning again. The assignment is called “Making Ends Meet”. It was created years ago with a teaching partner, but it has grown and developed over the years. In this task students take the role of new university graduates who are just moving out on their own. They need to determine how they will pay all of their costs on an entry-level salary. I created a list of entry-level jobs and their salaries. I cut up the list so that each item on the list is on a separate sheet of paper. The papers go into a jar, and then students pick their career out of a jar. I think I need to update the list for next year, as many starting salaries have increased since I first created the list.

After the initial excitement dies down, students begin to move on to the first part of the task, which is calculating take home pay after federal and provincial deductions. I chose to leave off EI (employment insurance) and CPP (Canada Pension Plan) deductions this year, but may put them back on in the future. After determining the yearly net salary the students then determine the monthly net salary, and then the real fun begins. The students proceed to determine the various costs that they will have, including food, housing, utilities, transportation, medical expenses, miscellaneous expenses, and savings. During this phase of the assignment I usually have many students trying to negotiate with me if they really need certain items or with how many people they can share a rental apartment or house, and the buzz in the room is full of excitement. As students are trying to find somewhere to live I encourage them to consider distance to work, safety of the neighbourhood, and proximity to public transportation. Students then come up with a monthly budget, hopefully including a portion for savings. In this phase of the task the students are free to talk with one another and share ideas.

The last phase of the task requires the students to answer questions under a “test” situation and the students are not allowed to share ideas at this point. The amount and content of questions has varied from year to year, but the general theme is that they need to analyze the effectiveness of their budget compared to financial planning strategies and they need to deal with and pay for 2 of 19 potential unexpected problems (flood, broken glasses, etc). I created a numbered list of those problems. I have assigned the problems in various ways in the past, but this year I had each student randomly pick two numbers between 1 and 19 and then I assigned those two unexpected problems to the student.

The students and parents all love this assignment. Students in grade 8 do not pay for much on their own, and for many this gave them their first exposure to what is involved with living on your own. This year I had a student actually thank me for making her realize how expensive life really is, and she said that she was now a lot more appreciative of all that her parents do for her.

You can access the main task here. The “test” situation portion is not part of this handout, as I don’t want my students to access it online.

Have a wonderful day.

Posted by Ilana Cyna in Math, 0 comments

Maths with Zombies


I cannot remember where I first came across this resource, but if you or your students are into apocalypse scenarios, then this might be a good resource for you. There are 25 zombie based questions, including worked solutions and pdf handouts of the problems. I am thinking that it might be a good activity for the last few days before winter or spring break, when a portion of my students have already left for vacation. I may even take some of the problems and make an escape game activity.

Access the resource here.

Posted by Ilana Cyna in Math, 0 comments

The Game of War….Math Style

I came across the MashUp Math activity below for reviewing finding mean, median, mode, and range while using a deck of cards, including an accompanying worksheet.

After watching the video, I thought that this might be interesting as a Game of War card game. It you don’t know how to play standard war, then you can read the instructions here.

Here is how I envision this activity can be modified into a game.

  • Use two decks of cards and the additional card set that I created
  • Playing cards get distributed similar to the original War card game
  • Players draw a card from the new card set, cards may be action or reaction cards:
    1. An Action Card may say to use 2, 3, 4, 5, 6, or 7 cards and then find the mean, median, mode, or range. For these cards, all players put out the designated amount of cards from their individual pile and determine the respective value. The player with the highest value wins all cards. With two players, if players have the same value then the action is repeated and the new highest value wins all cards. With three players, if the highest value is the same for two of the players then those two players repeat the action and the player with the highest value wins all cards for that action round. With three players, if the highest value is the same for all three of the players then all players repeat the action and the player with the highest value wins all cards for that action round. The action card is then placed in the discard pile.
    2. An Action Card may say to give 1, 2, or 3 cards to all other players or to receive 1, 2, or 3 cards from all other players. For these cards, the player who drew the card either gives cards to other players or receives cards from other players. The action card is then placed in the discard pile.
    3. A Reaction Card may say “No Thank You”. The player may hold on to this card and use it to counter action cards from step 2 at any point in the game. Once used, this card should go in the discard pile.
    4. A Reaction Card may say “Double Up”. The player may hold on to this card and use it to double the required number of cards in step 2 to be given to or received from other players at any point in the game. Once used, this card should go in the discard pile.
  • If at any point a player disagrees with the calculation of another player then a Challenge Card may be used. All players should check the disputed calculation. If the challenger is correct then the challenger wins all cards from that action round. If the challenger is incorrect then the player challenged wins all cards from that action round.
  • Play continues until one player has all of the cards or for a set amount of time

