Mathematics in the Middle School Middle School Mathematics

In collaboration and consultation with Upper School math teachers, IB coordinator and our Head of School, Middle School math teachers developed the following updates to our middle school math program to align with our newly adopted Common Core State Standards in Mathematics (CCSSM). Our math program provides our students with opportunities for depth of learning and acceleration without skipping over important foundational math content. We believe that building a strong foundation for future math achievement and success in Upper School is an essential goal for a Middle School math program. Parents will hear more information about our math program at Middle School Open House in September and can attend Grade Coffee to speak to teachers directly. What is the reasoning behind the decision in choosing Common Core? Our philosophy is to strive for depth of conceptual knowledge in mathematics versus procedural knowledge. This means achieving not just an ability to do drill and practice problems but bringing about lasting understanding of the concepts. In the past students were accelerated by skipping one or two course levels which caused them to have gaps in their Mathematics foundation. This has had serious consequences in the Upper School Algebra II Honors course in grade 9 as formerly strong math students struggled as concepts become more difficult in higher level courses. It became apparent that they had skipped over some essential foundational skills in earlier years. It is not developmentally appropriate to sort and track young students, particularly in grades 5 and 6, as their math conceptual thinking skills have not yet developed. The course pathway below reflects our differentiated approach to achieve proficiency in the Common Core State Math Standards.

�

Grade 6 Math 6 In Math 6, instructional time will focus 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. Grade 7

Math 7 In Math 7, instructional time will focus 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; and (4) drawing inferences about populations based on samples. Math 7 Accelerated* This course differs from the non-accelerated Math 7 course in that it contains content from Introduction to Algebra. While coherence is retained, in that it logically builds from the 6th Grade, the additional content when compared to the non- accelerated course demands a faster pace for instruction and learning. Content is organized into four critical areas, or units. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Prerequisite: B- or higher in Math 6 or similar course and teacher recommendation. *Accelerated Program Based on the idea that content will compact 3 years of content into 2 years (Math 7, Introduction to Algebra and Algebra I will be compacted into Math 7 Accelerated and 8th Grade Algebra I). Grade 8

8th Grade Introduction to Algebra In Introduction to Algebra, for 8th graders, instruction will focus 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 equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) and analyzing two- and three dimensional space and figures using distance, angle, similarity and congruence, and understanding and applying the Pythagorean Theorem.

8th Grade Algebra I* The fundamental purpose of 8th Grade Algebra I is to formalize and extend the mathematics that students learned through the end of seventh grade. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend. Students engage in methods for analyzing, solving, and using quadratic functions. In addition, the units will introduce methods for analyzing and using quadratic functions, including manipulating expressions for them, and solving quadratic equations. Students

understand and apply the Pythagorean theorem, and use quadratic functions to model and solve problems. This course differs from High School Algebra I in that it contains content from Introduction to Algebra. While coherence is retained, in that it logically builds from Math 7 Accelerated, the additional content when compared to the high school course demands a faster pace for instruction and learning. A scientific calculator with exponent and radical functions will be useful. Prerequisite: B- grade or higher in a Math 7 Accelerated or similar course and teacher recommendation. *Accelerated Program Based on the idea that content will compact 3 years of content into 2 years (Math 7, Introduction to Algebra and Algebra I will be compacted into Math 7 Accelerated and 8th Grade Algebra I). In addition, the following Mathematical Practice Standards will be incorporated throughout all of our courses to provide a more enriched mathematical program. 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 FAQs: Will my child in the Math 7 class be able to follow the IB math program in high school? Students enrolled in Math 7 might take the following path: 7th grade: Math 7 8th grade: Introduction to Algebra then in the high school: 9th grade: Algebra I (101) 10th grade: Geometry (202) 11th grade: Algebra II (302) 12th grade: Pre-Calculus or IB Math Studies (402) or

or

9th grade: Algebra I (101) 10th grade: Geometry (202) and Algebra II (302) 11th grade: Pre-Calculus or IB Math Standard Level year 1 (402) 12th grade: AP Calculus AB or IB Math Standard Level year 2 (502) 9th grade: Algebra I (101) 10th grade: Geometry Honors (201) and Algebra II Honors (301) 11th grade: IB Math Higher Level year 1 (401) 12th grade: IB Math Higher Level year 2 (501)

What are the math path options for students in the Math 7 Accelerated class? 7th grade: Math 7 Accelerated 8th grade: 8th Grade Algebra I 9th grade: Geometry (202) or Geometry Honors (201) 10th grade: Algebra II (302) or Algebra II Honors (301) 11th grade: IB Math Higher Level year 1 (401) 12th grade: IB Math Higher Level year 2 (501) To summarize, regardless of placement in Math 7 or Math 7 Accelerated, students can achieve the highest level of IB math in the Upper School. Some students blossom and develop mathematical and conceptual thinking later, some earlier. Our paths do not close doors for future math achievement. Math 7 Accelerated is a compacted course that covers all of Math 7 and most of Intro to Algebra (the rest of the Intro to Algebra curriculum is covered in the 8th Grade Algebra I). Students in the Math 7/Intro to Algebra path learn the same content as Math 7 Accelerated but they are allowed more time and practice to learn. How can you challenge my advanced math learner? Students may opt to participate in the Junior High Math Competition offered by our Upper School Math Department. Differentiation in the classroom will also take place, creating an enriching environment where all students have an opportunity to learn at the pace that works for them. If a student is showing readiness in grade 7, is it possible for them to move to the Grade 7 Accelerated class? Yes, depending on a variety of data: ■ Teacher Recommendation, including observations based on work habits (preparation, working collaboratively, self-reflection making one’s best effort) and motivation. ■ NWEA MAP Tests ■ Internal Assessments This decision needs to be made within a certain time frame/deadline. By Toussaint vacation in October, teachers will have reviewed all students’ placements and will have a better sense of the appropriate placement decision. We are committed to addressing the individual needs of our middle school math learners. Is a calculator required? For Grades 6 & 7 Math - Yes, students need a basic calculator with 5 operations (+, -, ×,÷,√) and +/- sign. For 8th Grade Algebra I - Yes, students need a scientific calculator with exponent and radical functions. What math supplies are required? Although most math classrooms have some school supplies on hand, students should have their own supplies: ■ a pencil case to hold the following:

■ ■ ■ ■ ■ ■ ■ ■

pencil and sharpener (or mechanical pencil) eraser small ruler or straightedge (15 cm) scissors glue stick calculator: please see calculator requirements per class in FAQ section above. colored pencils/pens/markers/highlighters spiral notebook or A4 paper (petits carrés, 0.5 cm squares graph paper) / folder or binder with A4 sized sleeves, and dividers or sections to file handouts and assessments (follow individual teacher guidance)