Transcript LCHS Auditorium

Math at La Cañada H.S.
LCHS AND THE NEW COMMON CORE STANDARDS —PARADIGM SHIFT
21st century workforce skills, the Common Core
State Standards and the changing assessments
Fortune 500 Survey On Needed Workforce Skills
Critical Thinking/Problem Solving
Oral and written communication
Teamwork/Collaboration
Diversity
Information Technology Application
Leadership
Creativity/Innovation
Lifelong Learning/Self-direction
Professionalism/Work ethic
Ethics/Social Responsibility
10th grade CST Geometry Standard:
Common Core State Standards for Mathematics:
10.0 Students compute areas of
polygons, including rectangles,
scalene triangles, equilateral
triangles, rhombi, parallelograms,
and trapezoids.
6.G.1 Find the area of right triangles, other triangles, special
quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these techniques in
the context of solving real-world and mathematical problems.
9.0 Students compute the volumes
and surface areas of prisms,
pyramids, cylinders, cones, and
spheres; and students commit to
memory the formulas for prisms,
pyramids, and cylinders
7.G.6 Solve real-world and mathematical problems involving area,
volume and surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
G-GMD.1 Give an informal argument for the formulas for the
circumference of a circle, area of a circle, volume of a cylinder, pyramid,
and cone. Use dissection arguments, Cavalieri’s principle, and informal
limit arguments.
G-GMD. 4 Identify the shapes of two-dimensional cross-sections of
three-dimensional objects, and identify three- dimensional objects
generated by rotations of two-dimensional objects.
Grade 11 Common Core Performance
Task – Math
Speeding Tickets
New York state wants to change its system for assigning speeding fines to drivers. The current
system allows a judge to assign a fine that is within the ranges shown in Table 1.
Table 1. New York Speeding Fines
Table 2. Massachusetts Speeding Fines
Miles per Hour over
Speed Limit
Minimum Fine
Miles per Hour over
Speed Limit
Fines
1-10
$45
1-10
$100 flat charge
11-30
$90
11 or more
31 or more
$180
$100 flat charge plus
$10 for each additional
mph above the first 10
mph
Performance Task Continued
Some people have complained that the New York speeding fine system is not fair. The New
Drivers Association (NDA) is recommending a new speeding fine system. The NDA is studying the
Massachusetts system because of the claims that it is fairer than the New York system.
In this task, you will:
Analyze the speeding fine systems for both New York and Massachusetts.
Use data to propose fairer speeding fine system for New York.
Sample Problem with Performance Task
Sample Problem – Algebra
Sample Problem - Geometry
Implementation
of the CCSS
Requires
Time
Resources
Patience
Perseverance
The Common
Core State
Standards
We have a
script for a
different
play…
The Common
Core State
Standards
Actors and
Directors need
training like…
The Key to Drive Successful
Implementation
Teacher
Professional
Development and
On-Going Support
Teachers Development Group (TDG)
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them
…start by explaining the meaning of a problem and looking for entry points to its solution
2. Reason abstractly and quantitatively
…make sense of quantities and their relationships to
problem situations
3. Construct viable arguments and critique the reasoning of others
…understand and use stated assumptions, definitions, and previously established results in
constructing arguments
4. Model with mathematics
…can apply the mathematics they know to solve problems arising in everyday life, society, and
the workplace
2011 © CA County Superintendents Educational Services Association
Standards for Mathematical Practice
5. Use appropriate tools strategically
…consider the available tools when solving a
mathematical problem
6. Attend to precision
…communicate precisely using clear definitions and calculate accurately and efficiently
7. Look for and make use of structure
…look closely to discern a pattern or structure
8. Look for and express regularity in repeated reasoning
…notice if calculations are repeated, and look for both general methods and for shortcuts
2011 © CA County Superintendents Educational Services Association
Regularity
Patterns
Structure
MAKE
SENSE
JUSTIFY
Mathematical
Representation
Connections
Mistakes and
Stuck Points
Metacognit
ion and
Reflection
Persevere and
Seek More
GENERALIZE
MATHEMATICAL HABITS OF MIND
MATHEMATICAL
HABITS OF
INTERACTION
Private
Reasoning
Time
Explain
Listen to
Understand
Genuine
Questions
Fixed Mindset vs. Growth Mindset
Carol Dweck
Fixed Mindset
Growth Mindset
Believe that ability is fixed Believe that math
and being good at math is a “smartness” grows with
“gift”
hard work
18
How to help your child at home
Your job is to help your child move towards an answer, not solve the
problem for him or her.
Have your child explain to you how he or she is thinking and reasoning
about the problem.
Let them grapple.
Resist the temptation to rescue your child.
Praise your child for qualities they can control like effort and
perseverance.
How to help your child at home
Ask open-ended questions:
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“Explain your thinking.”
“How do you know?”
“What confuses you?”
“What do you understand?”
“What do you know about the problem?”
“What are you being asked to do?”
“If your math teacher were here, what would he or she say?”
“What ideas do you have for solving the problem (i.e.
drawing, using manipulatives, role playing, etc.)
Source: Some of the slides have been taken from Torrey Pines Elementary School’s Math Night Presentation.
Implementation
of the CCSS
Requires
Community,
Students,
Teachers, Staff
coming
together