Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
Number Properties and Operations
Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop
multiplication and division. They move flexibly and fluently through basic number facts, operations and representations. Their understanding of the base-10 number system
expands to include decimals. They examine various meanings and models of fractions. They explore data, perform measurements and examine patterns as part of the
development process for number and operations, using other mathematics strands to enrich number. Computational fluency with whole numbers, relationships among decimals
and fractions and techniques for reasonable estimations represent elementary number.
Number Sense
MA-05-1.1.1
Students will:
• Apply multiple representations (e.g.,
drawings, manipulatives, base-10 blocks,
number lines, expanded form, symbols)
to represent whole numbers (0 to
99,999,999);
• Apply multiple representations e.g.,
drawings, manipulatives, base-10 blocks,
number lines, expanded form, symbols)
to describe commonly-used fractions,
mixed numbers, and decimals through
thousandths;
• Apply these numbers to represent realworld problems and
• Explain how the base-10 number system
relates to place value.
DOK 2
Create your own number and explain how to
use expanded form to show place value to the
ten millions place.
Kentucky Learns Links
(Number Line)
1
Math Vocabulary
Justify the placement of a decimal point in a
given whole number.
<, >, =, <, >, ≠
Tenths; Hundredths; Thousandths
Intervals
Positive/Negative, Integers
Unit segment
Denominator
Numerator
Reduce; simplify; lowest terms
Of -> multiplication
Is -> equal
Place Value
Construct a drawing representing the
following:
¾, 21/3, 1/2, 6/8
Kentucky Learns Links
(Fractions)
Dicey Decimals
Kentucky Learns Links
(Number Systems)
3
Fractions
(Unit)
Kentucky Learns Links
(The Number Line)
Construct a number line from -10 to 10
including whole numbers and fractions.
Describe patterns used in our number system.
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
1
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
MA-05-1.1.2
Students will read, write, and rename whole
numbers, fractions, and decimals, and apply to realworld and mathematical problems.
Joey went to the store with a certain amount
of money and he spent a fraction of it, how
would you determine how much money he
had left? Express answer in fraction &
decimal form.
Dicey Decimals
4
MA-05-1.1.3
Students will compare (<, >, =) and order whole
numbers), fractions and decimals, and explain
the relationships (equivalence, order) between
and among them.
DOK 2
Given any number, what is the place value of
each digit?
Explain the process of listing fractions and
decimals in a particular order. (least to
greatest, greatest to least)
Equivalent
<, >, =, <, >, ≠
Kentucky Learns Links
(Number Line)
Fractions
(Unit)
Math Vocabulary
3, 4
Kentucky Learns Links
(Fractions)
Submarine Sandwich OR
Pizza OR
Shaded Circles OR
Fraction Pie OR
Fraction Pizza OR
Fractions
(Unit)
Estimation
MA-05-1.2.1
Students will apply and describe appropriate
strategies for estimating quantities of objects and
computational results in real-world problems.
DOK 2
Given a set of data, estimate to the nearest
amount. Given the same data, calculate the
exact amount.
Kentucky Learns Links
(Multiply/Divide)
3, 4
Mowing OR
Assess when estimation and exact amounts
would be appropriate in real life situations.
Round, Approximate, Estimate
Tenths; Hundredths; Thousandths
Exact
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
2
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
Justify where to put the decimals in your
answers when you add & subtract decimal
numbers?
Bracelet OR
1, 2,3,4
Guessing Game OR
1
Number Operations
MA-05-1.3.1
Students will analyze real-world problems to
identify appropriate representations using
mathematical operations, and will apply
operations to solve real-world problems with the
following constraints:
• add, subtract, multiply, and divide whole
numbers (less than 100,000,000), using
technology where appropriate;
• add and subtract fractions with like
denominators through 16, with sums less than
or equal to one and
• add and subtract decimals through
hundredths.
DOK 2
The bus could carry __ students. The __
students from Room __ & the __ students
from Room 15 got on the bus. How many
more students can the bus carry?
Sum
Difference
Dividend; divisor; quotient;
Groups of; equal groups; array
Numerator; denominator, reciprocal; invert
Addend + addend = sum
Factor x factor = product
MA-05-1.3.2
Students will skip-count forwards and backwards.
Multiples, Patterns, Terms, Sequence
MA-05-1.3.3
Students will multiply decimals through tenths.
Justify where to put the decimal in the answer
when multiplying decimal numbers?
Sit-Ups OR
2, 3
Ratios and Proportional Reasoning
Properties of Numbers and Operations
MA-05-1.5.1
Students will identify and determine composite
numbers, prime numbers, multiples of a number,
factors of numbers, and least common multiples
(LCM), and will apply these numbers to solve
real-world problems.
