Galvin Middle School Mathematics The diagram below shows the typical math sequence for students at the Galvin Middle School. Grade 5

Grade 6

Grade 7

Grade 8

Math 5

Math 6

Math 7

Math 8

For students who have demonstrated exceptional achievement and are ready for a faster, more challenging pace, the Galvin offers an accelerated sequence, shown below. Grade 5

Grade 6

Grade 7

Grade 8

Math 5

Math 6

Math 7 Extended

Grade 8 Algebra 1

Both of these sequences offer rigorous curriculum aligned to the 2011 Massachusetts Curriculum Frameworks for Mathematics and the Common Core State Standards, and result in students graduating from high school, college and career ready. Accelerating a student’s math progress before they are ready can result in the student becoming frustrated or failing, and eventually losing interest in mathematics. In addition, the concepts taught in Algebra 1 are the foundation for all higher level math courses. It is crucial that students achieve full mastery of these concepts in order to be prepared for those higher level courses. Since a student’s placement and success in Algebra 1 can have such a significant impact on their future math success, we work very hard at identifying the best possible placement for each and every student. The course descriptions that follow describe the major content of each course, as well as the placement criteria for the accelerated courses.

Course Descriptions and Placement Criteria All math courses are aligned to the 2011 Massachusetts Curriculum Frameworks for Mathematics and the Common Core State Standards. The content focus for each course is described below. In addition to the grade level content, all courses incorporate the Standards for Mathematical Practice on a daily basis in order to develop students’ problem solving, reasoning and communication skills.

Math 5 The grade 5 content standards focus on three critical areas: (1) Fluency with addition and subtraction of fractions, and a beginning understanding of multiplication and division of fractions; (2) Fluency with all four decimal operations; and (3) An introduction to estimating and measuring volume.

Math 6 The focus of the grade 6 math content standards is on four critical areas: (1) Connecting students understanding of whole number multiplication and division to ratios and rates; (2) Extending understanding of rational numbers to include integers and a complete understanding of multiplying and dividing fractions; (3) Writing and operating with expressions and equations; and (4) An introduction to statistical analysis.

Math 7 The focus of the grade 7 math content standards is on four critical areas: (1) Ratios and Proportional Relationships; (2) Operations with rational numbers, expressions and linear equations; (3) Geometric principles of scale drawings, constructions, area, surface area and volume; and (4) Using samples to make inferences about populations.

Math 7 Extended Math 7 Extended covers all the topics in Math 7, in addition to the following eighth grade topics: (1) Linear Relationships; (2) Operations on equations with variables on both sides; (3) Geometric principles of similarity, congruence, transformations, angle relationships, and Pythagorean Theorem; and (4) Using two-way tables to display bivariate data. Due to the number of topics covered, the pace of this course will be significantly faster than Math 7. Students must meet three of the four 2016-2017 requirements listed below in order to be recommended for Math 7 Extended: 

A score of 85% or higher on the placement test for grade 7 math. The placement test for grade 7 math measures students’ mastery of basic numeracy and algebra skills.

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A score of 85% or higher on the grade 6 Mid-year Assessment The Mid-year Assessment measures students’ mastery of the grade 6 common core standards taught the first half of the year.

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92% or higher Math 6 average

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Sixth grade teacher recommendation See below for criteria considered in teacher recommendation.

Math 8 The focus of the grade 8 math content standards is on three critical areas: (1) Solving linear equations, solving systems of linear equations, and using linear equations to model associations of bivariate data; (2) An introduction to functions and using functions to model relationships; and (3) Geometric principles of similarity, congruence, transformations, angle relationships, and the Pythagorean Theorem.

Grade 8 Algebra 1 Grade 8 Algebra 1 covers the grade 8 math content standards not taught in Math 7 Extended. The focus of these standards is: (1) Solving systems of linear equations, and using linear equations to model associations of bivariate data; (2) An introduction to functions and using functions to model relationships. In addition to these 8th grade standards, the course also covers all standards taught in the high school Algebra 1 course. The focus of these standards is on four critical areas: (1) Developing a deep understanding of linear and exponential relationships; (2) Analyzing and solving quadratic functions; (3) Extending the laws of exponents to rational exponents; and (4) Using and interpreting linear models. Due to the number of topics covered, the pace of this course will be significantly faster than Math 8. Students must meet three of the four 2016-2017 requirements listed below in order to be recommended for Grade 8 Algebra 1:  

A score of 85% or higher on the placement test for grade 8 math. The placement test for grade 8 math measures students’ mastery of basic numeracy and algebra skills essential to success in Algebra 1.

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A score of 85% or higher on the grade 7 Mid-year Assessment The Mid-year Assessment measures students’ mastery of the grade 7 common core standards taught the first half of the year.

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92% or higher Math 7 or 90% or higher Math 7 Extended average.

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Seventh grade teacher recommendation See below for criteria considered in teacher recommendation.

Students recommended for Grade 8 Algebra 1 who did not take Math 7 Extended in seventh grade, will be required to complete a packet over the summer prior to eighth grade. Students who demonstrate a mastery of the content taught in Grade 8 Algebra 1 will take geometry in ninth grade.

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Considerations for Teacher Recommendation Student is motivated and has an interest in mathematics. Student takes responsibility for his/her own work (classwork, homework, extra help). Student has a desire to achieve. Student knows how to face challenges. Student is able to understand concepts the first time they’re presented. Student excels academically when the pace of the course quickens. Student is able to persist on a problem. Student demonstrates the ability to articulate their mathematical reasoning. Student is able to approach problems in different ways.