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NUMBER AND OPERATIONS

Putting Words into Action

Fifth Grade
Number and Operation

Content Standard 1.0 The student will develop number and operation sense needed to represent numbers and
number relationships verbally, symbolically, and graphically and to compute fluently and make reasonable
estimates in problem solving.

Learning Expectations:

1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.2 Understand meanings of operations and how they relate to one another.
1.3 Solve problems , compute fluently, and make reasonable estimates.

Accomplishments

5.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
a. read and write numbers from thousandths to millions;
b. name the place value of a given digit from thousandths to millions;
c. use various models to show relationships among whole numbers, fractions, mixed numbers, and decimals
(e.g., number lines , base ten blocks, Venn diagrams, hundreds boards);
d. communicate using mathematical language and symbols;
e. model proper fractions, improper fractions, and mixed numbers;
f. show the relationship between improper fractions and mixed numbers;
g. recognize and generate equivalent forms of commonly used fractions, decimals, and percents (e.g., 1/10,
1/4, 1/2, 3/4);
h. recognize relationships among commonly used fractions and decimals.

5.1.2 Understand meanings of operations and how they relate to one another.
a. use commutative, associative, and identity properties ;
b. explain and demonstrate the inverse nature of addition and subtraction;
c. explain and demonstrate the inverse nature of multiplication and division ;
communicate the effects of addition, subtraction, multiplication, and division on size and order of
numbers
.

5.1.3 Solve problems, compute fluently, and make reasonable estimates.
a. select appropriate methods and tools for computations (e.g., mental computation, estimation, calculators ,
paper and pencils)
b. explain why one from of a number might be more useful for computation than another form;
recognize reasonable estimates for operations;
c. add, subtract, multiply, and divide whole numbers and decimals;
use models, benchmarks, and equivalent forms to add and subtract commonly used fractions with like
and unlike denominators .
d. identify missing information and/or too much information in real-world problems;
solve multi- step real -world problems; solve real-world problems using decimals, fractions, and percents.

Fifth Grade Benchmarks
Performance Indicators State:

As documented through state assessment –
at Level 1, the student is able to
5.1.spi.1. read and write numbers from millions to thousandths;
5.1.spi.2. connect symbolic representations of proper and improper fractions to models of proper and improper
fractions;
5.1.spi.3. represent whole numbers and two-place decimals in expanded form.

at Level 2, the student is able to
5.1.spi.4. add, subtract, multiply, and divide whole numbers (multipliers and divisors no more than two-digits).
5.1.spi.5. identify the place value of a given digit from millions to thousandths;
5.1.spi.6. represent, compare, and order whole numbers and decimals to thousandths;
5.1.spi.7. use estimation to select a reasonable solution to a whole number computation;
5.1.spi.8. add, subtract, and multiply decimals;
5.1.spi.9. solve one- or two-step real-world problems involving addition, subtraction, and/or multiplication of whole
numbers and decimals;
5.1.spi.10. represent numbers as both improper fractions and mixed numbers;
5.1.spi.11. compare and order fractions using the appropriate symbol (<,>,=);
5.1.spi.12. add and subtract commonly used fractions.

at Level 3, the student is able to
5.1.spi.13. generate equivalent forms of commonly used fractions, decimals, and percents (e.g., 1/10, 1/4, 1/2,
¾);
5.1.spi.14. multiply a fraction by a multiple of its denominator ( denominator less than or equal to 10)

Performance Indicators Teacher:
As documented through teacher observation –
at Level 1, the student is able to
5.1.tpi.1. explain and demonstrate the inverse nature of addition and subtraction;
5.1.tpi.2. select appropriate methods and tools for computation (i.e., mental computation, estimation, calculators,
paper & pencil).

at Level 2, the student is able to
5.1.tpi.3. use various models to show relationships among fractions and decimals (e.g., number lines, base ten
blocks, Venn diagrams, hundreds boards);
5.1.tpi.4. explain and demonstrate the inverse nature of multiplication and division;
5.1.tpi.5. communicate using mathematical terms and symbols;
5.1.tpi.6. solve problems in more than one way and explain why one process may be more efficient than another;
5.1.tpi.7. use models and benchmarks to add and subtract commonly used fractions.

at Level 3, the student is able to
5.1.tpi.8. apply commutative, zero, associative, distributive, and identity properties;
5.1.tpi.9. explain relationships among commonly used fractions and decimals;
5.1.tpi.10. identify missing information and/or too much information in real-world problems
5.1.tpi.11. solve real-world problems using fractions, decimals, and percents.

