Class 4:Part 1

Common Core State Standards (CCSS) ClassApril 4, 2011

Reading – Chapter 8 Implementing Talk in the Classroom: Getting Started

Five Principals of Productive Talk

Principle 1: Establishing and Maintaining a Respectful, Supportive Environment

Principle 2: Focusing Talk on the Mathematics

Principle 3: Providing for Equitable Participation in Classroom Talk

Principle 4: Explaining Your Expectations About New Forms of Talk

Principle 5: Trying Only One Challenging New Thing at a Time

Journal Review by Your PeersRead and react to each other’s journal entries

about the five principals of productive talk

Use Post-it-Notes to record your comments in each journal

Pass the journals to the right until you get your own journal back

Discuss as a group – What stands out after reading all the journals?

Learning IntentionsWe Are Learning To …

Understand the Common Core State Standards Alignment Task

Reflect on how the mathematical tasks we select address the Standards for Mathematical Practice and Content Standards

Success CriteriaWe will know we are successful when we can explain to others the Common Core State Standards Alignment Task and when we can identify the Standards for Mathematical Practice and Content Standards in the mathematical tasks we teach.

Common Core State Standards Alignment Task 3

Present your completed Task 3 to the teachers at your table, briefly reviewing the task and student work.

Why did you select the task you did?

What did the students’ work reveal?

What did you see and hear when your students worked on this task?

Common Core Alignment Task 3

Discuss differences/ similarities between the three tasks in relation to the Standards for Mathematical Practices.

Final ProjectReview CCSS Project

Questions about expectations?

Developing Geometric Reasoning:

Grades 3-5 Common Core State Standards (CCSS)

Learning IntentionsWe Are Learning To:

Examine how students’ understanding of geometry develops through defined stages, the van Hiele Model.

Consider implications for instruction to move students along in developing their geometric reasoning.

Compare, contrast, and connect properties of quadrilaterals.

Success CriteriaWe will know we are successful when we can

articulate how Mathematical Practice Standards 1, 2 and 5—sense making, reasoning, and tools—are infused in mathematical tasks or lessons for a standards’ content progression.

Wisconsin Common Core Standards

Domain

Cluster

Standards

Content strand across grades: Geometry

“Big Idea” that groups together a set of related standards.

Statements that define what students should understand and be able to do at a grade level.

A Content Standards Progression

Domain: Geometry

Clusters:

3: Reason with shapes and their attributes

4: Draw and identify lines and angles, and classify shapes by properties of their lines and angles

5: Classify 2-dimensional figures into categories based on their properties

Standards: 3.G.1, 3.G.2, 4.G.1, 4.G.2, 4.G.3, 5.G.3, 5.G.4

van Hiele Levels of Geometric Reasoning

Level 0: Visualization Recognize figures as total entities, but do not recognize properties.

Level 1: Analysis (Description) Identify properties of figures and see figures as a class of shapes.

Level 2: Informal Deduction Formulate generalizations about relationships among properties of shapes; Develop informal explanations.

van Hiele Levels of Geometric Reasoning

Level 3: Deduction Understand the significance of deduction as a way of establishing geometric theory within an axiom system. See interrelationship and role of undefined terms, axioms, definitions, theorems and formal proof. See possibility of developing a proof in more than one way.

Level 4: Rigor Compare different axiom systems (e.g., non-Euclidean geometry). Geometry is seen in the abstract with a high degree of rigor, even without concrete examples.

How do students progress in developing geometric reasoning?How would you recognize each of these levels of

thinking in your students’ work?

Considering the first three levels, where would you place the majority of the lessons that you teach?

“I believe that development is more dependent on instruction than on age or biological maturation and that types of instructional experiences can foster, or impede, development.”

Pierre M. van Hiele

Quadrilateral Sorting Activity

Facilitator: Give all a voice. Recorder: Take notes on recording sheet.

Directions

1. Remove a card from the envelope.

2. Sort the quadrilateral shapes by the directions on the card.

3. Record the sort and discussion on the recording sheet.

4. Push all of the shapes back into a pile.

5. Pass the envelope to the left and repeat steps 1–4 with the next card.

Property CriteriaProperty Criteria

• all right angles • at least one right angle

• both pairs of opposite sides congruent

• both pairs of opposite sides parallel

• both pairs of opposite angles congruent

• congruent diagonals • diagonals bisect each other

• at least one pair of parallel sides

• exactly one pair of parallel sides

What is a Trapezoid?Some authors choose to define trapezoid as a

quadrilateral with at least one pair of parallel sides.

That definition is more inclusive and leads to the conclusion that all parallelograms are trapezoids.

Trapezoid definitionsEveryday Math Expressions Scott Foresman

A quadrilateralthat has exactlyone pair of parallel sides

(K & 1st)A quadrilateral withat least one pair ofparallel sides.

(5th)A quadrilateral withone pair of parallelsides.

(3rd & 4th)A quadrilateralwith only one pairof parallel sides.

(5th)A quadrilateralthat has exactlyone pair ofparallel sides

Maybe by Middle School?CMP Glencoe Holt

A quadrilateralwith at least onepair of oppositesides parallel.

(6th) A quadrilateralwith one pair ofopposite sidesparallel.

(7th) A quadrilateralwith one pair ofparallel sides.

(8th) A quadrilateralwith exactly onepair of parallelopposite sides.

A quadrilateralwith exactly onepair of parallelsides.

Parallelogram DefinitionsEveryday Math Expressions Scott Foresman

•A quadrilateral with two pairs of parallel sides.

•Opposite sides of aparallelogram arecongruent.

•Opposite angles ina parallelogram have the same measure.

(K-2nd)A quadrilateral in which both pairs of opposite sides are parallel andopposite angles arecongruent.

(3rd-5th)A quadrilateralwith both pairs ofopposite sidesparallel.

(3rd & 4th)A quadrilateral in which opposite sides are parallel.

(5th)A quadrilateral with both pairs of opposite sidesparallel.

True or FalseA square is

a special kind of rectangle.

It is a rectangle in which all four sides are the same length

A parallelogram is

a special kind of trapezoid.

It is a trapezoid with two pairs of parallel sides.

True or FalseA rhombus

is a special kind of kite.

It is a kite in which all four sides are the same length.

ReflectHow do these tasks engage you in the content

learning infused with practices? (Mathematical Practices Standards 1, 2, 5)

How do these tasks help you to better understand the mathematics?

Standards: 3.G.1, 3.G.A, 4.G.1, 4.G.2, 4.G.3, 5.G.3, 5.G.4

Big Ideas of GeometryTwo- and three-dimensional objects can be

described, classified and analyzed by their attributes.

Objects can be oriented in an infinite number of ways. The orientation of an object does not change the other attributes of the object.

Some attributes of objects (e.g. area, volume, perimeter, surface area) are measurable and can be quantified using unit amounts.

Objects can be constructed from or decomposed into other objects. In particular, any polygon can be decomposed into triangles.

Development Through the van Hiele Levels

Level is not affected by biological age.

Level is affected by degree of experience.

In order to progress through the levels, instruction must be sequential and intentional.

When instruction (or materials or vocabulary, etc.) is at an inappropriate level, students will not be able to understand the instruction. They may be able to memorize it, but with no understanding of material.

What other

practices were

infused in the

content learning?

Provide specific

examples.

SummaryWe were learning to recognize three of the Standards for Mathematical Practices—sense making, reasoning, and tools— within a chosen Content Standards progression.

We will know we are successful when we can articulate how both a Content Standard and a Standard for Mathematical Practice are infused in a math lesson in the classroom.