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.

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.
• #### 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.
• #### Mathematics 7

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 percentages. 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. Students work on a project that incorporates a variety of trimester 3 concepts including scale drawing, rates, and proportional reasoning. 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.