Blueprint for Learning

The Blueprint for Learning is a companion document for the Tennessee Curriculum
Standards which are located at. Although the curriculum
adopted by the State Board of Education in its entirety remains on the web for additional
reference, this reformatted version makes the curriculum more accessible to classroom
teachers.

Skills are coded and identified as Introduced (I), Developing (D), State CRT and Writing Assessed
(A), and Mastered and Maintained (M).

•Introduced (I) skills are new skills presented at that grade level. Even though a skill is considered
introduced at a grade level, some development would also occur.
•Developing (D) skills are skills that have been introduced at a previous grade level. At this stage of
development the skills are being refined and expanded.
•Assessed (A) skills are those skills that are correlated to the state performance indicators for the
CRT portion of the achievement test (grades 3-8) and the writing assessment (grades 5 and 8). The
identified skills are formally assessed through the CRT; however, all skills are informally assessed
in the classroom.

Key to Understanding Blueprint Codes

I= Introduced
D=Developing
A=State Assessed
M=Mastered

(M) Skills are mastered or maintained. This indicates a skill that has been introduced,
developed, and assessed. Even though a skill may be formally assessed, the
development and expansion of the skill still continues.

Note: “A” Indicates the state curriculum assessment only (CRT).
All skills marked “I” “D” “M” are assessed in the classroom.

Reporting Categories for Math

N=Number & Operations AT= Algebraic Thinking C= Computation
R= Real World DP= Data Analysis & Probability ME= Measurement
G= Geometry GR= Graphs & Graphing

MATHEMATICS
Fifth Grade
NUMBER AND OPERATIONS
The student will identify, represent, order, and compare numbers; and estimate, compute, and solve problems.

Key Reporting
Category
A N Read and write numbers from millions to thousandths.
A N Identify the place value of a given digit from millions to thousandths.
A N Represent whole numbers and two-place decimals in expanded form .
A N Represent, compare, and order whole numbers and decimals to thousandths.
D Order and compare (<, >, or =) whole numbers, fractions, mixed numbers, and decimals using models (e.g., number lines, base ten blocks, Venn diagrams, and hundreds boards).
A N Compare and order fractions using the appropriate symbol (<, >, and =).
D Demonstrate knowledge and understanding of grade level mathematical terms.
D Represent proper fractions, improper fractions, and mixed numbers using concrete objects, pictures, and the number line.
A N Connect symbolic representations of proper and improper fractions to models of proper and improper fractions.
A N Represent numbers as both improper fractions and mixed numbers.
D Identify and change improper fractions to mixed numbers and vice versa.
A N Generate equivalent forms of commonly used fractions, decimals, and percents (e.g., 1/10, 1/4, 1/2, .75, 50%).
D Recognize relationships among commonly used fractions and decimals.
A C Multiply a fraction by a multiple of its denominator (denominator less than or equal to 10).
M Use commutative, associative, and identity properties.
D Explain and demonstrate the inverse nature of addition and subtraction.
D Explain and demonstrate the inverse nature of multiplication and division.
D Explain how addition, subtraction, multiplication, and division affect the size and order of numbers.
D Select appropriate methods and tools for computations (e.g., mental computation, estimation, calculators, and paper and pencil).
I Explain why one form of a number might be more useful for computation than another form.
A N Use estimation to determine a reasonable solution to a whole number computation.
A C Add, subtract, multiply, and divide whole numbers (multipliers and divisors no more than two-digits).
A C Add, subtract, and multiply decimals.
A C Add and subtract commonly used fractions.
D Identify missing information and/or too much information in real-world problems.
A R Solve one- or two-step real-world problems involving addition, subtraction, and/or multiplication A R of whole numbers and decimals.
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