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Common Core Mapping for Grade 5

In Grade 5, instructional time should focus on three critical areas:
(1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
(2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
(3) developing understanding of volume.


Related Topics:
Common Core for Mathematics
Common Core Lesson Plans Grade 5

Operations and Algebraic Thinking







Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Order of Operations

Expressions with parentheses

Order of Operations Games


Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation ԡdd 8 and 7, then multiply by 2Ԡas 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

Numerical Expressions

Word Forms and Numerical Expressions

Equivalent Expressions

Expressions with parentheses

Order of Operations Games


Generate two numerical patterns using two given rules. 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 ԁdd 3Ԡand the starting number 0, and given the rule ԁdd 6Ԡand 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.

Numerical Patterns

Visualizing & interpreting relationships between patterns

Number Sequence Games

Number and Operations in Base Ten







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.

Place Values

Divide by 10 Patterns

Estimate Quotients

Place Values

Place Values

Regrouping decimals

Regrouping whole numbers

Place Value Games


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.


Multiply Decimals

Divide Decimals by Multiples of 10

Divide Decimals

Divide Decimal Word Problems

Patterns in zeros

Understanding moving the decimal

Multiply by Powers of 10

Divide by Powers of 10

Decimal Games


Read, write, and compare decimals to thousandths.

Check Below

Money and decimal place value intuition

Decimal Games


Read and write decimals to thousandths using base-ten 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).

Writing Decimals

Write Decimals in Expanded Form

Writing and interpreting decimals

Decimal Games


Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Compare Decimals

Compare Decimals

Compare Decimals

Comparing decimal place value

Comparing decimals



Use place value understanding to round decimals to any place.

Round Decimals

Round Decimals

Round Decimals

Rounding numbers

Estimation with decimals

Decimal Games


Fluently multiply multi-digit whole numbers using the standard algorithm.

Multi-digit Multiplication

Multiply 3-digit by 2-digit

Multiply 3-digit by 3-digit

Multi-digit multiplication

Multiplication Games


Find whole-number quotients 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.

Divide by 2 digits

Divide by Multiples of 10

2-digit Dividends and 2-digit Divisors

Up to 4-digit Dividends

Divide 3-digit by 2-digit (no remainder)

Divide 3-digit by 2-digit

Divide 4-digit by 2-digit (no remainder)

Divide 4-digit by 2-digit

Division Games


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.

Add & Subtract Decimals

Multiply & Divide Decimals

Relate Decimal and Fraction Multiplication

Add Decimals (Place Value Strategies)

Add decimals

Subtract decimals

Multiply decimal by number

Multiply decimal by decimal

Divide decimal by number

Divide decimal by decimal

Decimal Games

Number and Operations and Fractions







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. (In general, a/b + c/d = (ad + bc)/bd.)

Add & Subtract Fractions & Mixed Numbers

Make Equivalent Fractions

Add Fractions with Unlike Units

Subtract Fractions with Unlike Units

Add Fractions

Subtract Fractions

Add Mixed Numbers

Subtract Mixed Numbers

Fraction Games


Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. 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.

Fraction Word Problems

Two-Step Fraction Word Problems

Adding and subtracting fractions with unlike denominators word problems



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 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Fraction as Division

Fraction as Division Word Problems

Fraction as Division - Tape Diagrams

Understanding fractions as division



Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

See Below


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.)

Multiply Fractions

Fraction of a Set

Multipy Whole Number by Fraction

Repeated Addition

Fraction of Measurement

Multiply Fraction by Whole Number

Multiply Fractions

Understanding multiplying fractions by fractions

Fraction Games


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.

Area of Rectangle

Area of Rectangles with Fractional Side Lengths

Multiply Fractions



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.

Multiplication as Scaling

Multiply Unit Fractions

Fraction and Decimal Equivalence

Scaling Factor

Fraction multiplication as scaling



Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Multiply Mixed Numbers

Multiply Mixed Numbers

Multiply fractions word problems

Fraction Games


Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

See Below


Interpret division of a unit fraction by a non-zero 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.

Divide Unit Fractions by Whole Numbers

Divide Unit Fractions by Whole Numbers

Dividing fractions by whole numbers



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.

Divide Whole Numbers by Unit Fractions

Divide Whole Numbers by Unit Fractions

Dividing whole numbers by fractions



Solve real world problems involving division of unit fractions by non-zero 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 1/3-cup servings are in 2 cups of raisins?

Divide Fractions Word Problems

Dividing fractions word problems

Division with fractions and whole numbers word problems


Measurement and Data







Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Convert Measurements

Equivalent Measurements (Whole Numbers)

Equivalent Measurements (Decimals)

Equivalent Measurements Word Problems

Metric Length Conversion

Metric Weight Conversion

Convert customary units

Convert measurement word problems

Measurement Games


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.

Line Plots

Line Plots of Fraction Measurements

Interpreting line plots with fraction multiplication and division



Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

A. A cube with side length 1 unit, called a Եnit cube,ԍ is said to have ԯne cubic unitԠof 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.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Understand Volume

Measure Volume using Unit Cubes

Volume in Cubic Units

Volume with unit cubes

Volume Games


Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

A. Find 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 threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

B. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

C. Recognize 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.

Measure Volume

Use Multiplication to Calculate Volume

Decompose Rectangular Prisms

Volume as packing and as filling

Volume Word Problems

Design Prisms given Parameters


Volume word problems

Volume Games








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., x-axis and x-coordinate, y-axis and y-coordinate).

Coordinate System

Graphing points

Coordinate Plane Games


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.

Coordinate Plane Word Problems

Coordinate plane word problems in the first quadrant

Graphing points



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.

Classify two-dimensional figures in a hierarchy based on properties.

Attributes of Shapes

Properties of Quadrilaterals

Quadrilateral types

Properties of shapes

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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