Hardin County Schools Combined Curriculum Guide
Mathematics -- Fifth Grade – Number Properties and Operations
DRAFT
Big Idea
NUMBER PROPERTIES AND OPERATIONS
Academic Expectations
Students understand number concepts and use numbers appropriately and accurately.
Students understand various mathematical procedures and use them appropriately and accurately.
POS Understandings MA-5-NPO-U-1
9 Weeks
1 2 3 4
POS Skills & Concepts
2.7
2.8
Students will understand that numbers, ways of representing numbers, relationships
Taught
between numbers and number systems are means of representing real-world
quantities.
Date(s)
Core Content for Assessment
Objective
Taught
MA-5-NPO-S-NS1
Students will read, write, model, order, compare (using
relative magnitude) and apply multiple representations of
whole numbers.
MA-5-NPO-S-NS2
Students will compare and apply the relative sizes of
common and mixed fractions.
MA-5-NPO-S-NS3
Students will investigate multiple representations of
equivalent fractions (e.g.,
1 3 1 3
= , 1 = ) with
2 6 2 2
manipulatives, drawings and fractional notation.
MA-5-NPO-S-NS4
Students will explore the use of simple ratios to describe
problem situations.
MA-5-NPO-S-PNO1
Students will use factors to determine prime and
composite numbers.
MA-5-NPO-S-PNO2
Students will determine least common multiples.
MA-05-1.1.1
Students will:
apply multiple representations (e.g., drawings,
manipulatives, base-10 blocks, number lines,
expanded form, symbols) to represent whole
numbers (0 to 99,999,999);
apply multiple representations (e.g., drawings,
manipulatives, base-10 blocks, number lines,
symbols) to describe commonly-used fractions,
mixed numbers and decimals through
thousandths;
apply these numbers to represent real-world
problems and
explain how the base-10 number system relates to
place value.
DOK 2
MA-05-1.1.2
Students will read, write and rename whole numbers,
fractions and decimals, and apply to real-world and
mathematical problems.
MA-05-1.1.3
Students will compare (<, >, =) and order whole
numbers), fractions and decimals, and explain the
relationships (equivalence, order) between and among
them.
DOK 2
I can use place value to read
and write whole numbers
through 100 million.
I can use whole numbers
when solving real-world
problems.
Essential Vocabulary
Whole Numbers
Place Value
Standard Form
Expanded Form
Short Word Form
Round
I can explain how the base10 number system relates to
place value (e.g. Ten tens
make one hundred).
I can read, write and rename
whole numbers
I can compare and order
whole numbers and explain
their relationship by using
<,>, or=.
>(Greater Than)
<(Less Than)
=(Equal To)
MA-5-NPO-S-PNO3
Students will skip-count forwards and backwards with
fluency.
Hardin County Schools
Printed-11/5/2008
1
Hardin County Schools Combined Curriculum Guide
Mathematics -- Fifth Grade – Number Properties and Operations
DRAFT
Strategies & Activities
Hardin County Schools
Printed-11/5/2008
Resources
Common Assessments
Essential Questions
Higher Order Questions
2
Hardin County Schools Combined Curriculum Guide
Mathematics -- Fifth Grade – Number Properties and Operations
DRAFT
POS Understandings
POS Skills & Concepts
MA-5-NPO-U-2
9 Weeks
Students will understand that meanings of and relationships among operations
Taught
provide tools necessary to solve realistic problems encountered in everyday life.
Date(s)
Core Content for Assessment
Objective
Taught
MA-5-NPO-S-NS4
Students will explore the use of simple ratios to describe
problem situations.
MA-5-NPO-S-NS5
Students will explore, investigate, compare, relate and
apply relationships among whole numbers, fractions,
decimals and percents.
MA-5-NPO-S-NS6
Students will read, write, identify and compare decimals
through ten-thousandths.
MA-5-NPO-S-NO1
Students will develop and apply computational
procedures to add, subtract, multiply and divide whole
numbers using basic facts and technology as
appropriate.
MA-5-NPO-S-NO2
Students will add and subtract fractions with common
denominators using manipulatives or symbolic notation.
MA-5-NPO-S-NO3
Students will add and subtract decimals through onethousandths using manipulatives or symbolic notation.
MA-5-NPO-S-NO4
Students will extend multiplication to include one decimal
place.
MA-5-NPO-S-NO5
Students will explore the effects of operations on
numbers.
MA-5-NPO-S-PNO4
Students will use properties of numbers for written and
mental computation (e.g., combine commutative and
associative properties to rearrange multiplication
exercises such as 4 x (7 x 5) which can be rearranged
as (4 x 5) x 7 to simplify the multiplication).
Hardin County Schools
Printed-11/5/2008
MA-05-1.3.1
Students will analyze real-world problems to identify
appropriate representations using mathematical
operations, and will apply operations to solve real-world
problems with the following constraints:
add, subtract, multiply, and divide whole numbers
(less than 100,000,000), using technology where
appropriate;
add and subtract fractions with like denominators
through 16, with sums less than or equal to one
and
add and subtract decimals through hundredths.
DOK 2
MA-05-1.5.2
Students will use the commutative properties of addition and
multiplication, the associative properties of addition and
multiplication, the identity properties of addition and
multiplication and the zero property of multiplication in
written and mental computation.
I can add, subtract, multiply
and divide whole numbers.
I can use the commutative
property of addition to prove
that when the order of
addends is changed the sum
does not change it remains
the same. (3+5=5+3)
1
2
3
4
Essential Vocabulary
Operations
Addend
Sum
Difference
Factor
Product
Divisor
Dividend
Quotient
Remainder
Associative Property
Commutative Property
Identity Property
Distributive Property
I can use the commutative
property of multiplication to
prove when the order of
factors is changed the
product does not change it
remains the same. (3x5=5x3)
I can use the associative
property of multiplication to
prove that changing the
grouping of factors does not
change the product.
(6x4)x2 = 6x(4x2)
I can use the identity property
to prove that when I multiply
by 1 I will get the other
number. 3x1=3
3
Hardin County Schools Combined Curriculum Guide
Mathematics -- Fifth Grade – Number Properties and Operations
DRAFT
Use the zero property to
prove that the product of any
number multiplied by 0 is 0.
3x0=0
Strategies & Activities
Hardin County Schools
Printed-11/5/2008
Resources
Common Assessments
Essential Questions
Higher Order Questions
4
Hardin County Schools Combined Curriculum Guide
Mathematics -- Fifth Grade – Number Properties and Operations
DRAFT
POS Understandings
POS Skills & Concepts
MA-5-NPO-U-3
9 Weeks
Students will understand that computing fluently and making reasonable estimates
Taught
increases the ability to solve realistic problems encountered in everyday life.
Date(s)
Core Content for Assessment
Objective
Taught
MA-5-NPO-S-E1
Students will explore appropriate estimation procedures
for different situations.
MA-5-NPO-S-E2
Students will apply and explain appropriate strategies for
estimating quantities of objects and computational
results.
Strategies & Activities
Hardin County Schools
Printed-11/5/2008
MA-05-1.2.1
Students will apply and describe appropriate strategies
for estimating quantities of objects and computational
results in real-world problems.
DOK 2
I can estimate sums and
differences of whole
numbers.
1
2
3
4
Essential Vocabulary
Estimate
I can estimate products and
quotients of whole numbers.
Resources
Common Assessments
Essential Questions
Higher Order Questions
5