Tennessee Standards
Tennessee 5th Grade Math Standards
All 25 Tennessee math standards for 5th grade, each explained in plain English. The official wording is one click away under each one.
25 standards
Operations and Algebraic Thinking
3 standardsWrite and interpret numerical expressions.
5.OA.A.1
Group parts of whole-number expressions with parentheses or brackets and evaluate them in the standard order of operations, leaving out exponents.
Official wording
Use parentheses and/or brackets in numerical expressions involving whole numbers and evaluate expressions having these symbols using the conventional order by applying the Order of Operations. (When applying the order of operations, the evaluation of exponents need not be included.)
5.OA.A.2
Write expressions that record a calculation and read expressions without computing them, like seeing that 4 times a sum is four times as big as the sum.
Official wording
Write numerical expressions that record calculations with numbers and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 x (8 + 7). Recognize that 3 x (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.
Analyze patterns and relationships.
5.OA.B.3
Make two number patterns from two rules, like add 2 and add 4 starting at 0, compare their matching terms, and graph the pairs in the first quadrant.
Official wording
Generate two numerical patterns using two given rules. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences.aIdentify relationships between corresponding terms in two numerical patterns.bForm ordered pairs (limited to first quadrant) consisting of corresponding terms from two numerical patterns and graph the ordered pairs on a coordinate plane.
Number and Operations in Base Ten
7 standardsUnderstand the place value system.
5.NBT.A.1
Know that each place is worth ten times the place to its right and one tenth of the place to its left.
Official wording
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.2
Explain how the zeros and the decimal point move when a number is multiplied or divided by a power of 10, and write powers of 10 with exponents.
Official wording
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.A.3
Read and write decimals to thousandths in numerals, words and expanded notation, and compare two of them by place value using >, = or <.
Official wording
Read and write decimals to thousandths using standard form, word form, and expanded notation (e.g., the expanded notation of 347.392 is written as (3 x 100) + (4 x 10) + (7 x 1) + (3 x (1/10)) + (9 x (1/100)) + (2 x (1/1000))). Compare two decimals to thousandths based on meanings of the digits in each place and use the symbols >, =, and < to show the relationship.
5.NBT.A.4
Round decimals to the nearest whole number, tenth or hundredth using place value, and show the rounding on a number line.
Official wording
Round decimals to the nearest hundredth, tenth, or whole number using understanding of place value, and use a number line to explain how the number was rounded.
Perform operations with multi-digit whole numbers and with decimals to hundredths. (See Table 3 - Properties of Operations)
5.NBT.B.5
Multiply whole numbers fluently with efficient methods, up to a four-digit number times a three-digit number, like 2,415 × 136.
Official wording
Fluently multiply multi-digit whole numbers (up to three-digit by four-digit factors) using efficient strategies and algorithms.
5.NBT.B.6
Divide numbers up to four digits by two-digit divisors to find quotients and remainders, using place value strategies, and explain with equations, arrays or area models.
Official wording
Find whole-number quotients and remainders of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.B.7
Do all four operations with decimals to hundredths using models and strategies, check with estimates, keep products within thousandths and one number in division whole.
Official wording
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations. Assess the reasonableness of answers using estimation strategies. (Limit multiplication problems so that the product does not exceed thousandths. Limit division problems so that either the dividend or the divisor is a whole number.)
Number and Operations - Fractions
7 standardsUse equivalent fractions as a strategy to add and subtract fractions. (See Table 1 - Addition and Subtraction Situations for whole number situations that can be applied to fractions)
5.NF.A.1
Add and subtract fractions and mixed numbers with unlike denominators by rewriting them with a common denominator, like 1/4 + 2/3 = 3/12 + 8/12 = 11/12.
Official wording
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 or 3/5 + 7/10 = 6/10 + 7/10 = 13/10.
5.NF.A.2
Solve story problems that add or subtract fractions of the same whole, including unlike denominators, and use benchmarks like 1/2 to check if answers make sense.
Official wording
Solve contextual problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (See Table 2 - Multiplication and Division Situations for whole number situations that can be applied to fractions)
5.NF.B.3
Explain a fraction as a division, like 3/4 = 3 ÷ 4, and solve sharing story problems whose answers are fractions or mixed numbers, using models or equations.
Official wording
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). For example, 3/4 = 3 ÷ 4 so when 3 wholes are shared equally among 4 people, each person has a share of size 3/4. Solve contextual problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models or equations to represent the problem. For example, if 8 people want to share 49 sheets of construction paper equally, how many sheets will each person receive? Between what two whole numbers does your answer lie?
5.NF.B.4
Multiply a fraction by a whole number or by another fraction, like 3/4 × 8 or 1/2 × 3/5, using models, and find areas of rectangles with fraction side lengths.
