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Tennessee Math Standards - 5th Grade
MathScore aligns to the Tennessee Math Standards for 5th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the Tennessee Math Standards at other levels.
Numbers and Operations
5.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.a. read and write numbers from thousandths to millions; (Decimal Place Value )
b. name the place value of a given digit from thousandths to millions; (Decimal Place Value )
c. use various models to show relationships among whole numbers, fractions, mixed numbers, and decimals (e.g., number lines, base ten blocks, Venn diagrams, hundreds boards); (Compare Mixed Values , Positive Number Line , Fraction Comparison , Basic Fraction Comparison )
d. communicate using mathematical language and symbols;
e. model proper fractions, improper fractions, and mixed numbers; (Fraction Pictures )
f. show the relationship between improper fractions and mixed numbers; (Basic Fraction Simplification , Fraction Simplification )
g. recognize and generate equivalent forms of commonly used fractions, decimals, and percents (e.g., 1/10, 1/4, 1/2, 3/4); (Percentages , Percentage Pictures )
h. recognize relationships among commonly used fractions and decimals. (Fractions to Decimals , Decimals To Fractions )
5.1.2 Understand meanings of operations and how they relate to one another.
a. use commutative, associative, and identity properties; (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 )
b. explain and demonstrate the inverse nature of addition and subtraction; (Inverse Equations 1 )
c. explain and demonstrate the inverse nature of multiplication and division; (Inverse Equations 2 )
d. communicate the effects of addition, subtraction, multiplication, and division on size and order of numbers.
5.1.3 Solve problems, compute fluently, and make reasonable estimates.
a. select appropriate methods and tools for computations (e.g., mental computation, estimation, calculators, paper and pencil); (Many topics align to this standard)
b. explain why one from of a number might be more useful for computation than another form;
c. recognize reasonable estimates for operations;
d. add, subtract, multiply, and divide whole numbers and decimals; (Long Addition , Long Subtraction , Multiplication By One Digit , Long Multiplication , Long Division By One Digit , Long Division , Division with Remainders , Long Division with Remainders , Small Decimal Division , Money Multiplication , Money Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division )
e. use models, benchmarks, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators; (Basic Fraction Addition , Fraction Addition , Basic Fraction Subtraction , Fraction Subtraction )
f. identify missing information and/or too much information in real-world problems;
g. solve multi-step real-world problems; (Arithmetic Word Problems )
h. solve real-world problems using decimals, fractions, and percents. (Making Change , Unit Cost , Fraction Word Problems , Fraction Word Problems 2 , Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity )
Algebra
5.2.1 Represent and analyze patterns, relations, and functions.a. generalize and extend geometric and numerical patterns; (Patterns: Numbers , Patterns: Shapes )
b. represent and analyze patterns and functions using words, tables, and graphs; (Function Tables , Function Tables 2 )
c. apply basic function rules. (Function Tables , Function Tables 2 )
5.2.2 Represent and analyze mathematical situations and structures using algebraic symbols.
a. demonstrate understanding that an equation is a number sentence stating two quantities are equal;
b. solve open sentences using informal methods and knowledge of operations; (Missing Factor , Missing Term , Missing Operator , Compare Expressions )
c. represent the idea of a variable as an unknown quantity using a letter or a symbol; (Algebraic Word Problems , Algebraic Sentences )
d. express mathematical relationships using equations. (Algebraic Sentences )
5.2.3 Illustrate general properties of operations.
a. apply commutative, associative, zero, distributive, and identity properties; (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 , Distributive Property , Basic Distributive Property )
b. show that division is not commutative.
5.2.4 Analyze change in various contexts.
a. investigate how a change in one variable relates to a change in a second variable; (Line Graphs )
b. use a variety of methods to compare and describe situations involving constant and/or varying rates of change.
Geometry
5.3.1 Analyze characteristics and properties of two- and three-dimensional shapes.a. identify, compare, and analyze attributes of two- and three-dimensional figures; (Polygon Names )
b. use the attributes of geometric figures to develop definitions;
c. draw points, lines, line segments, rays, and angles;
d. identify and describe the attributes of a circle using appropriate mathematical language (e.g., radius, diameter, center); (Circle Measurements )
e. use properties to classify geometric figures; (Polygon Names )
f. investigate and describe the results of subdividing and combining geometric figures;
g. compare and contrast congruent and symmetrical geometric figures; (Congruent And Similar Triangles )
h. describe characteristics of lines and angles (e.g., parallel, perpendicular, intersecting, right, acute, obtuse); (Parallel and Perpendicular Lines )
i. make and test hypothesis about geometric properties;
j. explore similarity.
5.3.2 Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
a. describe location and movement using appropriate mathematical language; (Translations and Reflections )
b. find and specify points in Quadrant I of a coordinate system.
a. investigate, predict, and describe the results of transformations of two-dimensional figures (i.e., slides, flips, turns);
b. describe line and rotational symmetry in two-dimensional figures;
c. describe a motion or a series of motions that will show that two shapes are congruent.
5.3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.
a. construct and draw two- and three-dimensional geometric figures;
b. create and describe mental images of objects, patterns, and paths;
c. build a three-dimensional object from a two-dimensional representation (nets) of that object;
d. use visualization and spatial reasoning to solve real-world problems
Measurement
5.4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.a. demonstrate understanding of the concepts of length, perimeter, circumference, area, weight, capacity, volume, elapsed time, and angle measure;
b. demonstrate understanding that measurements are approximations;
c. understand how differences in units affect precision;
d. demonstrate understanding of the relationships among the units within the same system of measurements; (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Area and Volume Conversions )
e. explore what happens to measurements of a two-dimensional shape when the shape is changed in some way (e.g., perimeter, area). (Area And Volume Proportions )
5.4.2 Apply appropriate techniques, tools, and formulas to determine measurements.
a. apply and explain appropriate estimation strategies using standard units of measure;
b. select and apply appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles;
c. select and use appropriate tools for measuring in real-world situations;
d. solve real-world problems involving measurement and elapsed time; (Time Intervals )
e. read and record temperature using Fahrenheit and Celsius scales;
f. develop, understand, and use formulas to find the area of parallelograms and triangles; (Triangle Area , Parallelogram Area )
g. explain and demonstrate how scale in maps and drawings shows relative size and distance;
h. develop informal strategies to determine the surface area and volume of rectangular solids
Data Analysis and Probability
5.5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.a. collect data using observations, surveys, and experiments;
b. understand how data-collection methods affect the nature of the data set;
c. represent data using pictographs, bar graphs, tables, circle graphs, and line graphs;
d. interpret data displayed in pictographs, bar graphs, tables, circle graphs, and line graphs. (Tally and Pictographs , Bar Graphs , Line Graphs )
5.5.2 Select and use appropriate statistical methods to analyze data.
a. use measures of central tendency (i.e., mean, median, mode); (Mean, Median, Mode )
b. relate mean, median, and mode to a visual representation of a data set; (Mean, Median, Mode )
c. find the range of a data set. (Mean, Median, Mode )
5.5.3 Develop and evaluate inferences and predictions that are based on data.
a. make predictions and justify conclusions based on data; (Line Graphs )
b. design investigations to address a question;
c. examine various representations of data to evaluate how accurately the data is depicted;
d. explain the importance of sample size in investigations.
5.5.4 Understand and apply basic concepts of probability.
a. describe the likelihood or chance of events as likely, unlikely, certain, equally likely, or impossible;
b. use a sample space to predict the probability of an event;
c. understand that the measure of the likelihood of an event can be represented as a number from 0-1 (Probability )
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