Kennedy Middle School
Wilson Middle School
Family Math Night
November 15, 2012
7:00 PM – 8:30 PM
@WMS Auditorium
Evening Overview
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Overview of Evening
NPS Middle School Mathematics Programming
Transition to Common Core
Grade Level Expectations and Content
Math Placement Process
Options for classes/levels and High School
Grade Level Investigation Experiences
Q&A
Middle School Mathematics
• A comprehensive approach to:
• learn the concepts behind mathematical operations
• build mathematical understanding, number fact fluency,
and algebraic thinking
• incorporate all eight Standards for Mathematical Practice
to support comprehensive mathematics learning
• incorporate traditional skill building
• build a platform for success in high school coursework in
algebra and geometry
Provide students with a solid foundation of middle school math
skills for future high school and college study
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.
Grade 5 Overview
Operations and Algebraic Thinking
• Write and interpret numerical expressions.
• Analyze patterns and relationships.
Number and Operations in Base Ten
• Understand the place value system.
• Perform operations with multi-digit whole numbers and
with decimals to hundredths.
Number and Operations – Fractions
• Use equivalent fractions as a strategy to add and subtract
fractions.
• Apply and extend previous understandings of
multiplication and division to multiply and divide fractions.
Grade 5 Overview continued
Measurement and Data
• Convert like measurement units within a given
measurement system.
• Represent and interpret data.
• Geometric measurement: understand concepts of
volume and relate volume to multiplication and to
addition.
Geometry
• Graph points on the coordinate plane to solve realworld and mathematical problems.
• Classify two-dimensional figures into categories based
on their properties.
Grade 6 Overview
Ratios and Proportional Relationships
• Understand ratio concepts and use ratio reasoning to
solve problems.
The Number System
• Apply and extend previous understandings of
multiplication and division to divide fractions by
fractions.
• Multiply and divide multi-digit numbers and find
common factors and multiples.
• Apply and extend previous understandings of
numbers to the system of rational numbers.
Grade 6 Overview continued
Expressions and Equations
• Apply and extend previous understandings of arithmetic to
algebraic expressions.
• Reason about and solve one-variable equations and
inequalities.
• Represent and analyze quantitative relationships between
dependent and independent variables.
Geometry
• Solve real-world and mathematical problems involving
area, surface area, and volume.
Statistics and Probability
• Develop understanding of statistical variability.
• Summarize and describe distributions.
Grade 7 Overview
Ratios and Proportional Relationships
• Analyze proportional relationships and use them to
solve real-world and mathematical problems.
The Number System
• Apply and extend previous understandings of
operations with fractions to add, subtract, multiply,
and divide rational numbers.
Expressions and Equations
• Use properties of operations to generate equivalent
expressions.
• Solve real-life and mathematical problems using
numerical and algebraic expressions and equations.
Grade 7 Overview continued
Geometry
• Draw, construct and describe geometrical figures and
describe the relationships between them.
• Solve real-life and mathematical problems involving
angle measure, area, surface area, and volume.
Statistics and Probability
• Use random sampling to draw inferences about a
population.
• Draw informal comparative inferences about two
populations.
• Investigate chance processes and develop, use, and
evaluate probability models.
Grade 8 Overview
The Number System
• Know that there are numbers that are not rational,
and approximate them by rational numbers.
Expressions and Equations
• Work with radicals and integer exponents.
• Understand the connections between proportional
relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of
simultaneous linear equations.
Functions
• Define, evaluate, and compare functions.
• Use functions to model relationships between
quantities.
Grade 8 Overview continued
Geometry
• Understand congruence and similarity using physical
models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem.
• Solve real-world and mathematical problems
involving volume of cylinders, cones and spheres.
Statistics and Probability
• Investigate patterns of association in bivariate data.
Accelerated Mathematics In Middle School
• New “compacted” pathways for Grade 7, Grade 8, and the Model Algebra I
course could be compressed into an accelerated pathway for students in
grades 7 and 8, allowing students to enter the Model Geometry course in
grade 9.
• Selection and placement of students into accelerated opportunities must
be done carefully in order to ensure success.
• The compacted pathway is advanced work at an accelerated pace.
Students placed into the these courses will be challenged by significantly
more rigorous standards in a compressed time frame as they will master
all the grade 7, grade 8 and algebra standards within 2 years instead of 3
years.
• The Department of Education recommends that placement decisions be
made based upon common assessments to be reviewed by a team of
stakeholders that includes teachers and instructional leadership.
• Natick has a comprehensive placement process in place:
• Iowa Algebra Readiness, MCAS, Teacher-created assessments, Teacher
recommendation
Common Core Recommendations for Middle School
Acceleration
• Compacted courses should include the same Common
Core State Standards as the non-compacted courses.
• Decisions to accelerate students into the Common Core
State Standards for high school mathematics before ninth
grade should not be rushed.
• Decisions to accelerate students into high school
mathematics before ninth grade should be based on solid
evidence of student learning.
Common Core State Standards for Mathematics Appendix A
Accelerated 7th Grade Overview
Rational Numbers and Exponents
• Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers.
• Know that there are numbers that are not rational, and
approximate them by rational numbers.
• Work with radicals and integer exponents.
