Colorado State Standards for Mathematics: Grade 8

CO.1. Number Sense, Properties, and Operations

1.1. In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line. Students can:

1.1.a. Compare and order sets of integers and rational numbers that are expressed as fractions, decimals, or percents

1.1.b. Given a whole number from 0 - 100, determine whether it is a perfect square or find the two consecutive whole numbers between which its square root lies

1.1.c. Approximate the location of square roots between two whole numbers on a number line

1.2. Formulate, represent, and use algorithms with rational numbers flexibly, accurately, and efficiently. Students can:

1.2.a. Add, subtract, multiply and divide rational numbers including integers, positive and negative fractions and decimals

1.2.b. Apply computational methods to solve multi-step application problems involving percents and rational numbers

1.2.c. Analyze how credit and debt impact personal financial goals (PFL)

CO.2. Patterns, Functions, and Algebraic Structures

2.1. Linear functions model situations with a constant rate of change and can be represented algebraically, graphically, and using tables. Students can:

2.1.a. Convert from one representation of a linear function to another, including situations, tables, equations (slope-intercept form), and graphs

2.1.b. Use representations of linear functions to analyze situations and solve problems

2.1.c. Identify the dependent and independent variable in real-world situations

2.1.d. Identify and interpret the slope (rate of change) and y-intercept in graphs, in tables, and from equations in slope-intercept form

2.1.e. Model and graph two linear equations in slope-intercept form on the same coordinate plane and interpret the point of intersection as the solution to the system of equations

2.2. Properties of algebra, equality, and inequality are used to solve linear equations and inequalities. Students can:

2.2.a. Use the distributive, associative, and commutative properties to simplify algebraic expressions

2.2.b. Solve one-variable equations including those involving multiple steps, rational numbers, variables on both sides, and the distributive property

2.2.c. Solve inequalities in one variable including negative coefficients and graph the solution on a number line

2.2.d. Represent the distributive property in a variety of ways including numerically, geometrically, and algebraically

2.3. Graphs and tables can be used to distinguish between linear and nonlinear functions. Students can:

2.3.a. Given a table or graph determine if the function is linear

2.3.b. Explain the properties of linear functions in tables and graphs

CO.3. Data Analysis, Statistics, and Probability

3.1. Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge. Students can:

3.1.a. Given a scatter plot, calculate quadrant count ratio to quantify the magnitude and strength of the association between two variables for numeric data as positive, negative, or no correlation

3.1.b. Given a scatter plot suggesting a linear relationship, draw a line of fit to make predictions

3.1.c. Use time series plots (line graphs) to analyze the trend of a set of data over time

CO.4. Shape, Dimension, and Geometric Relationships

4.1. Objects in the plane and their parts and attributes can be analyzed. Students can:

4.1.a. Classify quadrilaterals and apply angle and side properties, including the sum of the interior angles

4.1.b. Apply properties of complementary, supplementary, and vertical angle relationships

4.1.c. Apply properties of parallel lines including corresponding angles and alternate interior angles

4.2. Direct and indirect measurements can be used to describe and make comparisons. Students can:

4.2.a. Use properties of similar triangles to find unknown lengths

4.2.b. Use the Pythagorean Theorem to find unknown lengths in right triangles

4.2.c. Use proportional reasoning to estimate distance, weight, and capacity

4.2.d. Use proportional reasoning to convert among measures including dimensional analysis

CO.5. Prepared Graduate Competencies in Mathematics: The prepared graduate competencies are the preschool through twelfth-grade concepts and skills that all students who complete the Colorado education system must master to ensure their success in a postsecondary and workforce setting.

5.1. Understand the structure and properties of our number system. At the most basic level numbers are abstract symbols that represent real-world quantities

5.2. Understand quantity through estimation, precision, order of magnitude, and comparison. The reasonableness of answers relies on the ability to judge appropriateness, compare, estimate, and analyze error

5.3. Are fluent with basic numerical and symbolic facts and algorithms, and are able to select and use appropriate (mental math, paper and pencil, and technology) methods based on an understanding of their efficiency, precision, and transparency

5.4. Make both relative (multiplicative) and absolute (arithmetic) comparisons between quantities. Multiplicative thinking underlies proportional reasoning

5.5. Recognize and make sense of the many ways that variability, chance, and randomness appear in a variety of contexts

5.6. Solve problems and make decisions that depend on understanding, explaining, and quantifying the variability in data

5.7. Understand that equivalence is a foundation of mathematics represented in numbers, shapes, measures, expressions, and equations

5.8. Make sound predictions and generalizations based on patterns and relationships that arise from numbers, shapes, symbols, and data

5.9. Apply transformation to numbers, shapes, functional representations, and data

5.10. Make claims about relationships among numbers, shapes, symbols, and data and defend those claims by relying on the properties that are the structure of mathematics

5.11. Communicate effective logical arguments using mathematical justification and proof. Mathematical argumentation involves making and testing conjectures, drawing valid conclusions, and justifying thinking

5.12. Use critical thinking to recognize problematic aspects of situations, create mathematical models, and present and defend solutions