﻿ Middle School Mathematics-Shanghai High School International Division Middle School Mathematics

## Middle School Mathematics

The main goal of theMiddle School Mathematics Department is for students to develop mathematical proficiency that will enable them to use efficiently mathematics to make sense of and improve the world around them.

We intend for our students to:

• Develop positive attitudes toward mathematics, including the confidence, creativity, enjoyment, and perseverance that come from achievement.

• Become proficient problem-solvers by posing appropriate questions, selecting appropriate methods, employing a variety of strategies, and exploring alternative approaches.

• Think logically, using inductive reasoning to formulate reasonable conjectures and using deductive reasoning for justification, formally and informally.

• Cooperatively and independently explore mathematics, using inquiry and technological skills.

• Make connections between mathematical ideas, between mathematics and other disciplines, and between mathematics and life.

• Communicate mathematics through writing, modeling, and visualizing, using precise mathematical language and symbolic notation.

Pre-algebra is a two-semester preparation course for students on the verge of Algebra I and offers rational number theory (including comparing and ordering on a number line), drawing conclusions from statistical data, ratios, proportions and percentages, spatial thinking (including congruency, translations, and symmetry), sequences and patterns, and polynomials and functions. Opportunities for the development of vital problem-solving skills at the middle school level are also included. These lessons are designed to be integrated into the regular curriculum or may be used as a stand-alone mini-unit course. Learning strategies include writing algebraic expressions, generating patterns, and problem simulations.

Objectives for Pre-algebra:

Objective 1: Compute fluently with understanding and make reasonable estimates with rational numbers.

Objective 2: Analyze relationships among rational numbers, including negative rational numbers, and operations involving these numbers.

Objective 3: Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

Objective 4: Model and illustrate meanings of ratios, percentages, and decimals.

Objective 5: Solve a wide variety of problems using ratios and proportional reasoning.

Objective 6: Recognize similar polygons and use properties of similar triangles to solve problems and define the slope of a line.

Objective 7: Generalize and express patterns using algebraic expressions.

Objective 8: Evaluate, simplify, and solve algebraic expressions, equations, and inequalities.

Objective 9: Represent relationships using graphs, tables, and other models.

Objective 10: Apply the properties of proportionality for different units of measure.

Objective 11: Derive formulas for surface areas and the volume of three-dimensional figures.

Objective 12: Calculate probabilities of events and compare theoretical and experimental probability.

Objective 13: Formulate questions and answer the questions by organizing and analyzing data.

Algebra 1 is a two-semester course that provides in-depth coverage of writing, solving and graphing a variety of equations and inequalities, as well as linear systems. Functions are a central theme of the course which include function notation, domain and range, rate of change, and transformations. Students use the properties of real numbers to explore, justify and simplify numeric and algebraic expressions, including laws of exponents, radicals and rational expressions. Lab activities provide students with opportunities to explore and discover algebraic principles on their own, often prior to the lecture. Students model and solve real world problems using algebra, functions, probability and data analysis. In the Making Connections sections, relevant, project-based learning activities provide students with a deeper understanding of the subject matter.

Objectives for Algebra 1:

Objective 1: Represent real numbers as points on the number line and distinguish rational numbers from irrational numbers.

Objective 2: Compute fluently and make reasonable estimates with rational and irrational numbers.

Objective 3: Represent and analyze the slope of a line.

Objective 4: Model and interpret problems having a constant rate of change using linear functions.

Objective 5: Represent and analyze linear relationships using algebraic equations, expressions, and graphs.

Objective 6: Simplify polynomials and the quotient of monomials.

Objective 7: Solve and interpret linear equations and inequalities in various situations involving real-world problems.

Objective 8: Solve and interpret pairs of linear equations and inequalities.

Objective 9: Factor polynomials with common monomial factors and factor simple quadratic expressions.

Objective 10: Solve quadratic equations using factoring or by taking square roots.

Objective 11: Summarize, display, and analyze data.