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This PowerPoint is from Day 3 of Math week. It covers…1. Questioning techniques2. Discourse in the Classroom3. Vocabulary4. The math of Unit 35. The math of part 3 of Unit 4

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High School MathThe Standards Based Way

Day 3

Nicole Spiller

West Georgia RESA

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Problem of the Day

  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?

A) 4 B) 8 C)12 D) 16 E) 32

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Essential Questions

• 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

• Breaks

• Cell Phones

• Restrooms

• Parking Lot

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Activator

• Word Association

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Questioning in the Classroom

• 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

• 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

– “What do you think about _______ explanation?”

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How many questions do you ask?

• Research Finding #1: – Teachers ask between one and 4 questions per

minute.

• Implication:– Questioning dominates a large portion of

instructional time. A few carefully prepared or selected questions are preferable to a large number of questions.

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What types of questions do you ask?

• Research Finding #2: – Most teacher question are at the lowest

cognitive level – fact, recall, or knowledge

• Implication:– Teachers should purposefully plan and ask

questions that require students to engage in high-level thinking.

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Do you hold all students accountable to questioning ?

• Research Finding #3:– Not all students are accountable for all questions.

Teachers frequently call on volunteers who constitute a select group of students.

• Implication:– Teachers should decide who will answer questions.

They should establish procedures and norms to give all students equal opportunity.

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How long do you wait after asking a question?

• 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)

• Implication:– Wait times promote student thinking and foster

more students formulating answers to more questions.

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How do you respond to incorrect or incomplete answers?

• Research Finding #5:– Teachers often accept incorrect answers without

probing and they frequently answer their own questions.

• Implication:– 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.

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How often do students ask questions?

• Research Finding #6: – Students ask very few content-related

questions.

• Implication:– Teachers need to value, encourage, and help

students learn to formulate good questions, and make time for student questions.

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Vocabulary

• 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

• 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

• Survey, Medical, and Area Learning Tasks

• These tasks apply the concept of probability to actual situations

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Overview of Unit 3

• 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 UnderstandingsEssential Questions

• 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• 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.

– Understand and use the triangle inequality, the side-angle 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

• 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

• Basic geometric constructions including…– Angle bisectors, perpendicular bisectors– Parallel and perpendicular lines

• Congruency

• Basic quadrilaterals

–

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Selected Terms and Symbols

• 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

• 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• 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 n-gon,

• Tasks 2 thru 6: Learning tasks that extend students knowledge of triangles

• 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.

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Poor Captain RobotA Learning Task

• 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

• Key Points– Congruence postulates and theorems of

triangles– Corresponding parts

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Middles and HalvesA Learning Task

• 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 TrianglesA Learning Task

• Key Points:– 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

• 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 DiagonalsA Learning Task

• 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

• This task incorporates all of the material learned in this unit in an applied setting.

• 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