We do math concerts in K-8 schools across Ontario with our band Joy of X, funded by the Fields Institute. Before we sing the song "Parallel lines" (see 2.b below) I invite volunteers to come to the stage. I ask, "Please tell me everything you know about parallel lines." The typical answer is "Two straight lines that never meet." When I ask, "How sure are you that this is always true?" there are no doubts. What's really interesting is that over 2,000 years ago, the Greek mathematician Euclid tried to prove his Parallel Line Postulate, but was not able to. And neither could any mathematician after him. Why is this the case?
The volunteers return to their seats and I then pose this riddle:
The solution to this riddle is the reason why Euclid could not prove his Parallel Line Postulate. It turns out that his Postulate is not a theorem but an assumption. If we assume "parallel lines never meet", then we have a flat surface, or a Euclidean geometry. Different assumptions lead to different geometries, which are just as valid as the flat surface geometry, like the spherical geometry of our Earth's surface.
Shouldn't children have opportunities at an early age to explore the wonderful geometry of our beautiful Earth?
Get the lesson plan.
1.a - How it unfolded in the classroom
|Students shared what they knew about parallel lines. They looked for parallel lines in their classroom, like in floor tiles, bookshelves, and wires on the guinea pig cage. Next they were given the bear riddle described above and they shared ideas. Then they read the story, Do Parallel Lines Meet? where Wolf and Piggy run on parallel paths and Piggy wonders if they will ever meet. Using hand-held globes (purchased from a dollar store) students explored how this might happen on the Earth. They used words, diagrams and pictures to record their thinking, which were used to write the songs "Parallel lines" (see 2.b below).|
1.b - Grade 2 classroom action
|Grade 2 students share how they recorded their thinking.|
1.c - Home connection
|Grade 2 students posed the bear riddle to their parents, they read the story Do Parallel Lines Meet? and parents recorded their children's sharing and thinking for the teacher to read. Such a home connection gives children the opportunity to play the role of "teacher" and consolidate their learning. Rich activities such as the one on parallel lines, where mathematically new, wonderful and surprising is experienced, make for students relating engaging math stories to family and friends.|
2.a - Using songs in the math classroom
|Students love singing, especially when the lyrics are a summary of their own thinking and ideas. Such songs represent the collective knowledge of the class and a celebration of student learning. This song was shared at the Math and Science Performance Festival.|
2.b - "Parallel lines" - student performance
Parallel, parallel, parallel lines
Molly in her tent
|Grade 2 students perform their song "Parallel lines."|
2.c - "Parallel lines" - music video
|Music video of "Parallel lines." Lyrics based on the writing and thinking of the grade 2 students from Pam King's class. Illustrated and animated by Jessica Taylor Charland. Music by Ian Parliament, Amanda Lewis, Ryan Casselman and Ricardo Scucugila.|
3.a - Using children's literature
|Children's literature helps students make emotional connections with math ideas, through the characters in the story. Stories are also easy to remember and help anchor student learning. In the story Do Parallel Lines Meet? Wolf and Piggy run on parallel paths and Piggy wonders if they will ever meet.|
3.b - Making cross-curricular connections
|Making cross-curricular connections helps students experience the richness of mathematical ideas. In the parallel lines activity, a number of other subject areas were integrated: social studies (mapping, continents, lines of longitude), art (student drawing), and music (student song and performance).|
3.c - Using cooperative learning
|Working with a partner or in a small group students get a chance to use their language, bounce ideas, help eachother focus, and have fun.|
4.a - Let's paint a math story!
Below is an artistic representation of "Where parallel lines meet." Artistically rendered by Ann Langeman (Faculty of Education, UWO). Designed by George Gadanidis.