Middle School
MS Curriculum

# Mathematics

Middle School mathematics builds and expands students’ skills foundation developed in the Lower School while transitioning them from self-generated pictorial models to using symbolic algebraic reasoning by the end of Middle School.
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.

By seventh grade, students begin to move away from visual models and toward a more algebraic and abstract method. Students begin the formal study of algebra in either seventh or eighth grade. 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 primary focus of the fifth grade math curriculum is to help our students make sense of mathematics in a meaningful way as they build upon the foundations established in the Lower School. The curriculum revolves around number sense in whole numbers, fractions and decimals, taught using pictorial models. In addition to developing discipline in their written work, students will gain mental math skills in all four operations. We will explore equivalence and proportionality through our work with fractions, ratios and percentages. Following our work on decimal operations, students will have an opportunity to practice converting within the metric system.

Many pre-algebra concepts, such as order of operations, exponents and prime factorization, are also investigated. Geometry and spatial relations are explored as a part of our course of study along with basic statistics and a variety of real-world problem-solving situations. In geometry, students will add the area of triangles to their knowledge of two-dimensional shapes. They will use protractors to measure angles, and they learn angle properties that will help to determine missing angles involving triangles, as well as intersecting lines.

Throughout the year, we supplement the content using manipulatives, games, videos, estimation, technology and hands-on activities. In addition, students generate math projects to extend or integrate with other subject areas, such as science, art and history. For example, students will create line designs and tessellations, they research mathematicians, and they will work in collaboration with science classes as they engage in a maple syrup project. Students are also asked to conduct an independent research project on a topic of their choice. This project culminates in a video presentation using Explain Everything on iPads.
• #### 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 develop the basic pre-algebra skills necessary to advance to the next level of our Middle School math program.
• #### Mathematics 7

During the first trimester, students build upon the foundations established in Math 6 regarding ratios, percentages and integer operations. Beginning with concrete scale models and moving to more abstract percentage ratio models, students will deepen their proportional reasoning skills and improve their accuracy working with signed decimals and fractions. Ideas of fairness and communicating accurately with scale and percentage are also highlighted.

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. They also study such statistical concepts as sampling and measures of central tendency. Students will also revisit ideas of fairness when analyzing graphs and statistical results and conclusions. These quotidian experiences enable students to develop general procedures and strategies for problem solving. Student engagement is regularly enhanced through games, puzzles and projects that capitalize upon longer block periods.

This is a course for students who have demonstrated that they are 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 covers one-variable equations and inequalities, graphing linear equations, and relations and functions. The second trimester deals with systems of equations, exponents and polynomials operations. In the third trimester, students study factoring, solving and graphing quadratic equations, and linear one-variable and two-variable equations.
• #### 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, such break-even scenarios 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, students 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.
• #### Geometry 8

This course assumes one year of algebra and some familiarity with the geometry taught earlier in 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.