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Toronto Catholic District School Board

 
It’s true Math IS everywhere.
 
That’s what I set out to convince our Gr. 8 students a few weeks ago. I started by reading them the book – The Math Curse – a fun read by Jon Sciezka when and if you find time.
The moral of the story – math is everywhere.
 
I followed this observation by telling students about my experience driving to school with my children Chantelle and Mark. While we were driving in, we heard a stat saying that the average American teenager eats 30 lbs of French fries a year. Interesting stat. But what did it mean?  Was 30 lbs of fries a lot for one year? How many fries do WE eat in one year? The conversation had begun. We started by converting 30 lbs to kg because we’re metric here. Next we started to figure out how many fries WE consumed a week and then month and then year. The documentation is all here for those so interested.
 
Next it was time for the Gr. 8s to think about what THEY wanted to research. Real Life Math was the challenge. Find a way to solve a multi step math problem that interested them.
The criteria for the assignment was developed together and then shared.
 
Attached below.
 
 
Next it was time for the students to go off and research thanks to our recently arrived ipads.
A few days later the mid point check took place to see where they were at.
 
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Brief conferencing took place and then it was time to prep for the final presentation exactly one week after we had begun.
 
We chose to do a gallery walk where students left their work on their desk and then wandered around to not just observe other students work but to comment on their work as well.
 
It was a unique experience and the range of topics and quality of work were both interesting. You can see some of the completed work below.
 
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Here's my work (not as visually appealing as what the Gr. 8 class came up with but some intriguing math.

 

Math is everywhere.pdfMath is everywhere.pdf
 

Students were asked to indicate what they enjoyed about the work, what they would change, and what question they might consider if they were to have this experience again. And again, there were some unique thoughts.

 

   
 “Honestly, I thought the experience was a great way to explore the wonders of math. I got to figure out and ask my own question instead of reading and solving questions in the textbook. I would love to do more of this in the future.”
 
“I would like to have explained more and made my work more organized.”
 
“I thought it was ok because some of the projects were unclear. We also wasted lots of paper. Remember we’re trying to be eco friendly. I would suggest that we use an app and view our projects that way instead.”  Ouch, the enviro guy takes a hit. In my defense, no one was told they needed to use paper and I posted the assignment online. None the less, a challenge ahead for the NEXT project.
 
“I liked doing the gallery walk because it’s easier to read information myself than to have someone read it for me. “
 
“I think the experience was amazing. I thought it was so interesting. I loved doing it and I really want to do it again.”
 

 

“This experience was horrible. Absolute rubbish. I Expected my partner to fork in some work but no. My partner just relaxes and messes around." A learning experience for sure. Students were given the choice to work on their own or with a partner. Clearly, this student learned a bit about what collaborative contributors are all about and I imagine a different partner or solo work will be chosen next time.

 

 
“I thought the experience was very good because I tend to not find interest in presenting up front and by doing the gallery walk, I could read the presentation in my voice and it’s better for me to understand. You can see how organized the presentations are also.”
 
I considered some of the common themes that emerged from the student feedback.
 
For the experiential piece
 
  • Gallery walk was a success for the most part
  • Students wanted to see quality work (and not everyone completed quality work)
  • Option of group or on own. Most choose group
  • Some regretted the group they chose
  • Evaluation of others – need to remember to be  positive and constructive
  • Always ask questions even at the end – life long learning
  
As I reflected on the work that was done, a math guru I know questioned the validity of the work. There needed to be a consolidation of the learning. There needed to be a more organically created success criteria based on their experiences from the work.
 
So in my best attempt at Bansho math, I began to group the learning trends that were evident in the students’ work. Here’s what I found.
 
Math learnings
 

 

a. cross multiplication is an  organized way to find answers (walking to vegas and currency project)

 

 

 

b. Comparing apples to apples – ie. Always need the same unit when you’re comparing (circumfrence of world project)

 

 

 

c. Comparative math (internet use – don’t stop with just you compared to the average. Compare to others part of world or other age groups or genders (internet, video games projects)

 

 

 

d. SHOW work (putting the answer is not enough – how did you find it – basketball and video game example vs the Elephant drinking example)

 

 
e. Analysis – WHY? Look for reasons to explain what you’re finding and look for ways to extend your thinking (every group could have extended in some way). See the analysis challenges in the challenge questions below
 
 
 
My next steps will be having the discussion with the students and trying to consolidate the learning by going over the 5 math learnings above.
 
At that point, the plan will be to extend the learning by having students choose one of the 6 options below and demonstrate their application of the new concepts. All the questions offer choice but all will involve a demonstration of their take away math skills from the work we have done.
 
