**Try Google Translate to translate these documents to another language!**

Tennessee Mathematics Standards

2009-2010 Implementation

Grade Five Mathematics

Standard 1 – Mathematical Processes

Grade Level Expectations:

State Performance Indicators:

Standard 2 - Number and Operations

Grade Level Expectations:

Checks for Understanding (Formative/Summative Assessment):

State Performance Indicators:

Standard 3 – Algebra

Grade Level Expectations:

Understand and use order of operations.

Tennessee Mathematics Standards

2009-2010 Implementation

Grade Five Mathematics

Standard 1 – Mathematical Processes

Grade Level Expectations:

**GLE 0506.1.1**Use mathematical language, symbols, and definitions while developing mathematical reasoning.**GLE 0506.1.2**Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.**GLE 0506.1.3**Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.**GLE 0506.1.4**Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution strategies.**GLE 0506.1.5**Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.**GLE 0506.1.6**Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.**GLE 0506.1.7**Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.**GLE 0506.1.8**Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and reliable models of mathematical concepts.**Checks for Understanding (Formative/Summative Assessment):**

**0506.1.1**Make and test conjectures about geometric properties and develop logical arguments to justify conclusions.**0506.1.2**Make reasonable estimates of fraction and decimal sums or differences using models.**0506.1.3**Explore different methods of estimation including rounding and truncating.**0506.1.4**Explore problems in different contexts to interpret the meaning of remainders as discrete values or not.**0506.1.5**Solve problems in more than one way and explain why one process may be more effective than another.**0506.1.6**Communicate answers in correct verbal and numerical form; including use of mixed numbers or fractions and use of units.**0506.1.7**Organize and consolidate verbal statements involving fractions and mixed numbers into diagrams, symbols, and numerical expressions.**0506.1.8**Use patterns, models, and relationships as contexts for writing inequalities and simple equations.**0506.1.9**Use age-appropriate books, stories, and videos to convey ideas of mathematics.State Performance Indicators:

**SPI 0506.1.1**Given a series of geometric statements, draw a conclusion about the figure described.**SPI 0506.1.2**Estimate fraction and decimal sums or differences.**SPI 0506.1.3**Recognize the unit associated with the remainder in a division problem or the meaning of the fractional part of a whole given in either decimal or fraction form.**SPI 0506.1.4**Identify missing information and/or too much information in contextual problems.Standard 2 - Number and Operations

Grade Level Expectations:

**GLE 0506.2.1**Extend the understanding of place value through millions and millionths in various contexts and representations.**GLE 0506.2.2**Write natural numbers (to 50) as a product of prime factors and understand that this is unique (apart from order).**GLE 0506.2.3**Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division.**GLE 0506.2.4**Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm.**GLE 0506.2.5**Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals.Checks for Understanding (Formative/Summative Assessment):

**0506.2.1**Identify prime numbers up to 50.**0506.2.2**Use the prime factorization of two whole numbers to determine the greatest common factor and the least common multiple.**0506.2.3**Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.**0506.2.4**Use divisibility rules to factor numbers.**0506.2.5**Make reasonable estimates of fraction and decimal sums and differences.**0506.2.6**Add and subtract mixed numbers.**0506.2.7**Understand the placement of the decimal point in calculations of multiplication and long division, including the placement in the estimation of the answer.**0506.2.8**Understand that division by zero is undefined.**0506.2.9**Explore numbers less than 0 by extending the number line through familiar applications (e.g., temperatures below zero, owing money, measuring elevation below sea level).**0506.2.10**Use exponential notation to represent repeated multiplication of whole numbers.State Performance Indicators:

**SPI 0506.2.1**Read and write numbers from millions to millionths in various contexts.**SPI 0506.2.2**Write the prime factorization of numbers through 50 using both exponential and standard notation.**SPI 0506.2.3**Select a reasonable solution to a real-world division problem in which the remainder must be considered.**SPI 0506.2.4**Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers.**SPI 0506.2.5**Solve addition and subtraction problems involving both fractions and decimals.**SPI 0506.2.6**Add and subtract proper and improper fractions as well as mixed numbers.**SPI 0506.2.7**Recognize equivalent representations for the same number.**SPI 0506.2.8**Write terminating decimals in the form of fractions or mixed numbers.**SPI 0506.2.9**Compare whole numbers, decimals and fractions using the symbols <, >, and =.Standard 3 – Algebra

Grade Level Expectations:

**GLE 0506.3.1****GLE 0506.3.2**Develop and apply the concept of variable.

**GLE 0506.3.3**Understand and apply the substitution property.

**GLE 0506.3.4**Solve single-step linear equations and inequalities.

**Checks for Understanding (Formative/Summative Assessment):**

**0506.3.1**Evaluate an expression by substituting non-negative rational number values for letter variables in the expression.

