# 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.

## Program of Studies

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.

##### Algebraic ExpressionsFractionsDecimalsRates, Ratios and ProportionsPercentEquations and InequalitiesRational Numbers (Integers)AreaVolume and Surface AreaData and Statistics

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.

##### Operations with Integers Expressions and Equations with Integers Operations with Rational Numbers Expressions and Equations with Rational Numbers Ratios and Proportions Percents Angles and TrianglesCircles and Area Surface Area and Volume of 3D figuresProbability and DataInequalities

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.

##### Operations with Integers Expressions and Equations with Integers Operations with Rational Numbers Expressions and Equations with Rational Numbers Ratios/Proportions Percents Angles and TrianglesCircles and Area Surface Area and Volume of 3D figures Probability and DataInequalities

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.

##### Operations with Integers Expressions and Equations with Integers Operations with Rational Numbers Expressions and Equations with Rational Numbers Ratios/Proportions Linear Equations PercentsAngles, Triangles & Parallel LinesPythagorean TheoremCircles and Area Probability and DataInequalities Rotations, Dilations and Transformations

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

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.

##### Essential Skills of Grade 8 MathEquationsLinear EquationsSystems of Linear EquationsFunctionsPythagorean Theorem and the Number SystemLaws of Exponents and Scientific NotationGeometryAngles & TrianglesTransformations on the Coordinate PlaneData 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.

##### EquationsLinear EquationsData Analysis & DisplaysInequalitiesSystems of Linear EquationsLinear FunctionsExponents, Scientific Notation and Exponential DecayPythagorean Theorem and the Number SystemGeometryTransformations on the Coordinate PlanePolynomials and Methods of factoringQuadratics

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.

##### Functions, Equations, Graphing LinearWriting Linear Equations, Inequalities, and Absolute Value Equations Linear Systems, Linear Programming, ExponentsGeometryPolynomialsQuadraticsRadicals and Rationals

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

### Catherine Anusauskas

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

### Megan Elder

Locations: Hopkinton Middle School
Email:

### Susan Fraser

Locations: Hopkinton Middle School
Email:

### Christine Kouris

Locations: Hopkinton Middle School
Email:

### Ann Marie Lockwood

Locations: Hopkinton Middle School
Email:

### Kristin Mascia

Locations: Hopkinton Middle School
Email:

### Catherine Mason

Locations: Hopkinton Middle School
Email:

### Monica McLean

Locations: Hopkinton Middle School
Email: