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Mathematics

Middle School

In the Middle School Math curriculum, students will be applying what they have learned in grades Pre-K to 5 within three major topics.  With all of these topics, they will learn about real life applications. The first major topic, introduced to students in the MA Curriculum Frameworks in grade 6, is the exploration of ratios and proportional relationships, which continues to develop through grade 7 and 8. The second major topic is rational numbers which now extends to negative numbers, irrational numbers and repeating decimals.  The third major topic is linear relationships.

 

Courses

Program of Studies

Grade 6

Math 6 is designed to be rigorous and to meet the needs of all students. Instruction in grade 6 math classes focuses on four critical areas:

1.       Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems;

2.       Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;

3.     Writing, interpreting, and using expressions  and equations; and

4.     Developing understanding of statistical thinking.

In addition to the four critical areas, instruction will build on students' knowledge of area by reasoning about relationships among shapes to determine area, surface area, and volume.

Grade 6 Math provides an extra block of math to grade 6 students on five days in our twelve day schedule. By expanding the time for students to learn, Grade 6 Math provides to students all the math standards in Grade 6 Math while also building foundational skills in a student-centered environment. In order to best meet students' individual needs, Grade 6 Math is taught by two educators. Students are placed into Grade 6 Math based on teacher recommendation combined with data from state, local and classroom assessments.


Curriculum Units and Learning Outcomes:
Algebraic Expressions
Fractions
Decimals
Rates, Ratios and Proportions
Percent
Equations and Inequalities
Rational Numbers (Integers)
Area
Volume and Surface Area
Data and Statistics

Grade 7

Instruction in all grade 7 math classes focuses on four critical areas:

1. Developing understanding of and applying proportional relationships;

2. Developing understanding of operations with rational numbers and working with expressions and linear equations;

3. Solving problems involving scale drawings and informal geometric constructions, and working with two and three dimensional shapes to solve problems involving area, surface area, and volume;

4. Drawing inferences about populations based on samples.

Co-Taught Math 7 is taught by two or more teachers. In addition to a diverse instructional model, having multiple teachers allows us to provide students with a wealth of resources in  order to  best meet individual needs: smaller class sizes, increased access to  teachers, tailored instruction for each individual student, and the ability to establish  flexible  student groups based on need.


Co-Taught Math 7 Curriculum Units and Learning Outcomes:
Operations with Integers
Expressions and Equations with Integers
Operations with Rational Numbers
Expressions and Equations with Rational Numbers
Ratios and Proportions
Percents
Angles and Triangles
Circles and Area
Surface Area and Volume of 3D figures
Probability and Data
Inequalities

 

Math 7 is designed to be rigorous and meet the needs of the majority of our students, focusing on the four critical areas listed above.


Math 7 Curriculum Units and Learning Outcomes:
Operations with Integers
Expressions and Equations with Integers
Operations with Rational Numbers
Expressions and Equations with Rational Numbers
Ratios/Proportions
Percents
Angles and Triangles
Circles and Area
Surface Area and Volume of 3D figures
Probability and Data
Inequalities

 

Grade Pre-Algebra focuses on the four critical areas listed above but differs from the other Math 7 courses in that students are instructed in some of the Grade 8 standards from the Massachusetts Mathematics Curriculum Framework. While coherence is retained in that it logically builds from grade 6, the additional content demands a faster pace for instruction and learning. Grade Pre-Algebra supports students who are ready for a math experience that delves deeper into grade level concepts and who are ready for a faster-paced class. The curriculum emphasizes a deep, authentic command of mathematical concepts. Grade Pre-Algebra is designed for students who regularly think about problems in ways that go beyond simple computation and are able to independently apply concepts to novel situations. Pre-Algebra students demonstrate a strong interest and passion for math and display an enthusiastic disposition to think critically and analytically while independently monitoring and evaluating their own progress.


Grade 7 Pre-Algebra Curriculum Units and Learning Outcomes:
Operations with Integers
Expressions and Equations with Integers
Operations with Rational Numbers
Expressions and Equations with Rational Numbers
Ratios/Proportions
Linear Equations
Percents
Angles, Triangles & Parallel Lines
Pythagorean Theorem
Circles and Area
Probability and Data
Inequalities
Rotations, Dilations and Transformations

 

Grade 7 Placement

Criteria for placement into each of the above grade 7 classes is based upon performance on:

•         MCAS

•         STAR Math Assessment (Winter)

•         IOWA Algebra Aptitude Test (Early Spring)

•         Teacher Rubric

  •       Fluency assessment

Grade 8

Instruction in all grade 8 math classes focuses on three critical areas:

1.       formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations;

2.       grasping the concept of a function and using functions to describe quantitative relationships; and

3.     analyzing two and three dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

Co-Taught Math 8 is taught by two or more teachers. In addition to a diverse instructional model, having multiple teachers in one class allows us to provide students with a wealth of resources in  order to best meet each individual's needs: smaller class sizes, increased access to teachers, tailored instruction for each individual student, and the ability to establish flexible  student  groups  based on need.

Math 8 is a rigorous course focused on the critical areas listed above.


Co-Taught and Math 8 Curriculum Units and Learning Outcomes:
Essential Skills of Grade 8 Math
Equations
Linear Equations
Systems of Linear Equations
Functions
Pythagorean Theorem and the Number System
Laws of Exponents and Scientific Notation
Geometry
Angles & Triangles
Transformations on the Coordinate Plane
Data Analysis & Displays

 

Grade 8 Honors Algebra I formalizes and extends the mathematics that students  learned  through  the end of grade 7 covering all of the grade 8 standards from the Massachusetts Mathematics Curriculum Framework in addition to the following Algebra 1 standards:

1.  deepen and extend understanding of linear relationships;

2.  contrast linear relationships with each other and engage in methods for analyzing, solving, and using quadratic functions;

3.  add, subtract, and  multiply  polynomials in addition to factoring polynomials; and

4.  work with inequalities and systems of inequalities  by solving them algebraically  and graphically.

All topics will be covered with extensive rigor to ensure mathematical success at high school and beyond. Honors Algebra I students must possess a strong work ethic as well as an ability to learn independently. This class is designed  for students seeking higher  level Calculus in  high school.


Grade 8 Honors Algebra I Curriculum Units and Learning Outcomes:
Equations
Linear Equations
Data Analysis & Displays
Inequalities
Systems of Linear Equations
Linear Functions
Exponents, Scientific Notation and Exponential Decay
Pythagorean Theorem and the Number System
Geometry
Transformations on the Coordinate Plane
Polynomials and Methods of factoring
Quadratics

 

Grade 8 Advanced Algebra I formalizes and extends the  mathematics that students learned  through  the end of grade 7 covering all of the grade 8 standards from the Massachusetts Mathematics Curriculum Framework as well as all Algebra  I standards. Grade 8 Advanced  Algebra I  supports students who are ready for a substantially  above-grade  level  math  experience. The curriculum  demands and  emphasizes a deep, authentic command of mathematical concepts. Grade 8 Advanced Algebra I  is designed  for students who  regularly think about  problems in ways that go beyond  simple computation  and  are  able to apply concepts to novel situations. Students demonstrate a strong interest and passion for math and display an enthusiastic disposition  to think critically  and  analytically  while independently  monitoring and evaluating their own progress. This class is designed for students to reach two years of high school Calculus. The main areas of concentration of Grade 8 Advanced Algebra I are to:

1.  deepen and extend understanding of linear and exponential relationships;

2.  contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions;

3.  apply linear models to data that exhibit a linear trend.

Students will summarize, interpret and represent one or two variable data distribution as well as simplify and solve rational expressions and equations using various operations. Students will explore aspects of functions and pre-calculus topics that will further develop in Algebra 11, including composition, inverse, and operations. Grade 8 Advanced Algebra I students must possess solid mathematical prerequisite skills, as well as a strong and independent work ethic.


Grade 8 Advanced Algebra I Curriculum Units and Learning Outcomes:
Functions, Equations, Graphing Linear
Writing Linear Equations, Inequalities, and Absolute Value Equations
Linear Systems, Linear Programming, Exponents
Geometry
Polynomials
Quadratics
Radicals and Rationals

 

Grade 8 Placement

Criteria for placement into each of the above grade 8 classes is based upon performance on:

•         MCAS

•         STAR Math Assessment (Winter)

•         IOWA Algebra Aptitude Test (Early Spring)

•         Teacher Rubric

Foundations

The objective of Foundations and Application of Numbers (FAN) is to reinforce essential building block math skills to help students become confident learners. FAN supplements mathematics classrooms by providing additional support to struggling math learners. The FAN experience is different for each student as we look closely at state, local and classroom assessments in order to create a program tailored to individual needs. Students begin to generate their own math goals and work towards reaching them while in FAN. Beyond this foundational work, students will preview and review concepts and skills taught in  their regular math class.

Resources

Contact Us

Catherine Anusauskas

Titles: Math Interventionist Teacher, MS Math CTL
Locations: Hopkinton Middle School
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Megan Elder

Titles: Teacher Grade 7
Locations: Hopkinton Middle School
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Susan Fraser

Titles: Teacher Grade 6
Locations: Hopkinton Middle School
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Christine Kouris

Titles: Teacher Grade 8
Locations: Hopkinton Middle School
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Ann Marie Lockwood

Titles: Teacher Grade 7
Locations: Hopkinton Middle School
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Kristin Mascia

Titles: Teacher Grade 8
Locations: Hopkinton Middle School
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Catherine Mason

Titles: Teacher Grade 6
Locations: Hopkinton Middle School
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Monica McLean

Titles: Teacher Grade 8
Locations: Hopkinton Middle School
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Richard Paquette

Titles: Teacher Grade 6, 8th Grade Outdoor Track Coach
Locations: Hopkinton Middle School
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Jane Sherwill

Titles: Teacher Grade 7
Locations: Hopkinton Middle School
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