Download 5th Grade Math - Dinwiddie County Public Schools

th
5 Grade
Math Curriculum
Dinwiddie County Public Schools provides each student the
opportunity to become a productive citizen, engaging the
entire community in the educational needs of our children.
1
Revised: 8/20/16
Nine Weeks
Approximate # of
Days Taught
Topic
Targeted SOL
Curriculum
Framework
1
6
Decimals: Place Value, Rounding
5.1
p. 2-3
1
3
Addition and Subtraction of Whole Numbers
Single and Multi-step Word Problems; Estimation
5.4
p. 9
1
5
Addition and Subtraction of Decimals
Single and Multi-step Word Problems; Estimation; Multiplication symbols
5.5 a b
p. 10-11
1
5
Multiplication of Whole Numbers
Single and Multi-step Word Problems; Estimation; Division symbols
5.4
p. 9
1
5
Multiplication of Decimals
Single and Multi-step Word Problems; Estimation
5.5 a b
p. 10-11
1
6
Division of Whole Numbers
Single and Multi-step Word Problems; Estimation
5.4
p. 9
1
4
Division of Decimals
Single and Multi-step Word Problems; Estimation
5.5a, b
p. 10-11
1
5
Order of Operations; Simplify expressions; Find the value of numerical expressions;
Describe which operation is completed first, second, etc.
5.7
p. 14
1
5
Review
1 Nine Weeks Benchmark
See Above
Review
st
2
Revised: 8/20/16
Nine Weeks
Approximate # of
Days Taught
Topic
Targeted SOL
Curriculum
Framework
2
5
Distributive Property of Multiplication over Addition
5.19
p. 39
2
3
Prime/Composite Numbers,
Odd/Even Numbers
5.3 a,b
p. 6-7
5
Fractions and Decimals:
Equivalent (Fractions to Decimals and vice versa),
Compare/Order
(Per State Blueprint items testing this standard will be completed without
the use of a calculator)
5.2 a, b*
p. 4-5
5.6
p. 12-13
2
Computation of Fractions and Mixed Numbers
Addition and Subtraction in Simplest Form
Single and Multi-step Word Problems
2
18
2
5
Data and Graphs: Line Graphs, Stem and Leaf Plots
5.15
p. 29-31
2
5
Statistics: Mean (fair share), Median, Mode,
Range (measure of variation)
*See standard for important descriptions.
5.16 a,b,c,d
p. 32-33
2
3
Review
2nd Nine Weeks Benchmark
See Above
Review
3
Revised: 8/20/16
Nine Weeks
Approximate
# of Days
Taught
Topic
Targeted SOL
Curriculum
Framework
3
2
Temperature (Celsius & Fahrenheit)
Water Freezes/Boils, Normal Body Temperature
5.8 c,d,e
p. 16-18
3
5
Linear Measurement (U.S. Customary & Metric):
Equivalent within Metric,
Estimate and Measure using both units and choosing appropriate unit for a given
situation using both units
5.8 c,d,e
p. 16-18
3
3
Weight/Mass Measurement (U.S. Customary & Metric):
Equivalent within Metric, Estimate and Measure Choose appropriate unit for a given
situation
5.8 c,d,e
p. 16-18
3
3
Liquid Measurement (U.S. Customary & Metric):
Equivalent within Metric, estimate and measure using both units and choosing
appropriate unit for a given situation using both units
5.8 c,d,e
p. 16-18
3
4
Elapsed Time: Hours and Minutes within a 24-Hour Period
(Review telling time on an analog clock)
5.10
p. 20
3
5
Angles : Classify and Measure Using Protractor (Right, Acute, Obtuse, Straight)
Classify Triangles
(Right, Acute and/or Obtuse, Equilateral, Scalene, Isosceles)
5.11
5.12a,b
p. 21, 23
3
4
Polygons: Plane Figures (square, rectangle, triangle, parallelogram, rhombus, trapezoid);
develop definitions; describe the results of combining and subdividing plane figures
5.13a,b
p. 24-25
5
ind Perimeter (Polygon)
Area(Square, Rectangle, Right Triangle)
Volume: Differentiate which is the appropriate unit of measure in a given situation
5.8a,b
p. 16-18
3
4
Revised: 8/20/16
Nine Weeks
Approximate
# of Days
Taught
Topic
Targeted SOL
Curriculum
Framework
3
5
Circles
5.9
p. 35-36
3
5
Probability: Make Predictions, Determine Outcome by constructing a sample space
(tree diagram, table, chart)
5.14
p. 27-28
3
5
Review/Test 3rd Nine Weeks Benchmark
See Above
Review
4
15
Algebra:
Describe a variable
Write an open sentence using a variable (all operations)
Using addition and subtraction, model one-step linear equations
Create and write a word problem using a single variable
5.18 a,b,c,d
p. 37-38
4
5
Number Patterns
Describe and Express Relationship
5.17
p. 35-36
4
5
Review
EOY Growth Assessment
4
Remainder
SOL Review
5
SOL
Review
Revised: 8/20/16
SOL 5.1 – 1st Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
Blueprint Categories
Number and Number Sense
The student, given a decimal through thousandths, will round
to the nearest whole number, tenth, or hundredth.
Grade 5 SOL
Number of Items
5.1, 5.2a-b, 5.3a-b
5
Prior Knowledge
4.1c – round whole numbers through millions to nearest thousand, 10 thousand, & 100
thousand
4.3a – read, write, represent, & identify decimals through thousandths
4.3b – round decimals to nearest whole number, tenth, & hundredth
Essential Understandings
Understanding the Standard


The structure of the Base-10 number system is based upon a simple
pattern of tens in which each place is ten times the value of the place
to its right. This is known as a ten-to-one place value relationship.

A decimal point separates the whole number places from the places
less than one. Place values extend infinitely in two directions from a
decimal point. A number containing a decimal point is called a decimal
number or simply a decimal.
Understand that decimals are rounded in
a way that is similar to the way whole
numbers are rounded.

Understand that decimal numbers can
be rounded to estimate when exact
numbers are not needed for the
situation at hand.

To read decimals,
– read the whole number to the left of the decimal point, if there is
one;
– read the decimal point as “and”;
– read the digits to the right of the decimal point just as you would
read a whole number; and
– say the name of the place value of the digit in the smallest place.

Decimals may be written in a variety of forms:
All students should
6
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Round decimal numbers to the
nearest whole number, tenth, or
hundredth.
Revised: 8/20/16
– Standard: 23.456
– Written: Twenty-three and four hundred fifty-six thousandths
– Expanded: (2  10) + (3  1) + (4  0.1) + (5  0.01) + (6  0.001)

To help students identify the ten-to-one place value relationship for
decimals through thousandths, use Base-10 manipulatives, such as
place value mats/charts, decimal squares, Base-10 blocks, and money.

Decimals can be rounded to the nearest whole number, tenth or
hundredth in situations when exact numbers are not needed.

Strategies for rounding decimal numbers to the nearest whole
number, tenth and hundredth are as follows:
– Look one place to the right of the digit to which you wish to
round.
– If the digit is less than 5, leave the digit in the rounding place as it
is, and change the digits to the right of the rounding place to
zero.
– If the digit is 5 or greater, add 1 to the digit in the rounding place
and change the digits to the right of the rounding place to zero.

Create a number line that shows the decimal that is to be rounded.

The position of the decimal will help children conceptualize the
number’s placement relative for rounding. An example is to round
5.747 to the nearest hundredth:
5.74
5.747 5.75
7
Revised: 8/20/16
Additional Instructional Strategies
Additional Math Curriculum Resources
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Word Wall Instructional Video
Decimal Number - A number written using base ten;
a number containing a decimal point.
Decimal point – A dot separating the ones and
tenths place in a decimal number
Digit - There are 10 digits; any one of the symbols: 0,
1, 2, 3, 4, 5, 6, 7, 8,
Lessons and TEI Items
Trade Books
Decimal Round-Up/Round-Down - Number and
Number Sense
A Place for Zero (A Math Adventure) by Angeline
Sparagna LoPresti)
Thinking Rationally about Fractions, Decimals and
Percent Instructional Activities (Grades 4-8) (PDF) –
lessons providing additional strategies for
elementary and middle school teachers in the areas
of fractions, decimals, percent and proportional
thinking
Piece = Part = Portion (Fractions = Decimals =
Percents by Scott Gifford
Coyotes All Around by Stuart J. Murphy
Picture Book Lessons
Number and Number Sense Lesson
Decimals in the Dugout Part I
Decimals in the Dugout Part II
Numeral - A symbol (not a variable) used to
represent a number.
Decimals in the Dugout Part III
Place value – A value a digit represents depending
on its place in the number.
Rounding - Reducing the digits in a number while
trying to keep its value similar.
8
Revised: 8/20/16
Whole number – The set of numbers containing (0,
1, 2, 3, …).
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Bite Size Math
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
Bite Size Maths (Videos)
9
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.4 – 1st Nine Weeks
Blueprint Categories
Grade 5 SOL
Computation and Estimation
The student will create and solve single-step and multistep
practical problems involving addition, subtraction,
multiplication, and division with and without remainders of
whole numbers.
5.4, 5.5a-b, 5.6, 5.7
Number of Items
9
Prior Knowledge
4.4 estimate; find the product and quotient of two numbers; +/- fractions with like and
unlike denominators up to 12; +/- decimals up through the thousandths place value
Understanding the Standard

An example of an approach to solving problems is Polya’s
four-step plan:
– Understand: Retell the problem; read it twice; take
notes; study the charts or diagrams; look up words
and symbols that are new.
– Plan: Decide what operation(s) to use and what
sequence of steps to use to solve the problem.
– Solve: Follow the plan and work accurately. If the first
attempt doesn’t work, try another plan.
– Look back: Does the answer make sense?

Estimation gives a rough idea of an amount. Strategies
such as front-end, rounding, and mental computation
may be used to estimate addition, subtraction,
multiplication, and division of whole numbers.

Examples of problems to be solved by using estimation
strategies are encountered in shopping for groceries,
Essential Understandings
All students should

Understand the meaning of mathematical
operations and how these operations
relate to one another when creating and
solving single-step and multistep word
problems.
10
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations to

Select appropriate methods and tools from
among paper and pencil, estimation, mental
computation, and calculators according to
the context and nature of the computation
in order to compute with whole numbers.

Create single-step and multistep problems
involving the operations of addition,
subtraction, multiplication, and division
with and without remainders of whole
numbers, using practical situations.

Estimate the sum, difference, product, and
Revised: 8/20/16
buying school supplies, budgeting allowance, and sharing
the cost of a pizza or the prize money from a contest.

quotient of whole number computations.

Solve single-step and multistep problems
involving addition, subtraction,
multiplication, and division with and
without remainders of whole numbers,
using paper and pencil, mental
computation, and calculators in which
– sums, differences, and products will not
exceed five digits;
– multipliers will not exceed two digits;
– divisors will not exceed two digits; or
– dividends will not exceed four digits.

