Mathematics
5th Grade Math Standard 1.1
5.Math.1.1 The decimal number system describes place value patterns and relationships that
are repeated in large and small numbers and forms the foundation for efficient algorithms
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Explain that in a multi-digit number, a digit
1. How can writing numbers in expanded form in one place represents ten times as much as it
using powers of ten, fractions and/ or decimals represents in the place to its right and 1/10 of
help you to understand the value of numbers?
what it represents in the place to its left.
2. How can finding a pattern in the number of
zeros help you to multiply by powers of ten?
3. How does the placement of the decimal
point change when multiplying or dividing by
a power of ten?
4. How do you use exponents to denote powers
of ten?
5. How do you read and write decimals to
thousandths using base-ten numerals, number
names, and expanded form?
6. How does understanding place value
help you to compare decimals?
2. Explain patterns in the number of zeros of
the product when multiplying a number by
powers of ten.
3. Explain patterns in the placement of the
decimal point when a decimal is multiplied or
divided by a power of ten.
4. Use whole-number exponents to denote
powers of ten.
5. Read and write decimals to thousandths
using base-ten numerals, number names, and
expanded form.
7. How can you use place value understanding
to round decimals?
6. Compare two decimals to thousandths based
on meanings of the digits in each place, using
>, =, and < symbols to record the results of
comparisons.
8. How do you convert units of measurement
within the same measurement system?
7. Use place value understanding to round
decimals to any place.
9. How can you use measurement conversions
to solve real-world problems?
8. Convert among different-sized standard
measurement units within a given
measurement system.
Academic Vocabulary:
place value
digit
multi-digit
pattern
product
9. Use measurement conversions in solving
multi-step, real world problems.
Assessment:
1. Use Build a Number Worksheet. Students
use this worksheet to create their own versions
of this activity. Students should select the
digits to be used and then write five to
ten Build a Number conditions. Students then
create answer keys on the back of their
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Mathematics
5th Grade Math Standard 1.1
power of ten
whole number
decimal
denote
tenths
hundredths
thousandths
standard form
expanded form
compare
<(is less than)
>(is greater than)
=(is equal to)
round
convert
metric system
customary system
papers. Use these student-generated activities
for future place-value practice.
2-3. Create custom assessments to evaluate
multiplication and division of whole numbers
and decimals with powers of ten using the
worksheet created at worksheetworks.com.
4. Use attachment to evaluate ability to
multiply powers of ten using exponents.
5. The assessment for "Decimal War" is
included in the attached lesson plan.
6. Use the attached Comparing Decimals
assessment for evaluation of ability to
accurately compare the value of decimals.
7. Create an assessment to evaluate ability to
round decimals accurately.
8. Use assessment worksheet to evaluate ability
to convert metric units.
9. Observe and assess students' abilities to
solve problems involving measurement
conversions.
Suggested Activities/Strategies:
1. Play the Place Value Game. Using
numerical cards, students actively play a game
learning place value.
2a. Introduce powers of ten using the
PowerPoint. (See attachment.)
1. Build a Number Worksheet
4. Exponents Assessment
6. Comparing Decimals Assessment
8. Assessment on Converting Metric Units
Resources/Technology:
Standards-Based Activities
Site for Teacher-Created Worksheets
Metric Conversions Lesson
Powers of Ten Tutorial
2b. Use the attached Powers of Ten
Performance Task to explore multiplying
whole numbers with powers of ten.
3. Use the attached Powers of Ten
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Mathematics
5th Grade Math Standard 1.1
Performance Task to explore patterns
when multiplying and dividing decimals by
powers of ten.
4. Use the attached video to introduce writing
powers of ten with exponents.
5. Use the Decimal War Lesson to teach and to
explore decimal place value through model
building.
6. Use the Illuminations Fraction Model to
explore different representations for fractions
(improper and mixed) and percentages.
7. Use attached Rounding Decimals
Performance Task to explore rounding
decimals to the nearest hundredth.
8. Use the PowerPoint on metric conversion
and Lesson #2 for practice converting between
units.
9. Use the attached Converting Units Word
Problems for practice solving measurement
conversions using real world situations.
