This PowerPoint is from Day 3 of
Math week. It covers…
1. Questioning techniques
2. Discourse in the Classroom
3. Vocabulary
4. The math of Unit 3
5. The math of part 3 of Unit 4
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High School Math
The Standards Based Way
Day 3
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Nicole Spiller
West Georgia RESA
Problem of the Day
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A rectangular pool 24 feet long, 8 feet
wide, and 4 feet deep is filled with water.
Water is leaking from the pool at the rate
of 0.40 cubic foot per minute. At this rate,
how many hours will it take for the water
level to drop 1 foot?
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A) 4 B) 8 C)12
D) 16
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E) 32
Essential Questions
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• What is the Math of Unit Three?
• What is the Math of part three of Unit Four?
• How can we change our questioning
techniques to improve student learning?
• What role does vocabulary play in content
development?
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Housekeeping
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Breaks
Cell Phones
Restrooms
Parking Lot
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Activator
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• Word Association
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Questioning in the Classroom
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• Complete the self-evaluation on your own
questioning techniques.
• Read the article from EdThoughts on the
role of teacher questioning. Highlight
statements with which you strongly agree
with which you strongly disagree.
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Priority 1: Change the Discourse of
the Classroom
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• Rephrase questions to start with “How” or
“Why”
• “Tell me about…”
• Frequent use of the think-pair-share strategy
• Think time … silence is not the enemy
• Encourage students to listen to one another
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– “What do you think about _______ explanation?”
How many questions do you ask?
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• Research Finding #1:
– Teachers ask between one and 4 questions per
minute.
• Implication:
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– Questioning dominates a large portion of
instructional time. A few carefully prepared or
selected questions are preferable to a large
number of questions.
What types of questions do you ask?
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• Research Finding #2:
– Most teacher question are at the lowest
cognitive level – fact, recall, or knowledge
• Implication:
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– Teachers should purposefully plan and ask
questions that require students to engage in
high-level thinking.
Do you hold all students
accountable to questioning ?
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• Research Finding #3:
– Not all students are accountable for all questions.
Teachers frequently call on volunteers who constitute a
select group of students.
• Implication:
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– Teachers should decide who will answer questions.
They should establish procedures and norms to give all
students equal opportunity.
How long do you wait after asking a
question?
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• Research Finding #4:
– Teachers typically wait less than one second
after asking a question before calling on a
student (wait time 1).
– Teachers wait less time before speaking after a
student has answered (wait time 2)
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• Implication:
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– Wait times promote student thinking and foster
more students formulating answers to more
questions.
How do you respond to incorrect or
incomplete answers?
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• Research Finding #5:
– Teachers often accept incorrect answers without
probing and they frequently answer their own
questions.
• Implication:
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– When students give either incomplete or incorrect
responses, teachers should seek to understand those
answers more completely by gently guiding student
thinking with appropriate probes.
How often do students ask
questions?
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• Research Finding #6:
– Students ask very few content-related
questions.
• Implication:
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– Teachers need to value, encourage, and help
students learn to formulate good questions, and
make time for student questions.
Vocabulary
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• Read the one page handout from Marzano
• Is there a statement you either strongly
agree or disagree with?
• Are there any implications for the High
School Math Class?
• How can the Math Support class support
vocabulary mastery?
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Robotic Gallery
A Learning Task
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• Introduction of exterior angle sum theorem. If a
polygon is convex, then the sum of the measure of
the exterior angles, one at each vertex, is 360o.
• Sum of the measures of the interior angles of a
convex polygon: 180o(n-2)
• Measure of each interior angle of a regular n-gon:
180o(n-2)/n
• Measure of each exterior angle of a regular n-gon:
360o/n
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Part Three of Unit Four
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• Survey, Medical, and Area Learning Tasks
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• These tasks apply the concept of probability
to actual situations
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Overview of Unit 3
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• The study of geometry requires an understanding
of the way we think. Inductive and deductive
reasoning has been introduced in Unit One.