Use two or more operational steps to solve
a multistep problem. Operations can be the
same or different.
Estimation can be used to check the reasonableness of
the results.
Additional Instructional Strategies
Box Method
Arrays for multiplication
Multistep word problems instructional videos
An estimate produces answers that are ―close enough‖ for the purpose. The situation determines what we need to know and, thus, the strategy we use for
estimation. Consider the sum: $349.29 + $85. 99 + $175.25. For the three prices, the question, ―About how much?‖ is very different from, ―Is it more than $600?‖
Students should consider the context when deciding what estimation strategy to use. They should be able to explain and justify their strategy and describe the
closeness of their estimate
Estimation can be used to check the reasonableness of the results, using the following types of strategies:
Compatible numbers are numbers that are easy to work with mentally. For example, 52 + 74 can be estimated using 50 + 75. The product 291 x 27 is close to 300 x
11
Revised: 8/20/16
25. The quotient 4929 ÷ 26 is close to 4800 ÷ 24 or 5000 ÷ 25.
Front-end or leading digit estimation is useful when totaling many large numbers, e.g. the number of people who attended football games in a season. Front-end
estimation of sums always gives a sum less than the actual sum; however, the estimate can be adjusted or refined so it is closer to the actual sum. For example,
9,162 + 5, 643 + 6,636 could be estimated using 9,000 + 5,000 + 6,000. (To refine the estimate, one might glance down the hundreds in each number and see that
the estimate could be increased by 1,000.)
Compensation is a strategy shoppers may use when mentally estimating a total purchase amount. For example, $2.38 + $5.22 + $0.39 may be estimated as $2 + $5
+ $1 (where the $1 represents an approximation of the accumulated cent amounts: $ .38 + $ .22 + $ .39)
Rounding the numbers to be added, subtracted, multiplied, or divided, to a given place is another method of estimation.
Never should the problem be solved and the answer rounded to find an estimate. If the exact answer is known, an estimate is not needed.
Students need additional practice solving multistep problems with whole numbers that involve the use of more than one operation. In this example students need
to use the information in the table and the information in the text. Many students will compute the answer to be $27, which is the amount of money Paul will save
on one tire.
Here is another example for SOL 5.4 that requires students to use more than one operation when solving the problem. Students would benefit from experiences
12
Revised: 8/20/16
that require them to consider how the remainder of a division situation impacts the outcome, as in the example provided. In this example students need to add to
find the total number of pictures (222) and then divide by 10 to decide how many posters are needed. Since the result is 22 R2 Maria will need a total of 23 posters
in order to display all of the pictures.
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Take a Trip - Computation and Estimation
Handout available: Working with Vocabulary /
Concept Development (Word)
Divison at the Carnival
Trade Books
Multiplying Menace: The Revenge of
Rumplestiltskin by Pam Calvert
Corkscrew Counts by Donna Jo Napoli
How Does Your Garden Grow
Word Wall Instructional Video
A Remainder of One by Elinor J. Pinczes
Multiplication Magic
Sum – The answer in an addition problem
March of the Dividing Ants
Amanda Bean’s Amazing Dream by Cyndi
Neuschwander
Enough for Everybody
Spaghetti and Meatballs for All by Marilyn Burns
Difference – The answer in a subtraction problem
Product – The answer in a multiplication problem
13
Revised: 8/20/16
Picture Book Lessons
Quotient – The answer in a division problem
Dividend – the number being divided
Divisor – the number that divides into another
number
Multi-step problem – a problem that requires more
than one step to solve
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
14
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.5 – 1st nine weeks
The student will
a)
find the sum, difference, product, and quotient of
two numbers expressed as decimals through thousandths
(divisors with only one nonzero digit); and
b)
create and solve single-step and multistep practical
problems involving decimals.
Blueprint Categories
Computation and Estimation
5.4, 5.5a-b, 5.6, 5.7
Number of Items
9
Prior Knowledge
4.4 estimate; find the product and quotient of whole numbers and decimals up through the
thousandths place value
Understanding the Standard

Addition and subtraction of decimals may be investigated using a
variety of models (e.g., 10-by-10 grids, number lines, money).

Decimal computation uses similar procedures as those developed for
whole number computation and applies them to decimal place values,
giving careful attention to the placement of the decimal point in the
solution.

Grade 5 SOL
Essential Understandings
All students should

Multiplication of decimals follows the same procedure as
multiplication of whole numbers. The only difference is that a decimal
point must be correctly placed in the product giving careful attention
to the placement of the decimal point in the solution.

The product of decimals is dependent upon the two factors being
multiplied.

In cases where an exact product is not required, the product of
decimals can be estimated using strategies for multiplying whole
numbers, such as front-end and compatible numbers, or rounding. In
each case, the student needs to determine where to place the
15
Use similar procedures as those
developed for whole number
computation and apply them to decimal
place values, giving careful attention to
the placement of the decimal point in
the solution.

Select appropriate methods and tools
from among paper and pencil,
estimation, mental computation, and
calculators according to the context and
nature of the computation in order to
compute with decimal numbers.

Understand the various meanings of
division and its effect on whole numbers.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Determine an appropriate
method of calculation to find the
sum, difference, product, and
quotient of two numbers
expressed as decimals through
thousandths, selecting from
among paper and pencil,
estimation, mental computation,
and calculators.

Estimate to find the number that
is closest to the sum, difference,
and product of two numbers
Revised: 8/20/16

decimal point to ensure that the product is reasonable.


Division is the operation of making equal groups or shares. When the
original amount and the number of shares are known, divide to find
the size of each share. When the original amount and the size of each
share are known, divide to find the number of shares. Both situations
may be modeled with Base-10 manipulatives.
Division with decimals is performed the same way as division of whole
numbers. The only difference is the placement of the decimal point in
the quotient.

The quotient can be estimated, given a dividend expressed as a
decimal through thousandths (and no adding of zeros to the dividend
during the division process) and a single-digit divisor.

Estimation can be used to check the reasonableness of a quotient.

Division is the inverse of multiplication; therefore, multiplication and
division are inverse operations.

Terms used in division are dividend, divisor, and quotient.
dividend  divisor = quotient

A multistep problem needs to incorporate no more than two
operational steps (operations can be the same or different).
Find the sum, difference, and
product of two numbers
expressed as decimals through
thousandths, using paper and
pencil, estimation, mental
computation, and calculators.

Determine the quotient, given a
dividend expressed as a decimal
through thousandths and a
single-digit divisor. For example,
5.4 divided by 2 and 2.4 divided
by 5.

Use estimation to check the
reasonableness of a sum,
difference, product, and
quotient.

Create and solve single-step and
multistep problems.

A multistep problem needs to
incorporate two or more
operational steps (operations
can be the same or different).
divisor dividend
dividend
divisor = quotient.
divisor )dividend
There are a variety of algorithms for division such as repeated
multiplication and subtraction. Experience with these algorithms may
enhance understanding of the traditional long division algorithm.

quotient
quotient

expressed as decimals through
thousandths.
dividend  divisor = quotient
The fair-share concept of decimal division can be modeled, using
manipulatives (e.g., Base-10 blocks).

Understand various representations of
division, i.e.,
16
Revised: 8/20/16
Additional Instructional Strategies
Multistep word problems instructional video
Teaching alternative algorithms is essential to student success and understanding.
Example:
For SOL 5.5a, students need additional practice multiplying decimals. Statewide results indicate that the most frequent error made by students on both multiplechoice and technology-enhanced items occurs when placing the decimal into the answer.
Using estimation strategies to verify the reasonableness of a product is mandatory for instruction. For example in #3, since 2 times 2 equals 4 and 3 times 3 equals
9, it is reasonable to decide that 2.5 times 2.5 should be between 4 and 9. Therefore, 6.25 is a reasonable answer. If the student incorrectly placed the decimal
and got 62.5 as an answer to #3, the student’s estimation should indicate that this is not a reasonable solution. All students are expected to use estimation when
multiplying decimals.
#1 20 x ½ (20/2)= 10; I know my answer is less than 10
because 0.4 is less than ½.
#2 ½ x.5 (.5/2)= 0.25 I know my answer is a little more than
0.25 because 0.55 is a little more than ½.
#3. See above
For SOL 5.5b, students need additional practice solving practical problems involving multiplication of decimals. Again, estimation should be used to check
17
Revised: 8/20/16
reasonableness of answer.
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Trade Books
Party Time - Computation and Estimation
Handout available: Working with Vocabulary /
Concept Development (Word)
Word Wall Instructional Video
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
18
Revised: 8/20/16
Sheppard Software
IQ Practice Tests
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
National Library of Virtual
Manipulatives
iPad™ Resources
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Worksheet Fun
Quia
RCPS Math Resources
19
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.7 – 1st Nine Weeks
The student will evaluate whole number numerical expressions,
using the order of operations limited to parentheses, addition,
subtraction, multiplication, and division.
Blueprint Categories
Grade 5 SOL
Number of Items
Computation and Estimation
5.4, 5.5a-b, 5.6, 5.7
9
Prior Knowledge
Understanding the Standard
Essential Understandings
 An expression, like a phrase, has no equal sign.
All students should
 Expressions are simplified by using the order of operations.

 The order of operations defines the computation order to follow in
simplifying an expression.
 The order of operations is as follows:
– First, complete all operations within grouping symbols. If there are
grouping symbols within other grouping symbols, do the
innermost operation first.
– Second, evaluate all exponential expressions.
– Third, multiply and/or divide in order from left to right.
– Fourth, add and/or subtract in order from left to right.
20
Understand that the order of operations
describes the order to use to simplify
expressions containing more than one
operation.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Simplify expressions by using the
order of operations in a
demonstrated step-by-step
approach.

Find the value of numerical
expressions, using the order of
operations.

Given an expression involving
more than one operation,
describe which operation is
completed first, which is second,
etc.
Revised: 8/20/16
Additional Instructional Strategies
Order of Operations Instructional Video
Handout available: Rules for Order of Operations (Word)
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Order Out of Chaos - Computation and Estimation
Handout available: Working with Vocabulary /
Concept Development (Word)
Pardon My Expression
Trade Books
Word Wall Instructional Video
Expression – A variable or combination of variables,
numbers, and symbols that represent a
mathematical relationship
Order of Operations – The order in which operations
must be completed in order to simplify an equation
(Parentheses, Exponents, Multiply, Divide, Add,
Subtraction) – Please Excuse My Dear Aunt Sally
21
Revised: 8/20/16
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
22
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.19 – 2nd Nine Weeks
Blueprint Categories
Probability, Statistics, Patterns,
Functions and Algebra
The student will investigate and recognize the distributive
property of multiplication over addition.
Grade 5 SOL
Number of Items
5.14, 5.15, 5.16b-d,
5.17, 5.18a-d, 5.19
13
Blueprint Categories
3.20 Commutative property of addition and multiplication
4.16 Associative property of addition and multiplication
Understanding the Standard

The distributive property states that multiplying a sum by a
number gives the same result as multiplying each addend
by the number and then adding the products (e.g.,
3(4 + 5) = 3 x 4 + 3 x 5,
Essential Understandings
All students should

5 x (3 + 7) = (5 x 3) + (5 x 7); or (2 x 3) + (2 x 5) = 2 x (3 + 5).

The distributive property can be used to simplify
expressions (e.g., 9 x 23 = 9(20+3) =180+ 27 = 207; or 5 x
19 = 5(10 + 9) = 50 + 45 = 95).
Understand that the distributive property
states that multiplying a sum by a number
gives the same result as multiplying each
addend by the number and then adding the
products.

Understand that using the distributive
property with whole numbers helps with
understanding mathematical relationships.

Understand when and why the distributive
property is used.
23
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to

Investigate and recognize the
distributive property of whole
numbers, limited to multiplication over
addition using diagrams and
manipulatives.

Investigate and recognize an equation
that represents the distributive
property, when given several whole
number equations, limited to
multiplication over addition.
Revised: 8/20/16
Additional Instructional Strategies
Distributive Property instructional video
Distributive Property Study Jam
Practice Distributive Property
Additional Math Curriculum Resources
24
Revised: 8/20/16
Vocabulary
Lessons and TEI Items
Vocabulary word wall
Trade Books
Exploring the Distributive Property - Patterns,
Functions, and Algebra
Handout available: Working with Vocabulary /
Concept Development (Word)
Patterns, Functions and Algebra K-5 (PDF)
Word wall instructional video
Distributive Property – a number and a sum can be
multiplied by multiplying the number by each
addend and then adding these products.
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
25
Revised: 8/20/16
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
26
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.3 – 2nd Nine Weeks
The student
a) identify and describe the characteristics of prime and
composite
b) numbers; and identify and describe the characteristics
of even and odd numbers.
Blueprint Categories
Grade 5 SOL
Number of Items
Number and Number Sense
5.1, 5.2a-b, 5.3a-b
5
Prior Knowledge
1.2 – skip counting by 2s to 100
2.4c – recognize odd & even numbers
3.5 – multiplication facts
4.5a – common multiples & factors
Understanding the Standard

A prime number is a natural number that has exactly two different
factors, one and the number itself.

A composite number is a natural number that has more than two
different factors.

The number 1 is neither prime nor composite because it has only one
factor, itself.

The prime factorization of a number is a representation of the
number as the product of its prime factors. For example, the prime
factorization of 18 is 2  3  3.

Prime factorization concepts can be developed by using factor trees.

Prime or composite numbers can be represented by rectangular
models or rectangular arrays on grid paper. A prime number can be
represented by only one rectangular array (e.g., 7 can be represented
by a 7  1 and a 1 x 7). A composite number can always be
represented by more than two rectangular arrays (e.g., 9 can be
Essential Understandings
All students should

27
Understand and use the unique
characteristics of certain sets of
numbers, including prime, composite,
even, and odd numbers.
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

Identify prime numbers less than or
equal to 100.

Identify composite numbers less
than or equal to 100.

Explain orally and in writing why a
number is prime or composite.

Identify which numbers are even or
odd.

Explain and demonstrate with
manipulatives, pictorial
representations, oral language, or
Revised: 8/20/16
represented by a 9  1, a 1 x 9, or a 3  3).

Divisibility rules are useful tools in identifying prime and composite
numbers.

Students should use manipulatives (e.g., Base-10 blocks, cubes, tiles,
hundreds board, etc.) to explore and categorize numbers into groups
of odd or even.

Students should use rules to categorize numbers into groups of odd or
even. Rules can include:
– An odd number does not have 2 as a factor or is not divisible by 2.
– The sum of two even numbers is even.
– The sum of two odd numbers is even.
– The sum of an even and an odd is odd.
– Even numbers have an even number or zero in the ones place.
– Odd numbers have an odd number in the ones place.
– An even number has 2 as a factor or is divisible by 2.
written language why a number is
even or odd.
Additional Instructional Strategies
Additional Math Curriculum Resources
28
Revised: 8/20/16
Vocabulary
Vocabulary word wall
Handout available: Working with Vocabulary /
Concept Development (Word)
Lessons and TEI Items
Trade Books
Sieve of Eratosthenes: An Ancient Algorithm to
Number and Number Sense
You Can Count on Monsters by Richard Evan
Schwartz
Partners and Leftovers - Number and Number Sense
Even Steven and Odd Todd by Kathryn Cristaldi
Number and Number Sense Lesson
Among the Odds and Evens by Priscillia Turner
Word Wall Instructional Video
Prime number - A natural number with exactly two
factors; one and itself
Missing Mittens by Stuart Murphy
Factors – A number that is multiplied by another
number to find a product
Ocean Counting: Odd Numbers by Jerry Pallotta
One is a Snail Ten is a Crab by April Pulley Sayre and
Jeff Sayre
Composite number – Any natural number with more
than two factors
One Odd Day by Doris Fisher and Danni Sneed
Natural number - The counting numbers (1, 2, 3, …)
My Even Day by Doris Fisher and Danni Sneed
Prime factorization - Finding the factors of a number
that are all prime
The Odds Get Even by Natale Ghert
Product – The answer in multiplication
If You Were and Even Number by Marcie Aboff
Even – Any number ending in 0, 2, 4, 6, or 8; divisible
by two
If You Were an Odd Number by Marcie Aboff
Picture Book Lesson Ideas
Odd – Any number ending in 1, 3, 5, 7, or 9
29
Revised: 8/20/16
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
30
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.2 – 2nd Nine Weeks
The student will
a) recognize and name fractions in their equivalent decimal
form and vice versa; and
b) compare and order fractions and decimals in a given set
from least to greatest and greatest to least.
Blueprint Categories
Grade 5 SOL
Number and Number Sense
5.1, 5.2a-b, 5.3a-b
Number of Items
5
Prior Knowledge
4.2 – compare, represent, & order fractions & mixed numbers; identify division statement
that represents a fraction
4.3 – read, write, & represent through thousandths; round through hundredths; compare, &
order; write equivalents
4.5d – problem solving with decimals
Understanding the Standard
Essential Understandings

Students should recognize, name, and focus on finding equivalent decimals
of familiar fractions such as halves, fourths, fifths, eighths, and tenths.

Students should be able to determine equivalent relationships between
decimals and fractions with denominators up to 12.

1
Students should have experience with fractions such as , whose decimal
8
1
representation is a terminating decimal (e. g., = 0.125) and with fractions
8
2
such as , whose decimal representation does not end but continues to
9
2
repeat (e. g., = 0.222…). The repeating decimal can be written with ellipses
9
All students should
(three dots) as in 0.222… or denoted with a bar above the digits that repeat
as in 0 .2 .
31

Understand the relationship between
fractions and their decimal form and
vice versa.

Understand that fractions and decimals
can be compared and ordered from
least to greatest and greatest to least.
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to

Represent fractions (halves, fourths,
fifths, eighths, tenths, and twelfths) in
their equivalent decimal form and vice
versa.

Recognize and name equivalent
relationships between decimals and
fractions with denominators up to 12.

Compare and order from least to
greatest and greatest to least a given set
of no more than five numbers written as
decimals, fractions, and mixed numbers
with denominators of 12 or less.
Revised: 8/20/16

To help students compare the value of two decimals through thousandths,
use manipulatives, such as place value mats/charts, 10-by-10 grids, decimal
squares, Base-10 blocks, meter sticks, number lines, and money.

A procedure for comparing two decimals by examining may include the
following:
– Line up the decimal numbers at their decimal points.
– Beginning at the left, find the first place value where the digits are
different.
– Compare the digits in this place value to determine which number is
greater (or which is less).
– Use the appropriate symbol > or < or the words greater than or less than
to compare the numbers in the order in which they are presented.
– If both numbers are the same, use the symbol = or words equal to.
Two numbers can be compared by examining place value and/or using a
number line.

Decimals and fractions represent the same relationships; however, they are
presented in two different formats. Decimal numbers are another way of
writing fractions. Base-10 models (e.g., 10-by-10 grids, meter sticks, number
lines, decimal squares, money) concretely relate fractions to decimals and
vice versa.
Additional Instructional Activities
Understanding Fractions Video
Models for teaching fractions instructional video
32
Revised: 8/20/16
For SOL 5.2b, students need additional practice comparing and ordering fractions. When given a multiple-choice question the most common errors are to order
the fractions by their numerators (as in option A) or to order them by their denominators (as in option D).
Students also need additional practice comparing and ordering a set of decimals and fractions.
Common mistakes include incorrectly converting when finding equivalent fractions and decimals (for instance, converting 3 3/4 to 3.34), incorrectly applying
whole number understanding when comparing decimals (for instance, stating 3.34 is greater than 3.5 because 34 is greater than 5), and incorrectly comparing
the fractions (stating 3 3/4 is less than 3 5/8 because the numerator of 3 is less than the numerator of 5 and the denominator of 4 is less than the denominator
of 8).
Additional Math Curriculum Resources
33
Revised: 8/20/16
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary word wall
Order Up! - Number and Number Sense
Fraction Action by Loreen Leedy
Handout available: Working with Vocabulary /
Concept Development (Word)
Number and Number Sense Lesson
Piece = Part = Portion by Scott Gifford
Thinking Rationally about Fractions, Decimals and
Percent Instructional Activities (Grades 4-8) (PDF) –
lessons providing additional strategies for
elementary and middle school teachers in the areas
of fractions, decimals, percent and proportional
thinking
Fraction Fun by David A. Adler
Word Wall Instructional Video
Compare – Seeing whether two numbers are equal,
greater than, or less than each other
Equivalent – Having the same value
Jump, Kangaroo, Jump! by Stuart J. Murphy
Hershey’s Fraction Book by Jerry Pallotta
Gator Pie by Louise Mathews
Don't Be Bugged By Decimals
Picture Book Lesson Ideas
Fractions on a Number Line
Marathon Markers (Comparing and Ordering
Fractions)
Rings Around Decimals
Fishing Derby Ad
Exploring Two-Digit Numbers with the Inequality
Symbols
34
Revised: 8/20/16
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
35
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.6 – 2nd Nine Weeks
The student will solve single-step and multistep practical
problems involving addition and subtraction with fractions
and mixed numbers and express answers in simplest form.
Blueprint Categories
Grade 5 SOL
Computation and Estimation
5.4, 5.5a-b, 5.6, 5.7
Number of Items
9
Prior Knowledge
4.5 estimate; find the product and quotient of two numbers; +/- fractions with like and
unlike denominators up to 12; +/- decimals up through the thousandths place value
Understanding the Standard

Essential Understandings
A fraction can be expressed in simplest form (simplest equivalent
fraction) by dividing the numerator and denominator by their greatest
common factor.

When the numerator and denominator have no common factors
other than 1, then the fraction is in simplest form.

Fractions having like denominators means the same as fractions
having common denominators.

Equivalent fractions name the same amount. To find equivalent
fractions, multiply or divide the numerator and denominator by the
same nonzero number.

Addition and subtraction with fractions and mixed numbers can be
modeled using a variety of concrete materials and pictorial
representations as well as paper and pencil.

To add, subtract, and compare fractions and mixed numbers, it often
All students should
36

Develop and use strategies to estimate
and compute addition and subtraction of
fractions.

Understand the concept of least
common multiple and least common
denominator as they are important
when adding and subtracting fractions.

Understand that a fraction is in simplest
form when its numerator and
denominator have no common factors
other than 1. The numerator can be
greater than the denominator.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Solve single-step and multistep
practical problems involving
addition and subtraction with
fractions having like and unlike
denominators. Denominators in
the problems should be limited
1 1
to 12 or less (e.g., 5 + 4 ) and
answers should be expressed in
simplest form.
Revised: 8/20/16
helps to find the least common denominator. The least common
denominator (LCD) of two or more fractions is the least common
multiple (LCM) of the denominators.

To add or subtract with fractions having the same or like
denominators, add or subtract the numerators and write in simplest
form.

To add or subtract with fractions that do not have the same
denominator, first find equivalent fractions with the least common
denominator. Then add or subtract and write the answer in simplest
form.

A mixed number has two parts: a whole number and a fraction. The
value of a mixed number is the sum of its two parts.

To add or subtract with mixed numbers, students may use a number
line, draw a picture, rewrite fractions with like denominators, or
rewrite mixed numbers as fractions.

Solve single-step and multistep
practical problems involving
addition and subtraction with
mixed numbers having like and
unlike denominators, with and
without regrouping.
Denominators in the problems
should be limited to 12 or less
(common denominator when
computing fractions could be
larger than 12), and answers
should be expressed in simplest
form.