1. Place Value Game
2a. Powers of Ten PowerPoint
2b. Multiplying Whole Numbers by Powers of
Ten
3. Multiplying Decimals with Powers of Ten
Activity
3. Dividing Decimals with Powers of Ten
4. Powers of Ten Exponents Video
5. Decimal War Activity
6. Illuminations Fraction/Decimal/Percent
Interactive Model
7. Rounding Decimals Performance Task
8. Metric Conversions Lesson PowerPoint
9. Converting Units Word Problems
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Mathematics
5th Grade Math Standard 1.2
5.Math.1.2 Formulate, represent, and use algorithms with multi-digit whole numbers and
decimals with flexibility, accuracy, and efficiency
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Fluently multiply multi-digit whole
numbers using standard algorithms.
1. What algorithms can be used to multiply
multi-digit numbers?
2. Find whole-number quotients of whole
2. What algorithms can be used to divide
numbers.
whole numbers?
3. Use strategies based on place value, the
3. How can you use the properties of
properties of operations, and/or the
relationship between multiplication and
operations to help solve problems?
division.
4. How can you explain your calculations
4. Illustrate and explain calculations by using
using equations or drawing arrays and area
models?
equations, rectangular arrays, and/or area
models.
5. How do you add and subtract decimals to
5. Add, subtract, multiply, and divide decimals
hundredths? How do you multiply decimals to
to hundredths.
hundredths? How do you divide decimals?
6. How can using drawings and/or making
drawings help you to solve problems?
7. How can you explain your reasoning and
strategies using a written method?
8. How can you use the order of operations to
write and solve numerical expressions using
parentheses, brackets, and braces?
9. How do you write and interpret numerical
expressions without evaluating them?
Academic Vocabulary:
factor
product
traditional algorithm
partial products algorithm
lattice multiplication
6. Use concrete models or drawings and
strategies based on place value, properties of
operations, and/or the relationship between
addition and subtraction.
7. Relate strategies to a written method and
explain the reasoning used.
8. Use parentheses, brackets, or braces in
numerical expressions, and evaluate
expressions with these symbols.
9. Write simple expressions that record
calculations with numbers, and interpret
numerical expressions without evaluating
them.
Assessment:
1. Use this worksheet to assess multiplication
with standard algorithms. Have students solve
the first column with the traditional algorithm,
the second column using lattice, and the third
column with partial products.
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Mathematics
5th Grade Math Standard 1.2
quotient
dividend
divisor
traditional division algorithm
partial quotients algorithm
properties of addition
properties of multiplication
array
area model
sum
difference
numerical expression
equation
order of operations
() (parentheses)
[] (brackets)
{} (braces)
2. Assess students’ knowledge of solving
division using this quiz.
3. Use this assessment in which students must
apply their knowledge of the relationship
between multiplication and division to solve
for unknown factors.
3-4. Give students base ten blocks and have
them model a multiplication or division
problem. Use a checklist to record who has
grasped the skill. After demonstrating
proficiency using the blocks, have students
represent a problem pictorially.
5a. Use this assessment for adding decimals.
5b. Use this assessment
for subtracting decimals.
5c. Use this assessment for multiplying
decimals.
5d. Use this assessment for dividing decimals.
6-7. Give students base ten blocks and have
them model an addition or
subtraction problem. Use a checklist to record
who has grasped the skill. After demonstrating
proficiency using the blocks, have students
represent a problem pictorially.
8. Use this worksheet to assess order of
operations.
9. Use this assessment to evaluate writing
numerical expressions.
9c. Use this rubric to assess the performance
task.
1. Multiplication Algorithms Assessment
2. Division Assessment
3. Missing Factor Worksheet
5a. Adding Decimals
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Mathematics
5th Grade Math Standard 1.2
Suggested Activities/Strategies:
1a-c. Use the attached resources and videos to
teach and practice the traditional, partial
products, and lattice algorithms for
multiplication.
2a. Explain long division using this colorful,
step-by-step tutorial.
2b. Practice long division using this practice
sheet which includes scaffolding.
5b. Subtracting Decimals
5c. Multiplying Decimals
5d. Division with Decimals
8. Order of Operations
9. Writing Numerical Expressions
9c. Rubric
Resources/Technology:
Pete's PowerPoints
Explanations of Multiplication Algorithms
Teacher Video Explaining Partial Products
Division Worksheet Creator
Decimal Worksheets
Operations with Decimals
Study Jams Videos
Performance Task Bank
2c. Use this PowerPoint to teach "short"
division. This method works well for
advanced students who can do some steps
mentally.
3-4. Use this interactive site to show students
how to demonstrate multiplication and
division using place value models.
5a. Watch this video to explain adding and
subtracting decimals.
