LESSON PLAN 4: Do Parallel Lines Meet?
IN BRIEF
The story Do Parallel Lines Meet? offers the following insights:
We've all learned in school that parallel lines never meet - but this
only holds true if we live on a flat surface.
We live on a sphere, where all parallel lines
meet! See an interview with mathematician
Megumi Harada of McMaster University at
www.fields.utoronto.ca/mathwindows/sphere
From www.BrainyDay.ca
o in English
o in French
o in Spanish
As an eBook from iTunes,
Amazon & Kobo
CLASSROOM-TESTED
Do Parallel Lines Meet? is classroom-tested in grades 2 and 4.
MATERIALS
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The story Do Parallel Lines Meet? (see www.BrainyDay.ca)
a flat map of the Earth
a large globe
string
Smart Math – Lesson Plan #4
www.BrainyDay.ca
page 1
LESSON DEVELOPMENT, Grades 2 and 4
Learning goals
Geometry
o Explore straight lines
o Explore parallel lines
o Explore lines on a globe (latitude and longitude)
Communication
o Use words, numbers, symbols, diagrams, and storytelling to communicate learning
Reading of Do Parallel Lines Meet?
Introduction
Ask students to share examples of parallel lines, especially ones they can see in the classroom, such as
tiles on the ceiling and doors on cupboards. Ask if they think that parallel lines ever meet and to
explain their thinking.
Pose the following riddle, and show the diagram on the right:
Molly stepped out of her tent, and walked south 100 metres. Then she
walked west 100 metres and came upon a bear. She got scared and ran
north 100 metres, arriving back at her tent. How is this possible, and
what colour was the bear?
Reading
Read the story Do Parallel Lines Meet? and pause at the end of page 9. Show students a flat map of the
Earth and have a student follow two lines of longitude with two fingers, to show that they are parallel.
Also show students a globe (as Wolf does with Piggy in the story) and have them share with their
partner how this might be a clue to two straight and parallel paths meeting. Share and discuss as a
whole class.
Finish reading the story and ask students to share what they learned.
Revisit the riddle and ask students to share and discuss possible solutions. (The tent is at the North Pole
and therefore the bear, being a polar bear, is white.]
Extension for grade 4 - the shortest path on the globe
Show students a globe and identify where Tokyo and New York City are located. Ask: when an
airplane flies from Tokyo to New York, what path does it follow? Have students make predictions and
show their airplane paths on the globe. Students typically predict that the plane would fly along a line
of latitude.
Suggest that the pilot wants to take the shortest path, to save time and to save fuel. Have two student
volunteers, standing about 3 metres apart, hold the ends of a 6 metre piece of string. Pull the centre of
the string to one side and ask: if you followed the string and walked from one student to the other,
would it be the shortest path?
Scaffold student thinking to the idea that a taut string would be the shortest path. Have the 2 volunteers
pull the string taut to demonstrate.
Smart Math – Lesson Plan #4
www.BrainyDay.ca
page 2
Have students come up in pairs and pull a string taut between Tokyo and New York City. They should
discover that the airplane follows a path that passes near Anchorage, Alaska.
Have students also use their string to determine which of the following are "shortest" paths between
two points on the globe: lines of latitude, lines of longitude, and the equator. Have students share and
discuss.
Students will discover that a taut string will match the path along a line of longitude and along the
equator, but not along a line of latitude.
The lines of longitude and the equator are great circles.
They are the largest circles you can draw on a sphere.
They are also the smallest circles through which the
sphere will fit.
Have students view the interview on this theme with Dr.
Megumi Harada of McMaster University, available at
http://www.fields.utoronto.ca/mathwindows/sphere.
Ask students to share and discuss what they learned
from the interview.
Communicating
Students summarize their learning using diagrams, pictures and words. They draw the riddle diagram or
the airplane path diagram and write to describe the solution. They also draw a diagram of the following
teacher prompts such as: “What did you learn? What surprised you? How did you feel?” They share
their learning with their peers, in a whole-class setting.
Sharing at home option. Students take their learning summaries home and share with parents.
Parent feedback option. Ask parents to send the following feedback:
o What did your child share with you?
o What did you learn from this activity?
Smart Math – Lesson Plan #4
www.BrainyDay.ca
page 3