Common Core
Skills available for Common Core fifthgrade math standards
Click on the name of a skill to practice that skill.
Operations and Algebraic Thinking.
Write and interpret numerical expressions.
 CC.5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
 CC.5.OA.2 Write simple 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 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Analyze patterns and relationships. Generate two numerical patterns using two given rules.
 CC.5.OA.3 Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. 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, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Number and Operations in Base Ten
Understand the place value system.
 CC.5.NBT.1 Recognize that in a multidigit 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.
 CC.5.NBT.2 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.
» I.05: Multiplication by multiples of 10  Assessment 1
» I.06: Multiplication by multiples of 10  Assessment 2
 CC.5.NBT.3 Read, write, and compare decimals to thousandths.
» L.02: Explore the values of Tenth, Hundredths, and Thousandths
» L.03: Comparing decimals using story telling problems
» L.04: Exploring equivalent decimals
» L.06: Compare decimals
» L.07: Order the decimal numbers
» L.09: Compare, order and round decimals  Assessment 1
» L.10: Compare, order and round decimals  Assessment 2
 CC.5.NBT.3a Read and write decimals to thousandths using baseten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
 CC.5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Understand the place value system.
Perform operations with multidigit whole numbers and with decimals to hundredths.
 CC.5.NBT.5 Fluently multiply multidigit whole numbers using the standard algorithm.
Perform operations with multidigit whole numbers and with decimals to hundredths.
 CC.5.NBT.6 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit 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.
» H.15: Divide 2 or 3 digit by 1 & 2 divisors to find out the quotients  Assessment 1
» H.16: Divide 2 or 3 digit by 1 & 2 divisors to find out the quotients  Assessment 2
 CC.5.NBT.7 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 addition and subtraction; relate the strategy to a written method and explain the reasoning used.
» I.03: Word problems on addition of Decimals
» I.04.01: Word problems on subtraction of decimals
» I.07.01: Multiplication of a decimal number by a whole number  Assessment 1
» I.08.01: Multiplication of two decimal numbers  Assessment 1
» I.09.01: Multiply three or more decimal numbers  Assessment 1
» I.10.01: Word problems on multiplication
» I.10.02: Review on multiplication of decimal
» I.11.02: Division of a decimal number by multiples of 10  Assessment 2
» I.12: Division of a decimal by a whole number
» I.13.01: Division with decimal quotient  Assessment 1
» I.13.02: Division with decimal quotient  Assessment 2
» I.13.03: Division with decimal quotient  Assessment 3
» I.14: Division of a whole number by a decimal number  Assessment 1
» I.15: Division of a whole number by a decimal number  Assessment 2
» I.16: Division of a decimal by a decimal  Assessment 1
» I.17: Division of a decimal by a decimal  Assessment 2
» I.18: Division of a decimal by a decimal  Assessment 3
» I.19: Division of a decimal by a decimal  Assessment 4
» I.23: Word problems on division
» L.11: Addition of decimals  Assessment 1
» L.12: Addition of decimals  Assessment 2
» L.13: Addition of decimals  Assessment 3
» L.14: Word problems on addition of decimals
» L.15: Review on addition of decimals
» L.16: Subtraction of decimals  Assessment 1
» L.23: Addition and Subtraction by using Decimals  Assessment 1
Number and Operations—Fractions
Use equivalent fractions as a strategy to add and subtract fractions.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 CC.5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
 CC.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 CC.4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
 CC.5.NF.4a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
 CC.5.NF.4b Find 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.
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
 CC.5.NF.5 Interpret multiplication as scaling (resizing) by:  a. Comparing 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.  b. Explaining 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); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a) / (n×b) to the effect of multiplying a/b by 1.
 CC.5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
 CC.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

CC.5.NF.7a Interpret division of a unit fraction by a nonzero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
» H.21: Division of fractions  Assessment 1
 CC.5.NF.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
 CC.5.NF.7c Solve realworld problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., 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 1/3cup servings are in 2 cups of raisins?
Measurement and Data
Convert like measurement units within a given measurement system.
Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8)
 CC.5.MD.2 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.
 CC.5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.  a. 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.  b. 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.
» R.05: Volume of irregular figures
 CC.5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
» O.17: Volume
 CC.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
 CC.5.MD.5a Find the volume of a right rectangular prism with wholenumber 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 threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication.
 CC.5.MD.5b Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real world and mathematical problems.
 CC.5.MD.5c Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the nonoverlapping parts, applying this technique to solve real world problems.
Geometry
Graph points on the coordinate plane to solve realworld and mathematical problems.
 CC.5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate).
 CC.5.G.2 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 twodimensional figures into categories based on their properties.
 CC.5.G.3 Understand that attributes belonging to a category of twodimensional 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.
Classify twodimensional figures into categories based on their properties.
 CC.5.G.4 Classify twodimensional figures in a hierarchy based on properties.


