T1PM3

4th and 5th grade Math Institute

Focus on Geometry, Measurement and Data & The Eight Mathematical PracticeSeptember 27, 2011

Welcome

• Introductions• Overview of Course

Goals

• To explore the Standards for Content and Practice.

• Consider how the CCSS Standards are likely to impact your mathematics program and to plan next steps.

• Organize and Practice games for use in the classroom

Common Core State Standards

Mathematics

• Standards for Content• Standards for Practice

Common Core Standards for Student Success

• Video Link

Common Core State Standards

Video Link

Looking at the Content Standards

The StandardsThe Common Core State Standards for Mathematics

Crosswalks from MDE4th Grade Crosswalk 5th Grade Crosswalk

Link to All Crosswalks

Transition Plan Assessment Plans

Number Talk

• 4.OA.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.

• 5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

• 5.G.1 and 5.G.2 Graph points on the coordinate plane to solve real world and mathematical problems.

Number Talk: Guess My Rule

InX

Outy

Number Talk: Guess My Rule

InX

Outy

10 27

9 24

8 21

7 18

6 15

5 12

4 9

3 6

2 3

1 0

0 -3

Standards for Mathematical Practice

1. Individually review the Standards for Mathematical Practice.

2. Choose a partner at your table and discuss a new insight you had into the practices, then discuss the following question:

What implications might the standards of mathematical practice have on your classroom?

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of

others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

Common Core State Standards for Mathematical Practice

In our work, we will examine the eight Standards for Mathematical Practice through a classroom vignette.

Consider:What is the nature of mathematical tasks in these classrooms?

What do you hear or see in a mathematics classroom that is working to build the Standards for Mathematical Practice?

Link to Video

The Button Task

Gina plays with her Grandmother’s collection of black and white buttons. She arranges them in patterns. Her first three patterns are shown below.

Pattern 1 Pattern 2 Pattern 3 Pattern 4

1. Draw Pattern 4 next to Pattern 3.

2. How many white buttons does Gina need for Patterns 5 and 6? Explain how you figured this out.

3. 3. How many buttons in all does Gina need to make Pattern 11?

Using Formative Assessment to Plan Instruction

Learner A

What does Learner A see staying the same? What does Learner A see as changing? Draw a picture to show how Learner A sees this pattern growing through

the first 3 stages. Color coding and modeling with square tiles may come in handy.

Using Formative Assessment to Plan Instruction

Learner B

What does Learner B see staying the same? What does Learner B see as changing? Draw a picture to show how Learner B sees this pattern growing through

the first 3 stages. Color coding and modeling with square tiles may come in handy.

www.Inside Mathematics.org

• http://insidemathematics.org/index.php/classroom-video-visits/public-lessons-numerical-patterning/219-numerical-patterning-introduction-part-a?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8

Exploring Standards for Mathematical Practice in a Classroom

• What mathematical practices did you see in this classroom?

• What evidence do you see that students are building this standard of practice?

Planning and Teaching to Develop Standards for Mathematical Practice

• What instructional decisions did the teacher make that seemed to support the development of Standards for Mathematical Practice for students?

Leading to Develop Standards for Mathematical Practice

Reflect on the status of your district/site in developing Standards for Mathematical Practice with respect to:• Students• Instructional decisions in

classrooms• The nature of instructional and

assessment materials• Collegial conversations• Professional development

Next steps and resources

• Review the implications you listed earlier, then discuss with your table group one or two next steps you might take as a district, school, and teacher.

Geometry

4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Assessment Code: 301, 308, DOK 1

4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

DOK 1 & 2

4.G.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Assessment Code: 301, 308, DOK1

Geometry

Classify two-dimensional figures into categories based on their properties.5.G.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

DOK 1 & 2

5.G.4. Classify two-dimensional figures in a hierarchy based on properties.

DOK 1&2

Van Hiele Levels of Van Hiele Levels of Geometric ThoughtGeometric Thought

Level 0: Visualization

DescriptionSee geometric shapes as a whole; does not focus on their particular attribute

ExampleA student would identify a square but would be unable to articulate that it has four congruent sides with right angles.

Teacher ActivityReinforce this level by encouraging students to group shapes according to their similarities

Shape SortShape Sort

van Hiele

• This is a level 0 activity because students are operating on shapes they see in front of them.

• These shapes may “change” or have different properties as they are rearranged or rotated.

The object of this activity is to begin to see that there are likenesses and differences in shapes.

Geometry

Game: Polygon Capture

van Hiele Levels of van Hiele Levels of Geometric ThoughtGeometric Thought

Level 1: Analysis

DescriptionRecognize that each shape has different properties; identify the shape by that property.

ExampleA student is able to identify that a parallelogram has two pairs of parallel sides, and that if a quadrilateral has two pairs of parallel sides it is identified as a parallelogram.

The products of thought at level 1 are the properties of shapes.

Goals

• To explore the Standards for Content and Practice.

• Consider how the CCSS Standards are likely to impact your mathematics program and to plan next steps.

• Organize and Practice games for use in the classroom

Reflections

1. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain.

2. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain.