This PowerPoint is from Day 3 of Math week. It covers… 1 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

High School Math The Standards Based Way Day 3 Nicole Spiller West Georgia RESA Need something for those who may finish early Need folders, handouts on ? Of students, ? Of teacher, math involved

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

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?

Housekeeping Breaks Cell Phones Restrooms Parking Lot

Activator Word Association

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.

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?”

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.

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.

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.

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.

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.

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.

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?

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

Part Three of Unit Four Survey, Medical, and Area Learning Tasks These tasks apply the concept of probability to actual situations

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.

Enduring Understandings Essential 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

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.

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

Concepts/Skills to Maintain Basic geometric constructions including… Angle bisectors, perpendicular bisectors Parallel and perpendicular lines Congruency Basic quadrilaterals

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

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

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.

Poor Captain Robot A 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

Triangles Learning Task Key Points Congruence postulates and theorems of triangles Corresponding parts

Middles and Halves A 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

Centers of Triangles A 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

Location Learning Task Key Points: This task gives students an opportunity to apply knowledge gained in the previous task to two new scenarios.

Constructing with Diagonals A Learning Task Key Points: Covers the properties of quadrilaterals Which quadrilaterals can be constructed based on specific information about the diagonals

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

End of Day 3