Use estimation to check the
reasonableness of a sum or
difference.
Additional Instructional Activities
Fraction Computation Instructional Video
Alternative Strategies to standard algorithms
37
Revised: 8/20/16
Statewide results indicate that students have difficulty when adding and subtracting fractions that require regrouping. When mixed numbers are included in the
problem, students frequently subtract the smaller fraction from the larger fraction and subtract the smaller whole number from the larger whole number. For
example, in this question many students would subtract one-eighth from three-fourths to get five-eighths and also subtract 54 from 55 to get 1, resulting in the
incorrect selection of option A.
This is another multistep problem involving fractions and mixed numbers. There are several strategies that could be used to solve this problem. One strategy that
could be used is to subtract 1¼ from 3½ to get 2¼ and then subtract 1/3 to get the answer. Another strategy would be to add 1¼ to 1/3 to get 1 7/12 and then
subtract 1 7/12 from 3½ to arrive at the same answer. Students would benefit from a discussion of different approaches to arrive at the solution.
Additional Math Curriculum Resources
38
Revised: 8/20/16
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Enough Room? - Computation and Estimation
Handout available: Working with Vocabulary /
Concept Development (Word)
Thinking Rationally about Fractions, Decimals and
Percent Instructional Activities (Grades 4-8) (PDF) –
lessons providing additional strategies for
elementary and middle school teachers in the areas
of fractions, decimals, percent and proportional
thinking
Word Wall Instructional Video
Fraction – a way of representing a part of a whole or
a part of a group
Trade Books
Simplest Form – a fraction whose numerator and
denominator have no common factor greater than
one
Equivalent Fraction – Fractions that represent an
equal amount
Numerator - the number above the line in a fraction;
the number that tells how many equal parts are
described by the fraction
Denominator – the number below the line in a
fraction; it tells the number of equal parts into which
a whole is divided
Greatest Common Factor – the largest number that
divides evenly into two or more numbers
Mixed Numbers – a number with an integer part
and fraction part
39
Revised: 8/20/16
Least Common Denominator (LCD) – the smallest
common multiple of the denominators of two or
more fractions
Least Common Multiple (LCM) – the smallest
common multiple of a set of two or more numbers
Improper Fraction- The numerator is greater or
equal to the denominator.
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
40
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL 5.15 – 2nd Nine Weeks
Blueprint Categories
Grade 5 SOL
Number of Items
Probability, Statistics, Patterns,
5.14, 5.15, 5.16b-d,
5.17, 5.18a-d, 5.19
13
The student, given a problem situation, will collect, organize,
and interpret data in a variety of forms, using stem-and-leaf
plots and line graphs.
Functions and Algebra
Prior Knowledge
4.13 predict the likelihood of an event occurring; create line/bar graphs; draw conclusions
and make predictions on line/bar graphs
Understanding the Standard


Essential Understandings
The emphasis in all work with statistics should be on the analysis and
the communication of the analysis, rather than on a single correct
answer. Data analysis should include opportunities to describe the
data, recognize patterns or trends, and make predictions.
All students should
Statistical investigations should be active, with students formulating
questions about something in their environment and finding
quantitative ways to answer the questions.

Investigations can be brief class surveys or more extended projects
taking many days.

Through experiences displaying data in a variety of graphical
representations, students learn to select an appropriate

Understand how to interpret collected
and organized data.

Understand that stem-and-leaf plots list
data in a meaningful array. It helps in
finding median, modes, minimum and
maximum values, and ranges.

41
Understand that line graphs show
changes over time.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Formulate the question that will
guide the data collection.

Collect data, using observations
(e.g., weather), measurement
(e.g., shoe sizes), surveys (e.g.,
hours watching television), or
experiments (e.g., plant growth).
Revised: 8/20/16
representation.


Line graphs are used to show how two continuous variables are
related. Line graphs may be used to show how one variable changes
over time. If one variable is not continuous, then a broken line is used.
By looking at a line graph, it can be determined whether the variable
is increasing, decreasing, or staying the same over time.
– The values along the horizontal axis represent continuous data on
a given variable, usually some measure of time (e.g., time in
years, months, or days). The data presented on a line graph is
referred to as “continuous data” because it represents data
collected over a continuous period of time.
– The values along the vertical axis are the scale and represent the
frequency with which those values occur in the data set. The
values should represent equal increments of multiples of whole
numbers, fractions, or decimals depending upon the data being
collected. The scale should extend one increment above the
greatest recorded piece of data.
– Each axis should be labeled and the graph should have a title.
– A line graph tells whether something has increased, decreased, or
stayed the same with the passage of time. Statements
representing an analysis and interpretation of the
characteristics of the data in the graph should be included (e.g.,
trends of increase and/or decrease, and least and greatest). A
broken line is used if the data collected is not continuous data
(such as test scores); a solid line is used if the data is continuous
(such as height of a plant).
Stem-and-leaf plots allow the exact values of data to be listed in a
meaningful array. Data covering a range of 25 numbers are best
displayed in a stem-and-leaf plot and are utilized to organize
numerical data from least to greatest, using the digits of the greatest
to group data.
– The data is organized from least to greatest.
– Each value should be separated into a stem and a leaf [e.g., twodigit numbers are separated into stems (tens) and leaves
42

Organize the data into a chart,
table, stem-and-leaf plots, and
line graphs.

Display data in line graphs and
stem-and-leaf plots.

Construct line graphs, labeling
the vertical axis with equal
whole number, decimal, or
fractional increments and the
horizontal axis with continuous
data commonly related to time
(e.g., hours, days, months, years,
and age). Line graphs will have
no more than six identified
points along a continuum for
continuous data (e.g., the
decades: 1950s, 1960s, 1970s,
1980s, 1990s, and 2000s).

Construct a stem-and-leaf plot
to organize and display data,
where the stem is listed in
ascending order and the leaves
are in ascending order, with or
without commas between
leaves.

Title the given graph or identify
the title.

Interpret the data in a variety of
forms (e.g., orally or in written
form).
Revised: 8/20/16
(ones)].
– The stems are listed vertically from least to greatest with a line to
their right. The leaves are listed horizontally, also from least to
greatest, and can be separated by spaces or commas. Every
value is recorded regardless of the number of repeats.
– A key is often included to explain how to read the plot.
Additional Instructional Strategies
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Mystery Data - Probability and Statistics
Bart’s Amazing Charts by Dianne Ochiltree
Handout available: Working with Vocabulary /
Concept Development (Word)
Super Duper Amusement Park
The Best Vacation Ever by Stuart Murphy
43
Revised: 8/20/16
Be Mathletic!
The Fly on the Ceiling: A Math Myth by Dr. Julie Glass
Vote the Facts
The Long Wait by Annie Cobb
Let's Get Physical
Picture Book Lesson Ideas
Word Wall Instructional Video
Stem-and-Leaf Plots – a data display that organizes
data points by separating each into a leaf (last digit)
and a stem (remaining digits).
Blast Off
Line Graphs – a type of graph in which points
representing data pairs are connected by line
segments.
Vertical Axis – the y-axis in the coordinate plane.
Horizontal Axis – the x-axis in the coordinate plane.
Title – the heading that identifies the topic of the
display.
Frequency – the number of times an event occurs.
Data – information, facts, or numbers that describe
something.
Key – a systematic explanation of abbreviations and
symbols
44
Revised: 8/20/16
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
45
Revised: 8/20/16
SOL 5.16 – 2nd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.16 – 2nd Nine Weeks
The student will
a) describe mean, median, and mode as measures of
center;
b) describe mean as fair share;
c) find the mean, median, mode, and range of a set of
data; and
d) describe the range of a set of data as a measure of
variation.
Statistics is the science of conducting studies to collect,
organize, summarize, analyze, and draw conclusions
from data.
Grade 5 SOL
Number of Items
Probability, Statistics, Patterns,
Functions and Algebra
5.14, 5.15, 5.16b-d,
5.17, 5.18a-d, 5.19
13
Prior Knowledge
Understanding the Standard

Blueprint Categories
Essential Understandings
All students should

Understand that mean, median, and mode are
described as measures of center.
A measure of center is a value at the center or middle of
a data set. Mean, median, and mode are measures of
center.

Understand that mean, median, and mode are
three of the various ways that data can be
described or summarized.

The mean, median, and mode are three of the various
ways that data can be analyzed.


Mean represents a fair share concept of the data.
Dividing the data constitutes a fair share. This is done
by equally dividing the data points. This should be
demonstrated visually and with manipulatives. The
arithmetic way is to add all of the data points then
divide by the number of data points to determine the
Understand that mean as fair share is described
as equally dividing the data set or the data set has
already been divided equally.


Understand how to find the mean, median, and
mode of a set of data as measures of center.

Understand values in the context of other
characteristics of the data in order to best
46
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

Describe and find the mean of a
group of numbers representing data
from a given context as a measure of
center.

Describe and find the median of a
group of numbers representing data
from a given context as a measure of
center.

Describe and find the mode of a
group of numbers representing data
Revised: 8/20/16
SOL 5.16 – 2nd Nine Weeks
average or mean.

describe the results.
The median is the piece of data that lies in the middle of
the set of data arranged in order.

The mode is the piece of data that occurs most
frequently in the data set. There may be one, more than
one, or no mode in a data set. Students should order
the data from least to greatest so they can better find
the mode.

The range is the spread of a set of data. The range of a
set of data is the difference between the greatest and
least values in the data set. It is determined by
subtracting the least number in the data set from the
greatest number in the data set. An example is ordering
test scores from least to greatest: 73, 77, 84, 87, 89, 91,
94. The greatest score in the data set is 94 and the least
score is 73, so the least score is subtracted from the
greatest score or 94 - 73 = 21. The range of these test
scores is 21.

Students need to learn more than how to identify the
mean, median, mode, and range of a set of data. They
need to build an understanding of what the number
tells them about the data, and they need to see those
values in the context of other characteristics of the data
in order to best describe the results.
from a given context as a measure of
center.

Describe mean as fair share.

Describe and find the range of a
group of numbers representing data
from a given context as a measure of
variation.

Describe the impact on measures of
center when a single value of a data
set is added, removed, or changed.†
†
Revised March 2011
Additional Instructional Strategies
Mean as a fair share Instructional Video
Mean as a balance point instructional video
Statistics Instructional video
47
Revised: 8/20/16
SOL 5.16 – 2nd Nine Weeks
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
What Does It Mean? - Probability and Statistics
Handout available: Working with Vocabulary /
Concept Development (Word)
Swimming in Data
Trade Books
All Aboard! Hop on the Averaging Train
Word Wall Instructional Video
Chocolate Festival
Mean – the sum of the values in a data set divided
by the number of values.
Median – the middle value or the average of the two
middle values in an ordered data set.
Line Plots: Frogs in Flight
Blast Off
Mode – the value in a data set that occurs most
often. A data set can have no mode, one mode, or
more than one mode.
Measures of Center – measures used to describe the
middle of a data set.
Fair Share – equally dividing the data; the mean
Range – the difference between the greatest and
least values in a set of data.
Measure of Variation – amount, rate, extent, or
degree of change
48
Revised: 8/20/16
SOL 5.16 – 2nd Nine Weeks
Statistics – collecting, classifying, analyzing, and
interpreting numerical facts or data
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
49
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.8 c,d,e – 3rd Nine Weeks
The student will
c) identify equivalent measurements within the metric
system;
d) estimate and then measure to solve problems, using U.S.
Customary and metric units; and
e) choose an appropriate unit of measure for a given situation
involving measurement using U.S. Customary and metric
units.
When measuring with U.S. Customary units, students should be able to
1 1 1
measure to the nearest part of an inch (2 , 4 , 8 ), foot, or yard.

Weight and mass are different. Mass is the amount of matter in an object.
Weight is determined by the pull of gravity on the mass of an object. The
mass of an object remains the same regardless of its location. The weight
that an object changes is dependent on the gravitational pull at its location.
In everyday life, most people are actually interested in determining an
object’s mass, although they use the term weight (e.g., “How much does it
weigh?” versus “What is its mass?”).

Number of Items
Measurement and Geography
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
8
4.6 Measuring weight and mass using US Customary and Metric
4.7 Length using US Customary and Metric
4.8 Volume using US Customary and Metric
Essential Understandings
All students should
U.S. Customary units for measurement of length include inches, feet, yards,
and miles. Appropriate measuring devices include rulers, yardsticks, and tape
measures. Metric units for measurement of length include millimeters,
centimeters, meters, and kilometers. Appropriate measuring devices include
centimeter ruler, meter stick, and tape measure.

Grade 5 SOL
Prior Knowledge
Understanding the Standard

Blueprint Categories

Appropriate measuring devices to measure mass in U.S. Customary units
50
Understand how to select a
measuring device and unit of measure
to solve problems involving
measurement.
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations
to

Identify whether the application of the
concept of perimeter, area, or volume is
appropriate for a given situation.

Identify equivalent measurements within
the metric system for the following:
– length: millimeters, centimeters,
meters, and kilometers;
– mass: grams and kilograms;
– liquid volume: milliliters, and liters.

Solve problems involving measurement by
selecting an appropriate measuring device
and a U.S. Customary or metric unit of
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
(ounces, pounds) and metric units (grams, kilograms) are balances.
measure for the following:
U.S. Customary units to measure liquid volume (capacity) include cups, pints,
quarts, and gallons. Metric units to measure liquid volume (capacity) include
milliliters and liters.
–

Temperature is measured using a thermometer. The U.S. Customary unit of
measure is degrees Fahrenheit; the metric unit of measure is degrees Celsius.

Practical experience measuring familiar objects helps students establish
benchmarks and facilitates students’ ability to use the units of measure to
make estimates.
–
–
–

–
–
1 1 1
length: part of an inch (2 , 4 , 8 ),
inches, feet, yards, millimeters,
centimeters, meters, and kilometers;
weight: ounces, pounds, and tons;
mass: grams and kilograms;
liquid volume: cups, pints, quarts,
gallons, milliliters, and liters;
area: square units; and
temperature: Celsius and Fahrenheit
units.
– Water freezes at 0C and 32F.
– Water boils at 100C and 212F.
– Normal body temperature is about
37C and
98.6F.
Additional Instructional Activities
Play Video Converting Units (grades 3-8)
Handout available: Converting Units (Word)
Liquid measure instructional video
Units of measure instructional video
51
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
NOTE: Decimals are to be used in conversions!!
There are several helpful strategies that students can use to help them convert. One strategy is “King Henry Died Unexpectantly By Drinking Chocolate Milk”.
(There are several versions of this phrase.) There is an Active Inspire Lesson in the Shared (Z) Drive on the county web site (Elementary/Grade 5
Math/Measurement).
King Henry Drinks Ucky Dark Chocolate Milk
Additional Math Curriculum Resources
52
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Measurement Mania - Measurement
Measuring Penny by Loreen Leedy
Handout available: Working with Vocabulary /
Concept Development (Word)
Line Plots: Frogs in Flight
Pastry School in Paris: An Adventure in Capacity by
Cindy Neuschwander
Word wall instructional video
U.S. Customary Unit – a standard for
measurement, used in the United States.
Measurement: Using a Ruler to Measure Sea
Creatures to the Nearest Eighth Inch
For Good Measure by Ken Robbins
Inchology-The Study of Inches
The 100 Pound-Problem by Jennifer Dussling
What's Your Capacity?
Balancing Act by Ellen Stoll Walsh
Metric – a decimal system of measurement used
internationally.
Beanstalk; the Measure of a Giant by Ann McCallum
Length – the measure of a path or object in one
dimension from end to end.
The Biggest Fish by Sheila Keenan
Biggest, Strongest, Fastest by Steve Jenkins
Width – the measure of a path or object in one
dimension from end to end.
Counting on Frank by Rod Clement
Inch – a customary unit of length
The Dragon’s Scales by Sarah Albee
Foot – Customary (English) system unit of length;
12 inches.
Equal Shmequal by Virginia Kroll
Hottest, Coldest, Highest, Deepest by Steven Jenkins
Yard – Customary (English) system unit of length; 3
feet.
How Big is a Foot by Rolf Myller
Mass – amount of matter; commonly measured in
grams, kilograms, and metric tons.
How Big is It? by Ben Hillman
How Long is It? by Donna Loughman
53
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
How Long or How Wide by Brian Cleary
Weight – the force of gravity acting on an object;
can be used to measure mass.
How Tall, How Short, How Faraway by David Adler
Ounces – a unit for measuring weight in the English
system.
Inch by Inch by Leo Lionni
Inchworm and a Half by Elinor Pinczes
Pounds – a unit of measure of weight in the
customary (English) system; 16 oz.
Incredible Comparisons by Russell Ash
Tons – a unit of measure of weight in the
customary (English) system; 2000 lbs.
Is a Blue Whale the Biggest Thing There Is? by Robert
Wells
Grams – the basic unit of mass in common usage in
the metric system.
Jim and the Beanstalk by Raymond Briggs
Length by Henry Arthur
Kilograms – unit of measure of mass in the metric
system; 1000 grams
.
Millimeters – unit of measure of length in the
metric system which is 1/1000 of a meter.
The Librarian Who Measured the Earth by Kevin
Hawkes
Me and the Measure of Things by Joan Sweeney
Centimeters – a unit of measure of length in the
metric system which is 1/100 of a meter.
Millions to Measure by David Schwartz
More for Me by Sydnie Meltzer Kleinhenz
Meters – the basic unit of length in the metric
system.
Pigs in the Pantry by Amy Axelrod
Kilometers – a unit of measure of length in the
metric system; 1000 meters.
Racing Around by Stuart J. Murphy
Slower than a Snail by Anne Schreiber
Liquid Volume – the amount a container can hold;
capacity.
Super Sand Castle Saturday by Stuart Murphy
Cup – a unit of capacity in the English system of
measurement; 2 cups = 1 pint.
Twelve Snails to One Lizard by Susan Hightower
54
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Twenty-One Elephants by Phil Bildner
Pints – a unit of capacity in the English system of
measurement; 2 cups.
Twenty-One Elephants and Still Standing by April Jones
Prince
Quarts – a unit of capacity in the customary system
of measurement; 8 pints.
Weight by Henry Arthur
What’s Smaller Than a Pygmy Shrew by Robert Wells
Gallon – a unit of capacity in the customary system
of measurement; 4 quarts.
Who Sank the Boat? by Pamela Allen
Milliliters – a unit of capacity in the metric system
of measurement; 1/1000 liter.
Picture Book Lesson Ideas
Liter – the basic unit of capacity of liquids and gases
in the metric system.
55
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
56
Revised: 8/20/16
SOL 5.10 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.10 – 3rd Nine Weeks
The student will determine an amount of elapsed time in
hours and minutes within a 24-hour period.
Blueprint Categories
Grade 5 SOL
Number of Items
Measurement and Geography
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
8
Prior Knowledge
4.9 Elapsed time hours and minutes within a 12 hour time period
Understanding the Standard

Elapsed time is the amount of time that has passed between two
given times.

Elapsed time can be found by counting on from the beginning time to
the finishing time.
– Count the number of whole hours between the beginning time
and the finishing time.
– Count the remaining minutes.
– Add the hours and minutes. For example, to
find the elapsed time between 10:15 a.m. and 1:25 p.m.,
count on as follows:
from 10:15 a.m. to 1:15 p.m., count 3
hours;
from 1:15 p.m. to 1:25 p.m., count 10
minutes; and then
add 3 hours to 10 minutes to find the total
elapsed time of 3 hours and 10 minutes.
Essential Understandings
All students should

Understand that elapsed time can be
found by counting on from the beginning
time to the finishing time.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

57
Determine elapsed time in hours
and minutes within a 24-hour
period.
Revised: 8/20/16
SOL 5.10 – 3rd Nine Weeks
Additional Instructional Activities
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
What Time is It? - Measurement
All About Time by Jeunesse and Verdet
Handout available: Working with Vocabulary /
Concept Development (Word)
Elapsed Time in the Real World
All in a Day by Mitsumasa Anno et al
It's About Time
Picture Book Lesson Ideas
Word wall instructional video
A Day in Time
Elapsed Time – the amount of time between a start
time and an end time.
58
Revised: 8/20/16
SOL 5.10 – 3rd Nine Weeks
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
59
Revised: 8/20/16
SOL 5.11 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.11 – 3rd Nine Weeks
The student will measure right, acute, obtuse, and straight
angles.
Blueprint Categories
Grade 5 SOL
Number of Items
Measurement and Geography
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
8
Prior Knowledge
4.10 Identify angles
Understanding the Standard

Angles are measured in degrees. There are up to 360 degrees in an
1
angle. A degree is 360 of a complete rotation of a full circle. There are
360 degrees in a circle.

To measure the number of degrees in an angle, use a protractor or an
angle ruler.

A right angle measures exactly 90°.

An acute angle measures less than 90°.

An obtuse angle measures greater than 90° but less than 180°.

A straight angle measures exactly 180°.

Before measuring an angle, students should first compare it to a right
angle to determine whether the measure of the angle is less than or
greater than 90°.
Essential Understandings
All students should

Understand how to measure acute, right, obtuse,
and straight angles.
60
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections,
and representations to

Identify the appropriate tools (e.g.,
protractor and straightedge or
angle ruler as well as available
software) used to measure and
draw angles and triangles.

Measure right, acute, straight, and
obtuse angles, using appropriate
tools, and identify their measures in
degrees.

Recognize angle measure as
Revised: 8/20/16
SOL 5.11 – 3rd Nine Weeks

additive. When an angle is
decomposed into nonoverlapping
parts, the angle measure of the
whole is the sum of the angle
†
measures of the parts.
Students should understand how to work with a protractor or angle
ruler as well as available computer software to measure and draw
angles and triangles.

†
Solve addition and subtraction
problems to find unknown angle
measures on a diagram in practical
and mathematical problems, (e.g.,
by using an equation with a symbol
†
for the unknown angle measure).
Revised March 2011
Additional Instructional Activities
Finding Unknown Angle on a Straight Angle
Additional Math Curriculum Resources
61
Revised: 8/20/16
SOL 5.11 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Angles Are Everywhere! - Measurement
Handout available: Working with Vocabulary /
Amusement Angles
Trade Books
Sir Cumference and the Great Knight of Angleland by
Cindy Neuschwandr
Concept Development (Word)
Hamster Champs by Stuart Murphy
Classifying Triangles
Word Wall Instructional Video
Picture Book Lesson Ideas
What's Your Angle?-Classifying & Measuring Angles
Angles – the union of two rays with a common
endpoint, called the vertex.
Geometry for Elementary School Teachers K-5
(Word)
Degree – a unit of measure of an angle.
Right Angle – an angle that has a measure of exactly
90º.
Acute Angle – an angle with a measure greater than
0º and less than 90º.
Obtuse Angle – an angle whose measure is between
90º and 180º.
Straight Angle – an angle whose measure is exactly
180º
62
Revised: 8/20/16
SOL 5.11 – 3rd Nine Weeks
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
63
Revised: 8/20/16
SOL 5.12 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.12 – 3rd Nine Weeks
Blueprint Categories
Grade 5 SOL
Measurement and Geography
The student will classify
a) angles as right, acute, obtuse, or straight; and
b) triangles as right, acute, obtuse, equilateral, scalene,
or isosceles.
Number of Items
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
8
Prior Knowledge
4.10a – identify & draw points, lines, segments, rays, angles (endpoints & vertices)
Understanding the Standard

A right angle measures exactly 90.