5b. Display these tips for adding and
subtracting decimals.
5c. Use this interactive site to practice adding
and subtracting decimals.
5d. Watch this PowerPoint presentation for
explaining multiplication with decimals.
5e. Use this interactive site to allow students
to practice multiplying decimals.
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Mathematics
5th Grade Math Standard 1.2
5f. Watch this video for explaining division
with decimals.
5g. Use these StudyJams videos and tutorials
to teach operations with decimals. Click on the
"decimals and percents" tab at top of the page.
6, 7a, & 7b. Use these virtual manipulatives to
teach modeling addition and subtraction based
on place value.
8a. Watch this rap video explaining PEMDAS.
8b. Use this interactive site to explain/practice
using order of operations.
8c. Play the linked game to practice order of
operations.
9a. Watch the PowerPoint presentation to
teach writing numeric expressions.
9b. Play the matching game to practice
numeric expressions.
9c. Complete "Sam the Slippery Spider"
Performance Task.
1a. Standard Multiplication Algorithm
1b. Lattice Multiplication
1c. Video Modeling Partial Products with
Base Ten Blocks
2a. Long Division Tutorial
2b. Long Division Practice
2c. Short Division PowerPoint
3-4. Interactive Model for Modeling
Multiplication
5a. Video on Adding and Subtracting
Decimals
5b. Tips for Adding/Subtracting Decimals
5c. Adding/Subtracting Decimals Interactive
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Mathematics
5th Grade Math Standard 1.2
Site
5d. Multiplying Decimals PowerPoint
5e. Practice Multiplying Decimals
5f. Dividing Decimals Video
5g. Study Jams Videos
6-7a. Place Value Addition
6-7b. Modeling Subtraction
8a. Order of Operations Video
8b. Order of Operations Practice
8c. Order of Operations Game
9a. PowerPoint on Numeric Expressions
9b. Matching Game
9c. "Sam ..." Performance Task
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Mathematics
5th Grade Math Standard 1.3
5.Math.1.3 Formulate, represent, and use algorithms to add and subtract fractions with
flexibility, accuracy, and efficiency
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Use benchmark fractions and number sense
1. How can estimation be used with fractions
of fractions to estimate mentally and assess the
to see if your answer is reasonable?
reasonableness of answers.
2. How can finding equivalent fractions with
like denominators help you to add and subtract
fractions?
2. Add and subtract fractions with unlike
denominators (including mixed numbers) by
replacing given fractions with equivalent
fractions with like denominators.
3. How can word problems be solved involving
the adding and subtracting fractions?
3. Solve word problems involving addition and
subtraction of fractions referring to the same
whole.
Academic Vocabulary:
Assessment:
fraction
benchmark fractions
mixed number
improper fraction
mixed number
simplest form/lowest terms
numerator
denominator
equivalent fraction
estimate
reasonable
1. Complete the comparing fractions worksheet
for assessment.
2a-c. Use these assessments for adding and
subtracting unlike fractions.
1-3a & b. Use the assessments included within
the units.
1-3c. Use this rubric to assess the performance
task.
3. Use this worksheet as an assessment for
fraction word problems.
1. Comparing Fractions Worksheet
2a. Adding Unlike Fractions Assessment
2b. Adding Unlike Fractions for Advanced
Learners
2c. Unlike Fractions for Learners Needing
Additional Assist
1-3a. Fabulous Fractions Unit
1-3b. Fractions Unit
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Suggested Activities/Strategies:
1a. Watch the video explaining how to
estimate using benchmark fractions.
1b. Compare fractions using fraction strip
worksheets in order to give the students a
visual model of fractional parts.
2a. Watch the “Thirteen Ways of Looking at a
Half” slideshow and play the linked game.
2b. Watch the video explaining equivalent
fractions.
2-3. View the Study Jams step-by-step
tutorial explaining adding and subtracting
unlike fractions. The demonstration uses a real
world example.
1-3a. Follow the "Fabulous Fractions Unit" to
find equivalent fractions and to add, subtract,
and compare fractions.
1-3b. Use this comprehensive unit to teach
adding and subtracting fractions. Performance
Tasks are included.
1-3c. Complete the "Lots of Chocolate"
Performance Task.
3. Use this interactive site to practice solving
word problems involving fractions.
