Singapore Math

Course Description:

The sixth grade math course is designed to introduce concepts and procedures involving rational numbers, geometry, measurement, probability and data. Each unit is designed to activate students' prior knowledge of mathematical concepts previously learned throughout elementary school and strengthen their skills. Throughout the year, students will be introduced to algebraic concepts with each unit. Students will study relations and procedures and represent these relationships and procedures into formulas or rules. 

Course Objectives:

• Students will develop mathematical thinking and problem solving skills. 

• Students will learn about factors, multiples, divisors, products, prime numbers, composite numbers, greatest common factors and least common multiples.

• Students will develop an understanding of fractions, decimals, and percents along with computation and how to work with these in real world situations.

• Students will recognize, analyze, measure, and reason about the shapes and visual patterns that are important features of our world.

• Students will develop an understanding of perimeters and areas of rectangles, triangles, parallelograms, and circles.

• Students will learn to make line plots, bar graphs, and coordinate graphs and will learn to interpret patterns shown in these displays.

Curricular Sequence

Course Description:

In seventh grade, students extend and apply many of the concepts they've learned in sixth grade in order to discover new types of relationships, new and efficient ways to solve problems, and new ways to analyze and look at data and associations. Students will investigate proportional relationships and use this understanding to solve real-world problems involving discounts, interest, and taxes. Building off of their sixth-grade understanding of integers, seventh-grade students will apply the properties of operations to all rational numbers in order to efficiently and thoughtfully work with the real number system, including how it applies to expressions and equations. 

Course Objectives

     Students will:

• Be introduced to Irrational Numbers and the Real Number System

• Learn how to solve numerous Rational Number Operations such as adding, subtracting, multiplying, and dividing integers

• Further their knowledge of Algebraic Expressions by including fractional and decimal coefficients

• Solve algebraic equations with variables on both sides of the equation

• Learn to solve algebraic equations in factored form and will have the knowledge to check if their solutions are correct

• Learn to graph the solution set of an inequality on a Number Line

• Understand what a direct proportion is and will be able to identify it from a table

• Represent direct proportions graphically and will use a graph to interpret inverse proportions

• Explore the properties of complementary, supplementary and adjacent angles

• Use their previous knowledge of ratios to find unknown angle measures

• Construct bisectors, triangles, and quadrilaterals through the use of a protractor

• Be introduced to the concept of measures of variation and will begin to understand quartiles and interquartile range

Curricular Sequence

Course Description:

In eighth grade, students make several advances in their algebraic reasoning, particularly as it relates to linear equations. Students extend their understanding of proportional relationships to include all linear equations, and they consider what a “solution” looks like when it applies to a single linear equation as well as a system of linear equations. They learn that linear equations can be a useful representation to model bivariate data and to make predictions. Functions emerges as a new domain of study, laying a foundation for more in-depth study of functions in high school. Lastly, students study figures, lines, and angles in two-dimensional and three-dimensional space, investigating how these figures move and how they are measured.

Course Objectives

     Students will:

• Know that there are numbers that are not rational, and approximate them by rational numbers

• Work with radicals and integer exponents 

• Understand the connection between proportional relationships, lines, and linear equations

• Analyze and solve linear equations and pairs of simultaneous linear equations

• Define, evaluate, and compare functions

• Use functions to model relationships between quantities

• Understand congruence and similarity using physical models, transparencies, or geometry software

• Understand and apply the Pythagorean Theorem

• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

• Investigate patterns of association in bivariate data

Curricular Sequence