Download common core math standards

COMMON CORE MATH STANDARDS
Grade 7 & 8 Math Curriculum
Compacted Vs. Standard
Objective
To provide a standards-based math program
to meet the needs of all learners in order that:
All students will build a strong foundation in
mathematics at a pace which develops each
student’s mathematical understanding and ability
to apply concepts to problems;
All students will demonstrate at least grade level
proficiency on Common Core Assessments.
Key Changes
New standards provide focus and coherence
New framework highlights the Standards for
Mathematical Practices
New content standards rely on mastery of
prior content to ‘Push Down’ curriculum
2000-2011 MA State Frameworks
5 Strands carried throughout each year
Number Sense and Operations
Patterns, Relations and Algebra
Geometry
Measurement
Data Analysis, Statistics and Probability
Common Core Standards
PK-8
Common Core Standards 9-12
The high school standards are listed in conceptual
categories:
Number and Quantity (N)
Algebra (A)
Functions (F)
Modeling ()
Geometry (G)
Statistics and Probability (S)
Standards for Mathematical Practices
Make sense of problem solving and persevere in solving
them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of
others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
New content standards rely on mastery of prior content to
‘Push Down’ curriculum
What is ‘Push Down’
Introduction of new material
higher level thinking skills
Movement from concrete to abstract thinking
Mathematical Modeling
Examples of ‘Push Down’
New to Grade 7:
Use proportional relationships to solve multi-step ratio and percent
problems.
Understand that rewriting an expression in different forms in a
problem context can shed light on the problem and how the
quantities in it are related.
Solve word problems leading to inequalities of the form px + q > r or
px + q < r, where p, q, and r are specific rational numbers. Graph the
solution set of the inequality and interpret it in the context of the
problem.
Describe the two-dimensional figures that result from slicing three-
dimensional figures, as in plane sections of right rectangular prisms
and right rectangular pyramids.
Examples of ‘Push Down’
New to Grade 8
Solve linear equations with rational number coefficients, including
expanding expressions using the distributive property and collecting
like terms.
Solve systems of two linear equations in two variables algebraically,
and estimate solutions by graphing the equations.
Compare properties of two functions each represented in a different
way (algebraically, graphically, numerically in tables, or by verbal
descriptions).
Use informal arguments to establish facts about geometric properties
Know that straight lines are widely used to model relationships between
two quantitative variables. For scatter plots…informally fit a straight
line, and informally assess the model fit by judging the closeness of
the data points to the line.
Examples of ‘Push Down’
New to Algebra 1
Extend the properties of exponents to rational exponents.
Use properties of rational and irrational numbers.
Interpret the structure of expressions including linear, quadratic and exponential
expressions
Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically.
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for
specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using
technology.
Distinguish between situations that can be modeled with linear functions and with
exponential functions.
Use the mean and standard deviation of a data set to fit it to a normal distribution and
to estimate population percentages.
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Challenge: Pacing
‘Pushing Down’ curriculum impacts
instructional pacing
Student readiness
Importance of strong foundation
Grade 7 and 8 Presently
7th grade
8th grade
9th grade
Grade 7 Math
Algebra 1
Geometry
Grade 7 Math
Grade 8 Math
Algebra 1
Grade 7 Presently
Grade 7 Curriculum presently assumes all
students are ready for High School Level
Math in Grade 8
Grade 7 & 8 Standards are Compacted
5 Strands
39 Standards
Grade 8 Presently
Grade 8 (based on gr. 7 performance) has two
course offerings:
Algebra 1 (approx. 80% of students)
5 Strands
19 Standards
Grade 8 Math
5 Strands
9 Standards
Review of Grade 8
Grade 7 and 8 Moving Forward
7th grade
Compacted
Grade 7 Math
Standard
Grade 7 Math
8th grade
9th grade
Algebra 1
Geometry
Standard
Grade 8 Math
Algebra 1
Grade 7 Standard Curriculum
25 Content Standards
Unit 1: Rational Numbers
Unit 2: Proportionality and
Linear Relationships
Unit 3: Introduction to Sampling
and Inference
Unit 4: Creating, Comparing,
and Analyzing Geometric
Figures
Compacted Curriculum
40 Content Standards
Unit 1: Rational Numbers and
Exponents (6 additional standards)
Unit 2: Proportionality and Linear
Relationships (3 additional
standards)
Unit 3: Introduction to Sampling
and Inference (no additional
standards)
Unit 4: Creating, Comparing, and
Analyzing Geometric Figures
(6 additional standards)
Grade 8 Standard Curriculum
28 Content Standards
(grade 8)
Unit 1: Formulating, Reasoning
and Modeling with Linear
Equations
Unit 2: Linear Functions
Unit 3: Patterns of Association
with Bivariate Data
Unit 4: Creating, Comparing, and
Analyzing Geometric Figures
Unit 5: Expressions and
Equations
Compacted Curriculum
63 Content Standards
(13 grade 8 and 50 Alg 1)
Unit 1: Relationships between
Quantities and Reasoning with
Equations
Unit 2: Linear and Exponential
Functions
Unit 3: Descriptive Statistics
Unit 4: Expressions and
Equations
Unit 5: Quadratic Functions and
Modeling
Grade 9
• Algebra 1
• 50 Content Standards
• Geometry
• 44 Content Standards
• Unit 1: Relationships between
• Unit 1: Congruence, Proof, and
•
•
•
•
Quantities and Reasoning with
Equations
Unit 2: Linear and Exponential
Functions
Unit 3: Descriptive Statistics
Unit 4: Expressions and Equations
Unit 5: Quadratic Functions and
Modeling
•
•
•
•
•
Constructions
Unit 2: Similarity, Proof, and
Trigonometry
Unit 3: Extending to Three
Dimensions
Unit 4: Connecting Algebra and
Geometry Through Coordinates
Unit 5: Circles With and Without
Coordinates
Unit 6: Applications of Probability
Placement Process
Inform Parents/Guardians
Course Descriptions
Placement Process-3 Parts
Teacher Recommendation
Preliminary Math MCAS Score
Grade Level Cumulative Exam Score
Placement Recommendations
Late June via letter to Parents
Parent choice to Opt out of Recommendation
Students are evenly distributed among grade level teams
Math placement does not effect any other subject area
Let’s Revisit the Objective
To provide a standards-based math program
to meet the needs of all learners in order that:
All students will build a strong foundation in
mathematics at a pace which develops each
student’s mathematical understanding and ability
to apply concepts to problems;
All students will demonstrate at least grade level
proficiency on Common Core Assessments.
What Does Placement in the
Standard Course Mean Long Term?
Gr 7 Standard Course & Gr 8 Standard Course
High School Algebra 1, Geometry, Algebra 2, PreCalculus
Or
Summer Program between grade 7 & 8 for students who have
demonstrated ability to master content quickly
Taking HS Geometry and Algebra 2 simultaneously in Gr 10, gr 11
PreCalculus, gr 12 Calculus
Adaptations as needed-
Overall: Strong Foundation, Content Mastery, Confidence, Success
What Does Placement in the
Compacted Course Mean Long Term?
Gr 7 Compacted Course & Gr 8 Compacted Algebra 1 Course
High School Geometry, Algebra 2, PreCalculus, Calculus
Adaptations as needed-
Overall: Strong Foundation, Content Mastery, Confidence, Success