A math lesson for Grade 5, Grade 6, Grade 7 or Grade 8
Lesson title: Pure Geometric Constructions
Free to use math lessons. Thank you for posting a comment.
Brief lesson summary/general objectives
The objectives of Math Magic lessons are expanding students’ knowledge beyond the curriculum, learning math without being concerned about grades, and thus developing love for math --- all as early as possible.
In this lesson students are introduced to a new presentation tool – Prezi. In an effort to improve the given Prezi presentation students will learn about Euclidean geometry and pure geometric constructions. This learning experience is further enhanced by strong cross-curriculum connections.
Connections to the British Columbia (K-7) curriculum
The lesson is connected to the Space and Shape Unit for grades 6 and 7 math.
Additional Connections and Enrichment Opportunities
Other curriculum connections are with:
· Math units on number systems (position versus non-position) and measurement (invention of protractor).
· Art based on Albrecht Durer’s quote “Geometry is the foundation of all painting."
· Social studies through learning about ancient Greek and Egyptian societies.
· Technology by using its presentation tools to support individual learning.
Manipulatives/Supplies Needed
- Compass, straightedge and paper for each student
- Computers with internet connections for each student / student pairs
Grouping Strategies
A teacher keeps to his/her usual grouping strategies, except for the Main activity. For that activity, the grouping is based on students’ preferences. For every unconnected lesson, students shall choose to work either individually, or in groups of up to 4 students, organized by themselves.
A teacher follows the same strategy for all Math Magic lessons. Hook/Warm–up and Debrief /Consolidation activities are done as a full class body. Then, the end-of-class reflection write-up is done as individual journal entry by each student. The Main Activity grouping is done as explained above, and all participants from it will exchange learning points by way of shared activities during classes or in virtual reality.
Assessment
Math Magic lessons are envisaged to be an evaluation-free zone, in order to enhance the students’ creativity and enjoyment of learning mathematics, free from the stress of achieving good grades.
Warm-Up (10 to 15 min)
S/he demonstrates how to construct a 30º angle in two different ways:
1st: using a protractor,
2nd: using only compass and straightedge: the teacher will construct a 60º angle, the angle bisector of it, and the result, a half of 60º angle is a 30º angle.
The teacher also demonstrates how to construct a line bisector using only a compass and straightedge. S/he tells students that pure geometric constructions are performed without any measurements. They are important as they provide a greater insight into geometric concepts. In his book “Elements” the ancient Greek mathematician Euclid used these construction techniques extensively therefore they have become a part of the study of geometry.
Main Activity (20 to 25 min)
Students and the teacher discuss how the presentation could be improved.
The teacher will present a list of ideas on how the content of the presentation could be improved by adding more:
- about Euclidean geometry,
- non-Euclidean geometries,
- the ancient Greek number system, or
- applications of learning pure geometric construction.
E.g. after learning how to construct a triangle students will see clearly why a triangle with sides 2, 3 and 6 could not exist.
2nd: Students practice geometric constructions learned through websites such as:
3rd: Students start planning how to improve/ replace the above Prezi presentation.
Consolidation and Reflection (10 to 15 minutes)
The teacher shares with students “Where to go from here” and then students write journals. Students can use the following prompts:
I liked the most the construction of ___________
I am not sure that I understand ______________
I would like to know more about ___________
Where to go from here
1st: The teacher will choose to give students more class time to work on the presentation or assign it as homework. OR
2nd: Students will make and share a new presentation on any math topic related to the lesson.
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