If you have suggestions that would make this better, please send them along. Access the instructions and card set here.


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Ready, Set, Laugh

I am getting lost on the internet.

As I prepare my lessons for next year I am constantly searching for new ideas and resources. Today’s search somehow led me to a term that I had not yet heard, Cartoon Science. My first exploration of that term took me to a website by the same name. The owner of this site, Matteo Farinella, believes that cartoons can provide visual narratives that can communicate scientific information and bridge gaps between the public and academic worlds. Visit his Visualization page to find a source of authors and publishers who are sharing comics, videos, animations, and other similar type resources.

I already had a few of my own favourite comic and cartoon creators bookmarked, but I was intrigued to discover what else was easily available. Below you will find my updated list of math and science cartoons and comic resources, aside from the one mentioned above. Most sites have search features to allow you to find the topic of your choice.

Sydney Harris Math and Science Cartoons (he has been one of my favourites for years)

Randy Glasbergen and the Glasbergen Cartoon Service


Foxtrot (search Comics by Tag)

Frank & Ernest

Chris Madden

Science and Ink

I also love Calvin and Hobbes, but Bill Watterson’s website does not contain all of his comic strips. However, you can find his work on Go Comics. Alternately you could search Go Comics for specific comics, cartoons, and themes.

How can you incorporate these in the classroom? It is important to recognize that most of these cartoons and comics are bound by copyright rules, and so you or your students cannot just download them for personal use. However, here are a few ideas of how to incorporate comics and cartoons in the classroom:

  • Have a website link prepared before class to show a comic or cartoon (perhaps it would already be open as students enter the room) and have students explain what they see, how it relates to their learning, and why it is funny
  • Have students look through samples and then generate their own comic or cartoon based on curriculum content – these student generated creations could then be displayed on class websites with the permission of the creator
  • Show the cartoon or comic without the tagline or script and have students generate their own
  • Only show the tagline and have students draw a cartoon that represents that tagline, then compare to the original cartoon

Finally, I came across an interesting journal article titled Use of Cartoons and Comics to Teach Algebra in Mathematics Classrooms by Tim Lam Toh that shows how cartoons and comics can be used with students.

Posted by admin in General Education, 0 comments

Making Ends Meet

Husband who broke his foot + car in the shop all week = missed #MTBos SundayFunday blog deadline.

One of my favourite math tasks is a financial planning activity for my grade 8 students titled “Making Ends Meet”. Unfortunately we did not get to complete it last year due to time constraints, and so the version that I am sharing is from the previous year.

In this task, students are given the role of a recent university graduate just entering the work force. Each student is given a job or career (picked randomly out of a jar) and must determine how to pay bills with a starting salary for that job or career. In order to prepare for this assignment, I researched starting salaries for those fields in Canadian dollars. Students begin by calculating take home pay after taxes (my students needed assistance with this step). They then use the net salary to determine a monthly budget for food, housing, utilities, transportation, medical expenses, miscellaneous expenses, and savings. Once students have completed the budget and presented their work in an orderly and logical manner, they are presented with an unexpected problem. I have created a whole list of problems, and they are variations of this:

“You were filling the bath when the phone rang. A friend’s car broke down and she needed you to pick her up. You left immediately to go help her, but you forgot about the bathtub. When you returned, there was water everywhere and the floor was ruined. Unfortunately, insurance does not cover this type of flooding. The repair bills were $750. Calculate and explain how this will affect your budget.”