Proportionality and Linear Relationships
• Analyze proportional relationships and use them to solve realworld and mathematical problems.
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and
algebraic expressions and equations.
• Understand the connection between proportional relationships,
lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous
linear equations.
Accelerated 7th Grade Overview
continued
Introduction to Sampling Inference
• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.
• Investigate chance processes and develop, use, and evaluate
probability models.
Creating, Comparing, and Analyzing Geometric Figures
• Draw, construct and describe geometrical figures and describe
the relationships between them.
• Solve real-life and mathematical problems involving angle
measure, area, surface area, and volume.
• Understand congruence and similarity using physical models,
transparencies, or geometry software.
• Solve real-world and mathematical problems involving volume of
cylinders, cones and spheres.
8th Grade Algebra I Overview
Relationships Between Quantities and Reasoning with Equations
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Reason quantitatively and use units to solve problems.
Interpret the structure of expressions.
Create equations that describe numbers or relationships.
Understand solving equations as a process of reasoning and explain the reasoning.
Solve equations and inequalities in one variable.
Linear and Exponential Relationships
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Extend the properties of exponents to rational exponents.
Analyze and solve linear equations and pairs of simultaneous linear equations.
Solve systems of equations.
Represent and solve equations and inequalities graphically.
Define, evaluate, and compare functions.
Understand the concept of a function and use function notation.
Use functions to model relationships between quantities.
Interpret functions that arise in applications in terms of a context.
Analyze functions using different representations.
Build a function that models a relationship between two quantities.
Build new functions from existing functions.
Construct and compare linear, quadratic, and exponential models and solve problems.
Interpret expressions for functions in terms of the situation they model.
8th Grade Algebra I Overview continued.
Descriptive Statistics
• Summarize, represent, and interpret data on a single count or measurement variable.
• Investigate patterns of association in bivariate data.
• Summarize, represent, and interpret data on two categorical and quantitative
variables.
• Interpret linear models.
Expressions and Equations
• Interpret the structure of expressions.
• Write expressions in equivalent forms to solve problems.
• Perform arithmetic operations on polynomials.
• Create equations that describe numbers or relationships.
• Solve equations and inequalities in one variable.
• Solve systems of equations.
Quadratics, Functions and Modeling
• Use properties of rational and irrational numbers.
• Understand and apply the Pythagorean theorem.
• Interpret functions that arise in applications in terms of context.
• Analyze functions using different representations.
• Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Construct and compare linear, quadratic and exponential models and solve problems.
Compacting in Middle School/Acceleration
Grade 6
Grade 7 +
Part of
Grade 8
Part of
Grade 8 +
Algebra I
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Acceleration Point
Geometry
Algebra II
Precalc
Calculus
Grades 7, 8, and 9
High School
Grade 7 Mathematics
Grade 8 Mathematics
Algebra I
(Honors or College Prep)
Accelerated 7th Grade
Mathematics
8th Grade
Geometry
Algebra I
(Honors or College Prep)
The Process
• Data is collected throughout the year and shared with parents
• Data is analyzed and compared to placement criteria
• Recommendations are made for the next year’s placement and shared
with parents
• Conversations between school and parents
• Option to override school’s recommendation*
*Forms due first week in June because class sections are created
based on the number of eligible students (changes yearly)
Portfolio of Assessment
• Many opportunities to demonstrate skill/knowledge
• Variety of assessments to give complete picture of learner’s
skill/knowledge
o Nationally-normed
o State
o Locally created
o Skill assessments
o Writing tasks
o Inquiry tasks
o Computation tasks
o Readiness tasks
Placement Assessment Information
• 6th to 7th Grade
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• 7th to 8th Grade
5th Grade MCAS
Scantron Performance Series
(Nationally Norm
Referenced, Aligned to the
MA Standards)
6th Mid-Year Exam
Nationally Norm Referenced
Algebra Readiness test
Teacher Recommendation
Grades from Term 1 & 2
6th Grade MCAS
7th Mid-Year Exam
Nationally Norm
Referenced Algebra
Readiness test
o Teacher
Recommendation
o Grades from Term 1 & 2
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Threshold Scores
• Criteria for placement remains consistent
MCAS: (both grades)
(90%)
MidYear: (both grades) (90%)
Scantron: (grade 6 to 7) (90%)
Iowa:
• Grade 6 to 7: 51+ (85%)
• Grade 7 to 8: 54+ (90%)
Dates of Assessments
Assessment
Date of Administration
MCAS (all grades)
May 2012
6th Grade –Scantron Nationally
Norm Referenced Assessment
October 2012
April 2013
Mid-year Tests (all grades)
January 2013
Nationally Norm Referenced Algebra
Assessment – 7th Grade
April 2013
Nationally Norm Referenced Algebra
Assessment – 6th Grade
May 2013
Websites
• Massachusetts Department of Elementary and Secondary
Education (explanation of acceleration in middle school)
• http://www.doe.mass.edu/candi/commoncore/MakingDecisio
ns.pdf
• Illustrative Mathematics (sample tasks aligned to CCSS)
• http://illustrativemathematics.org/
• Khan Academy (reinforcement, extra practice)
• http://www.khanacademy.org/about