Transcript region_8_math_collaborative_summer_workshop_day_onex

Region 8 Math Collaborative
Summer Workshop
Jamie Ashby, Texarkana College
What Do You See?
Map of
Washington D.C.
area
What Do You See?
Map of
Washington D.C.
area Metro
subway stops
What Do You See?
West Rose Stained Glass
window in the
Washington National
Cathedral
What Do You See?
Library of Congress, Great Hall view of ceiling and cove
Masonic symbol found on
American currency, buildings, etc.
What Do You See?
Stained glass
What Do You See?
Wassily Kandinsky
(1886 – 1944), the father
of abstract art, also a
skilled musician, strongly
associated music with art.
Kandinsky, who named
works after musical terms,
saw color when he
listened to music, and
believed color could
visually express music’s
timber, pitch and volume.
At age 30, Kandinsky’s
artistic career began
when he left a legal
career to pursue artistic
studies after seeing
Monet’s “Haystacks.”
Passionately compelled
to create, Kandinsky
believed that the purity
of this desire would
communicate itself to
viewers of his work.
What Do You See?
Map of Maze from
the Overlook
Hotel featured in
“The Shining”
Day 1: Foundations of Geometry
4.1/5.1 Mathematical process standards. The student uses mathematical
processes to acquire and demonstrate mathematical understanding. The
student is expected to:
•
4.1/5.1A Apply mathematics to problems arising in everyday life, society, and
the workplace.
•
4.1/5.1C Select tools, including real objects, manipulatives, paper and pencil,
and technology as appropriate,…, to solve problems.
•
4.1/5.1D Communicate mathematical ideas, reasoning, and their implications
using multiple representations, including symbols, diagrams, graphs, and
language as appropriate.
•
4.1/5.1E Create and use representations to organize, record, and
communicate mathematical ideas.
•
4.1/5.1F Analyze mathematical relationships to connect and communicate
mathematical ideas.
•
4.1/5.1G Display, explain, and justify mathematical ideas and arguments
using precise mathematical language in written and oral communication.
Day 1: Foundations of Geometry
4.6 Geometry and measurement. The student applies mathematical
process standards to analyze geometric attributes in order to develop
generalizations about their properties. The student is expected to:
•
4.6A Identify points, lines, line segments, rays, angles,
and perpendicular and parallel lines. Supporting
Standard
•
4.6C Apply knowledge of right angles to identify
acute, right and obtuse triangles. Supporting
Standard
•
4.6D Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular
lines or the presence or absence of angles of a
specified size. Readiness Standard.
Day 1: Foundations of Geometry
5.5 Geometry and measurement. The student applies mathematical
process standards to classify two-dimensional figures by attributes and
properties. The student is expected to:
• 5.5A Classify two-dimensional figures
in a hierarchy of sets and subsets
using graphic organizers based on
their attributes and properties.
Readiness Standard.
Building Blocks of Geometry
 4.6A Identify points, lines, line segments, rays, angles, and perpendicular
and parallel lines. Supporting Standard
 The most basic figures in geometry are undefined terms, which cannot be
defined by using other figures. The undefined terms point, line, and plane
are the building blocks of geometry.
Note: Parallel lines must be in
the same plane.
Sidebar Explanation on Parallel Lines:
What Do You See?
What Do You See?
Make a list of at
least one each of
the basic
geometric
concepts
discussed.
Share your
answers with your
partner and
discuss other ways
students may
recognize basic
geometric
principles in the
real world.
Virtual Scavenger Hunt
Search online for examples of the basic
concepts of geometry in the real world.
Make a collage of your images in Word or
PowerPoint.
Share your findings with your tablemates.
Angle Basics
Practice
Angle Types and Names
Using a
Protractor
and
AngLegs
Scavenger Hunt: Angles in Real Life
Two Dimensional Figure Basics
 4.6D Classify two-dimensional figures based on the presence or absence of
parallel or perpendicular lines or the presence or absence of angles of a
specified size. Readiness Standard.

Two Dimensional Figure Basics
 4.6D Classify two-dimensional figures based on the presence or absence of
parallel or perpendicular lines or the presence or absence of angles of a
specified size. Readiness Standard.