DOK 2
Choose a number between 50 and 100,
identify its factors, and explain if it is prime or
composite.
Factors/Multiples
Composite, Prime, Factors, LCM and GCF
Odd; even; prime; composite; multiples;
exponent base; powers; square root
Let’s Eat
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
3
Fractions & Decimals
3
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
Fractions
(Unit)
MA-05-1.5.2
Commutative properties, associative
2
properties, identity properties, zero property
Students will use the commutative properties of
addition and multiplication, the associative
properties of addition and multiplication, the
identity properties of addition and multiplication
and the zero property of multiplication in written
and mental computation.
Measurement
Students progress from measuring using nonstandard units to using standard units of measurement. They identify measurable attributes of objects, estimate and measure weight,
length, perimeter, area, angles, temperature, time and money. They convert units within the same measurement system.
Measuring Physical Attributes
MA-05-2.1.1
Students will apply standard units to measure
length (to the nearest eighth-inch or the nearest
centimeter) and to determine:
• weight (ounce, pound; gram, kilogram);
• perimeter;
• area (figures that can be divided into
rectangular shapes);
• time (nearest minute);
• temperature (Fahrenheit and Celsius) and
• angle measures (nearest degree).
DOK 2
MA-05-2.1.2
Students will choose appropriate tools (e.g.,
protractor, meter stick, ruler) for specific tasks and
apply skills to solve real-world and mathematical
problems.
MA-05-2.1.3
Students will use measurements to identify,
describe, sort, and compare attributes of objects
Weight (ounce, pound; gram, kilogram);
Length (nearest eighth-of-an-inch or nearest
centimeter);
Perimeter; Circumference of Circle
Area (figures that can be divided into
rectangular shapes) A = L x W;Square
Time (nearest minute);
Temperature (Fahrenheit and Celsius); and
Angles (nearest degree) o –degree symbol
Choose a unit of measurement and design a
playground including fencing & mulch.
Explain the process of determining the area
and perimeter of your playground.
Explain which measurement tool would be
used to measure the length of the room,
distance to town, degree of an angle, etc.
Faces, Edges, Vertices - 3D figures
Sides, Vertices, Angles – 2D figures
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
Kentucky Learns Links
(Prop of Lines)
1,2,3,4
Temperature
Perimeter Art
Place Mat Perimeter
Geometry
(Unit)
Measurement
(Unit)
Measurement
(Unit)
Geometry
(Unit)
Geometry
(Unit)
3, 4
3, 4
4
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
and apply these to solve real-world and
mathematical problems.
MA-05-2.1.4
Students will measure volume of rectangular
prisms, liquid capacity, and money using standard
units and apply these skills to solve real-world and
mathematical problems
MA-05-2.1.6
Students will estimate weight, length, perimeter,
area, angle measures and time using appropriate
units of measurement.
DOK 2
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
Given a rectangular solid explain how many
cubes would it take to build it without
counting?
US Standard & Metric Units
Volume = Length x Width x Height
Cubic
Choose an object and describe each by
estimating the units of measurement. Justify
how to estimate the weight, length, perimeter,
area, and angle measures, of objects in your
everyday life.
GRADING
PERIOD
3, 4
Kentucky Learns Links
(Geometric Figures)
3
Geometry
(Unit)
Systems of Measurement
MA-05-2.2.1
Students will determine elapsed time.
DOK 3
MA-05-2.2.2
Students will describe, define, give examples of and
use to solve real-world and mathematical problems
nonstandard and standard (U.S. Customary, metric)
units of measurement.
MA-05-2.2.3
Students will convert units within the same
measurement system [U.S. customary (inches,
feet, yards, miles; ounces, pounds, tons), metric
(millimeters, centimeters, meters, kilometers;
grams, kilograms), money, or time] and use the
units to solve problems.
DOK 2
Create a field trip schedule and determine the
elapsed time for each activity.
US Customary & Metric
Standard & Non-standard measurements
(paper clips, candy, etc.)
Explain how to convert units of measurement
within the same system.
U.S. customary (inches, feet, yards, miles;
ounces, pounds, tons), metric (millimeters,
centimeters, meters, kilometers; grams,
kilograms), money, or time (seconds, minutes,
hours)
Elapsed time
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
Kentucky Learns Links
(Geometric Figures)
Measurement
(Unit)
Kentucky Learns Links
(Measurement)
3
3, 4
Measurement
(Unit)
5
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
Geometry
Students explore and find basic geometric elements and terms, two-dimensional shapes and three-dimensional objects. They find and use symmetry. They move twodimensional figures in a plane and explore congruent and similar figures.
