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.
Paradigm Shift in Core Subject Areas –
Student Cognitive Demand: CCSS vs. CCS
CCSS
CCS
Explore
Identify
Master
Simplify
Analyze and explain
Solve
Interpret and translate
Verify
Extend
Add, subtract, multiple, and divide
Compare and contrast
Determine
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
The Key to Drive Successful
Implementation
Teacher
Professional
Development and
On-Going Support
Teachers Development Group (TDG)
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
12
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
How will the Implementation of Common
Core Impact Math Pathways at LCHS ?
Why we chose the Traditional Pathway?
◦Freedom from the state to go with either pathway
◦Teacher Input
◦Lack of quality CCSS aligned textbooks
◦No data available on either pathway
Math Readiness Is The Goal
Current math standards emphasize deep understanding of concepts,
application of skills and solving novel (non-routine) problems.
Basic math computation, memorization of formulas, plugging numbers into
equations to derive an answer do not prepare students for advanced level
math courses in high school and beyond.
Providing opportunities to every student to access calculus by her/his senior
year
Overview of LC Math Pathways 2015-16
7th Grade
7th
8th Grade
8th
Algebra 1
9th Grade
Geometry
Honors
LC Math 1
Advanced
7th Grade
CCSS
10th Grade
Algebra II/Trig. H
LC Math 2
Advanced
11th Grade
Pre-Calc.
Honors
LC Math 3
Advanced
12th Grade
AP
Calculus
BC
AP Calculus
AP Statistics
8th Grade CCSS
LC Math 1
Applied
Statistics
LC Math 2
LC Math 3
Other 4th
Course
College Preparatory Pathway
7th Grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
7th Grade
CCSS
8th Grade
CCSS
LC Math 1
LC Math 2
LC Math 3
Advanced
Math
• KEY GOAL: Students master the CCSS curriculum by 11th grade and complete a 4th
course in math in their senior year.
• 7th and 8th grade build solid foundations in basic math and the SMPs
• Students can choose this pathway entering 9th grade but can still access the
Advanced Pathway by taking summer school after 9th grade
LC Math 1 – Subject Content
Semester 1 Essential Course Content :
Quarter 1
Quarter 2
Introduction to variables, quantities,
functions, and equations
Graph linear functions
Properties of real numbers
Apply rate of change and slope to
describe linear function behavior
Solving linear equations and inequalities
Analyze lines of best fit and linear
regression
Problem solving with systems of linear
equations and inequalities
Advanced College Preparatory Pathway
7th Grade
7th
8th Grade
8th
Algebra 1
9th Grade
LC Math 1
Advanced
10th Grade
11th Grade
LC Math 2
Advanced
LC Math 3
Advanced
12th Grade
AP or
College
Course
• KEY GOAL: 7th and 8th grade build solid foundations in basic math and SMPs
• 8th grade curriculum contains about 60% of former Algebra I curriculum
• This contains CCSS Algebra I, Geometry and Algebra II covering 50% of traditionally PreCalculus topics --statistics and probability, basic function analysis and advanced
trigonometry
LC Math 1 Advanced – Key Concepts
1st Course in 9-12 Math Compaction
Includes Algebra I plus Algebra II and Pre-Calculus Concepts
1st Course in Pathway that concludes in Advanced Placement Calculus
Takes key course concepts of LC Math 1 and expands upon them – 2 Examples
 LC Math 1 will study linear, quadratic and exponential functions
 LC Math 1 Advanced begin with these and adds learning about radical and
polynomial functions
 Analysis of exponential and quadratic functions, with real and non-real
solutions.
LC Math 1 Advanced – Subject Content
Quarter 1 Essential Course Content :
Quarter 1
Introduction to variables, quantities,
functions, and equations
Apply rate of change and slope to describe
linear function behavior
Properties of real numbers
Analyze lines of best fit and linear
regression
Graphing and solving linear functions,
equations and inequalities
Problem solving with systems of linear
equations and inequalities
Overview of LC Math Pathways – 2019-2020
7th Grade
CC Math 7
Advanced
8th Grade
9th Grade
11th Grade
12th Grade
CC Math 8
Advanced
LC Math 1
Advanced
CC Math 7
10th Grade
LC Math 2
Advanced
LC Math 3
Advanced
CC Math 8
AP Calculus
AP
Statistics
LC Math 1
LC Math 2
LC Math 3
Applied
Statistics
Other 4th
Course
Next Steps
Select teachers to teach the courses
Work with the consultant to design the pacing guides and
assessments for these courses
Align Science course descriptions to reflect changes in math
sequencing
Continue to communicate with students and their families on math
pathways
If You Are Considering Summer School…
Math in Summer School –Intensive Study
Options available to students
High School Credits earned through Summer School