An acute angle measures greater than 0 but less than 90.

An obtuse angle measures greater than 90 but less than 180.

A straight angle forms an angle that measures exactly 180°.

A right triangle has one right angle.

An obtuse triangle has one obtuse angle.

An acute triangle has three acute angles (or no angle measuring 90 or
greater).

A scalene triangle has no congruent sides.

An isosceles triangle has two congruent sides.

To facilitate the exploration of relationships, ask students whether a right
triangle can have an obtuse angle. Why or why not? Can an obtuse triangle
have more than one obtuse angle? Why or why not? What type of angles are
the two angles other than the right angle in a right triangle? What type of
angles are the two angles other than the obtuse angle in an obtuse triangle?
64
Essential Understandings
All students should

Understand that angles can be
classified as right, acute, obtuse,
or straight according to their
measures.

Understand that a triangle can be
classified as either right, acute, or
obtuse according to the measure
of its largest angle.

Understand that a triangle can be
classified as equilateral, scalene,
or isosceles according to the
number of sides with equal length.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Classify angles as right, acute,
straight, or obtuse.

Classify triangles as right,
acute, or obtuse.

Classify triangles as
equilateral, scalene, or
isosceles.
Revised: 8/20/16
SOL 5.12 – 3rd Nine Weeks
Additional Instructional Strategies
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Triangle Sort - Geometry
Handout available: Working with Vocabulary /
Concept Development (Word)
Geometry for Elementary School Teachers K-5
The Greedy Triangle by Marilyn Burns
(Word)
Picture Book Lesson Ideas
Word wall instructional video
Right Triangle – a triangle with one right angle.
Obtuse Triangle – a triangle with one obtuse angle.
Acute Triangle – a triangle in which all three angles
are acute.
Scalene Triangle – a triangle with three sides of
different lengths.
Congruent – having the same measure.
65
Revised: 8/20/16
SOL 5.12 – 3rd Nine Weeks
Isosceles Triangle – a triangle with at least two sides
of the same length.
Equilateral – a triangle with three sides of the same
length
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
66
Revised: 8/20/16
SOL 5.13 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.13 – 3rd Nine Weeks
The student will, using plane figures (square, rectangle,
triangle, parallelogram, rhombus, and trapezoid), will
a) develop definitions of these plane figures; and
b) investigate and describe the results of combining and
subdividing plane figures.
Blueprint Categories
Grade 5 SOL
Number of Items
Measurement and Geography
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
8
Prior Knowledge
4.10b – intersection, parallelism, perpendicularity
4.11 – congruence, flips, slides, & turns
4.12 – polygons
Understanding the Standard

Essential Understandings
A triangle is a polygon with three sides. Triangles may be classified
according to the measure of their angles, i.e., right, acute, or obtuse.
Triangles may also be classified according to the measure of their sides,
i.e., scalene (no sides congruent), isosceles (at least two sides congruent)
and equilateral (all sides congruent).

A quadrilateral is a polygon with four sides.

A parallelogram is a quadrilateral in which both pairs of opposite sides are
parallel. Properties of a parallelogram include the following:
– A diagonal (a segment that connects two vertices of a polygon but is
not a side) divides the parallelogram into two congruent triangles.
– The opposite sides of a parallelogram are congruent.
– The opposite angles of a parallelogram are congruent.
– The diagonals of a parallelogram bisect each other. To bisect means to
cut a geometric figure into two congruent halves. A bisector is a line
segment, line, or plane that divides a geometric figure into two
67
All students should

Understand that simple plane
figures can be combined to make
more complicated figures and that
complicated figures can be
subdivided into simple plane
figures.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections and
representation to

Develop definitions for squares,
rectangles, triangles,
parallelograms, rhombi, and
trapezoids.

Investigate and describe the
results of combining and
subdividing plane figures.
Revised: 8/20/16
SOL 5.13 – 3rd Nine Weeks
congruent halves. A sample of a bisected parallelogram is below.

A rectangle is a parallelogram with four right angles. Since a rectangle is a
parallelogram, a rectangle has the same properties as those of a
parallelogram.

A square is a rectangle with four congruent sides. Since a square is a
rectangle, a square has all the properties of a rectangle and of a
parallelogram.

A rhombus is a parallelogram with four congruent sides. Opposite angles of
a rhombus are congruent. Since a rhombus is a parallelogram, the rhombus
has all the properties of a parallelogram.

A trapezoid is a quadrilateral with exactly one pair of parallel sides. The
parallel sides are called bases, and the nonparallel sides are called legs. If
the legs have the same length, then the trapezoid is an isosceles trapezoid.

Two or more figures can be combined to form a new figure. Students
should be able to identify the figures that have been combined.

The region of a polygon may be subdivided into two or more regions that
represent figures. Students should understand how to divide the region of
a polygon into familiar figures.
68
Revised: 8/20/16
SOL 5.13 – 3rd Nine Weeks
Additional Instructional Strategies
Properties of Polygons Instructional Video
Students need additional practice identifying the similarities among and differences between squares, rectangles, parallelograms, rhombi, and trapezoids. Through
constructing, drawing, measuring, comparing, and classifying geometric figures, students develop definitions for quadrilaterals. These activities will help definitions
become meaningful and help students understand the relationships among figures. Students would benefit from opportunities to compare and contrast properties
of quadrilaterals. Additionally, having students draw figures that disprove the incorrect answer options may help them develop a better understanding of the
characteristics of quadrilaterals.
Additional Math Curriculum Resources
69
Revised: 8/20/16
SOL 5.13 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
All Cracked Up - Geometry
Handout available: Working with Vocabulary /
Capturing Polygons
Concept Development (Word)
Word Wall Instructional Video
Quadrilateral – polygon that has four sides.
Trade Books
The Amazing Book of Shapes: Explore Math Through
Shapes and Patterns by Lydia Sharman
Does Poly Want a Polygon?
Captain Invincible and the Space Shapes by Stuart J .
Murphy
Qualifying Quadrilaterals
Grandfather Tang’s Story by Ann Tompert
Geometry for Elementary School Teachers K-5
Polygon – simple closed plane figure that is formed
by three or more line segments.
(Word)
Icky Bug Shapes by Jerry Pallota
If You Were a Polygon by Marcie Aboff
Parallelogram – a quadrilateral with two pairs of
parallel sides which are also congruent.
If You Were a Quadrilateral by Molly Blasidell
A Light in the Attic (poem “Shapes”) by Shel
Silverstein
Diagonal – a line segment joining two vertices that
are not next to each other.
Mouse Shapes by Ellen Stoll Walsh
Rectangle – a parallelogram with four right angle
and opposite sides congruent.
Museum Shapes by Metropolitan Museum of Art
Square – a special rectangle four congruent sides
Shapes, Shapes, Shapes by Tana Hoban
Rhombus – a parallelogram with four congruent
sides.
The Silly Story of Goldie Locks and the Three Squares
by Grace Maccarone
Plane Figures – a figure with only two dimensions
The Village of Round and Square Houses by Ann
Grifalconi
Trapezoid – a quadrilateral with at least one pair of
parallel sides.
When a Line Bends….A Shape Begins by Rhonda
Greene
Base(s) – the parallel sides of a trapezoid.
70
Revised: 8/20/16
SOL 5.13 – 3rd Nine Weeks
Picture Book Lesson Ideas
Legs – the two sides of a right triangle that form the
right angle.
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
Pearson Success Net
New York State Assessments
*Multiple Languages
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
71
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.8 a, b – 3rd Nine Weeks
Blueprint Categories

Perimeter is the distance around an object. It is a
measure of length. Area is the number of square units
needed to cover a surface. Volume is a measure of
capacity and is measured in cubic units.

To find the perimeter of any polygon, add the lengths of
the sides.

Students should label the perimeter, area, and volume
with the appropriate unit of linear, square, or cubic
measure.

Area is the number of square units needed to cover a
surface or figure.

Students should investigate, using manipulatives, to
discover the formulas for the area of a square,
rectangle, and right triangle; and volume of a
rectangular solid.
Number of Items
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
Measurement and Geography
The student will
a) find perimeter, area, and volume in standard units of
measure;
b) differentiate among perimeter, area, and volume and
identify whether the application of the concept of
perimeter, area, or volume is appropriate for a given
situation
Understanding the Standard
Grade 5 SOL
8
Prior Knowledge
3.9 US Customary and Metric length, volume, weight, area, and perimeter
3.10 Perimeter and area
Essential Understandings
All students should

Understand the concepts of perimeter,
area, and volume.

Understand and use appropriate units of
measure for perimeter, area, and volume.

Understand the difference between using
perimeter, area, and volume in a given
situation.
72
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations to

Determine the perimeter of a polygon, with
or without diagrams, when
– the lengths of all sides of a polygon that is
not a rectangle or a square are given;
– the length and width of a rectangle are
given; or
– the length of a side of a square is given.

Estimate and determine the perimeter of a
polygon, and area of a square, rectangle, and
right triangle following the parameters listed
above, using only whole number
measurements given in metric or U.S.
Customary units, and record the solution with
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
– Area of a rectangle = Length  Width
– Area of a square = Side  Side
1
– Area of a right triangle = Base  Height
2
– Volume of a rectangular solid = Length x Width x
Height

Length is the distance along a line or figure from one
point to another.

U.S. Customary units for measurement of length include
inches, feet, yards, and miles. Appropriate measuring
devices include rulers, yardsticks, and tape measures.
Metric units for measurement of length include
millimeters, centimeters, meters, and kilometers.
Appropriate measuring devices include centimeter
ruler, meter stick, and tape measure.

the appropriate unit of measure (e.g., 24
square inches).
When measuring with U.S. Customary units, students
should be able to measure to the nearest part of an inch
1 1 1
(2 , 4 , 8 ), foot, or yard.
73

Estimate and determine the area of a square,
with or without diagrams, when the length of
a side is given.

Estimate and determine the area of a
rectangle, with or without diagrams, when
the length and width are given.

Estimate and determine the area of a right
triangle, with or without diagrams, when the
base and the height are given.

Differentiate among the concepts of area,
perimeter, and volume.

Develop a procedure for finding volume using
manipulatives (e.g., cubes).

Determine volume in standard units.

Describe practical situations where area,
perimeter, and volume are appropriate
measures to use, and justify their choices
orally or in writing.

Identify whether the application of the
concept of perimeter, area, or volume is
appropriate for a given situation.

