Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Operations and Algebraic Thinking
Math Standard: 5.OA.1
Math Standard: 5.OA.2
Use parentheses, brackets, or braces in numerical
Write simple expressions that record calculations with
expressions, and evaluate expressions with these
numbers, and interpret numerical expressions without
symbols. In fifth grade students begin working more
evaluating them.
formally with expressions. They write expressions to
For example, express the calculation “add 8 and 7,
express a calculation, e.g., writing 2 x (8 + 7) to express then multiply by 2” as 2 × (8 + 7). Recognize that 3 ×
the calculation “add 8 and 7, then multiply by 2.”
(18932 + 921) is three times as large as
They also evaluate and interpret expressions, e.g.,
18932 + 921, without having to calculate the indicated
using their conceptual understanding of multiplication sum or product.
to interpret 3 x (18932 + 921) as being three times as
large as 18932 + 921, without having to calculate the
indicated sum or product. Thus, students in Grade 5
begin to think about numerical expressions in ways
that prefigure their later work with variable
expressions (e.g., three times an unknown length is 3 .
L). In Grade 5, this work should be viewed as
exploratory rather than for attaining mastery;
for example, 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,
e.g., (8 + 27) + 2 or (6 x 30) (6 x 7).
5.OA.1 Essential Skills and Concepts:
1. Evaluate how to use numerical expressions with
parentheses, brackets, and braces
evaluate a numerical expression
identify parentheses, brackets, and braces
evaluate the relationship between parentheses,
brackets, and braces.
determine the order of operations by solving the
expression in the parentheses, then in the
brackets and then in the braces
2. Explain how to use numerical expressions with
parentheses, brackets, and braces
explain a numerical expression
identify parentheses, brackets, and braces
explain the relationship between parentheses,
brackets, and braces.
determine the order of operations by solving the
expression in the parentheses, then in the
brackets, and then in the braces
(see middle column for Mathematical Language)
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 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.
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.
5.OA.2 Essential Skills and Concepts:
1. Identify and write a simple expression
create a simple expression with (+, -, x, ÷)
recognize the different components of a simple
expression
2. Describe numerical expressions
verbally explain the relationship between
expressions without calculating them.
verbally explain the relationship between
numbers
5.OA.3 Essential Skills and Concepts:
1. Generate patterns with two rules
describe the pattern
extend the pattern to formulate the rules
2. Form ordered pairs
explain how to write an ordered pair
identify the relationship of the ordered pair
identify the ordered pairs using the table
3. Plot ordered pairs on a coordinate plane
explain how the numbers in the ordered pair
are graphed on the coordinate plane
plot the ordered pair on a coordinate plane
5.OA.1: Mathematical Language: parentheses,
brackets, braces, numerical expressions, operation
5.OA.3: Mathematical Language: numerical patterns,
rules, ordered pairs, coordinate plane
5.OA.2: Mathematical Language: parentheses,
brackets, braces, numerical expressions, calculate,
computation
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Number and Operations in Base Ten
Math Standard: 5.NBT.1
Math Standard: 5.NBT.2
Recognize that in a multi-digit number, a digit in one
Explain patterns in the number of zeros of the product
place represents 10 times as much as it represents in
when multiplying a number by powers of 10, and
the place to its right and 1/10 of what it represents in
explain patterns in the placement of the decimal point
the place to its left (i.e. recognize that place values are when a decimal is multiplied or divided by a power of
either 10 times greater or 1/10th of a number).
10. Use whole-number exponents to denote powers of
10.
