Research Ideas

Mathematics (funded by SSHRC + Fields)

1. Infinity in my hand (gr. 3: fractions, infinity, limit)
2. Making sums of 10 (gr. 3-4: patterning, linear functions)
3. How to fence a pen (gr. 2-4: area, perimeter, optimization)
4. Where parallel lines meet (gr. 2: geometry of a sphere)
5. Probability race (gr. 2-4: probability with dice)
6. Odds and evens (gr. 2, 7: growth patterns, odds, evens)
7. Low floor, high ceiling (big ideas for young mathematicians)
8. I don't like math anymore (I love it now! - math-for-teachers)
9. Math performance (what did you do in math today?)
10. Research performance (arts-informed research dissemination)
Mathematics (funded by KNAER)
1. How much is a billion? (gr. 3: Fermi questions, social justice)
2. Math pattern trains (gr. 1-4: growth patterns, slope, linear functions)
3. Math waves around us (gr. 3-4: patterning, trigonometry)
Science
1. Cough, cough (gr. 4: pollution, social justice)
2. Eating plastic (gr. 3-4: the great plastic dump, social justice)
3. Refraction action (gr. 2-3: refraction)
4. Will it float, will it sink? (gr. 2-3: density, buoyancy)
5. Gravity's pull (gr. 2-3: gravity, density)
Peter Jaffe on violence & abuse
1. Never met a happy bully (bullying and breaking the silence)
2. The lizard in your brain (violence in the media)

Parent feedback

"It was a nice refresher of math for me and I loved to watch her excitement. Considering I [her mother] had difficulty in math in grade school I enjoy watching her complete understanding and explanation of it all."

"My daughter learned that adding is fun when you use patterns. She also liked using a story with math."

"She learned how to match number patterns with graph patterns. She said this is "cooool". This was fun!"

"I found this exercise to be an interesting was to start teaching younger children basic patterns that will help them with more complicated algebra later on. I had a lot of fun making a math train with my son."

"I think it's great these activities are helping to prepare them for more advanced math concepts."

"I learned that you can teach math concepts by telling a story."

"The visual story helped my son describe what he did during the activity."

"My son likes the math stories. He said he can't wait for the next story and that he wants to learn more."

"Math does not have to be difficult or boring, it can be a fun learning experience and kids can enjoy doing math!"

"I learned that you can teach younger children algebra in simple terms. The patterns make it understandable and fun at the same time."

Math Pattern Trains

In grade 9, students study linear functions like y = x + 1 and y = 3x + 3, which have terms whose values vary (like x and 3x) and terms whose values remain constant (like 1 and 3).

In the Math Trains activities below, grades 1-2 and grade 4 students explore patterns that are combinations of both changing and constant elements, using concrete materials, tables, and bar graphs. While developing skills in number sense, patterning, and data management, students also have opportunities to explore complex math relationships (constants, variables, and slope) that draw their attention, engage their imagination, and offer them the pleasure of mathematical insight and beauty. Using children's literature, students experience the emotional math moments of story characters.

Resources to support this activity

 Lesson plan Get the lesson plan (pdf) Materials grid paper cylinder and rectangular prism containers markers Children's literature The straight line wonder (lines as characters, identity, social justice) ... used to introduce lines and curves in a social justice setting Math Trains (growth patterns with concrete materials, bar graphing, constant and variable patterns, linear functions)

Math Trains in Grades 1-2 and in Grade 4

1 - Introducing the problem through story

 Grades 1-2 students are introduced to the first math train puzzle posed through the story Math Trains.
 Grade 4 students are introduced to the first math train puzzle posed to the Second Little Piggy by Wolf, through the story "Math Trains."

2 - Exploring the first math train pattern (y = x + 1)

 Grades 1-2 students explore and discuss the first math train puzzle posed to the Second Little Piggy by Wolf. A table is used to record the numeric patterns, as a way of checking or proving their solutions.

3 - Extending the first math train pattern

 Grades 1-2 students consider an extension to the first math train puzzle: Can they determine the 10th or 100th stage of the pattern without building the stages in-between?

4 - Exploring the second math train pattern (y = 3x + 3)

 Grades 1-2 students explore to the second math train puzzle posed to the Second Little Piggy by Wolf. A table is used to record the numeric patterns, as a way of checking or proving their solutions.
 Grade 4 students explore to the second math train puzzle posed to the Second Little Piggy by Wolf.