Identify equivalent measurements within the
metric system for the following:
– length: millimeters, centimeters, meters,
and kilometers;
– mass: grams and kilograms;
– liquid volume: milliliters, and liters
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Additional Instructional Activities
Measurement of square units instructional video
For SOL 5.8a, students need additional practice finding the area of a figure, particularly when the figure is not provided. The example in the model asks students to
find the area of a square. In problems similar to the one shown, the most common error occurs when students confuse area and perimeter.
Students also need additional practice finding the area and/or perimeter of a right triangle. In this example, all three side lengths are given. Students have to
decide which measures to use to calculate area and which to use to calculate perimeter. In addition, they should be able to select the appropriate unit of measure
to label their answers.
Additional Math Curriculum Resources
74
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Rolling Rectangles - Measurement
Handout available: Working with Vocabulary /
Concept Development (Word)
Extreme Room Make Over
Trade Books
Sir Cumference and the Isle of Immeter by Cindy
Neuschwandr
GeoDesign: Finding Perimeter and Area
Zachary Zormer, Shape Transformer by Joanne
Reisberg
Discovering Perimeter and Area
Picture Book Lesson Ideas
Word Wall Instructional Video
Perimeter – the distance around a plane figure,
measured in linear units.
Geometry for Elementary School Teachers K-5
(Word)
Area – the amount of surface.
Volume – the amount of space that a solid
occupies; capacity.
Height – the perpendicular distance between a
base and its opposite side.
Additional Links and Resources – 5th Grade
Student Links
ABCya
Practice Test Items
Virtual Manipulatives
DOE Practice Items
Allen Interactive Assessment
75
Instructional Resources
Grade Level Technology Folder
Revised: 8/20/16
SOL 5.8 – 3rd Nine Weeks
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
76
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.9 – 3rd Nine Weeks
Blueprint Categories
Grade 5 SOL
Measurement and Geography
The student will identify and describe the diameter, radius,
chord, and circumference of a circle.
Number of Items
5.8a-e, 5.9, 5.10, 5.11,
5.12a-b, 5.13 a-b
8
Prior Knowledge
3.14 Characteristics of plane and solid figures
Understanding the Standard




A circle is a set of points on a flat surface (plane)
with every point equidistant from a given point
called the center.
A chord is a line segment connecting any two
points on a circle. Students will benefit from
understanding that a chord goes from one side of
the circle to the other, but does not need to pass
through the center.
A diameter is a chord that goes through the center
of a circle. The diameter is two times the radius. A
radius is a segment from the center of a circle to
any point on the circle. Two radii end-to-end form
a diameter of a circle.
Circumference is the distance around or perimeter
of a circle. The circumference is about 3 times
larger than the diameter of a circle.
Essential Knowledge and Skills
Essential Understandings
All students should

Understand that a chord is a line segment that
extends between any two unique points of a circle.

Understand that a diameter is also a special chord
that goes through the center of a circle.

Understand the relationship between the measures
of diameter and radius and the relationship between
the measures of radius and circumference.

Understand that a radius is a line segment that
extends between the center and the circumference
of the circle.

Understand that the circumference is the distance
around the circle. Perimeter is the measure of the
circumference.
77
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to

Identify and describe the diameter,
radius, chord, and circumference of a
circle.

Describe the relationship between
– diameter and radius;
– diameter and chord;
– radius and circumference; and
– diameter and circumference.

The length of the diameter of a circle is
twice the length of the radius.
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Additional Instructional Strategies
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Trade Books
Vocabulary Word Wall
Human Circles - Measurement
Handout available: Working with Vocabulary /
Concept Development (Word)
So Many Circles, So Many Squares by Tana Hoban
'Round -N-'Round We Go: A Math Adventure with
Circles
Word wall instructional video
Geometry for Elementary School Teachers K-5
(Word)
The Village of Round and Square Houses by Ann
Gifalconi
Diameter – a chord that passes through the center
of a circle.
When a Line Bends… A Shape Begins by Rhonda
Radius – a line segment from the center of a circle
78
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
to any point on the circle.
Greene
Chord – a line segment joining two points of a
circle.
Sir Cumference and the 1st Round Table by Cindy
Neuschwandr
Circumference – the distance around a circle.
Circle – the set of all points in a plane that are the
same distance from a fixed point, called the center.
Sir Cumference and the Dragon of Pi by Cindy
Neuschwandr
Center – the point in the interior of a circle that is
the same distance from all the points on the circle
Picture Book Lesson Ideas
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
IQ Practice Tests
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
Jefferson Lab
Interactivate
Internet 4 Classrooms
Sheppard Software
New York State Assessments
iPad™ Resources
StarrMatica
*Multiple Languages
National Library of Virtual
Manipulatives
79
Math Study Jams
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Turtle Diary
NCTM Illuminations
Pearson Success Net
Promethean Planet
Super Teacher Worksheets
Worksheet Fun
RCPS Math Resources
80
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.14 - 4th Nine Weeks
The student will make predictions and determine the
probability of an outcome by constructing a sample space.
Blueprint Categories
Grade 5 SOL
Number of Items
Probability, Statistics, Patterns, Functions,
and Algebra
5.14, 5.15, 5.16b-d,
5.17, 5.18a-d, 5.19
13
Prior Knowledge
4.10b – intersection, parallelism, perpendicularity
4.11 – congruence, flips, slides, & turns
4.12 - polygons
Understanding the Standard
Essential Understandings
Probability is the chance of an event occurring.
All students should


·Understand that the basic concepts of
probability can be applied to make
predictions of outcomes of simple
experiments.

·Understand that a sample space
represents all possible outcomes of an
experiment.


·The probability of an event occurring is the ratio of desired outcomes
to the total number of possible outcomes. If all the outcomes of an
event are equally likely to occur, the probability of the event =
number of favorable outcomes
total number of possible outcomes.
·The probability of an event occurring is represented by a ratio
between 0 and 1. An event is “impossible” if it has a probability of 0
(e.g., the probability that the month of April will have 31 days). An
event is “certain” if it has a probability of 1 (e.g., the probability that
the sun will rise tomorrow morning).
·When a probability experiment has very few trials, the results can be
misleading. The more times an experiment is done, the closer the
experimental probability comes to the theoretical probability (e.g., a
81
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

·Construct a sample space,
using a tree diagram to identify
all possible outcomes of a single
event.

·Construct a sample space,
using a list or chart to represent
all possible outcomes of a single
event.

·Predict and determine the
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
coin lands heads up half of the time).
probability of an outcome by
constructing a sample space.
The sample space will have a
total of 24 or less possible
outcomes

·Students should have opportunities to describe in informal terms
(i.e., impossible, unlikely, as likely as unlikely, as likely as, equally
likely, likely, and certain) the degree of likelihood of an event
occurring. Activities should include practical examples.

·For any event such as flipping a coin, the equally likely things that can
happen are called outcomes. For example, there are two equally likely
outcomes when flipping a coin: the coin can land heads up, or the coin
can land tails up.

·A sample space represents all possible outcomes of an experiment.
The sample space may be organized in a list, chart, or tree diagram.

·Tree diagrams show all possible outcomes in a sample space. The
Fundamental Counting Principle describes how to find the number of
outcomes when there are multiple choices. For example, how many
different outfit combinations can you make from 2 shirts (red and
blue) and 3 pants (black, white, khaki)? The sample space displayed in
a tree diagram would show that there are 2  3 = 6 (Fundamental
Counting Principle) outfit combinations: red-black; red-white; redkhaki; blue-black; blue-white; blue-khaki.
·
A spinner with eight equal-sized sections is equally likely to
land on any one of the sections, three of which are red, three
green, and two yellow. Have students write a problem
statement involving probability, such as, “What is the
probability that the spinner will land on green?”
82
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Additional Instructional Activities
Students need additional practice constructing a sample space from given information and interpreting a sample space to determine a probability.
Example 1 The first part of this question requires students to use the information in the table to construct a sample space. One way the sample space could be
represented is shown in the example. There are other correct representations of this sample space. The second part of the question requires students to use the
sample space to determine a probability.
Example 1
Example 2
Students also need additional practice interpreting a sample space that has been constructed for them. In example 2, students have been given information and
a tree diagram has been constructed to display the information. The students must determine the number of possible outcomes. The most common error
made by students is to count each word in the tree diagram
Additional Math Curriculum Resources
83
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
It's in the Bag - Probability and Statistics
Handout available: Working with Vocabulary /
Concept Development (Word)
Word wall instructional video
Passionate About Probability
Probability – a measure of the likelihood that an
event will occur.
Probability: How Much Can I Earn?
Trade Books
Do You Wanna Bet? Your Chance to Find Out
About Probability by Jean Cushman
Pigs at Odds by Amy Axelrod
Potato Possibilities
Probability Pistachio by Stuart J. Murphy
Probability CHEX©plorations
Socrates and The Three Little Pigs by Mitsumasa
Anno
Carnival Craze: What are Your Chances?
A Very Improbable Story by Edward Einhorn
Summer Vacation Combinations
Picture Book Lesson Ideas
Outcomes – a possible result of an experiment.
Event – a set of outcomes for an experiment.
Number of Favorable Outcomes – number of
outcomes corresponding to a specified event.
Number of Possible Outcomes – the number of
results that could occur
Ratio – a comparison of one number to another
number.
Impossible – an event that will never happen. An
event with a probability of zero.
Unlikely – the chance of an event happening is not
good, but it is not impossible.
As likely as – comparing two or more probable
outcomes
84
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Equally Likely – events that have the same
probability of occurring.
Likely – the chance of an event happening is very
good, but not certain.
Certain – an event that will happen for sure. An
event with a probability of 1.
Sample Space – the set of all possible outcomes for
an experiment.
Tree Diagram – a branching diagram that shows all
the possible choices or outcomes of a process
carried out in several stages
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
85
Revised: 8/20/16
SOL 5.9 – 3rd Nine Weeks
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
86
Revised: 8/20/16
SOL 5.18– 4th Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.18 -4th nine weeks
The student
a) investigate and describe the concept of variable;
b) write an open sentence to represent a given
mathematical relationship, using a variable;
c) model one-step linear equations in one variable,
using addition and subtraction; and
d) create a problem situation based on a given open
sentence, using a single variable
Blueprint Categories
Probability, Statistics, Patterns,
Functions, and Algebra
A variable is a symbol that can stand for an unknown number or
object.

·A variable expression is like a phrase: as a phrase does not have
a verb, so an expression does not have an equals sign (=).

·A verbal expression involving one operation can be represented
by a variable expression that describes what is going on.
Numbers are used when they are known; variables are used
when the numbers are unknown. For example, “a full box of
cookies and four extra” can be represented by b + 4; “three full
boxes of cookies” by 3b; “a full box of cookies shared among
four” by b/4.

·An open sentence contains a variable and an equals sign (=).
For example, the sentence, “A full box of cookies and four extra
5.14, 5.15, 5.16b-d,
5.17, 5.18a-d, 5.19
Number of Items
13
Prior Knowledge
4.16a Meaning of equality in an equation.
Understanding the Standard

Grade 5 SOL
Essential Understandings
All students should

·Understand that a variable is a symbol
that can stand for an unknown number
or object.

·Understand that a variable expression
is a variable or combination of
variables, numbers, and symbols that
represents a mathematical relationship.

·Understand that verbal expressions can
be translated to variable expressions.

·Understand that an open sentence has
a variable and an equal sign (=).
87
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication,
mathematical reasoning, connections, and
representations to

·Describe the concept of a variable
(presented as boxes, letters, or other
symbols) as a representation of an
unknown quantity.

·Write an open sentence with
addition, subtraction, multiplication,
or division, using a variable to
represent a missing number.

·Model one-step linear equations
Revised: 8/20/16
SOL 5.18– 4th Nine Weeks
equal 24 cookies.” can be written as b + 4 = 24, where b stands
for the number of cookies in one full box. “Three full boxes of
cookies equal 60 cookies.” can be written as 3b = 60.

·Another example of an open sentence is b + 3 = 23 and
represents the answer to the word problem, “How many
cookies are in a box if the box plus three more equals 23
cookies, where b stands for the number of cookies in the box?