5.NBT.1 Essential Skills and Concepts:
5.NBT.2 Essential Skills and Concepts:
1. Identify place value using base ten
1. Explain how to multiply and divide by powers of ten
identify numbers using base ten place value
determine the relationship of numbers when
recognize one place value represents 10 times
multiplying by the powers of ten
the amount as the number to its right
determine the relationship of numbers when
recognize the digit to the right is one tenth to
dividing by the powers of ten
the number to its left
2. Explain and use exponents with the powers of ten
evaluate the relationship between the digits and
define an exponent
its place value
define exponents to the powers of ten
analyze problems with exponents using the
powers of ten
3. Investigate the relationship of a decimal to the
powers of ten
explore the placement of the decimal point
based on the multiplication of the powers of ten
explore the placement of the decimal point
based on the division of the powers of ten
Mathematical Language: place value, decimal,
decimal point, patterns, multiply, divide, tenths,
thousandths, greater than, less than, equal to, ‹, ›, =,
compare/comparison, round
Mathematical Language: place value, decimal,
decimal point, patterns, multiply, divide, tenths,
thousandths, greater than, less than, equal to, ‹, ›, =,
compare/comparison, round
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 5.NBT.3
Read, write, and compare decimals to thousandths.
5.NBT.3 Essential Skills and Concepts:
1. Write decimals to the thousandths
write decimals to the thousandths place using
base ten, number names, and expanded form
2. Read decimals to the thousandths
read decimals to the thousandths place using
base ten, number names, and expanded form
3. Compare decimals to the thousandths using >, =,
and <
compare decimals to the thousandths place
using base ten, number names, and expanded
form
http://insidemathematics.org/common-core-mathtasks/5th-grade/5-2005%20Fractions.pdf
http://insidemathematics.org/common-core-mathtasks/5th-grade/5-2009%20Decimals.pdf
Mathematical Language: place value, decimal,
decimal point, patterns, multiply, divide, tenths,
thousandths, greater than, less than, equal to, ‹, ›, =,
compare/comparison, round
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Number and Operations in Base Ten
Math Standard: 5.NBT.4
Math Standard: 5.NBT.5
Use place value understanding to round decimals to
Fluently multiply multi-digit whole numbers using the
any place.
standard algorithm.
5.NBT.4 Essential Skills and Concepts:
1. Explore understanding of place value to round
decimals to a given place value
identify benchmark numbers (0, 0.5, 1, 1.5)
use benchmark numbers for comparing and
rounding numbers
explain and reason why a number is rounded to a
given place value
5.NBT.5 Essential Skills and Concepts:
1. Fluently multiply multi-digit whole numbers using
the standard algorithm and/or alternative
strategies
rewrite the problem by using strategies related
to the distributive property or breaking numbers
apart.
solve the problem using the standard algorithm
solve the problem using alternative strategies
http://insidemathematics.org/common-core-mathtasks/5th-grade/5http://insidemathematics.org/problems-of-themonth/pomthroughthegrapevine.
pdf
Mathematical Language: place value, decimal,
decimal point, patterns, multiply, divide, tenths,
thousandths, greater than, less than, equal to, ‹, ›, =,
compare/comparison, round
Mathematical Language: multiplication/multiply,
division/division, decimal, decimal point, tenths,
hundredths, products, quotients, dividends,
rectangular arrays, area models, addition/add,
subtraction/subtract, (properties)-rules about how
numbers work, reasoning, distributive property
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 5.NBT.6
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.
5.NBT.6 Essential Skills and Concepts:
1. Explore various strategies to divide up to four digit
dividends and two digit divisors.
identify different components of a division
problem
divide using place value
divide using the properties of operation i.e.
repeated subtraction.
explain the relationship between multiplication
and division
http://insidemathematics.org/common-core-mathtasks/5thgrade/52004%20Fruits%20&%20Vegetables.pdf
2. Illustrate and explain a division calculation
draw a picture to illustrate the division process
illustrate division using an equation
illustrate division using rectangular arrays
illustrate division using area models
Mathematical Language: multiplication/multiply,
division/division, decimal, decimal point, tenths,
hundredths, products, quotients, dividends,
rectangular arrays, area models, addition/add,
subtraction/subtract, (properties)-rules about how
numbers work, reasoning, distributive property
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC
Grade: Fifth – Number and Operations in Base Ten
Math Standard: 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.