Official wording
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction by a fraction.aInterpret the product a/b x q as a x (q ÷ b) (partition the quantity q into b equal parts and then multiply by a). Interpret the product a/b x q as (a x q) ÷ b (multiply a times the quantity q and then partition the product into b equal parts). For example, use a visual fraction model or write a story context to show that 2/3 x 6 can be interpreted as 2 x (6 ÷ 3) or (2 x 6) ÷ 3. Do the same with 2/3 x 4/5 = 8/15. (In general, a/b x c/d = ac/bd.)bFind the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles and represent fraction products as rectangular areas.
5.NF.B.5
Think of multiplying as resizing, predict whether a product is bigger or smaller than a factor, and explain why fractions above 1 enlarge a number and below 1 shrink it.
Official wording
Interpret multiplication as scaling (resizing).aCompare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. For example, know if the product will be greater than, less than, or equal to the factors.bExplain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explain why multiplying a given number by a fraction between 0 and 1 results in a product less than the given number; and relate the principle of fraction equivalence a/b = (a x n)/(b x n) to the effect of multiplying a/b by 1.
5.NF.B.6
Solve real-life problems that multiply fractions and mixed numbers, showing them with fraction models or equations, like 1 1/2 batches using 2/3 cup each.
Official wording
Solve real-world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations to represent the problem.
5.NF.B.7
Divide a unit fraction by a whole number and a whole number by a unit fraction, like 1/3 ÷ 4 = 1/12 and 4 ÷ 1/5 = 20, and use this in real-world problems.
Official wording
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.aInterpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3. In other words, when thirds are partitioned into 4 equal groups, they become twelfths.bInterpret division of a whole number by a unit fraction and compute such quotients. For example, use visual models and the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4 (i.e., there are 20 groups of 1/5 inside 4 wholes and connect this to ? x (1/5) = 4).cSolve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and non-unit fractions by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?
Measurement and Data
5 standardsConvert like measurement units within a given measurement system from a larger unit to a smaller unit.
5.MD.A.1
Convert bigger units to smaller ones within the customary or metric system, like 2.5 liters to 2,500 milliliters, and use this in multi-step real-life problems.
Official wording
Convert customary and metric measurement units within a single system by expressing measurements of a larger unit in terms of a smaller unit. Use these conversions to solve multi-step real-world problems involving distances, intervals of time, liquid volumes, masses of objects, and money (including problems involving simple fractions or decimals). For example, 3.6 liters and 4.1 liters can be combined as 7.7 liters or 7700 milliliters.
Represent and interpret data.
5.MD.B.2
Make a line plot with measurements in halves, quarters and eighths, and use fraction operations to answer questions about it.
Official wording
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
5.MD.C.3
Understand volume as the space inside a solid, measured by how many unit cubes fill it without gaps or overlaps.
Official wording
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.aUnderstand that a cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume and can be used to measure volume.bUnderstand that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.C.4
Find volume by counting unit cubes in cubic centimeters, cubic inches, cubic feet, or made-up units.
Official wording
Measure volume by counting unit cubes, using cubic centimeters, cubic inches, cubic feet, and improvised units.
5.MD.C.5
Find the volume of rectangular prisms by packing cubes and using V = l × w × h or V = B × h, and add volumes of two joined prisms to solve problems.
Official wording
Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume of right rectangular prisms.aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent whole-number products of three factors as volumes (e.g., to represent the associative property of multiplication).bKnow and apply the formulas V = l x w x h and V = B x h (where B represents the area of the base) for rectangular prisms with whole number edge lengths in the context of solving real-world and mathematical problems.cRecognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world problems.
Geometry
3 standardsGraph points on the coordinate plane to solve real-world and mathematical problems.
5.G.A.1
Plot and name points on a first-quadrant grid, reading an ordered pair as steps right along the x-axis from zero, then steps up along the y-axis.
Official wording
Graph ordered pairs and label points using the first quadrant of the coordinate plane. Understand in the ordered pair that the first number indicates the horizontal distance traveled along the x-axis from the origin and the second number indicates the vertical distance traveled along the y-axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.G.A.2
Graph real-world data as points in the first quadrant of a coordinate grid and explain what each point’s coordinates mean.
Official wording
Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane and interpret coordinate values of points in the context of the situation.
Classify two-dimensional figures into categories based on their properties.
5.G.B.3
Sort flat shapes into a family tree by their properties, knowing a subgroup has every feature of its group, like squares having right angles because they are rectangles.
Official wording
Classify two-dimensional figures in a hierarchy based on properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
The official Tennessee documents
- Tennessee Mathematics Standards · adopted February 2021 · since 2023-24
Tennessee Academic Standards for Mathematics, Tennessee Department of Education, tn.gov/education.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
The plain-English lines are EMStudio's own explanations, shown beside the official wording. They are not part of the standards.