Math

6th Grade Math

Open Up Resources is an engaging middle school mathematics course designed to develop students' mathematical skills, problem-solving abilities, and analytical thinking. This course covers a wide range of topics, including number and quantity, algebraic reasoning, ratios, percentages, geometry and more. Students will explore real-world applications, strengthen their computational fluency, and develop a solid foundation in mathematical concepts.

Learning Goals

Numbers and Operations

• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 
•  Interpret and compute quotients of fractions involving a combination of division of fractions by fractions, whole numbers and mixed numbers.
• Apply computation skills to solve real-world problems. 

Expressions and Equations

• Write and evaluate numerical expressions involving the order of operations (PEMDAS).
• Write, read, and evaluate expressions in which letters represent numbers.
• Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.
• Solve one step equations.

Ratios, Unit Rates, and Percentages

• Understanding the concept of a ratio and use ratio language to describe a ratio relationship between two or more concepts. 
• Understand the concept of a unit rate.
• Recognizes a percent of a quantity as a rate per 100.
• Use understanding of ratios and percentages to solve real-world and mathematical problems.

Geometry

• Find the area of quadrilaterals, triangles, and polygons by composing into rectangles or decomposing into triangles and other shapes
• Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.
• Apply these skills to solve real-world problems.

7th Grade Math

Open Up Resources is an engaging middle school mathematics course designed to develop students' mathematical skills, problem-solving abilities, and analytical thinking. This course covers a wide range of topics, including number and quantity, algebraic reasoning, ratios, percentages, geometry and more. Students will explore real-world applications, strengthen their computational fluency, and develop a solid foundation in mathematical concepts.

Learning Goals

Scale Drawings

• Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Proportional Relationships

• Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
• Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• Represent proportional relationships by equations. 
• Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Area and Circumference of Circles 

• Know the formulas for the area and circumference of a circle and use them to solve simple and more complex problems.

Percents 

• Use proportional relationships to solve multistep ratio and percent problems, including tax, tips, discounts, markups, commission, simple interest, percent increase, and percent decrease.

Operations with Rational Numbers 

• add, subtract, multiply, divide positive and negative integers, fractions, mixed numbers, and decimals

Expressions, Equations, and Inequalities

• write and solve basic one variable expressions, equations, and inequalities

8th Grade Math

Open Up Resources is an engaging middle school mathematics course designed to develop students' mathematical skills, problem-solving abilities, and analytical thinking. This course covers a wide range of topics, including similarity, congruence, proportional relationships, systems of equations, volume, and more. Students will explore real-world applications, strengthen their algebraic competency, and develop a solid foundation in mathematical concepts.

Learning Goals

The Number System

• Students understand and use notation such as 2 and 35 for square and cube roots and they understand the terms “rational number” and “irrational number.” 

Expressions and Equations

• Students deepen their understanding of slope, and they learn to recognize connections among rate of change, slope, and constant of proportionality, and between linear and proportional relationships.
• Students write and solve linear equations in one variable. These include equations with no solutions, exactly one solution, and infinitely many solutions.
• Students learn about the properties of exponents, apply these concepts to the base-ten system, and learn about orders of magnitude and scientific notation

Functions

• Students are introduced to the concept of a function. They learn to understand and use the terms “input,” “output,” and “function.”

Geometry

• Students learn to understand and use the terms “reflection,” “rotation,” “translation,” recognizing what determines each type of transformation.
• Students learn to understand and use the term “dilation,” and to recognize that a dilation is determined by a point called the “center” and a number called the “scale factor.” 

Statistics and Probability

• Students generate and work with bivariate data sets. They learn to understand and use the terms “scatter plot” and “association,” and describe associations as “positive” or “negative” and “linear” or “nonlinear.”

Algebra

This course allows students to strengthen their understanding of Pre-Algebra concepts while studying topics in Algebra I attached to the Common Core standards: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability.  

**Students interested in this course will be considered by the following: Teacher recommendation, statewide assessment scores, classroom data.

Algebra 1 Topics Include:

The language and tools of Algebra

• Maintain fluency in the addition, subtraction, multiplication, and division of rational numbers.
• Reason quantitatively, create expressions and solve equations that model real-life mathematical problems.
• Understand the structure of expressions and use foundational skills to write, simplify and apply properties of operations to algebraic expressions.

Solving linear equations

• Analyze linear equations and understand the process of reasoning associated with creating and solving them in one variable.

Functions and patterns

• Understand the concept of a function, to include the representation of functions using tables, graphs, mappings and basic function notation.

Analyzing linear equations

• Represent and solve linear equations graphically and understand the connections between lines and their equations.
• Use basic graphical and numerical techniques to analyze data in one and two variables and make inferences to justify conclusions.

Solving systems of linear equations

• Solve systems of equations by graphing, substitution, elimination and apply these methods to solve real-life mathematical problems.

Solving linear inequalities

• Analyze linear inequalities algebraically and graphically and understand the process of reasoning associated with creating and solving them in one variable.

Polynomials 

• Perform basic arithmetic operations on monomials and polynomials.

Factoring

• Understand the process of factoring as the inverse of multiplying and use it to generate equivalent expressions and to solve algebraic equations.