5.NBT.7 Essential Skills and Concepts:
1. Add, subtract, multiply, and divide decimals to the
hundredths place value
use concrete models to add, subtract, multiply
and divide decimals to the hundredths place
value
use a pictorial representation to add, subtract,
multiply and divide decimals to the hundredths
place value
use algorithms to add, subtract, multiply and
divide decimals to the hundredths place value
2. Explain how to add, subtract, multiply, and divide
decimals to the hundredths place value
explain in writing the reasoning I used to add,
subtract, multiply and divide decimals to the
hundredths place value
Mathematical Language: place value, decimal,
decimal point, patterns, multiply, divide, tenths,
thousandths, greater than, less than, equal to, ‹, ›, =,
compare/comparison, round
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Number and Operations - Fractions
Math Standard: 5.NF.1
Math Standard: 5.NF.2
Add and subtract fractions with unlike denominators
Solve word problems involving addition and
(including mixed numbers) by replacing given fractions subtraction of fractions referring to the same whole,
with equivalent fractions in such a way as to produce
including cases of unlike denominators, e.g., by using
an equivalent sum or difference of fractions with like
visual fraction models or equations to represent the
denominators.
problem. Use benchmark fractions and number sense
of fractions to estimate mentally and assess the
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In
reasonableness of answers.
general, a/b + c/d = (ad + bc)/bd.).
5.NF.1 Essential Skills and Concepts:
1. Use a model to represent the addition and
subtraction of fractions with unlike denominators.
identify the common denominator by finding
the product of both denominators
replace fractions with an equivalent fraction
use visual fraction models to build an
understanding
use standard algorithms to add and subtract
fractions
http://www.math-play.com/adding-and-subtractingfractions-game.html
http://www.illustrativemathematics.org/illustrations/
848
http://www.illustrativemathematics.org/illustrations/
839
http://www.illustrativemathematics.org/illustrations/
848
http://www.illustrativemathematics.org/illustrations/
855
http://www.illustrativemathematics.org/illustrations/
861
http://insidemathematics.org/common-core-mathtasks/5th-grade/52007%20Cindy's%20Cats.pdf
For example, recognize an incorrect result 2/5 + 1/2 =
3/7, by observing that 3/7 < ½.
5.NF.2 Essential Skills and Concepts:
1. Solve word problems using addition and
subtraction of fractions including like and unlike
denominators
write a number equation to solve word
problems involving fractions with like and
unlike denominators
use visual fraction models to represent the
problem
http://www.illustrativemathematics.org/illustrations/
847
5.NF Do These Add Up?
http://www.illustrativemathematics.org/illustrations/
481
5.NF Salad Dressing
http://www.illustrativemathematics.org/illustrations/
1172
2. Use benchmark fractions and number sense of
fractions to estimate mentally and check for
reasonableness
use knowledge of benchmark fractions to
estimate mentally
use knowledge of benchmark fractions to
check for reasonableness
use number sense of fractions to estimate
mentally
use number sense of fractions to check for
reasonableness
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 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.
5.NF.3 Essential Skills and Concepts:
1. Use models to solve division problems using
fractions
create a fraction model to solve a division
problem
solve a division problem using a fraction
model
2. Solve word problems including the division
of whole numbers with answers in forms of
mixed numbers
solve word problems using division by
interpreting the quotient as a mixed
number
use visual fraction models or equations to
represent and solve the problem
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC
Grade: Fifth – Number and Operations - Fractions
http://themathworksheetsite.com/numline.html
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L2
49
5.NF How Much Pie?
http://www.illustrativemathematics.org/illustrations/
858
5.NF What is 23 ÷ 5?
http://www.illustrativemathematics.org/illustrations/
292
5.NF and 5.MD Converting Fractions of a Unit into a
Smaller Unit
http://www.illustrativemathematics.org/illustrations/
293
5.NF.1: Mathematical Language: fraction,
equivalent, addition/ add, sum, subtraction/subtract,
difference, unlike denominator, numerator,
benchmark fraction, estimate, reasonableness, mixed
numbers, partitioning
5.NF.2: Mathematical Language: fraction,
equivalent, addition/ add, sum, subtraction/subtract,
difference, unlike denominator, numerator,
benchmark fraction, estimate, reasonableness, mixed
numbers
Math Standard: 5.NF.4
Apply and extend previous understandings of
multiplication to multiply a fraction or whole number
by a fraction. 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.