Option 1 – Measurement  via proportion
 
Kristina’s problem re how many of her would be needed to go around the circumference of the world
 
Measurement connection  - Her height in cm but circumference of the world is in km
 
Math step needed to take:  Change her height to km. Always need to compare like units
 
155 cm to km
 
1 m = 100 cm
 
1 km = 1000 m
 
Difference from cm to km is therefore 5 places or multiplied by .00001
 
Kristina divided the circumference of the world by .00155 and found her answer (she previously found that arm span is approximately equivalent to your height.
 
Application question – Find how many of you would need to be stacked on top of each other to reach the height of 3 different large stuctures (eg  cn tower, Burj Khalifa, etc)
 
Show your work and remember we follow the metric system in Canada
 
Analysis – what goes into constructing such tall structures and why do they fascinate us
 
 
 
Option 2 – Time and distance
 
 
Gracy found how many km you travel by minute when you fly from Toronto to Beijing
 
She knew it was 13 hours to Beijing but converted that to minutes. Always need to compare like units
 
13 hours  x 60 = 780 minutes
 
Next use cross multiplication
 
 
 
9396 km (distance to Beijing)      780 minutes
 
X  km                                      1 minute
 
9396 = 780 x
 
X = 12 km
 
You travel 12km every 1 minute when you’re flying to Beijing
 
Application – Find the time it would take to travel to 3 different places in the world by at least 2 different methods   e.g   Las Vegas by car and plane  or India by boat and plane
 
Use cross multiplication to find out by the minute and by the hour
 
Extension – try Jessica E’s method of adding in swimming time and walking time (you’d need to do some experimentation with that one) . I’m going to try this one
 
Analysis – how has the airplane and the car changed our methods and ability to travel in the last 2000 years OR if you were to walk or swim somewhere far, what sorts of costs would you need to consider for your journey
 
 
 
Option 3 – Currency conversions
 
Jessica L considered the differences in currency between India and Canada and the buying power.
 
She needed to cross multiply
 
1 dollar = 49 rupees
 
25 dollars = x rupees
 
X = 1225
 
This means 25 dollars = 1225 rupees
 
Application – Find the cost of three different items in another country. Then find out how much this would be in Canadian dollars
 
Analysis – what is the buying power in different countries for the average citizen  e.g.  if we spend one dollar on a chocolate bar in Canada, that means someone in India would spend 49 rupees. The question is, can they get 49 rupees as easily as most of us can get one dollar or is it much more difficult for them? Think how you will be able to find the answer to this question.
 
 
 
Option 4 – Sports stats and comparative work
 
Tyrell/Jack/Joshua  did a comparison of how much a player makes and how this relates to the goals they score
 
 
 
g  A player makes 12 500 000 and scores 21 goals. How much are they making for every goal they score?
 
 
 
12 500 000           x dollars
 
21 goals              1 goal
 
21 x = 12 500 000
 
X = $595 238 per goal  scored
 
Application  Choose three different sports stars and find their salary. Next determine how much they make per something (eg  goals, assists, baskets, rebounds, saves)
 
Show your work
 
Analysis: How does this compare to other jobs. For instance how do we measure the worth of  a police officer, firefighter, teachers, doctor, grocery store clerk, etc
 
 
 
Option 5   - Comparative graphs
 
Several groups spent time on internet use or tv use or video games
 
5 hours of net use       1 day
 
X hours                        30 days (1 month but needed to convert first)
 
X = 150 which means 150 hours over one month
 
Application:  compare tv use or internet use or video use by age groups or different parts of world
 
Use graphs (Bar graph, or circle graph, or pictograph) to show your answers
 
Analysis: How has electronics changed the way we use our free time and is this for the better or the worse?
 
 
 
Option 6 – comparative math and proportional representation using animals
 
 
150 L               x litres
 
1 day               365 days (comparing same units)
 
X = 365 x 150 = 54 750
 
She then compared this to her own water intake
 
Application
 
Compare water or food intake of 3 different mammals. Show your results by day, month and year.
 
Show your work
 
Include a comparative graph (eg  broken line graph, bar graph, pictograph)
 
Analysis  I haven’t figured out an analysis for this one – any thoughts?

You can send your work to roy.fernandes@tcdsb.org if you choose.

Work is due by Tuesday, March 24 but save yourself March break work and hand in or send in by Friday, March 13

And one more bonus challenge - go through the Gr. 8 math curriculum (simple google ontario math curriculum gr. 8) and find out what curriculum expectations your work is covering. I know this won't be something many might take on but that's why it's a challenge.
 
 
 
It’s true…math is everywhere and inquiry is alive and well. This all started with a 30 second radio news piece about how much fries the average American teenager eats. By being alert to the world around and tuning into the learning process, I think some fairly engaging math has taken place, with new learnings and most importantly the further creation of life long learners. And guess what…science is everywhere, and so is geography and language and …..well life! Happy learning and happy soon to be March Break. I wonder what we’ll learn next.