Download Construction Junction - National Council of Teachers of Mathematics

Construction Junction, What’s your
Function?
Brian Shay
Teacher and Department Chair
Canyon Crest Academy
[email protected]
@MrBrianShay
Session Goals
• Familiarize ourselves with CCSS and the GSE
Geometry Standards
• Explore tasks involving constructions and
proof
• Connect these tasks to prior and future
knowledge
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Standards for Math Practice
1. Make sense of problems & persevere in solving
them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
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reasoning.
PtA’s Math Teaching Practices
1. Establish mathematics goals to focus learning.
2. Implement tasks that promote reasoning and problem
solving.
3. Use and connect mathematical representations.
4. Facilitate meaningful mathematical discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual
understanding.
7. Support productive struggle in learning mathematics.
8. Elicit and use evidence of student thinking.
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CCSS Geometry Standards
• G.CO.12 Make formal geometric constructions with a variety of
tools and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.). Copying
a segment; copying an angle; bisecting a segment; bisecting an
angle; constructing perpendicular lines, including the perpendicular
bisector of a line segment; and constructing a line parallel to a given
line through a point not on the line.
• G.CO.13 Construct an equilateral triangle, a square, and a regular
hexagon, each inscribed in a circle.
• G.C.3 Construct the inscribed and circumscribed circles of a triangle,
and prove properties of angles for a quadrilateral inscribed in a
circle.
• G.C.4 Construct a tangent line from a point outside a given circle to
the circle.
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Tools for Construction
• Real Old School: String and Chalk!
– https://flipagram.com/f/mvcrxhP269
• Less Old School: Compass and Straightedge
• New School: Dynamic Geometry Software
(GeoGebra)
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The Basics
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Copying a segment
Copying an angle
Bisecting a segment
Bisecting an angle 
Constructing Perpendicular Lines
Constructing Parallel Lines
Better than Basic
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Equilateral Triangle Inscribed in a Circle
Square Inscribed in a Circle
Regular Hexagon Inscribed in a Circle
Inscribed Circle for a Triangle
Circumscribed Circle for a Triangle
Tangent Line to a Circle
– http://www.mathopenref.com/consttangents.html
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These are gonna stretch ya…
• Before you start, draw the final image.
– Think about its properties and relationships
– Think about how you can work your way
backwards
– Think about how to use the basics to get there
• Construct an isosceles triangle ABC, given
base angle B and the altitude CD to one of its
legs.
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More stretches (#2)
• Construct a right triangle ABC, given angle B,
one of its acute angles, and CD, the altitude to
the hypotenuse.
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Stretch #3
• Construct a triangle ABC, given two if its
angles, A and B, and the angle bisector to the
angle B.
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Stretch #4
• Construct a parallelogram ABCD, given the
diagonals AC and BD, and <AEB, where E is the
intersection of the diagonals.
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Stretch #5
• Construct a triangle ABC, given the angles A
and B and the radius of the circle inscribed in
the triangle.
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Stretch #6
• Given a circle C1 and lines AX and AY, that are
tangent to the circle at points X and Y,
respectively. Construct a circle C2 that is
tangent to the circle C1, AX and AY.
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Constructions….FUNctions!
• Constructions are awesome!
– Connect all of the following together
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Angle and line properties
Circle properties
Triangle properties
Quadrilateral properties
• Tactile Proofs
• No, Low, or High Tech Integration
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Thank you!
• Construction Junction!
• Brian Shay
• [email protected]
• @MrBrianShay
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Disclaimer
The National Council of Teachers of Mathematics is a public voice
of mathematics education, providing vision, leadership, and
professional development to support teachers in ensuring
equitable mathematics learning of the highest quality for all
students. NCTM’s Institutes, an official professional development
offering of the National Council of Teachers of Mathematics,
supports the improvement of pre-K-6 mathematics education by
serving as a resource for teachers so as to provide more and
better mathematics for all students. It is a forum for the
exchange of mathematics ideas, activities, and pedagogical
strategies, and for sharing and interpreting research. The
Institutes presented by the Council present a variety of viewpoints.
The views expressed or implied in the Institutes, unless otherwise
noted, should not be interpreted as official positions of the Council.
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