The Greene School’s accelerated and enriched middle school mathematics curriculum provides opportunities for our highly able students to increase the depth and breadth of their learning of mathematics by studying advanced-level concepts and skills. Our curriculum allows students to complete Algebra I, Algebra II, and Geometry in middle school.

Students are provided opportunities to apply mathematical content to real-life situations. Challenging outside projects and long-term assignments are used as an integral part of the program to enable students to extend and apply the mathematics learned in the classroom. Students are expected to read technical matter on a regular basis, in order to gather information about challenging mathematical concepts. Technology is integrated throughout our math program in order to facilitate students’ problem-solving skills. Students learn to use scientific calculators, graphing calculators, and spreadsheets in their solutions and explanations. Students are assessed using math journals, checklists, informal observations, quizzes, tests, and projects.

Sixth Grade Algebra I Topics and Units Covered Include:

• Relationships Between Quantities and Reasoning with Equations

• Linear Relationships

• Expressions and Equations

• Functions and Modeling

• Descriptive Statistics

Mathematics

The fifth grade curriculum is a transition from the arithmetic-based curriculum of fourth grade to the algebra that is developed in middle school. The course reinforces the comprehension, computation, and application skills necessary for a solid foundation in mathematics, while also exposing students to algebraic concepts and developing their abstract reasoning skills. Word problems are incorporated throughout the course of the year to support and strengthen students in applying their knowledge. In fifth grade, students extend their computational skills with whole numbers, decimals, and fractions to include operations with integers, exponents, and rational numbers. They are also introduced to the concepts of ratio, proportion, and percent, as well as the language of algebra used to write and solve expressions and equations. In addition, students will further develop their knowledge of concepts in geometry, measurement, probability, and statistics. To enhance their comprehension and deepen their foundation, Pearson’s Envision Math textbook and the internet, including iXL, serve as resources for projects, additional problems, and review activities.

Mathematical skills taught in fifth grade include:

Number Sense and Operations with Whole Numbers

• Use place value, including how to read, write, and compare whole numbers to the hundred-trillions place.

• Write numbers in standard, expanded, and word form.

• Know the language of addition, subtraction, multiplication, and division, and understand the relationship between the operations.

• Use estimation to solve problems including all four operations.

• Understand the properties of addition and multiplication including the identity, inverse, commutative, associative, distributive and zero property of multiplication.

• Express very large and very small numbers using expanded and scientific notation.

• Solve single and multi-step real-life problems involving number operations.

• Determine key vocabulary words and concepts, check for reasonableness, and identify relevant and irrelevant information with problems.

Number Sense and Operations with Integers

• Order, compare, and graph integers with and without a number line.

• Solve mathematical operations of addition, subtraction, multiplication, and division with integers.

• Solve numeric expressions with integers using order of operations.

• Solve real-life problems involving integers.

Number Sense and Operations with Fractions and Decimals

• Use place value, including how to read, write, and compare decimals to the ten-thousandths place.

• Use models and number lines to identify, compare, and represent the order of fractions and decimals.

• Recognize the relationship between fractions and decimals.

• Add, subtract, multiply, and divide fractions and mixed numbers with like and unlike denominators.

• Convert between mixed numbers and improper fractions.

• Solve real-life problems involving fractions and decimals.

Number Sense and Operations with Ratios, Proportions, and Percent

• Write ratios in three different ways.

• Find unit rate.

• Solve problems involving ratios and rate with proportional reasoning.

• Understand the meaning of percent.

• Discover the relationship between fractions, decimals, and percentages.

• Convert between fractions, decimals, and percent.

• Perform calculations with percentages.

• Apply concepts learned to real life applications such as interest, discounts, taxes, tips, and sale prices.

Geometry and Spatial Sense

• Identify congruent and similar figures.

• Use proportions to find the missing side of similar figures.

• Use formulas to find perimeter, area, and volume on singular and compound shapes.

• Identify and define parts of a circle.

• Use formulas to find the circumference and area of a circle and semicircle.

• Graph and identify ordered pairs on a four-quadrant plane.

• Identify the quadrant for a given ordered pair.

Measurement

• Convert measurements within the same system, customary and metric.

• Simplify ratios with measurement.

Data Analysis, Statistics, and Probability

• Read and interpret various types of tables, including tally charts and line plots, and simple graphs, including bar, line, circle, and pictographs.

• Calculate mean, median, mode, and range from a given set of data.

• Find the probability of simple and compound events including independent and dependent events.

Patterns, Functions, and Pre-Algebra

• Use order of operations to solve numeric expressions.

• Solve single and multi-step algebraic equations including all four operations.

• Read, write, and solve algebraic expressions and equations.

• Convert between word phrases and algebraic expressions or equations.