Shapes and Relationships
MA-05-3.1.1
Students will describe and provide examples of
basic geometric elements and terms [points,
segments, lines (perpendicular, parallel,
intersecting), rays, angles (acute, right, obtuse),
sides, edges, faces, bases, vertices, radius,
diameter] and will apply these elements to solve
real-world and mathematical problems.
DOK 2
MA-05-3.1.2
Students will describe and provide examples of
basic two-dimensional shapes [circles, triangles
(right, equilateral), all quadrilaterals, pentagons,
hexagons, octagons], and will apply these shapes
to solve real-world and mathematical problems.
DOK 2
MA-05-3.1.3
Students will describe and provide examples of
basic three-dimensional objects (spheres, cones,
cylinders, pyramids, cubes, triangular and
rectangular prisms), will identify three-dimensional
objects from two-dimensional representations
(nets) and will apply the attributes to solve realworld and mathematical problems.
DOK 2
MA-05-3.1.5
Students will identify and describe congruent
and similar figures in real-world or
Classify the angles in your classroom by
describing their attributes.
Points, segments, lines (perpendicular,
parallel, intersecting), rays, angles (acute,
right, obtuse), sides, edges, faces, vertices,
radius, diameter
Math Vocabulary
Kentucky Learns Links
(Geometric Figures)
Geometry
(Unit)
Identify real-world objects using attributes of
two-dimensional shapes.
Kentucky Learns Links
(Probability of Events)
Circles, triangles (right, obtuse, acute,
equilateral, scalene, isosceles), all
quadrilaterals (trapezoid, rectangle, square,
parallelogram, rhombus, trapezium),
pentagons, hexagons, octagons
radius, diameter
Create a net that would form the 3-D shape.
Attributes of Polygons
Create/construct net for a 3D models such as
cylinders or cubes.
Classify plane and 3D figures by their
attributes.
Net
Draw a figure then draw a figure that is
congruent and a figure that is similar to the
first figure. Label each and explain for each.
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
1,2,3,4
4
Geometry
(Unit)
3
Kentucky Learns Links
(Probability of Events)
Geometry
(Unit)
Kentucky Learns Links
(Symmetry, Similarity, Congruence)
2,3
6
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
mathematical problems.
Congruent, Similar
Create a portion of a design, complete the
symmetrical portion.
Kentucky Learns Links
(Data Analysis)
3
Line of Symmetry, Symmetrical
Alphabet Symmetry
Draw and identify 90º rotations, reflections,
and translations of basic shapes within a
plane.
Kentucky Learns Links
(Graphs)
DOK 2
Transformations of Shapes
MA-05-3.2.1
Students will describe and provide examples of
line symmetry in real-world and mathematical
problems or will apply line symmetry to
construct a geometric design.
DOK 3
MA-05-3.2.2
Students will identify or draw 90º rotations,
reflections or translations of basic shapes within
a plane.
DOK 1
3
Transformations, Rotations (turn), Reflections
(flip), Translations (slide)
Coordinate Geometry
MA-05-3.3.1
Students will identify and graph ordered pairs
on a positive coordinate system scaled by ones,
twos, threes, fives, or tens; locate points on a
grid; and apply graphing in the coordinate
system to solve real-world problems.
DOK 2
When could the coordinate system be applied
to a real-world situation? (latitude/longitude,
GPS, grid maps)
Kentucky Learns Links
(Graphs)
3
The Game “Battleship”
Ordered pairs, Point of origin, Quadrants,
Units
Data Analysis and Probability
Students pose questions, plan and collect data, organize and display data and interpret displays of data. They generate outcomes for simple probability activities, determine
fairness of probability games and explore likely and unlikely events.
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
7
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
What data is represented by the x-axis?
What data is represented by the y-axis?
What categories are represented by the Venn
Diagram?
Which data is common to both categories in
the Venn Diagram?
Predict future trends based on the graph.
Give possible reasons for the trend shown by
the data.
Kentucky Learns Links
(Functions)
2
Data Representations
MA-05-4.1.1
Students will analyze and make inferences from
data displays (drawings, tables/charts, tally
tables, pictographs, bar graphs, circle graphs,
line plots, Venn diagrams, line graphs).
DOK 3
Kentucky Learns Links
(Graphs)
Kentucky Learns Links
(Graph/Coordinate Plane)
Insect Information
MA-05-4.1.2
Students will collect data (e.g., tallies, surveys) and
explain how the skills apply in real-world and
mathematical problems.
Survey, Legend, Icon
Function Table, input/output, drawings,
tables/charts, frequency tables, pictographs,
bar graphs, circle graphs, line plots, Venn
diagrams, line graphs
Explain the process used to conduct the
survey.
