Operations & Algebraic Thinking
(5% – 10%)
5.OA.1  5.OA.2
Write & interpret numerical expressions using properties of operations & order of operations.
5.OA.3
Analyze patterns & relationships.

5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Note: Students begin working more formally with expressions. Expressions should not contain nested grouping symbols, and they should be no more complex than the expressions one finds in an application of the associative or distributive property. The numbers in expressions need not always be whole numbers.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.


5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

5.OA.3 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.
Review All OA Standards
As of 31015, 3 items are from the OA Domain on the
NC READY Math 5 EOG.

Number and Operations in Base Ten  Includes Decimals to Hundredths (+,,x,÷) &Thousandths (read, write, compare)
(22% 27%)
5.NBT.15.NBT.4
Understand the place value system to read, write, compare, and order decimals to thousandths.
5.NBT.55.NBT.7
Perform operations with multidigit whole numbers and with decimals to hundredths.

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.
5.NBT.2 Explain patterns in the number of 0’s 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 wholenumber exponents to denote powers of 10.
5.NBT.3 Read, write, and compare decimals to thousandths.
a. Read & write decimals to thousandths using baseten numerals (standard form), number names (written form), and expanded form.
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, < symbols to record the results of comparisons.
5.NBT.4 Use place value understanding to round decimals to any place.
5.NBT.5 Fluently multiply multidigit whole numbers using the standard algorithm. Underlying this algorithm are the properties of operations and the baseten system.
Note: The size of the numbers should not exceed a 4digit factor by a 2digit factor unless students are using previously learned strategies such as properties of operations.

5.NBT.6 Find wholenumber quotients of whole numbers with up to 4digit dividends and 2digit 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.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 + and ; relate the strategy to a written method and explain the reasoning used.

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 + and ; relate the strategy to a written method and explain the reasoning used.

Review All NBT Standards
with a Focus on 5.NBT.6 & 5.NBT.7
As of 31015, 11 items are from the NBT Domain on the
NC READY Math 5 EOG.
The NBT Domain is a
Major Work of the Grade!

Number and Operations  Fractions
(47%– 52%)
5.NF.15.NF.2
Use equivalent fractions as a strategy to add and subtract fractions with unlike denominators.
5.NF.35.NF.7
Apply and extend previous understandings of multiplication and division to multiply & divide fractions.
Note: In grade 5 …
Multiply a fraction or whole number by a fraction.
Divide unit fractions by whole numbers & Divide whole numbers by unit fractions.

5.NF.1 Add & 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. In general,
a/b + c/d = (ad + bc)/bd.
Note:  builds on the work in 4^{th} grade where students add fractions with like denominators.
5.NF.2 Solve word problems involving addition & 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.

5.NF.1 Continue … Add & 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.
In general, a/b + c/d = (ad + bc)/bd.
5.NF.2 Continue … Solve word problems involving addition & 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.
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.
Note: 5^{th} grade students should connect fraction with division (equal sharing).

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations: a x q ÷ b.
In general, (a/b) x (c/d) = ac/bd.
b. 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.
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 that 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 x a)/(n x b) to the effect of multiplying a/b by 1.
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.

5.NF.4; 5.NF.5; 5.NF.6 Continue
 Apply & extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 Multiplication as scaling (resizing)
 Solve real world problems involving multiplication of fractions & mixed numbers.
5.NF.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Note: 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 grade 5.
a. Interpret division of a unit fraction by a nonzero whole number, & compute such quotients.
(1/b) ÷ d = 1/(b x d) because
1/(b x d) x d = (1/b)
 relationship between x & ÷.
b. Interpret division of a whole number by a unit fraction, & compute such quotients.
d ÷ (1/b ) = (b x d) because
(b x d) x (1/b) = d
 relationship between x & ÷.
c. Solve real world 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.
Review All NF Standards
As of 31015, 22 items are from the NF Domain on the
NC READY Math 5 EOG.
The NF Domain is a
Major Work of the Grade!