5 - Extending the second math train pattern

 Grades 1-2 students consider an extension to the second math train puzzle: Can they determine the 10th stage of the pattern without building the stages in-between? What about the 100th or 1000th stage?

6 - Comparing growing patterns using bar graphs

 Grades 1-2 students represent the patterns as bar graphs. How are the bar graphs similar? How are they different? What makes one graph steeper than the other? Is it the red blocks, the blue blocks, or both that make the graph steeper?
 Grade 4 students use bar graphs, such as the ones below, to represent patterns and compare slopes. Which bar graph pattern is steeper? Why? Is it the red blocks or the blue blocks or both that make the graph steeper?
 Grade 4 students create new growth patterns. They explore how they grow and then compare slopes.

7 - Using comics

 Grades 1-2 students create new patterns. They explore how they grow and they compare slopes.

8 - Students sharing their learning though song

 A little easy, a little hard a little easy and a little hard I like making growing patterns a little easy and a little hard and lots of fun I found school math hard so I loved to watch her excitement her complete understanding and explanation of it all it seemed so easy for her a nice refresher for me nice to see every day objects can be used in math patterns a little easy and a little hard I like making growing patterns a little easy and a little hard and lots of fun an interesting way to teach young children basic patterns that lead to more complex algebra I was surprised how advanced the math exercises were and how so very easily my son grasped it all a little easy and a little hard I like making growing patterns a little easy and a little hard and lots of fun Grades 1-2 students perform their song "A little easy, a little hard." 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).
 Growing patterns are cool 3 blue blocks and 1 red 6 blue blocks and 1 red 9 blue blocks and 1 red 12 blue blocks and 1 red the blue blocks grow by 3's the red blocks never change 31 blocks to make the 10th stage 301 to make the 100th stage growing patterns are cool they grow grow and grow growing by twos growing by ones growing by threes or even shrinking growing patterns are cool growing patterns shrinking patterns growing fast or slow a bar graph with bingo dabbers looks like a staircase take bigger steps to grow faster make the bar graph steeper and steeper growing patterns are cool they grow grow and grow growing by twos growing by ones growing by threes or even shrinking growing patterns are cool Grade 2 students perform their song "Growing patterns are cool." 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. Their math performance was also shared at the Math Performance Festival. Download the professional recording (mp3).
 Math with my Mommy she enjoyed the bingo dabbers creating her own math trains it was fun and interactive gets kids more excited about math she wants to buy bingo dabbers to do more bar graphs at home he shared about patterns how to make them grow one pattern grows by ones the other grows by threes some patterns grow faster their graphs are steep, steep, steep math does not have to be difficult or boring it can be really fun and kids can enjoy it and kids can enjoy it she understood the red blocks didn't change from car to car the blue blocks they increased she explained the difference between their bar graphs and why one was steeper he was able to explain patterns how each train was different I liked it when he said "I am very smart in math!" "I am very smart in math!" and "it was fun doing it with my Mommy" math does not have to be difficult or boring it can be really fun and kids can enjoy it and kids can enjoy it Grades 1-2 students perform their song "Math with my Mommy." 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).
 N'y number Learning at school and at home Our parents think it's hard This is easy we can do it Using tables, making graphs Making graphs, yeah Getting bigger, getting smaller Repeat, repeat, repeat Patterns go higher, some go lower Repeat, repeat, repeat Linear algebra is cool Patterns, patterns, patterns We can tell you "N"y number Patterns, patterns, patterns Learning at school and at home Our parents think it's hard This is easy we can do it Using tables, making graphs Making graphs, yeah Constants move you up Constants move you down The bigger the increasing number The steeper is the graph This is really fun We can make patterns It's interesting to learn Constants and variables Learning at school and at home Our parents think it's hard This is easy we can do it Using tables, making graphs Making graphs, yeah Grade 4 students perform their song "N'y number." 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. Their math performance was also shared at the Math Performance Festival. Download the professional recording (mp3).

4 - Let's paint a math story!

Below is an artistic representation of "Math Train patterns ." Artistically rendered by Ann Langeman (Faculty of Education, UWO). Designed by George Gadanidis. Download the poster for printing.