• In this unit students will explore, understand, and
use the formal language of reasoning and
justification. Students will be presented with the
opportunity to use logical reasoning and proofs.
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Enduring Understandings
Essential Questions
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• Properties of angles, triangles,
quadrilaterals, and polygons are connected
• Geometric ideas are significant in all math
areas
• Geometric ideas are appropriate for
describing many aspects of our world
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Key Standards
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MM1G3. Students will discover, prove, and
apply properties of triangles, quadrilaterals and
other polygons. Determine the sum of interior
and exterior angles in a polygon.
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Understand and use the triangle inequality, the sideangle inequality, and the exterior-angle inequality.
Understand and use congruence postulates and
theorems for triangles (SSS, SAS, ASA, AAS, HL).
Understand, use, and prove properties of and
relationships among special quadrilaterals:
parallelogram, rectangle, rhombus, square, trapezoid,
and kite.
Find and use points of concurrency in triangles:
incenter, orthocenter, circumcenter, and centroid.
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Related Standards
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• MM1G2: Students will understand and use the language of
mathematical argument and justification
• MM1P1: Students will solve problems (using appropriate
technology)
• MM1P2: Students will reason and evaluate mathematical
arguments
• MM1P3: Students will communicate mathematically
• MM1P4: Students will make connections among
mathematical ideas and to other disciplines
• MM1P5: Students will represent mathematics in multiple
ways
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Concepts/Skills to Maintain
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• Basic geometric constructions including…
– Angle bisectors, perpendicular bisectors
– Parallel and perpendicular lines
• Congruency
• Basic quadrilaterals
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Selected Terms and Symbols
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Centroid
Circumcenter
Incenter
Orthocenter
Sum of the measures of the interior angles
Measure of interior angel of a regular n-gon
Exterior angle of a polygon
Remote interior angles of a triangle
Measure of the exterior angle of a triangle
Exterior Angle Inequality
22 Theorems
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Evidence of Learning
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• Students will be able to prove conjectures
through multiple forms of justification
• Students will apply properties of triangles,
and special quadrilaterals
• Students will be able to find and use points
of concurrency in triangles
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Tasks
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• Task 1: A guided discovery task for the exterior angle sum
theorem, sum of the measures of interior angles of convex
polygons, measures of interior and exterior angles of a regular ngon,
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• Tasks 2 thru 6: Learning tasks that extend students knowledge of
triangles
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• Task 7: Learning task that extends students knowledge of
quadrilaterals
• Task 8: Designed to demonstrate the type of assessment
activities students should be comfortable with by the end of the
unit.
Poor Captain Robot
A Learning Task
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• Key Points:
– Students learn that the measure of an exterior
angle of a triangle equals the sum of the two
remote interior angles
– Students learn that the sum of the lengths of
any two sides of a triangle is greater than the
length of the third side
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Triangles Learning Task
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• Key Points
– Congruence postulates and theorems of
triangles
– Corresponding parts
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Middles and Halves
A Learning Task
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• Key Points:
– Review of triangle classification
– Review of basic constructions
– Review of definitions of angle bisectors,
perpendicular bisectors, and altitudes
– New term: Median
– Special properties of isosceles and equlateral
triangles
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Centers of Triangles
A Learning Task
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Incenter
Orthocenter
Circumcenter
Centroid
Studens need to remember the significance of
points on a perpendicular bisector of a segment
and the points on an angle bisector
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Location Learning Task
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• Key Points:
– This task gives students an opportunity to apply
knowledge gained in the previous task to two
new scenarios.
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Constructing with Diagonals
A Learning Task
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• Key Points:
– Covers the properties of quadrilaterals
– Which quadrilaterals can be constructed based
on specific information about the diagonals
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Landscaping Culminating Task
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• This task incorporates all of the material
learned in this unit in an applied setting.
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• It may be appropriate for students to work
on this task throughout the unit with
periodic deadlines
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End of Day 3
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