Kentucky Learns Links
(Functions)
2
Kentucky Learns Links
(Functions)
3
When is estimation appropriate?
When are exact tabulations appropriate?
MA-05-4.1.3
Students will construct data displays
(pictographs, bar graphs, line plots, line graphs,
Venn diagrams, tables).
DOK 2
Combination, Frequency chart
Which type of data is appropriate for each
type of graph?
Do a survey and create a graph and label
appropriately with titles & correct intervals?
Candy Sales
X axis, Y axis
Characteristics of Data Sets
MA-05-4.2.1
Students will determine and apply the mean,
median, mode and range of a set of data.
Given the average (mean) what could be the
student’s 10 possible math grades?
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
Calculator Patterns
1
8
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
DOK 2
Average, Measure of Central Tendencies ,
Mean, Median, Mode, Range
Kentucky Learns Links
(# Rules/Patterns)
GRADING
PERIOD
Probability
Math Vocabulary
Kentucky Learns Links
(Central Tendency)
Passing the Test OR
Experiments and Samples
MA-05-4.3.1
Students will describe and give examples of the
process of using data to answer questions (e.g.,
pose a question, plan, collect data, organize and
display data, interpret data to answer questions).
List the data you would need to collect & the
experimental steps you would take to conduct
a particular investigation.
Problem-solving
Kentucky Learns Links
(Sequence/Series)
1
Kentucky Learns Links
(Graphs)
Kentucky Learns Links
(Graphs)
Probability
MA-05-4.4.1
Students will determine all possible outcomes of
an activity/event with up to 12 possible outcomes.
DOK 2
Given an event determine all possible
outcomes.
Kentucky Learns Links
(Data Analysis)
Probability (fractions), Chance (Percent),
Combinations, Favorable Outcomes
Chips in a Hat OR
MA-05-4.4.2
Students will determine the likelihood of an
event and the probability of an event (expressed
as a fraction).
DOK 2
Name an event that would produce the same
outcome.
Certain = 1
Impossible = 0
Unlikely = fraction < 1/2
Likely = fraction > ½
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
Chris’ Sandwich Shop OR
Kentucky Learns Links
(Probability of Events)
2
2
Probability
9
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
Algebraic Thinking
Students explore and examine patterns and develop rules to go with patterns. They generate input-output for functions and create tables to analyze functions. They use ordered
pairs and plot points in the first quadrant of the Cartesian plane. Students use number sentences with missing values.
Patterns, Relations, and Functions
MA-05-5.1.1
Students will extend patterns, find the missing
term(s) in a pattern or describe rules for patterns
(numbers, pictures, tables, words) from realworld and mathematical problems.
DOK 3
Create a pattern, determine its rule, and
describe it.
Kentucky Learns Links
(# Rules/Patterns)
Sequence, Tessellations, Patterns
Calculator Patterns
1
Kentucky Learns Links
(# Rules/Patterns)
Kentucky Learns Links
(Sequence/Series)
MA-05-5.1.2
Students will describe functions (input-output)
through pictures, tables, or words, and will
construct tables to analyze functions based on
real-world or mathematical problems.
DOK 2
MA-05-5.1.3
Students will determine an output value or an
input value for a function rule given the other
value.
DOK 2
Design an Input/Output table and describe its
function.
Kentucky Learns Links
(Functions)
3
Number changing machine, Input/Output,
Function Machine
Given a function rule determine the output
value.
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
10
updated 4/8/08
Math
5th grade
GRADE LEVEL STANDARDS/DOK
ESSENTIAL QUESTIONS/
CONTENT/TERMS
SUGGESTED ACTIVITIES/
ASSESSMENTS
GRADING
PERIOD
Write a story problem with a missing value.
Create an expression using a variable to model
the problem.
Kentucky Learns Links
(Basic Equations)
4
Kentucky Learns Links
(Basic Equations)
4
Variables, Expressions, and Operations
MA-05-5.2.1
Students will model verbal descriptions of realworld and mathematical problems using a
variable or a missing value in an expression.
Story problems, Variable
DOK 2
Equations and Inequalities
MA-05-5.3.1
Students will model real-world and
mathematical problems with simple number
sentences (equations and inequalities) with a
variable or missing value (e.g., 4 = 2 x N, ___+ 5
> 14) and apply simple number sentences to solve
mathematical and real-world problems.
DOK 2
Explain the process to determine the missing
variable in an equation.
Equation, Inequalities, Variable
Bold – State Assessment Content Statement
Italics – Supporting Content Statement
11
updated 4/8/08