Research Ideas
Do the math workshops
Mathematics (funded by SSHRC + Fields)
- Infinity in my hand (gr. 3: fractions, infinity, limit)
- Making 10 (gr. 3-4: patterning, linear functions)
- How to fence a pen (gr. 2-4: area, perimeter, optimization)
- Where parallel lines meet (gr. 2: geometry of a sphere)
- Probability race (gr. 2-4: probability with dice)
- Odds and evens (gr. 2, 7: growth patterns, odds, evens)
- Low floor, high ceiling (big ideas for young mathematicians)
- I don't like math anymore (I love it now! - math-for-teachers)
- Math performance (what did you do in math today?)
- Research performance (arts-informed research dissemination)
- How big is a billion? (gr. 3: Fermi questions, social justice)
- Math trains (gr. 1-4: growth patterns, slope, linear functions)
- Math waves (gr. 3-4: patterning, trigonometry)
- Cough, cough (gr. 4: pollution, social justice)
- Eating plastic (gr. 3-4: the great plastic dump, social justice)
- Refraction action (gr. 2-3: refraction)
- Will it float, will it sink? (gr. 2-3: density, buoyancy)
- Gravity's pull (gr. 2-3: gravity, density)
- Never met a happy bully (bullying and breaking the silence)
- The lizard in your brain (violence in the media)
Parent feedback
"This was a very interactive activity. We bonded really well while doing it. It was a great learning experience for me as a parent. I am confident that this activity will leave a long term effect of the wave function concept on both of our minds."
Educator feedback
"... such exciting work you do. I HAVE to do the clock activity next week."
Tweet
Math Waves
In grades 11 and 12, students study periodic functions, like y = sin(x) and y = cos(x).
Problems to explore
Grades 3-4 students explored periodic patterns that emerged from the following problem situations, which they encountered in the story Math Waves.
- Problem 1. Imagine a yellow dot on a car tire, turning as the car moves forward. If the dot leaves a trail as it moves, what will the trail look like?
Problem 2. A grandfather clock has one piece of cheese placed on each of the hours 1-12. A mouse runs up the clock and eats the cheese at one o'clock. Then it runs back down. If it repeats the process for all 12 pieces of cheese, what would a bar graph of the 12 heights it travelled look like?- Problem 3. What is the shape of a bar graph representing average monthly temperatures for the months January to December in Toronto? What is the shape of a bar graph representing the sunrise times in Toronto over a year?
Resources to support this activity
Lesson plan
and activity handouts
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Math Waves in Grades 3 and 4
1 - Introducing Problem #1 through story
| Grade 3 students are introduced to the following problem, through the story Math Waves: "Imagine a yellow dot on a car tire, turning as the car moves forward. If the dot leaves a trail as it moves, what will the trail look like?" Students record and share their initial ideas about this problem. |
| Grade 4 students are introduced to the following problem, through the story Math Waves: "Imagine a yellow dot on a car tire, turning as the car moves forward. If the dot leaves a trail as it moves, what will the trail look like?" Students record and share their initial ideas about this problem. |
2 - Explore problem #2
Grade 3 students are introduced to the following problem, through the story Math Waves: "A grandfather clock has one piece of cheese placed on each of the hours 1-12. A mouse runs up the clock and eats the cheese at one o'clock. Then it runs back down. If it repeats the process for all 12 pieces of cheese, what would a bar graph of the 12 heights in travelled look like?" Get the activity handout: clock bar graph (pdf). |
Grade 4 students are introduced to the following problem, through the story Math Waves: "A grandfather clock has one piece of cheese placed on each of the hours 1-12. A mouse runs up the clock and eats the cheese at one o'clock. Then it runs back down. If it repeats the process for all 12 pieces of cheese, what would a bar graph of the 12 heights in travelled look like?" |
| Grade 4 students use bar graphs to explore Problem #2. |
| Grade 4 students discuss Problem #2. |
3 - Exploring problem #1
| Grade 3 students test their predictions of the path of the yellow dot on a car tire, using cylindrical cracker containers and markers. |
| Grade 4 students use toy cars to explore Problem #1. |
| Grade 4 students discuss Problem #1. |
4 - Extending Problem #1
Grade 3 students test their predictions of the path of the yellow dot on a square car tire, using square-top cracker containers and markers. |
| Grade 4 students extend Problem #1: "Imagine a yellow dot on a square car tire, turning as the car moves forward. If the dot leaves a trail as it moves, what will the trail look like?" |
5 - Exploring problem #3
| Grade 3 students explore bar graphs of average monthly temperature and sunrise times over the year, and compare their findings with the graphs from problem 1 (path of yellow dot on a car tire) and problem 2 (heights of the hours on a clock). Get the activity handout: sunrise times bar graph (pdf). |
| Grade 4 students explore Problem #3: "What is the shape of a bar graph representing average monthly temperatures for the months January to December in Toronto?" Get the activity handout: average monthly temperatures bar graph (pdf). |
6 - Reflecting: What did you learn and feel?
| Grade 3 students record what they learned and what the felt during the activities. |
7 - Communicating through comics: "What did you do in math today?"
Grade 3 students create comics to share with family and friends about their learning. The dialog for the comics comes from their statements about what they learned and how they felt, which were recorded by students in the three grade 3 classes. |
| Grade 4 students create comics to represent dialogues they might have with family and friends when answering the question: "What did you do in math today?" |
8 - Sharing collective learning through songs
Dots, clocks and waves my daughter explained she was amazed a dot on a car tire the wave pattern it's great to see my son excited |
my son enjoyed he shared his comics the height of every hour like the height of a dot it's great to see my daughter excited |
Grade 3 students perform their song "Dots, clocks and waves." Song lyrics are statements made by parents after students shared with them what they learned in math. Students' song performance was also shared at the Math Performance Festival. Download the professional recording (mp3). |
Math can actually be fun! what does a dot on a tire We tested with a wheel simple experiences the story was entertaining I learned that math |
I liked the bonding time reading with my child my daughter tends to be it's all new to me I learned that math |
Grade 3 students perform their song "Math can actually be fun!" Song lyrics are statements made by parents after students shared with them what they learned in math. Students' song performance was also shared at the Math Performance Festival. Download the professional recording (mp3). |
Math waves I have a math surprise for you, Mom will it be a straight line? the clock on the wall, Mom round and round |
take the average temperature, will it be like a mountain? good thinking, Mom good thinking, Mom |
Grade 4 students perform their song "Math Waves." Students recorded what they learned and how they felt during the activities. Their statements were used to create a class song that summarizes and celebrates their learning. Students' math performance was also shared at the Math Performance Festival. Download the professional recording (mp3). |