Kennedy Middle SchoolWilson Middle School

Family Math Night

November 15, 20127:00 PM – 8:30 PM@WMS Auditorium

Evening Overview• 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 real-world

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 real-world 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 continuedIntroduction 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 OverviewRelationships Between Quantities and Reasoning with Equations• 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• 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

Geometry

Algebra II

Precalc

Calculus

Acceleration Point

Grades 7, 8, and 9Grade 7 Mathematics

Grade 8 Mathematics

High SchoolAlgebra I

(Honors or College Prep)

Accelerated 7th Grade Mathematics

8th Grade Algebra I

Geometry(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/knowledgeo Nationally-normedo Stateo Locally createdo Skill assessmentso Writing taskso Inquiry taskso Computation taskso Readiness tasks

Placement Assessment Information

• 6th to 7th Grade

o 5th Grade MCASo Scantron Performance Series (Nationally Norm

Referenced, Aligned to the MA Standards)

o 6th Mid-Year Examo Nationally Norm Referenced

Algebra Readiness testo Teacher Recommendationo Grades from Term 1 & 2

• 7th to 8th Grade

o 6th Grade MCASo 7th Mid-Year Examo Nationally Norm

Referenced Algebra Readiness test

o Teacher Recommendation

o Grades from Term 1 & 2

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 AssessmentsAssessment Date of Administration

MCAS (all grades) May 2012

6th Grade –Scantron Nationally Norm Referenced Assessment

October 2012April 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