Mathematics Standards

Fifth Grade

B= Beginning D= Developing S= Secure

Problem Solving

Solves problems that arise in math and in other content areas:

• Builds new mathematical knowledge through problem solving
• Makes, investigates, and applies a variety of strategies to solve problems
• Monitors and reflects on solutions
• Develops and evaluates inferences and predictions that are based on data 

Communicates mathematical thinking coherently and clearly:

• Uses mathematical language to express ideas
• Shows connections among mathematical ideas
• Creates and uses representations to organize, record, and communicate mathematical ideas

Number and Operations

Understands Numbers, ways of representing numbers, relationships among numbers, and number systems:

• Renames numbers written in exponential notation  (B/D)
• Identifies prime and composite numbers  (S)
• Draws arrays to model multiplication  (S)
• Identifies even and odd numbers  (S)
• Rounds numbers to designated places  (D)
• Identifies place value in numbers to billions  (S)
• Knows place value to hundredths  (S)
• Understands and applies powers of 10  (D)
• Understands and applies order of operations to evaluate expressions and solve number sentences  (D)
• Compares and orders integers  (D/S)
• Orders and compares fractions  (D/S)

Understands meanings of operations and how they relate to one another:

• Uses a divisibility test to determine if a number is divisible by another number  (D/S)
• Understands how square numbers and their square roots are related  (S)
• Converts between fractions and mixed or whole numbers  (S)
• Finds common denominators  (S)
• Converts between fractions, decimals, and percents  (S)
• Understands the function and placement of parentheses in number sentences  (D/S)
• Finds a percent of a number  (D)

Computes fluently and makes reasonable estimates:

• Knows multiplication facts  (S)
• Writes and solves open sentences for number stories  (B/D)
• Makes magnitude estimates  (D/S)
• Finds the sum and difference of multi-digit whole numbers and decimals  (S)
• Finds the product of multi-digit whole numbers and decimals  (D/S)
• Divides decimal numbers by whole numbers with no remainders  (B/D)
• Writes and solves number sentences with variables for division number stories  (B/D)
• Finds the quotient and remainder of a whole number divided by a 1-digit whole number  (D/S)
• Finds the quotient and remainder of a whole number divided by a 2-digit whole number  (D)
• Makes magnitude estimated for quotients of whole and decimal numbers divided by whole numbers  (D)
• Interprets the remainder in division number stories  (D/S)
• Adds and subtracts fractions with like denominators  (D)
• Adds and subtracts fractions with unlike denominators  (D)
• Adds and subtracts integers  (D)
• Uses an algorithm to multiply mixed numbers  (B)
• Uses an algorithm to multiply fractions  (D)
• Uses an algorithm to subtract mixed numbers with like denominators  (D)
• Uses algorithm to add mixed numbers  (D/S)
• Finds the greatest common factor of two numbers  (D)
• Finds the least common multiple of two numbers   (D)
• Finds the prime factorization of numbers  (B/D/S)

Algebra

Understands patterns, relations and functions:

• Determines the value of a variables; use this value to complete a number sentence  (D/S)

Represents and analyzes mathematical situations and structures using algebraic symbols:

• Determines whether number sentences are true or false  (D/S)

• Writes algebraic expressions to represent situations  (D)

Uses mathematical models to represent and understand quantitative relationships:

• Solves on-step pan-balance problems  (D/S)
• Solves two-step pan-balance problems  (B)
• Represents rate problems as formulas, tables, and graphs  (D)
• Finds equivalent fractions  (D/S)

Geometry

Analyzes characteristics and properties of two-and three-dimensional geometric shapes and develops mathematical arguments about geometrical relationships:

• Identifies types of triangles  (D/S)

• Knows properties of polygons  (S)
• Identifies the base and height of triangles and parallelograms  (D/S)
• Uses a formula to find the area of triangles and parallelograms  (D/S)
• Understands the concept of area of a figure  (S)
• Uses a formula to find the area of rectangles  (S)
• Uses formulas to find circumference and area of a circle  (D)
• Distinguishes between circumference and area of a circle  (D)
• Finds the surface area of prisms  (B)
• Understands how to find the surface area of cylinders  (B)
• Knows the properties of geometric solids  (S)
• Uses formulas to find the area of polygons and circles  (S)

Specifies locations and describes spatial relationships using coordinate geometry and other representational systems:

• Determines angle measures based on relationships between angles  (D)
• Estimates the measure of an angle  (D/S)
• Measures an angle to within 2 degrees  (D/S)
• Identifies types of angles  (D/S)
• Plots ordered pairs on a one-quadrant coordinate grid  (S)
• Plots ordered pairs on a four-quadrant coordinate grid  (D)

Applies transformations and uses symmetry to analyze mathematical situations:

• Defines and creates tessellations  (S)

Measurement

Understands measurable attributes of objects and the units, systems, and processes of measurement:

• Understands the concept of volume of a figure  (D/S)
• Understands the relationship between the volume of pyramids and prisms, and the volume of cones and cylinders  (B)
• Understands the concept of and calculate capacity  (B)

Applies appropriate techniques, tools, and formulas to determine measurements:

• Uses formulas to find the volume of prisms and cylinders  (D/S)

Data Analysis and Probability

Formulates questions that can be addressed with data and collects, organizes, and displays relevant data to answer them:

• Draws a circle graph for a set of data  (D)
• Measures pieces of a circle graph; interpret a circle graph  (D)
• Constructs a stem-and-leaf plots  (B/D)
• Reads and interprets stem-and-leaf plots  (B/D)
• Interprets mystery line plots and graphs  (D)
• Understands and uses tree diagrams to solve problems  (B)

Selects and uses appropriate statistical methods to analyze data:

• Identifies the maximum, minimum, median, mode, and mean for a data set  (S)
• Identifies and uses data landmarks  (S)

Develops and evaluates inferences and predictions that are based on data:

• Understands how sample size affects results  (D)

Understands and applies basic concepts of probability:

• Computes the probability of outcomes when choices are equally likely  (B)
• Uses the Multiplication Counting Principle to find the total number of possible outcomes of a sequence of choices  (B/D)