·At this level, discuss how the symbol  used to represent
multiplication can often be confused with the variable x.
Students can minimize this confusion by using parentheses [e.g.,
4(x) = 20 or 4x = 20] or a small dot raised off the line to
represent multiplication [4 • x = 20].

·By using story problems and numerical sentences, students
begin to explore forming equations and representing quantities
using variables.

·An open sentence containing a variable is neither true nor false
until the variable is replaced with a number.

using a variety of concrete materials
such as colored chips on an equation
mat or weights on a balance scale.
·Understand that problem situations
can be expressed as open sentences

88
·Create and write a word problem to
match a given open sentence with a
single variable and one operation.
Revised: 8/20/16
SOL 5.18– 4th Nine Weeks
Additional Instructional Activities
Modeling one step equations instructional video
For SOL 5.18c, students need additional practice creating the model to represent a given one-step linear equation. It is important to note that the answer is also
correct if the student places ten triangles on the left side of the equation mat and the star and four triangles on the right side. Active Inspire Lessons can be
found on the Shared (Z) Drive. (Elementary/5th/Math/Algebra)
For SOL 5.18d, students need additional practice creating or identifying a problem situation that is represented by a given open sentence. In addition to multiple
choice answer options, students would benefit from opportunities to create their own situations that could be represented by the same open sentence.
Additional Math Curriculum Resources
89
Revised: 8/20/16
SOL 5.18– 4th Nine Weeks
Vocabulary
Vocabulary Word Wall
Handout available: Working with Vocabulary /
Lessons and TEI Items
Trade Books
Variables and Open Sentences - Patterns, Functions,
and Algebra
Concept Development (Word)
Variables: A Quest for the Unknown
Word Wall Instructional Video
Playworld Amusement Park
Expression – a mathematical phrase which can
contain numbers, operators, and at least one
variable. Expressions do not contain an = sign.
The Crazy Carnival
Variable – a symbol, usually a letter, that
represents one or more numbers.
The King's Rule
Planting Patterns and Fun with Functions!
Patterns, Functions and Algebra K-5 (PDF)
Unknown – a quantity, usually represented by a
letter, that does not have a numeric value assigned
to it.
Open Sentence – a mathematical sentence
containing one or more variables.
Story Problem – a real-world situation that can be
represented by an expression.
Algebraic Expression – an expression involving
numbers, variables, and/or operations. An algebraic
expression is not an equation.
90
Revised: 8/20/16
SOL 5.18– 4th Nine Weeks
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
91
Revised: 8/20/16
SOL 5.17 – 4th Nine Weeks
Dinwiddie County Public Schools
Math Curriculum
SOL 5.17 – 4th Nine Weeks
The student will describe the relationship found in a number
pattern and express the relationship.
Blueprint Categories
Grade 5 SOL
Number of Items
Probability, Statistics, Patterns,
Functions and Algebra
5.14, 5.15, 5.16b-d,
5.17, 5.18a-d, 5.19
13
Prior Knowledge
4.15 Geometric patterns (recognize, create, and extend)
Understanding the Standard

There are an infinite number of patterns.

The simplest types of patterns are repeating patterns. In such
patterns, students need to identify the basic unit of the pattern and
repeat it.

Growing patterns are more difficult for students to understand than
repeating patterns because not only must they determine what
comes next, they must also begin the process of generalization.
Students need experiences with growing patterns.

Essential Understandings
All students should
Sample numerical patterns are
6, 9, 12, 15, 18, ;
5, 7, 9, 11, 13, ;
1, 2, 4, 7, 11, 16, ;
92

Understand that patterns and functions
can be represented in many ways and
described using words, tables, and
symbols.

Understand the structure of a pattern
and how it grows or changes using
concrete materials and calculators.

Understand that mathematical
relationships exist in patterns.

Understand that an expression uses
symbols to define a relationship and
shows how each number in the list, after
the first number, is related to the
preceding number.
Essential Knowledge and Skills
The student will use problem
solving, mathematical
communication, mathematical
reasoning, connections, and
representations to

Describe numerical and
geometric patterns formed by
using concrete materials and
calculators.

Describe the relationship found
in patterns, using words, tables,
and symbols to express the
relationship.
Revised: 8/20/16
SOL 5.17 – 4th Nine Weeks
2, 4, 8, 16, 32, ;

32, 30, 28, 26, 24…; and
Understand that expressions can be
numerical or variable or a combination
of numbers and variables.
1, 5, 25, 125, 625,.

An expression, like a phrase, has no equal sign.

When the pattern data are expressed in a T-table, an expression can
represent that data. An example is:
X
Y
6
9
7
10
11
14
15
18
This example defines the relationship as x + 3.

Expressions are simplified by using the order of operations.

A verbal quantitative expression involving one operation can be
represented by a variable expression that describes what is going on.
Numbers are used when they are known; variables are used when the
numbers are unknown. For example, “a full box of cookies and four
extra” can be represented by b + 4; “three full boxes of cookies” by
b
3b; “a full box of cookies shared among four” by 4 .

A mathematical expression contains a variable or a combination of
variables, numbers, and/or operation symbols and represents a
mathematical relationship. An expression cannot be solved.
93
Revised: 8/20/16
SOL 5.17 – 4th Nine Weeks
Additional Instructional Activities
Additional Math Curriculum Resources
Vocabulary
Lessons and TEI Items
Vocabulary Word Wall
Pick Your Pattern - Patterns, Functions, and Algebra
Handout available: Working with Vocabulary /
Concept Development (Word)
Exploring Growing Patterns
Trade Books
Growing Patterns: Fibonacci Numbers in Nature by
Sarah C. Campbell
Function Fever
Patterns in Peru: An Adventure in Patterning by Cindy
Neuschwander
Patterns Rule
Pattern Bugs by Trudy Harris
Doing It Again, Repeating Patterns
Pattern Fish by Trudy Harris
Patterns, Functions and Algebra K-5 (PDF)
The Rabbit Problem by Emily Graves
Word wall instructional video
Numerical Pattern – a sequential list of numbers
with a consistent relationship between them.
Geometric Pattern – a sequential list of objects with
a consistent relationship between them.
Picture Book Lesson Ideas
Infinite – never ending, not finite.
Repeating Pattern – a pattern whose
numbers/objects repeat in a consistent manner.
Growing Pattern – a pattern whose
numbers/objects increase in a consistent manner.
94
Revised: 8/20/16
SOL 5.17 – 4th Nine Weeks
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Turtle Diary
New York State Assessments
*Multiple Languages
Math Study Jams
NCTM Illuminations
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
95
Revised: 8/20/16
Dinwiddie County Public Schools
Math Curriculum
SOL Review – 4th Nine Weeks
Blueprint Categories
Grade 5 SOL
Teachers should use data from county and released SOL
assessments to plan remediation and practice of all Standards
of Learning.
SOL Blueprint (PDF)
All
Number of Items
Prior Knowledge
Additional Instructional Activities
See County Shared (Z) Drive for additional resources. (Elementary/Grade 5/Math/SOL Review)
IMPORTANT!! The following 5th grade online practice is required for all students! All students must be exposed to practice items. This is NOT the same as the
practice conducted with the Guidance Counselor using the sign-in sheets with username and password. Teachers should use the script found in the Guide to
guide students through the practice. This practice will take several math blocks to complete if covered sufficiently. These practice items are good for
reteaching as well as exposing students to the tools available for testing.
Grade 5 Practice Items
Practice Items – Audio
Guide
View a narrated demonstration with examples of various technology-enhanced item types that appear on the new Mathematics SOL tests. These new SOL tests
may consist of approximately 15 percent technology-enhanced items. To download this narrated demonstration as a MOV file, right-click here. MOV video files
require the free Apple QuickTime player plug-in.
Mathematics Tools Practice: The online Mathematics Tools Practice allows students to practice using the online tools (such as the ruler, protractor or compass)
available within TestNav, the online testing software used in Virginia. All tools that are available for any grades 3-8 test are provided within the Grades 3-8 Tools
96
Revised: 8/20/16
Practice. Likewise, all tools that are available for any EOC test are provided within the End-of-Course Tools Practice. This means that the tools included within each
application do not necessarily indicate the tools that will be available for a particular test. To reference the tools available for a particular online mathematics test,
see Online Tools Available on the Mathematics SOL Tests (PDF) Grades 3-8 Tools Practice
Released Spring Test 2015: Online PDF
Answer Sheet
For Released Tests prior to Spring 2012, see: Archived Released Tests
Released SOL tests and test items can be found on Interactive Achievement. Students should be exposed to these (especially TEI items) throughout the year.
The following Student Response Activities (formatted in Notebook but can be used with Active Inspire/Expressions). See ITRT if you need assistance.
2004 SOL Released Test Items Part 1 Senteo Notebook (Preview with Notebook Express)
2. 2004 SOL Released Test Items Part 2 Senteo Notbeook (Preview with Notebook Express)
3. 2005 SOL Released Test Items Part 1 Senteo Notebook (Preview with Notebook Express)
4. 2005 SOL Released Test Items Part 2 Senteo Notebook (Preview with Notebook Express)
5. 2008 Senteo (SMART Response) SOL Computation & Estimation Test (Preview with Notebook Express)
6. 2008 Senteo (SMART Response) SOL Measurement & Geometry Test (Preview with Notebook Express)
7. 2008 Senteo (SMART Response) SOL Number Sense Test (Preview with Notebook Express)
8. 2008 Senteo (SMART Response) SOL Patterns, Functions & Algebra Test (Preview with Notebook Express)
9. 2008 Senteo (SMART Response) SOL Probability & Statistics Test (Preview with Notebook Express)
10. Senteo/SMART Response SOL Math Notebook files
11. 2000 SOL Math 5 Senteo/SMART Response Notebook file Part 1 (Preview with Notebook Express)
97
Revised: 8/20/16
12. 2000 SOL Math 5 Senteo/SMART Response Notebook file Part 2 (Preview with Notebook Express)
13. 2001 SOL Math 5 Senteo/SMART Response Notebook file Part 1 (Preview with Notebook Express)
14. 2001 SOL Math 5 Senteo/SMART Response Notebook file part 2 (Preview with Notebook Express)
15. Several Math Interactive & SMARTBoard Resources by Math SOLS
16. Elementary SMARTBoard Notebook lessons
17. Harvey Almarode's SMARTBoard Math Files
18. Jeopardy on Geometry, Circles, Fractions, Pologons & Measurement PowerPoint
19. Are you Smarter Than a 5th Grader PowerPoint
20. VDOE Technology Enhanced Items Practice Tests
21. Multi Step Math Word Problem Practice
22. SOL TEI Math Practice
23. TEI Practice Items
24. Joe Hill's Math PortaPortal Interactive Math Websites
More TEI Practice Items (From Interactive Assessments Allenteacher.com)
Additional Math Curriculum Resources
98
Revised: 8/20/16
Additional Links and Resources – 5th Grade
Student Links
Practice Test Items
Virtual Manipulatives
Instructional Resources
ABCya
DOE Practice Items
Allen Interactive Assessment
Grade Level Technology Folder
Recess Room
DOE Released Tests and Item Sets
Interactivate
Internet 4 Classrooms
Sheppard Software
IQ Practice Tests
National Library of Virtual
Manipulatives
iPad™ Resources
StarrMatica
Jefferson Lab
Math Study Jams
NCTM Illuminations
Turtle Diary
New York State Assessments
*Multiple Languages
Pearson Success Net
Promethean Planet
Interactive Achievement
Super Teacher Worksheets
Quia
Worksheet Fun
RCPS Math Resources
99
Revised: 8/20/16