Ratios and Proportional Relationships

Understands ratio concepts

 Trimester NS AS MS (Target) ES 1st - 3rd Student demonstrates limited ability in the understanding and reasoning of ratio, proportion, and/or  percentages.Student demonstrates limited ability to calculate percentages with tips, sales, tax, and interest. Student inconsistently demonstrates an understanding and use of ratios and proportions in context.Student inconsistently calculates percentages with tips, sales, tax, and interest. Student frequently interprets and uses ratios and proportions in different contexts.Student frequently calculates percentages with tips, sales, tax, and interest. Student consistently interprets and understands when to use ratios and proportions in real life scenarios.Student consistently calculates percentages with tips, sales, tax, and interest.

Uses ratio reasoning to solve problems

 Trimester NS AS MS (Target) ES 1st - 3rd Student demonstrates limited ability in the understanding and reasoning of ratio, proportion, or  percentages to solve problems. Student inconsistently demonstrates the use of proportions to solve problems. Student frequently uses ratios and proportions to solve problems. Student consistently solves problems and  applies the use of ratios and proportions in real life scenarios.Student consistently calculates and applies the concept of percentages to problem-solving situations.

 The Number System

Applies concepts of multiplication and division to divide fractions by fractions

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability to solve problems involving addition, subtraction, multiplication, and division of positive fractions.Student has limited ability to order and compare simple fractions and decimals. Student  inconsistently solves problems involving addition, subtraction, multiplication, and division of positive fractions.Student inconsistently orders and compares simple fractions and decimals. Student frequently solves problems involving addition, subtraction, multiplication, and division of positive fractions.Student frequently orders and compares simple fractions and decimals. Student consistently solves problems, compares and orders positive and negative fractions, decimals, and mixed numbers, and can place them on a number line.Student consistently  computes and/or solves addition, subtraction, multiplication, and division problems with multi-digit numbers.

Computes fluently with multi-digit numbers

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability to compute and/or solve addition, subtraction, multiplication, and division problems with multi-digit numbers. Student inconsistently  computes and/or solves addition, subtraction, multiplication, and division problems with multi-digit numbers. Student frequently computes and/or solves addition, subtraction, multiplication, and division problems with multi-digit numbers. Student consistently computes and/or solves addition, subtraction, multiplication, and division problems with multi-digit numbers.

Finds common factors and multiples

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability to  find common factors and/or multiples. Student inconsistently   finds common factors and/or multiples. Student frequently finds common factors and/or multiples. Student consistently understands the least common multiple and the greatest common divisor of whole numbers and uses them to solve problems with fractions.

Applies positive and negative numbers in given scenarios

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability  to identify and/or apply positive and negative numbers in given scenarios.Student has limited ability to compare and order positive and negative fractions, decimals, and mixed numbers and places them on a number line. Student inconsistently  identifies and/or applies positive and negative numbers in given scenarios.Student inconsistently  compares and orders positive and negative fractions, decimals, and mixed numbers and places them on a number line. Student frequently identifies and/or applies positive and negativenumbers in given scenarios. Student frequently compares and orders positive and negative fractions, decimals, and mixed numbers and places them on a number line. Student consistently identifies, applies, and/or  extends positive and negative numbers in given scenarios. Student consistently compares and orders positive and negative fractions, decimals, and mixed numbers and places them on a number line.

 Expressions and Equations

Reads, writes, and evaluates expressions, equations, and inequalities using numbers, variables, and mathematical terms

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability to write or solve simple algebraic equations.Student has limited ability to read, write and evaluate algebraic expressions, equations, and/or inequalities using numbers and variables using mathematical terms. Student inconsistently writes and solves simple algebraic equations with one variable by substituting given values. Student inconsistently writes and evaluates algebraic expressions equations, and/or inequalities using variables and mathematical terms. Student frequently understands and solves one-step linear equations with one variable . Student  frequently writes and evaluates algebraic expressions, equations, and/or inequalities for a given situation using variables using and mathematical terms. Student consistently solves multi-variable, multi-step linear equations and inequalities.Student is consistently evaluates expressions, equations, and/or inequalities with two or more variables and multiple operations using mathematical terms.