There are 19 problems of this type on my list, and the students get a random problem by picking one out of a jar. I cannot share the full problem list here, as I don’t want my students to have access to them.

My students have told me that this was one of their favourite assignments and it made them aware about real life expenses. Hopefully I can fit it in this year, as it takes quite some time to complete. You can access the document here. I am happy to hear suggestions as to how to improve this activity.

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Posters for the Math Classroom

Once again, I have Sara Carter to thank for many of the wonderful posters that I have put up in my classroom. Two of the posters that I put up were her ‘Types of Errors’ and ‘Always Show Your Thinking’ posters. A few of my math colleagues were in my classroom and we began a discussion about these posters, and as a result of the discussion we made a few changes:

  • We changed the word ‘parentheses’ to ‘brackets’. This is more of a USA vs Canada thing. (Similarly, for order of operations we use BEDMAS instead of PEMDAS.)
  • We decided to take out the word ‘failure’ under Problem Solving and we adjusted some of the descriptors for that section.

We discussed the fact that we like the ‘Types of Errors’ poster and think it is important, and we agreed that it reflects the types of errors that we point out to our students. However, we felt that we also wanted to focus on positive things the students can do to achieve success. We decided to put up a new series of posters under the ‘Types of Errors’ poster. These posters will be framed in the positive, with the heading ‘Aim for Success’. The posters are as follows:

  • Always Show Your Thinking (Sarah already did a fabulous job with this one, no changes were necessary.)
  • Read and Follow Instructions Carefully
  • Show Your Work Vertically
  • Line Up Your Equal Signs
  • Explain Your Understanding
  • Check Your Work
  • Write Neatly
  • Ask Questions
  • Work Collaboratively
  • Solve Using Multiple Strategies

Did we miss anything essential? It may end up being too many posters, but we will live with it for a bit and see how it works. You can download the Word and PDF versions of the posters here.

Posted by admin in General Education, Math, 0 comments

Need a Break?

I have been incredibly inspired by Sarah Carter @mathequalslove. She has so many amazing resources that she generously shares. As we prepare for and begin the new school year, I also want to be part of the giving community. I have been scouring the #MTBoS and other sources for “one off” activities that I can pull out and use at any moment. Our school is moving from 40 minute to 60 minute periods, and I know that I will need to incorporate new strategies to engage students for these longer periods of time. I want to build a collection of games, tasks, and activities that can be used either to introduce the class, to end the class, or as a brief interlude in the middle.

Pentanim is a game that comes from the NRICH database. It is a short logic game that can be used as a break in any subject. I have created student game boards should you want students to play in pairs with bingo chips, as well as a Notebook file to play this game as a class. When playing as a class, students could take turns, or you could still have two students play in a match against each other. One reminder, do not save the Notebook file before closing. This will allow it to open in proper format the next time you want to play.

You can access the files here.


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Videos in the Classroom…Part 2

I don’t have as many math YouTube channel suggestions as I had for science. Although I am sure there are many out there, today I am going to stick to the two with which I have been following for a few years.

The first is Numberphile. Here you will find videos on math and other number based problems. It is not a site that teaches all math concepts, rather it looks at interesting connections. The site is run by Brady Haran, and the name of the site means “lover of numbers”. To get a sample of their videos, check out Calculating Pi with Real Pies and The Monty Hall Problem.

The second site is that of Vi Hart. I am not sure if all who watch her videos like her work, but I am a fan. She talks fast and she doodles as she speaks, which is one of the features that draws me to her work. My favourite of her videos is Wind and Mr. Ug, and I also enjoy her Doodling in Math Class playlist.

Enjoy the weekend.

Posted by admin in Math, 0 comments