Measurement and Data
(10% – 15%)
5.MD.1
Convert like measurement units within a given measurement system.
5.MD.2
Represent and interpret data.
5.MD.35.MD.5
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.


5.MD.1 Convert among differentsized standard measurement units within a given measurement system (e.g.,
convert 5 cm to 0.05 m), and use these conversions in solving multistep, real world problems.
Note: Time could be used in this standard.
5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit ( ½, ¼, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
Note: The line plot should also include mixed numbers in grade 5.

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 on n cubic units.
5.MD.4 Measure volume by counting unit cubes, using cubic cm, cubic in, cubic ft, & improvised units.
5.MD.5Relate 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 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.
b. Apply the formulas
V=l x w x h
V=b x 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.
c. 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.

Review All MD Standards
with a Focus on 5.MD.1 & 5.MD.5
As of 31015, 5 items are from the MD Domain on the
NC READY Math 5 EOG.

Geometry
(2% – 7%)
5.G.15.G.2
Graph points on the coordinate plane to solve realworld and mathematical problems.
5.G.35.G.4
Classify 2D figures into categories based on their properties.
Note: Polygon, triangle, quadrilateral , rhombus, rectangle, square, kite, trapezoid, pentagon, hexagon,half/quarter circle,
circle




5.G.1Use 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 it 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).
5.G.2Represent 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.
5.G.3 Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category.
5.G.4 Classify twodimensional figures in a hierarchy based on properties.
As of 31015, 2 items are from the Geometry Domain on the
NC READY Math 5 EOG.
Note: Understanding concepts of volume and relating volume to multiplication & addition are a Major Work of the Grade!

Always use NC DPI’s Grade 5 Math Unpacking Document
Supplement with Textbook as Appropriate.
Textbook
envision Math Common Core, © 2012

5.OA.1; 5.OA.2; 5.OA.3
Topic 8: Numerical expressions, patterns & relationships
5.NBT.1; 5.NBT.2; 5;NBT.3
Topic 1: Place Value
5.NBT.4
Topic 2: Adding & Subtracting Decimals
5.NBT.5; 5.NBT.6
Topic 3: Multiplying Whole Numbers
Topic 4: Dividing by 1Digit Divisors
Topic 5: Dividing by 2Digit divisors
5.NF.1;5.NF.2
Topic 9: Adding & Subtracting Fractions
Topic 10: Adding & Subtracting Mixed Numbers

5.NBT.5; 5.NBT.6
Topic 3: Multiplying Whole Numbers
Topic 4: Dividing by 1Digit Divisors
Topic 5: Dividing by 2Digit divisors
5.NBT.7
Topic 2: Adding & Subtracting Decimals
5.NF.1;5.NF.2
Topic 9: Adding & Subtracting Fractions
Topic 10: Adding & Subtracting Mixed Numbers
5.NF.3; 5.NF.4; 5.NF.7; 5.NF.5; 5.NF.6
Topic 11: Multiplying & Dividing
Fractions & Mixed Numbers
5.MD.1
Topic 13:Units of Measure
5.MD.2
Topic 14: Data

5.OA.1; 5.OA.2; 5.OA.3
Topic 8: Numerical expressions, patterns & relationships
5.NBT.7
Topic 6: Multiplying Decimals
Topic 7: Dividing Decimals
5.NF.3; 5.NF.4; 5.NF.7; 5.NF.5; 5.NF.6
Topic 11: Multiplying & Dividing
Fractions & Mixed Numbers
5.MD.3; 5.MD.4; 5.MD.5
Topic 12: Volume of Solids

5.OA.1; 5.OA.2; 5.OA.3
Topic 8: Numerical expressions, patterns & relationships
5.NF.3; 5.NF.4; 5.NF.7; 5.NF.5; 5.NF.6
Topic 11: Multiplying & Dividing
Fractions & Mixed Numbers
5.G.1; 5.G.2
Topic 16: Coordinate Geometry
5.G.3; 5.G.4
Topic 15: Classifying Plane Figures