Math Standard: 5.NF.5
Interpret multiplication as scaling (resizing), by:
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.)
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..
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.
5.NF.3: Mathematical Language: fraction,
numerator, denominator, operations,
multiplication/multiply, division/divide, mixed
numbers, product, quotient, partition, equal parts,
equivalent, factor, unit fraction, area, side lengths,
fractional sides lengths, scaling, comparing
Math Standard: 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.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Number and Operations - Fractions
5.NF.4 Essential Skills and Concepts:
5.NF.5 Essential Skills and Concepts:
1. Create and solve problems using models to multiply 1. Use the factors to compare the products without
a fraction or whole number by a fraction
using multiplication.
create a model to solve multiplication fraction
examine the relationship of the two different
problems
factors when one factor is a whole number and
solve multiplication fraction problems using
one factor is a fraction of a whole number
visual fraction models
2. multiply with whole numbers and fractions
2. Find the area of rectangle with fractional side
recognize the product is greater than the given
lengths
number when multiplying with numbers greater
use tiles to find the area of rectangles with
than 1
fractional side lengths
recognize the product is less than the given
use grids to find the area of rectangles with
number when multiplying with numbers less
fractional side lengths
than 1
http://www.illustrativemathematics.org/illustrations/
explain why the product is less than the given
609
number when multiplying with numbers less
than 1
5.NF Connor and Makayla Discuss Multiplication
explain why the product is greater than the given
http://www.illustrativemathematics.org/illustrations/
number when multiplying with numbers greater
321
than 1
5.NF Folding Strips of Paper
Tasks
that illustrate content standard 5.NF.B.5
http://www.illustrativemathematics.org/illustrations/
5.NF Calculator Trouble Alignment 1: 5.NF.B.5
965
http://www.illustrativemathematics.org/illustrations/
151
5.NF Comparing a Number and a Product Alignment 1:
5.NF.B.5
http://www.illustrativemathematics.org/illustrations/
164
5.NF Fundraising Alignment 1: 5.NF.B.5
http://www.illustrativemathematics.org/illustrations/
150
5.NF Grass Seedlings Alignment 1: 5.NF.B.5
http://www.illustrativemathematics.org/illustrations/
143
5.NF Reasoning about Multiplication Alignment 1:
5.NF.B.5
http://www.illustrativemathematics.org/illustrations/
49
5.NF Running a Mile Alignment 1: 5.NF.B.5
http://www.illustrativemathematics.org/illustrations/
22
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
5.NF.6 Essential Skills and Concepts:
1. Solve real world problems using multiplication of
fractions and mixed numbers
use fraction models to represent real
world problem
use equations to represent real world
problems
Tasks that illustrate content standard 5.NF.B.6
5.NF Drinking Juice Alignment 1: 5.NF.B.6
http://www.illustrativemathematics.org/
illustrations/295
5.NF Half of a Recipe Alignment 1: 5.NF.B.6
http://www.illustrativemathematics.org/
illustrations/296
5.NF Making Cookies Alignment 1: 5.NF.B.6
http://www.illustrativemathematics.org/illustrations/
297
5.NF Running to School Alignment 1: 5.NF.B.6
http://www.illustrativemathematics.org/illustrations/
294
5.NF To Multiply or not to multiply? Alignment 1:
5.NF.B.6, 5.NF.A
http://www.illustrativemathematics.org/illustrations/
609
http://www.illustrativemathematics.org/illustrations/
609
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Number and Operations - Fractions
5.NF.4: Mathematical Language: fraction,
5.NF.5: Mathematical Language: fraction,
numerator, denominator, operations,
numerator, denominator, operations,
multiplication/multiply, division/divide, mixed
multiplication/multiply, division/divide, mixed
numbers, product, quotient, partition, equal parts,
numbers, product, quotient, partition, equal parts,
equivalent, factor, unit fraction, area, side lengths,
equivalent, factor, unit fraction, area, side lengths,
fractional sides lengths, scaling, comparing, formula
fractional sides lengths, scaling, comparing
Math Standard: 5.NF.7
Apply and extend previous understandings of division
to divide unit fractions by whole numbers and whole
numbers by unit fractions.
a. 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.
