Middle School
MS Curriculum

Mathematics

Middle School mathematics builds and expands students’ skills foundation developed in the Lower School while transitioning them from manipulative-based learning towards a self-generated pictorial model and, by the end of Middle School, to using symbolic algebraic reasoning.
In the fifth and sixth grades, the Singapore Math program encourages the use of skills in the context of multi-step word problems, building understanding for a concept by first using manipulatives like tiles or chips to explore the topic, moving to a pictorial model using bars to represent the concept and finally developing an abstract method using reasoning to apply the particular skill. These techniques introduce new concepts such as ratio, proportion and percent, allowing students new to the system a natural entrance into the pictorial modeling that is unique to this program.

We test students beginning in the sixth and seventh grades to determine whether or not they are ready for Algebra I. By seventh grade, students begin to move away from visual models and towards a more algebraic and abstract method. By the end of eighth grade, all Middle School students will have studied the linear topics of Algebra I.

Mathematics Courses

List of 6 items.

  • Mathematics 5

    The fifth grade math curriculum focuses on number sense in whole numbers, fractions and decimals. Students work to make sense of mathematics using pictorial models, develop discipline in their written work, and gain mental math skills in all four operations. Students explore equivalence and proportionality with fractions, ratios and percentages. Following their work on decimal operations, students practice converting within the metric system. Investigations into concepts such as order of operations, exponents and prime factorization begin building students’ pre-algebra skills. Foundational geometry and spatial relations are also extended from the Lower School curriculum. Students add the area of triangles to their knowledge of 2-dimensional shapes. They measure angles with protractors and learn angle properties to determine missing angles in triangles and intersecting lines diagrams. Basic statistical measures are discussed along with a variety of real-world problem solving situations.

    Throughout the year, the content is supplemented with a variety of manipulatives, games, videos, estimation exercises, and calculating and computing technology. In addition, students generate math projects to extend or integrate with other subject areas, such as science, art and history. Past examples include creating line designs and tessellations, researching a mathematician, and working in collaboration with science classes on maple syrup or bottle rocket projects. Students end the year with an independent research project on a topic of their choice. This project culminates in a video presentation using Explain Everything on iPads.

    Texts:
    • Marshall Cavendish International, Primary Mathematics CC ED Textbook 5A
    • Marshall Cavendish International, Primary Mathematics CC ED Textbook 5B Marshall Cavendish International, Primary Mathematics CC ED Workbook 5A Marshall Cavendish International, Primary Mathematics CC ED Workbook 5B
    • SingaporeMath.com Inc.

  • Mathematics 6

    This course emphasizes the development of students’ critical-thinking skills in mathematics. We build upon the foundations established in Math 5 regarding fractions, decimals, and whole number sense. Students use their knowledge of these three topics to make connections to percentages, probability, proportional thinking, and integers. Students also investigate two- and three-dimensional figures to expand their spatial reasoning and visual thinking skills.

    During our longer blocks, students are engaged in group activities, projects, exercises with manipulatives, games, and other non-routine materials such as Percento, Pentominoes, and Brain Maths puzzles to further extend their knowledge of mathematics. A variety of creative problems are consistently woven into the curriculum using the Primary Mathematics materials. Through our course work, students will have developed the basic pre-algebra skills necessary to advance to the next level of our Middle School math program.

    Texts:
    • Discovering Mathematics CC Textbook 6A
    • Marshall Cavendish International, Primary Mathematics Textbook 6B US Edition
    • Marshall Cavendish International, Primary Mathematics Workbook 6B US Edition
    • SNP Panpac, Primary Mathematics Challenging Word Problems 6 US Edition

  • Mathematics 7

    The focus of Math 7 is to build accuracy and formalization in students’ written math work while enhancing students’ self-advocacy and self-monitoring study skills. During the first trimester, students build upon the foundations established in Math 6 regarding ratios, percentages, and integer operations. Students extend their knowledge in these areas by studying operations with signed decimals and fractions and studying statistic concepts involving mean, median and mode. The second trimester introduces students to the fundamental algebraic concepts of evaluating and simplifying algebraic expressions. They then apply these skills to writing algebraic expressions for verbal phrases and analyzing algebraic equations and formulas. Students also solve basic algebraic equations. Students then apply these new algebraic tools to extend their knowledge in the areas of ratios and percent. During the third trimester, students explore sequences and connect patterns in tables to equations and graphs. Students also apply algebraic problem solving methods to geometric concepts, including finding missing angles, perimeters and areas of plane figures, and volumes and surface areas of solids. Student engagement is regularly enhanced through games, puzzles, and projects that capitalize upon longer block periods. Collaborative dialogue about mathematics is encouraged in class and students develop the skills to monitor their own progress through generating their own test question and solution for most units.

    Texts:
    • Discovering Mathematics CC Textbook 7A DMCCT7A
    • Discovering Mathematics CC Workbook 7A DMCCW7A
    • Discovering Mathematics CC Textbook 7B DMCCT7B
    • Discovering Mathematics CC Worktbook 7B DMCCW7A

  • Algebra I (Grade 7) & Algebra I (Grade 8)

    This is a course for students judged ready for a rigorous algebra course in the eighth grade, as well as for a select group of seventh graders who are ready to accelerate. The first trimester formalizes patterns with algebraic expressions and explores one-variable equations and inequalities along with several word problem examples, including break-even and distance-rate-time scenarios. The second trimester focuses on graphing linear equations, solving systems of equations, simplifying exponential expressions, and polynomials operations. In the third trimester, students study factoring, simplifying radical expressions and solving radical equations, solving and graphing quadratic equations, including quadratic word problem scenarios. absolute value and inequalities.

    Text: Pearson, Elementary Algebra, Fourth Edition, Sullivan, Struve, Mazzarella

  • Linear Topics in Algebra 8

    This course is designed to reinforce the skills and extend the algebra concepts developed during Math 7. Over the year, students study the linear topics of the Algebra curriculum while also preparing for the ninth-grade physics course work. During the first trimester, students explore the relationships between linear tables, graphs, and equations by studying numerical sequences, break-even scenarios such as cost comparisons and revenue-expense situations, and distance-speed-time correlations. In the second trimester, students study simplifying algebraic expressions, solving one-variable linear equations, and applying these skills to various word problem scenarios. In the third trimester, they expand their knowledge for graphing lines, relating tables of values to slopes and intercepts. Students continue their work on linear graphing concepts and word problems for two linearly related variables. Student engagement is regularly enhanced through games, puzzles, and projects that capitalize upon longer block periods. Technology supports instruction throughout the year.

    Text: Pearson, Elementary Algebra, Fourth Edition, Sullivan, Struve, Mazzarella

  • Geometry 8

    This course assumes one year of algebra and some familiarity with the geometry taught earlier in the middle school. The first trimester covers inductive reasoning, introduction to two-column proofs, properties of parallel lines, and basic constructions. During the second trimester, students study congruent triangles, similarity, the Pythagorean theorem, and special right triangles. In the third trimester, students learn about circles, the area of polygons and circles, surface area and volume, and trigonometry. In addition, students learn to interpret statistical graphs, including dot, stem, box and whisker plot, and scatter plots.
     
    Text: Geometry by Jurgensen, Brown, Jurgensen