Transcript The National Council of Supervisors of Mathematics

T1PM3
4th and 5th grade Math Institute
Focus on Geometry, Measurement and Data & The Eight Mathematical Practice
September 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 Standards
The Common Core State Standards for
Mathematics
Crosswalks from MDE
4th Grade Crosswalk
Link to All Crosswalks
Transition Plan
Assessment Plans
5th Grade Crosswalk
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
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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-lessonsnumerical-patterning/219-numerical-patterning-introduction-parta?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 twodimensional 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 twodimensional 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 Geometric
Thought
Level 0: Visualization
Description
See geometric shapes as a whole; does not focus on their particular
attribute
Example
A student would identify a square but would be unable to articulate
that it has four congruent sides with right angles.
Teacher Activity
Reinforce this level by encouraging students to group shapes
according to their similarities
Shape 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 Geometric
Thought
Level 1: Analysis
Description
Recognize that each shape has different properties; identify the
shape by that property.
Example
A 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.