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.
b. 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.
c. 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.
5.NF.7 Essential Skills and Concepts:
1. Interpret and solve division of fractions by a whole
number and/or within a story context
identify unit fractions
create a number sentence (equation) to
represent the story problem
solve the number sentence (equation) for the
story problem
solve real world problems using visual fraction
models
2. Interpret and solve division of whole numbers by
unit fractions and/or within a story context
identify unit fractions
create a number sentence (equation) to
represent the story problem
solve the number sentence (equation) for the
story problem
solve real world problems using visual fraction
models
Tasks that illustrate content standard 5.NF.B.7
5.NF Banana Pudding Alignment 1: 5.NF.B.7
http://www.illustrativemathematics.org/illustrations/
1196
For example, how much chocolate will each person get
if 3 people share ½ lb of chocolate equally? How many
1/3-cup servings are 2 cups of raisins?
5.NF Dividing by One-Half Alignment 1: 5.NF.B.7
http://www.illustrativemathematics.org/illustrations/
12
5.NF How many servings of oatmeal? Alignment 1:
5.NF.B.7
http://www.illustrativemathematics.org/illustrations/
829
(see middle column for skills and concepts)
(see next column for Mathematical Language)
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
5.NF.6: Mathematical Language: fraction,
numerator, denominator, operations,
multiplication/multiply, division/divide, mixed
numbers, product, quotient, partition, equal parts,
equivalent, factor, unit
fraction, area, side lengths, fractional sides lengths,
scaling, comparing
5.NF.7 Essential Skills and Concepts: (continued)
Tasks that illustrate part 5.NF.B.7.b
5.NF How many marbles? Alignment 1: 5.NF.B.7.b,
5.NF.B.7.c
http://www.illustrativemathematics.org/illustrations/
1120
5.NF Origami Stars Alignment 1: 5.NF.B.7.b
http://www.illustrativemathematics.org/illustrations/
958
5.NF Painting a room Alignment 1: 5.NF.B.7.a
http://www.illustrativemathematics.org/illustrations/
957
Mathematical Language: fraction, numerator,
denominator, operations, multiplication/multiply,
division/divide, mixed numbers, product, quotient,
partition, equal parts, equivalent, factor, unit
fraction, area, side lengths, fractional sides lengths,
scaling, comparing
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Measurement and Data
Math Standard: 5.MD.1
Math Standard: 5.MD.2
Convert among different-sized standard measurement Make a line plot to display a data set of measurements
units within a given measurement system (e.g.,
in fractions of a unit (1/2, 1/4, 1/8). Use operations on
convert 5 cm to 0.05 m), and use these conversions in
fractions for this grade to solve problems involving
solving multi-step, real world problems.
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.
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
Math Standard: 5.MD.3, 4 and 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 of
n cubic units.
5.MD.4 Measure volumes by counting unit cubes,
using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.5 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 nonoverlapping parts, applying this technique to solve real
world problems.
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design:
Grade: Fifth – Measurement and Data
5.MD.1 Essential Skills and Concepts:
5.MD.2 Essential Skills and Concepts:
1. Convert standard measurement units within a given 1. Make a line plot to display a data set of fractions
measurement system
using different measurement units (1/2, 1/4, 1/8)
use conversions in solving multi-step problems
create line plots to the nearest 1/2, 1/4, 1/8
use conversions to solve real world problems
use the base-ten system when converting within
the metric system.
Units of Measurement
http://studyjams.scholastic.com/studyjams/jams/mat
h/measurement/unitsofmeasurement.htm
Customary Units of Length
http://studyjams.scholastic.com/studyjams/jams/mat
h/measurement/unitsoflength.htm
http://insidemathematics.org/common-core-mathtasks/5th-grade/52004%20Fruits%20&%20Vegetables.pdf
Mathematical Language: conversion/convert, metric
and customary measurement, metric measurement,
standard measurement, hours, minutes, seconds
From Previous Grades: relative size, liquid volume,
mass, length, kilometer (km), meter (m), centimeter
(cm), kilogram (kg), gram (g), liter (L), milliliter (mL),
inch (in), foot (ft), yard (yd), mile (mi), ounce (oz),
pound (lb), cup (c), pint (pt), quart (qt), gallon (gal),
hour, minute, second
Mathematical Language: line plot, length, mass,
liquid volume
OASIS, LLC
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.
