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Daily Organizer MATH 2001 Fall 2017

Week 1: Angles: relationships and problem solving

Tuesday, August 15: Welcome to MATH 2001!

  • What is geometry?

  • What are angles and why do we have them?

  • What's a connection between angles and the eclipse next week?

  • What makes an angle big or small?

 

Thursday, August 17: If you have your book, please bring the class activities from section 10.1 to class.

  • Relating two ways to think about angles: Angle as two rays and the space between them; angle as an amount of turning

  • Angle at grade 4 in the Common Core

  • Making angles by folding paper and measuring angles with our paper "protractors"

  • Interesting angle relationships

    • angles formed by 2 lines in a plane

    • angles formed by 3 lines in a plane

    • can we explain these relationships?

 

CCSS Grade 4: An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

 

Week 2: Angles: relationships and problem solving 

 

Monday, August 21: Solar Eclipse! Woohoo, it was great!

 

Tuesday, August 22: Please bring the class activities from section 10.1 to class.

Interesting angle relationships:

  • angles formed by 2 lines in a plane: opposite angles

  • angles formed by 3 lines in a plane

  • can we explain these relationships?

 

Thursday, August 24: Please bring the class activities from section 10.1 to class.

  • Why do the angles in a triangle always add to 180 degrees?

  • What angle relationships can we discover when we walk around a triangle?

  • Angle problem solving

 

Week 3: Angles: relationships and problem solving 

 

Tuesday, August 29:   Please bring the class activities from section 10.1 to class.

  • Angle problem solving. Things we can use to help us solve angle problems:

    • The parallel postulate

    • Ideas about walking and turning

    • Add in extra lines

    • The sum of the angles in a triangle

 

Thursday, August 31:   Please bring the class activities from sections 10.1 and 10.2 to class.

  • Angle problem-solving

  • Eratosthenes method for determining the circumference of the earth.

 

Week 4: Defining, constructing, and classifying shapes: circles, triangles, quadrilaterals, polygons  

 

Tuesday, September 5:  Please bring the class activities from section 10.3 to class.

  • What are circles mathematically?

  • Using circles to solve problems

 

Thursday, September 7:  Please bring the class activities from section 10.4 to class.

  • How can we define and classify 2D shapes?

 

Week 5:  Defining, constructing, and classifying shapes: circles, triangles, quadrilaterals, polygons

 

Tuesday, September 12:  No class because of the storm. We will make up the class with an online assignment.

 

Thursday, September 14:  Please bring the class activities from section 10.4 to class.

  • How can we define and classify various 2D shapes?

    • We use properties to categorize shapes

    • A category of shapes can be defined in different ways, using different sets of properties

    • Categories of shapes can have subcategories.

 

Week 6: Defining, constructing, and classifying shapes: circles, triangles, quadrilaterals, polygons 

 

Tuesday, September 19:   Please bring the class activities from section 10.4 to class.

  • Using short lists of properties to define categories of shapes: square, rectangle, rhombus, parallelogram, trapezoid

  • Classifying shapes in a hierarchy based on properties of the shapes

  • Constructing shapes with a compass and ruler: triangles and rhombuses 

 

Thursday, September 21:  Please bring the class activities from section 10.4 to class.

  • Test discussion

  • Constructing shapes:

    • using a compass and straightedge

    • by folding and cutting paper

    • by walking and turning (think: programming a robot!) 

 

Week 7:  Measurement; Area: moving and additivity principles

 

Tuesday, September 26:   Please bring the class activities from sections 10.4 and 11.1 to class.

  • Constructing shapes

    • By folding and cutting paper

    • By walking and turning (think: programming a robot!)

  • Measurement and measurable attributes

  • What concepts are involved in length measurement?

 

Thursday, September 28: Please bring the class activities from section 11.1 to class.

  • Measurement and measurable attributes

  • What concepts are involved in length measurement?

  • What concepts are involved in area measurement?

  • Why can we find the area of a rectangle by multiplying two side lengths?

 

Week 8: Explaining and solving problems about area  

 

Tuesday, October 3:   Please bring the class activities from section 12.1 to class.

  • Area of a rectangle

    • By counting squares

    • Why can we find the area of a rectangle by multiplying two side lengths?

  • The moving and additivity principles about area

    • Applying the principles to determine areas

 

Thursday, October 5:  Please bring the class activities from section 12.3 to class.

  • Finding areas of triangles in progressively sophisticated ways

  • Choosing the base and height of a triangle

  • Explaining why the area formula for triangles is valid

 

Week 9: Explaining and solving problems about area    

 

Tuesday, October 10:  Please bring the class activities from section 12.3 to class.

  • Explaining why the area formula for triangles is valid

  • Area problem solving

 

Thursday, October 12:  Please bring the class activities from sections 12.3 and 12.4 to class.

  • Area problem solving

  • Areas of parallelograms

    • Why is there no formula for the area of a parallelogram that is only in terms of side lengths?

    • Developing and explaining an area formula for parallelograms and trapezoids

 

Week 10: Area of parallelograms, trapezoids, circles;  

 

Tuesday, October 17:   Please bring the class activities from sections 12.4 and 12.6 to class.

  • Areas of parallelograms and trapezoids

    • Developing and explaining area formulas for parallelograms and trapezoids

    • Using a paper towel roll to explain the area of a parallelogram!

  • How are the circumference and diameter of a circle related?

 

Thursday, October 19:  Please bring the class activities from sections 12.6 to class.

  • Where does the area formula for circles come from?

  • Area problem solving

  • How can we find the area of an irregular shape?

 

Week 11: Perimeter versus area; The Pythagorean theorem; 

 

Tuesday, October 24:  Please bring the class activities from sections 12.7 and 12.8 to class. 

  • Do we want some “group quizzes” instead of a third test??

  • Test discussion

  • How can we find the area of an irregular shape?

  • Area versus perimeter

 

Thursday, October 26:  Please bring the class activities from sections 12.8 and 12.9 to class.

  • How are perimeter and area related for rectangles?

  • How are perimeter and area related for 2D shapes more generally?

  • Using area to find the side lengths of “tilted squares”

  • Group quiz

 

FALL BREAK Friday, October 27

 

Week 12: The Pythagorean theorem; Solid shapes: prisms, pyramids, cylinders, cones   

 

Tuesday, October 31:  BOO!!!! Please bring the class activities from section 12.9 to class.

  • Homework comment: r squared versus 2r

  • Group quiz (finish)

  • Using area to find the side lengths of “tilted squares”

  • Where does the Pythagorean theorem come from? Why is it true?

 

Thursday, November 2:  Please bring the class activities from sections 13.1 and 13.2 to class.

  • Some basic 3D shapes: prisms, cylinders, pyramids, cones.

    • What are they?

    • What features do they have?

    • How can we make them?

 

Week 13: Volume: developing formulas, problem solving 

 

Tuesday, November 7:  Please bring the class activities from section 13.3 to class.

  • Next week's schedule. Group quizzes next week?

  • Volumes of prisms

  • Volumes of pyramids

  • Volume problem solving

  • Volume versus surface area

 

Thursday, November 9:  Please bring the class activities from sections 13.3 and 13.4 to class.

  •  Volume problem solving

  • Volume versus surface area

 

Week 14:  Surface area and patterns/nets

 

Tuesday, November 14: Please bring the class activities from section 13.2 to class.

  • Problem solving with patterns and surface area of prisms, pyramids, and cylinders

  • Group quiz

 

Thursday, November 16:  Please bring the class activities from section 13.2 to class.

  • Problem solving with patterns, surface area, and volumes of cones

  • Group quiz

 

THANKSGIVING BREAK: November 20 - 24

 

Week 15: Reasoning about similarity  

 

Tuesday, November 28:  Please bring the class activities from section 14.5 to class.

  • Similarity: mathematical similarity versus similarity in everyday language

  • How can we reason to solve problems about similar shapes?

Geogebra sketch: scaling in two directions  https://ggbm.at/xAzE2Azi

  • a few more minutes on the group quiz

 

Thursday, November 30:  Last day of class. Bring your questions. We will review material based on your question.  

 

Week 16: Review   

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