PowerPoint Presentation

The Arizona Mathematics Partnership: Week 1 Geometry

Ted Coe, June 2014

cc-by-sa 3.0 unported unless otherwise noted1Ways of doing Ways of thinkingHabits of thinkingTeaching and Learning MathematicsSpeak meaningfully what you say should carry meaning to others; Exhibit intellectual integrity base your conjectures on a logical foundation; dont pretend to understand when you dont; Strive to make sense persist in making sense of problems and your colleagues thinking. Respect the learning process of others allow them the opportunity to think, reflect and construct. When assisting your peers, pose questions to help them construct meaning rather than show them how to get the answer. Marilyn Carlson, Arizona State University, Project Pathways THE Rules of Engagement

http://hub.mspnet.org/media/data/Classroom_Rules_of_Engagement-Carlson.pdf?media_000000007898.pdfThe Plot...

08/13/09408/13/094The Foot

DefineSquareTriangleAngleTrue or False? A square is a rectangle.

Quadrilaterals

Quadrilaterals

Quadrilaterals

Downloaded from the PARCC website 6/2/2013

From the AZ Glossary, 2008:

But that isnt the only possibilitySome are based on symmetryAn Example of CCSS 5.GFrom Illustrativemathematics.org

From Illustrativemathematics.org

From Illustrativemathematics.org

Wolframalpha.com (6/11/2013)

From the Progression Documents http://ime.math.arizona.edu/progressions/

http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_g_k6_2012_06_27.pdf

http://ime.math.arizona.edu/progressions/Act I Scene II

From http://www.healthreform.gov/reports/hiddencosts/index.html (6/3/2011) The Broomsticks

08/13/092708/13/0927

The RED broomstick is three feet longThe YELLOW broomstick is four feet longThe GREEN broomstick is six feet long

The Broomsticks08/13/092808/13/0928The Willis tower (formerly the Sears tower) is 1730 feet high. The Burj Khalifa (formerly Burj Dubai) is 2717 feet high. The Burj is ______________ times as large as the Willis tower.The Willis tower is _____________times as large as the BurjThe Burj is _____________ percent the size of the Willis tower.The Willis tower is _____________ percent the size of the Burj.

08/13/092908/13/0929From the CCSS: Grade 330Source: CCSS Math Standards, Grade 3, p. 24 (screen capture)

From the CCSS: Grade 3313.OA.1:Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7.Soucre: CCSS Grade 3. See: Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. Daro, et al., 2011. pp.48-49From the CCSS: Grade 432Source: CCSS Grade 4

4.OA.1, 4.OA.2Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

From the CCSS: Grade 433Source: CCSS Grade 4

4.OA.1, 4.OA.2Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

From the CCSS: Grade 534Source: CCSS Grade 5

5.NF.5aInterpret multiplication as scaling (resizing), by:Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.Source: Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. Daro, et al., 2011. p.49

In Grades 6 and 7, rate, proportional relationships and linearity build upon this scalar extension of multiplication. Students who engage these concepts with the unextended version of multiplication (a groups of b things) will have prior knowledge that does not support the required mathematical coherences.What is it?

Is the perimeter a measurement?

or is it something we can measure?

Perimeter08/13/093608/13/093608/13/0936Is perimeter a one-dimensional, two-dimensional, or three-dimensional thing?

Does this room have a perimeter?

Perimeter08/13/093708/13/0937

08/13/093808/13/093808/13/0938

08/13/093908/13/093908/13/0939From the AZ STD's (2008)Perimeter: the sum of all lengths of a polygon.

Discuss08/13/094008/13/094008/13/0940ProgressionsProgressions:http://ime.math.arizona.edu/progressions/http://commoncoretools.files.wordpress.com/2012/07/ccss_progression_gm_k5_2012_07_21.pdf p.16.

Wolframalpha.com4/18/2013:

From the CCSS, Grade 3:What do we mean when we talk about measurement?Measurement08/13/0944Technically, a measurement is a number that indicates a comparison between the attribute of an object being measured and the same attribute of a given unit of measure.Van de Walle (2001)But what does he mean by comparison?MeasurementVan de Walle, J. (2001) Elementary School Mathematics : Elementary & Middle School Mathematics Teaching Developmentally.08/13/094508/13/0945How about this?Determine the attribute you want to measureFind something else with the same attribute. Use it as the measuring unit.Compare the two: multiplicatively.Measurement08/13/094608/13/0946

From Fractions and Multiplicative Reasoning, Thompson and Saldanha, 2003. (pdf p. 22)http://pat-thompson.net/PDFversions/2004FracsMultRsng.pdf 47Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriately tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.

Mathematic Practices from the CCSS/ACCRSWhich is a circle?

What is circumference?From the AZ STD's (2008)the total distance around a closed curve like a circleCircumference5208/13/0952So.... how do we measure circumference?Circumference5308/13/0953

The circumference is three and a bit times as large as the diameter.http://tedcoe.com/math/circumference54Tennis Balls

The circumference is about how many times as large as the diameter?

The diameter is about how many times as large as the circumference?08/13/095608/13/095656CircumferenceIf I double the RADIUS of a circle what happens to the circumference?

How many Rotations?What is an angle?Angles5908/13/0959Using objects at your table measure the angleAngles6008/13/0960What attribute are we measuring when we measure angles?Angles6108/13/0961

CCSS, Grade 4, p.31

tedcoe.comYou can download all of the geometry files from the week at tedcoe.com under STUFF

CCSS, p.89