Solves real world and mathematical problems using expressions, equations, and inequalities

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability to demonstrate and/or understand the commutative, associative, and distributive properties to evaluate expressions.Student has limited ability to demonstrate and/or understand thealgebraic order of operations. Student inconsistently demonstrates and/or understands the commutative, associative, and distributive properties to evaluate expressions.Student inconsistently demonstrates and/or understands the algebraic order of operations. Student frequently applies the algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions. Student frequently solves problems manually by understanding the correct order of operations or by using a calculator. Student consistently explains applies, and extends understanding of the algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions and solve real world mathematical problems.  Student  consistently solves problems manually by understanding the correct order of operations or by using a calculator.

 Geometry

Solves real world problems involving area, surface area, and volume

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited ability to  understand the mathematical concept of a constant such as pi.Student has limited ability to identify angles as vertical, adjacent, complementary, or supplementary or provide descriptions of these terms.Student has limited ability to identify, describe, and use properties of angles to solve problems including those with unknown angles.Student has limited ability to  identify, describe, and use properties of quadrilaterals and triangles to solve problems.Student has limited ability to  understand or  solve  real-world and mathematical problems involving area, surface area, and volume. Student inconsistently   understands the mathematical concept of a constant such as pi.Student inconsistently identifies angles as vertical, adjacent, complementary, or supplementary and inconsistently provides descriptions of these terms.Student inconsistently identifies, describes, and uses properties of angles to solve problems including those with unknown angles.Student inconsistently identifies, describes, and uses properties of quadrilaterals and triangles to solve problems.    Student  inconsistently  solves  real-world and mathematical problems involving area, surface area, and volume. Student  frequently   understands the mathematical concept of a constant such as pi.Student frequently identifies angles as vertical, adjacent, complementary, or supplementary and provides descriptions of these terms. Student  frequently uses the properties of complementary and supplementary angles, and the sum of the angles of a triangle, to solve problems involving those with unknown angles.Student frequently   demonstrates and explains properties of quadrilaterals and triangles to solve problems. Student frequently solves and applies real-world and mathematical problems involving area, surface area, and volume. Student consistently uses ‘n’ (pi symbol) and the formulas for the circumference and area of a circle in problem solving. Student consistently   applies concepts and creates own problems to identify angles as vertical, adjacent, complementary, or supplementary and provides descriptions of these terms. Student consistently applies concepts and creates own problems with identifying, describing, and using properties of angles to solve problems including those with unknown angles. Student consistently applies concepts and creates own problems with identifying, describing, and using properties of quadrilaterals and triangles to solve problems. Student consistently solves and applies real-world and mathematical problems involving area, surface area, and volume.

 Statistics and Probability

Understands statistical questions and their variability

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited understanding of sampling, statistical questions, and their variability. Student inconsistently   demonstrates an understanding of sampling, statistical questions, and their variability. Student frequently demonstrates understanding of sampling, statistical questions, and their variability. Student consistently identifies statistical questions and uses different methods of selecting a sample of variability.

Summarizes and describes distributions

 Trimester NS AS MS (Target) ES 1st - 3rd Student has limited  ability to represent, describe, and/or summarize sample selection, possible outcomes and/or distributions for compound events. Student inconsistently demonstrates an understanding of a sample selection to represent a population. Student inconsistently   demonstrates an understanding of possible outcomes and/or distributions for compound events. Student frequently  identifies different ways of selecting a sample and which method makes a sample more representative for a population.Student frequently represents all possible outcomes for compound events in an organized way and expresses the probability of each outcome. Student consistently  identifies different  approaches of selecting a sample and which method makes a sample more representative for a population.Student consistently represents, explains, and analyzes  all possible outcomes for compound events in an organized way and expresses the probability of each outcome.