# Mathematics

#### Lower School

This is our sixth year teaching Singapore Math at Montgomery. This program teaches the “why before the how.” Math is no longer just about accepting an approach to solving a problem, it’s about developing a true understanding of the methodology. Singapore mathematics lessons begin by engaging students in hands-on learning, followed by pictorial representations, which help them form a mental image of mathematical concepts. This is followed by an abstract stage, where they solve problems using numbers and symbols. This approach makes the learning of mathematics fun and meaningful, and helps students develop positive attitudes about math.

Our teachers have spent over 400 hours in training to teach Singapore Math effectively. They see the difference and truly believe that this is the best way for our Lower School students to learn math.

Here are some of the comments about Singapore Math that have been shared by our teachers:

- “The repetition in Singapore Math has helped to solidify the concepts the students learn.”
- “We are building strong skills. The building blocks are clear.”
- “I love the combination of language skills and the problem solving in math.”
- “The C-P-A (concrete to pictorial to abstract) model makes total sense to the students and the teacher. It builds strong retention”
- “Differentiation is easily provided. Moving students forward is not a problem.”
- “Students love math! It’s fun!

#### Middle School

Middle school is a time for students to continue to grow and expand their understanding of mathematics. Students are homogeneously grouped in order to best challenge their individual abilities. All courses are designed to implement the National Council of Teachers of Mathematics Curriculum and Evaluation Standards, and the Common Core State Standards Initiative. They focus on helping students develop their mathematical powers through reasoning,critical thinking, and problem solving.

6TH GRADE MATHEMATICS

On-Grade Math and Above-Grade Math Groups:

The sixth grade class is split into two math groups based on their previous experiences in math. Both groups study pre-algebra. This program allows students to move at a pace designed to fit their needs. They begin their study by revisiting basic arithmetic topics, then expand their knowledge of operations and mathematical properties to include the use of variables. Mastery and understanding are the objectives for each class. Emphasis is placed on applying knowledge to real life word problems. The program is based on investigations, discovery, and application of mathematics. Students communicate their ideas orally and in writing using appropriate mathematical terminology. Students frequently work in cooperative groups to help them understand the concepts being explored.

7TH GRADE MATHEMATICS

Above-Grade Math Group: The above-grade group is undertaking a one-year course of study of Algebra I. The students focus on expressing mathematical relationships verbally, pictorially, graphically, and symbolically. The course emphasizes the skills necessary to analyze real world problems and determine the most appropriate ways to solve them. It also stresses the importance of working as a member of a problem solving team and being able to communicate using mathematical terminology. A graphing calculator is frequently used to facilitate the visualization of a given algebraic function and the comparison of groups of algebraic functions. By the end of the year, the students should understand the relationships between any given linear and quadratic functions and their graphs.

Accelerated Math Group: The accelerated students will continue their individualized study of Algebra I and/or Algebra II. The course continues to emphasize the skills necessary to analyze real world problems and determine the most appropriate ways to solve them. It also stresses the importance of working as a member of a problem solving team and being able to communicate using mathematical terminology. A graphing calculator is frequently used to facilitate the visualization of a given algebraic function and the comparison of groups of algebraic functions. By the end of the year, the students will understand the relationships between any given quadratic function and its graph and solving rational functions. From time to time one or more students may be identified by faculty to start an accelerated course of study in mathematics in seventh grade. At that time, they will begin on a similar path as all other independent students.

8TH GRADE MATHEMATICS

On-Grade Math Group: The on-grade group completes its study of Algebra I this year. The students focus on expressing mathematical relationships verbally, pictorially, graphically, and symbolically. The course emphasizes the skills necessary to analyze real world problems and determine the most appropriate ways to solve them. It also stresses the importance of working as a member of a problem solving team and being able to communicate using mathematical terminology. A graphing calculator is frequently used to facilitate the visualization of a given algebraic equation and the comparison of groups of algebraic equations. The course concludes with an in depth study of quadratic functions.