Mathematics Instructional Design Lesson Planning Template
Class: _Geometry____
Lesson: ___3.2_____
Date: ______
Important Mathematics to Develop
Geometric constructions
Making conjectures
Standards for Mathematical Practice and Content
Geometry-Constructions
Make geometric constructions
G-CO.12
Learning Intention
We are learning to use geometric constructions to understand geometric relationships.
Success Criteria
We will know we are successful when we can construct and explain the Perpendicular Bisector Conjecture and its
converse.
Mathematical Task and needed material
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Additional notes
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Use classroom data to choose some students to work on
One Step. Students will make their own decisions about
tools necessary to construct a perpendicular bisector.
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Others students will have guided investigation. Do not
copy conjecture box!
One Step
Investigation 1:
Investigation 2:
Finding the Right Bisector
Constructing a Perpendicular Bisector
Math_Lesson Planning Template Geometry_07.27.11_v1
Launch
5-10 minutes
Ask students to come up with pairs of words. The pair of words should
be one adjective and one noun.
Explore
Notes/reflection
Allow students to come up with many examples
and chart. Surface relationship between the noun
and the adjective. Stress importance of the two
words, both must “happen” together.
20 minutes
Bring up Launch to discuss “perpendicular bisector”.
Turn and Talk:
“What do you think a perpendicular bisector of a segment is?”
Discuss answers and come to a consensus. Have students sketch an
example of it on the board.
Have students work in their assigned groups. These flexible groupings
were formed based on classroom observations and RIT scores from the
MAP test.
One Step worksheet-(Jimmy, Sally, Bob, Hank), (Katie, Astrid
Pandora, Beth)
For students working on the investigation, allow
students to explore using patty paper and then
verify their observations using the protractor and
ruler.
While students are working on the conjectures,
have them draw a picture next to the conjecture in
their journal.
Investigations 1&2 – Finding the Right Bisector and
Constructing the Perpendicular Bisector
Summarize
15 minutes
Students present their results to the class. As they present, have them
mark the congruent segments formed by bisectors.
To ensure that students understand the vocabulary, ask them to explain
the meaning of midpoint, perpendicular, and bisector of a line in their
own words. When students share, ask if they agree or disagree and
explain why.
What does equidistant mean?
Ask students to think-pair-share on the following prompts:
“If you needed to construct a midpoint of a segment, what modifications
would you make in the construction you just performed?”
“Give a situation where you’ve heard the word median in other
contexts.”
Explicit Instruction: After the teacher has facilitated a summary of the
investigation and collected formative assessment data, use the results to
model an example to clarify how to construct perpendicular bisectors.
Math_Lesson Planning Template Geometry_07.27.11_v1
Address any difficulties students are having in
realizing that the compass is marking off lengths
that are the same. Clear up any confusion as
students share.
Make sure the whole class agrees on a conjecture
that is formulated from their own words.
The intersection of a segment and a bisector is the
midpoint of the segment. The median of a sorted
list of numbers is the” middle number”, just as a
median of a triangle is a “middle segment”
between a vertex and the opposite side.
Refer back to the Launch and connect the
learning intention and success criteria of the
explore.
Check for understanding, paying attention to
misconceptions in order to bring them up in the
explicit instruction piece.
Apply
p. 152 #7
Construct triangle ALI. Construct the perpendicular bisectors of each
side. What do you notice about the three bisectors?
Math_Lesson Planning Template Geometry_07.27.11_v1
Students should discover that the perpendicular
bisectors all intersect in one point.