**0506.3.2**Use variables appropriately to represent numbers whose values are not yet known.

**0506.3.3**Solve single-step linear equations using inverse operations.

**0506.3.4**Solve single-step linear inequalities and graph solutions on a number line.

**0506.3.5**Determine if a given value is a solution to a linear equation/inequality.

**0506.3.6**Recognize there are many numbers between any two whole numbers on the number line.

**State Performance Indicators:**

**SPI 0506.3.1**Evaluate algebraic expressions involving decimals and fractions using order of operations.

**SPI 0506.3.2**Evaluate multi-step numerical expressions involving fractions using order of operations.

**SPI 0506.3.3**Find the unknown in single-step equations involving fractions and mixed numbers.

**SPI 0506.3.4**Given a set of values, identify those that make an inequality a true statement.

**Standard 4 – Geometry and Measurement**

**Grade Level Expectations:**

**GLE 0506.4.1**Use basic formulas and visualization to find the area of geometric figures.

**GLE 0506.4.2**Describe polyhedral solids and analyze their properties, including volume and surface area.

**GLE 0506.4.3**Describe length/distance relationships using the first quadrant of the coordinate system.

**GLE 0506.4.4**Solve problems that require attention to both approximation and precision of measurement.

**Checks for Understanding (Formative/Summative Assessment):**

**0506.4.1**Develop the formula for the area of a triangle as it relates to the area of a parallelogram/rectangle.

**0506.4.2**Find the area of a convex polygon by decomposing it into triangles/rectangles.

**0506.4.3**Build, draw, and work with prisms by means of orthogonal views, projective views, and nets.

**0506.4.4**Describe and identify the five regular (Platonic) solids and their properties with respect to faces, shapes of faces, edges, and vertices.

**0506.4.5**Quantify total volume as filling space with same-sized units of volume without gaps or overlap.

**0506.4.6**Decompose prisms to calculate surface area and volume.

**0506.4.7**Understand, select and use units of appropriate size and type to measure angles, lengths/distances, area, surface area and volume.

**0506.4.8**Identify characteristics of the set of points that define vertical and horizontal line segments.

**0506.4.9**Correctly interpret significant digits in the accuracy of measurements and associated calculations.

**0506.4.10**Recognize that measurements are never exact.

**0506.4.11**Understand the usefulness of approximations.

**0506.4.12**Develop strategies for choosing correct tools of measurement.

**0506.4.13**Recognize and use measures of weight and temperature.

**State Performance Indicators:**

**SPI 0506.4.1**Solve contextual problems that require calculating the area of triangles and parallelograms.

**SPI 0506.4.2**Decompose irregular shapes to find perimeter and area.

**SPI 0506.4.3**Identify a three-dimensional object from two-dimensional representations of that object and vice versa.

**SPI 0506.4.4**Solve problems involving surface area and volume of rectangular prisms and polyhedral solids.

**SPI 0506.4.5**Find the length of vertical or horizontal line segments in the first quadrant of the coordinate system, including problems that require the use of fractions and decimals.

**SPI 0506.4.6**Record measurements in context to reasonable degree of accuracy using decimals and/or fractions.

**Standard 5 – Data, Probability and Statistics**

**Grade Level Expectations:**

**GLE 0506.5.1**Make, record, display and interpret data and graphs that include whole numbers, decimals, and fractions.

**GLE 0506.5.2**Describe the shape and important features of a set of data using the measures of central tendency.

**Checks for Understanding (Formative/Summative Assessment):**

**0506.5.1**Construct and analyze double bar and line graphs.

**0506.5.2**Represent data using ordered pairs in the first quadrant of the coordinate system.

**0506.5.3**Design investigations to address a question and consider how data collection methods affect the nature of the data set.

**0506.5.4**Recognize the differences in representing categorical and numerical data.

**0506.5.5**Evaluate how different measures of central tendency describe data.

**0506.5.6**Identify outliers and determine their effect on mean, median, mode and range.

**State Performance Indicators:**

**SPI 0506.5.1**Depict data using various representations, including decimal and/or fractional data.

**SPI 0506.5.2**Make predictions based on various data representations, including double bar and line graphs.

**SPI 0506.5.3**Calculate measures of central tendency to analyze data.

Standards copied from http://tennessee.gov/education/ci/math/index.shtml