Two Dimensional Figure Basics
Types of Polygons
Name
Number of Sides
& Vertices
Type of Sides
Type of Angles
Triangle
3
No parallel sides
Possible acute,
obtuse, and/or
right angles
Quadrilateral
4
Possible parallel
and/or
perpendicular
sides
Possible acute,
obtuse, and/or
right angles
Pentagon
5
Possible parallel
and/or
perpendicular
sides
Possible acute,
obtuse, and/or
right angles
Hexagon
6
Possible parallel
and/or
perpendicular
sides
Possible acute,
obtuse, and/or
right angles
Triangle Basics
 4.6C Apply knowledge of right angles to identify acute, right and obtuse
triangles. Supporting Standard
Triangle Basics
Other Types of Triangles: Scalene
3 sides,
3 vertices,
No congruent
sides,
No parallel sides,
Up to one possible
pair of
perpendicular
sides
Types of
Triangles:
Isosceles
3 sides,
3 vertices,
At least 2
congruent sides,
No parallel sides,
Up to one possible
pair of
perpendicular
sides
Types of Triangles: Equilateral
(a special type of isosceles triangle)
3 sides,
3 vertices,
All sides congruent,
No parallel or perpendicular sides,
All angles congruent
Types of Triangles:
I came across this diagram at www.cut-the-knot.org
who credits seeing it in [Jacobs, p. 149] who credits First Steps in
Geometry by G. A. Wentworth and G. A. Hill (Ginn, 1901).
Types of Quadrilaterals: Trapezoid
4 sides,
4 vertices,
Exactly on pair of parallel sides,
Up to two possible pairs of perpendicular sides
Types of Quadrilaterals: Parallelogram
4 sides,
4 vertices,
Opposite sides congruent,
2 pairs of parallel sides,
Opposite angles congruent
Types of Parallelograms: Rectangle
4 sides,
4 vertices,
Opposite sides congruent,
2 pairs of parallel sides,
2 pairs of perpendicular sides
4 right angles
Types of Parallelograms: Rhombus
4 sides,
4 vertices,
All sides congruent,
2 pairs of parallel sides,
Opposite angles congruent
Types of ParallelogramsExamples/Non-Examples
Types of Parallelograms: Square
4 sides,
4 vertices,
All sides congruent,
2 pairs of parallel sides,
2 pairs of perpendicular sides
4 right angles
Types of Quadrilaterals: Summary
5.5 Geometry and measurement. The student applies mathematical process
standards to classify two-dimensional figures by attributes and properties. The
student is expected to:
Classify two-dimensional figures in a hierarchy of sets and subsets using graphic
organizers based on their attributes and properties. Readiness Standard
Discuss with your partners possible graphic
organizers that could be used to classify twodimensional figures that we have discussed so
far.
Types of Parallelograms
5.5 Geometry and measurement. The student applies mathematical process
standards to classify two-dimensional figures by attributes and properties. The
student is expected to:
Classify two-dimensional figures in a hierarchy of sets and subsets using graphic
organizers based on their attributes and properties. Readiness Standard
Construct both a Tree Diagram and a Venn Diagram of Triangle Types
Tree Diagram of Triangle Types
Venn Diagram of Triangle Types
Create two different graphic
organizers for Quadrilaterals
On your own at first, list as many generalizations as you can about
sets and subsets of two-dimensional figures.
Share ideas with your partner to expand your list.
What Do You See?
West Rose Stained Glass
window in the
Washington National
Cathedral, also flags,
arches, and other
geometric shapes
What Do You See?
Library of Congress, Great Hall view of ceiling and cove
Masonic symbol found on
American currency, buildings, etc.
Creating a Geometric Stained Glass
Using the materials provided, create your own “stained glass” or
Kandinsky-type art.
You must include representations of as many geometric
concepts as possible that were discussed today.
Day 1: Foundations of Geometry
4.1/5.1 Mathematical process standards. The student uses mathematical
processes to acquire and demonstrate mathematical understanding. The
student is expected to:
•
4.1/5.1A Apply mathematics to problems arising in everyday life, society, and
the workplace.
•
4.1/5.1C Select tools, including real objects, manipulatives, paper and pencil,
and technology as appropriate,…, to solve problems.
•
4.1/5.1D Communicate mathematical ideas, reasoning, and their implications
using multiple representations, including symbols, diagrams, graphs, and
language as appropriate.
•
4.1/5.1E Create and use representations to organize, record, and
communicate mathematical ideas.
•
4.1/5.1F Analyze mathematical relationships to connect and communicate
mathematical ideas.
•
4.1/5.1G Display, explain, and justify mathematical ideas and arguments
using precise mathematical language in written and oral communication.
Day 1: Foundations of Geometry
4.6 Geometry and measurement. The student applies mathematical
process standards to analyze geometric attributes in order to develop
generalizations about their properties. The student is expected to:
•
4.6A Identify points, lines, line segments, rays, angles,
and perpendicular and parallel lines. Supporting
Standard
•
4.6C Apply knowledge of right angles to identify
acute, right and obtuse triangles. Supporting
Standard
•
4.6D Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular
lines or the presence or absence of angles of a
specified size. Readiness Standard.
Day 1: Foundations of Geometry
5.5 Geometry and measurement. The student applies mathematical
process standards to classify two-dimensional figures by attributes and
properties. The student is expected to:
• 5.5A Classify two-dimensional figures
in a hierarchy of sets and subsets
using graphic organizers based on
their attributes and properties.
Readiness Standard.
Assessment Practice