5.MD.3, 4 and 5 Essential Skills and Concepts:
1. Recognize and identify the volume of solid figures
and their measurements
define volume
identify the measurement used with volume
2. Measure volume by counting cubic units
use concrete manipulatives to measure volume
in cubic inches, centimeters and feet
3. Identify the volume using the formula
use the formula, length x width x height to find
volume of a rectangular prism
explain the formula, length x width x height as it
relates to the volume of a rectangular prism
4. Relate volume to multiplication and addition to
solve real world problems
explore volume using multiplication and addition
solve real-world mathematical problems
involving area of a base, in order to find the
volume
http://insidemathematics.org/common-core-mathtasks/5thgrade/%2052004%20How20%20Many%20Cubes.pdf
Mathematical Language: measurement, attribute,
volume, solid figure, right rectangular prism, unit,
unit cube, gap, overlap, cubic units (cubic cm, cubic
in. cubic ft. nonstandard cubic units), multiplication,
addition, edge lengths, height, area of base, solid
figure, gaps, overlaps, cubic unit, formula
Essential MATH Skills Alignment – Math Standards
Content Source: 2013-2014 Iredell-Statesville Schools– Format Design: OASIS, LLC
Grade: Fifth – Geometry
Math Standard: 5.G.1 and 5.G.2
Math Standard: 5.G.3 and 5.G.4
5.G.1 Use a pair of perpendicular number lines, called 5.G.3 Understand that attributes belonging to a
axes, to define a coordinate system, with the
category of two-dimensional figures also belong to all
intersection of the lines (the origin) arranged to
subcategories of that category.
coincide with the 0 on each line and a given point in
For example, all rectangles have four right angles and
the plane located by using an ordered pair of
squares are rectangles, so all squares have four right
numbers, called its coordinates. Understand that the
angles.
first number indicates how far to travel from the origin
5.G.4 Classify two-dimensional figures in a hierarchy
in the direction of one axis, and the second number
based on properties.
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 x-coordinate, y-axis and y-coordinate).
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.
5.G.1 and 5.G.2 Essential Skills and Concepts:
1. Identify axes in the first quadrant of the coordinate
plane
identify the x-axis and y-axis
2. Plot ordered pairs in the first quadrant of the
coordinate plane
identify the x-coordinate and y-coordinate
plot ordered pairs using the x and y coordinates
on a coordinate grid.
connect the ordered pairs on the coordinate grid
3. Graph real world mathematical problems on a
coordinate grid
interpret the problem in order to graph ordered
pairs on a coordinate gird.
4. Real world mathematical problems on a
coordinate grid
interpret the graph in order to solve the real
world problem
http://insidemathematics.org/common-core-mathtasks/5thgrade/
5-2007%20Granny's%20Balloon%20Trip.pdf
Mathematical Language: coordinate system,
coordinate plane, first quadrant, points, lines, axis/axes,
x-axis, y-axis, horizontal, vertical, intersection of lines,
origin, ordered pairs, coordinates, x-coordinate, ycoordinate
5.G.3 and 5.G.4 Essential Skills and Concepts:
1. Classify two-dimensional figures by their attributes
compare two-dimensional figures and categorize
them by their attributes
2. Classify two-dimensional figures in a hierarchy
based on properties
classify two-dimensional figures in a hierarchy
based on the properties
http://insidemathematics.org/common-core-mathtasks/5th-grade/52006%20Sorting%20Shapes.pdf
Mathematical Language: attribute, category,
subcategory, hierarchy, (properties)-rules about how
numbers work, two dimensional, kite
From Previous Grades: polygon, rhombus/rhombi,
rectangle, square, triangle, quadrilateral, pentagon,
hexagon, cube, trapezoid,
half/quarter circle, circle
The academic vocabulary or content language
is listed under each standard. There are 30-40
words in bold that should be taught to mastery.