1-3c. "Lots of Chocolate" Rubric
3. Fraction Word Problems
Resources/Technology:
Free Printables
Fabulous Fractions Unit
Performance Task Bank
1a. Estimation with Fractions Video
1b. Fraction Strips Printable
2a. Thirteen Ways Video
2b. Equivalent Fractions Video
2-3. Study Jams Tutorial
1-3a. Fabulous Fractions Unit
1-3b. Fractions Unit
1-3c. "Lots of Chocolate" Performance Task
3. Fraction Word Problems
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Mathematics
5th Grade Math Standard 1.4
5.Math.1.4 The concepts of multiplication and division can be applied to multiply and divide
fractions
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Interpret a fraction as division of the
1. How is a fraction related to division?
numerator by the denominator (a/b = a ÷ b).
2. How can the answer to a division problem
be written as a fraction or mixed number?
3. What are some different ways to represent
multiplying a fraction by a whole number?
4. How can you use tiling to show that the area
of a rectangle can be found by multiplying the
side lengths?
5. How can you use multiplication to find the
area of a rectangle with fractional side lengths?
6. How is scaling related to multiplication?
7. How can you use the size of the factor to
estimate the size of the product?
8. How can you find equivalent fractions by
multiplying by a fraction equivalent to one?
9. How can you solve real-world problems
involving multiplying fractions and mixed
numbers?
10. How do you divide a unit fraction by a
whole number?
11. How do you divide a whole number by a
unit fraction?
12. How can you solve real-world problems
involving division of fractions and whole
numbers?
2. Solve word problems involving division of
whole numbers leading to answers in the form
of fractions or mixed numbers.
3. Interpret the product (a/b) × q as a parts of a
partition of q into b equal parts; equivalently,
as the result of a sequence of operations a × q
÷ b. In general, (a/b) × (c/d) = ac/bd.
4. Find the area of a rectangle with fractional
side lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and show
that the area is the same as would be found by
multiplying the side lengths.
5. Multiply fractional side lengths to find areas
of rectangles, and represent fraction products
as rectangular areas.
6. Interpret multiplication as scaling (resizing).
7. Compare the size of a product to the size of
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
8. Apply the principle of fraction equivalence
a/b = (n × a)/(n × b) to the effect of
multiplying a/b by one.
9. Solve real world problems involving
multiplication of fractions and mixed numbers.
10. Interpret division of a unit fraction by a
non-zero whole number, and compute such
quotients.
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Mathematics
5th Grade Math Standard 1.4
11. Interpret division of a whole number by a
unit fraction, and compute such quotients.
Academic Vocabulary:
fraction
numerator
denominator
whole number
mixed number
equivalent
tiling
area
scaling (resizing)
factor
unit fraction (a fraction with a numerator of 1)
product
quotient
12. Solve real world problems involving
division of unit fractions by non-zero whole
numbers and division of whole numbers by
unit fractions.
Assessment:
1. Turn in the completed chart from Activity
#1 for assessment.
2. Use this quiz to assess solving word
problems with quotients involving fractional
remainders.
3. Use this sheet to assess multiplying fractions
by whole numbers.
4-5. Use this assessment on finding the area of
rectangles with fractional side lengths. You can
also give students the problems and let them
draw their own models.
6-7a-b. Choose worksheets from these sites to
assess multiplication as scaling.
7. Choose practice sheets from this site for
assessment and have the students estimate the
product before solving.
8. Use this assessment for equivalent fractions.
9. Use this practice sheet to assess word
problems involving multiplication of fractions.
10-11. Use this assessment for dividing
fractions by whole numbers, and whole
numbers by fractions. To increase the depth of
knowledge, have students draw models of each
problem and then solve.
12b. Assess the modified recipe for accuracy.
If the students calculated and measured
correctly, the cookies will be edible and the
students receive an "A" for the project!
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Mathematics
5th Grade Math Standard 1.4
1-12. Use the assessments included in the
unit. Ideas for differentiation are included.
Suggested Activities/Strategies:
1. Complete this chart to show how a fraction
is another way to write division.
2. Use this interactive site to teach division
with fractional remainders. An explanation and
practice problems are included.
2. Word Problems with Fractional Remainders
3. Multiplying Fractions by Whole Numbers
4-5. Area of Rectangles with Fractional Sides
6-7a. Scaling and Resizing 1
6-7b. Scaling and Resizing 2
7. Fractions Worksheets
8. Equivalent Fractions Assessment
9. Multiplying Fractions Word Problems
10-11. Dividing Fractions and Whole
Numbers Assessment
1-12. Fractions Unit
Resources/Technology:
Equivalent Fractions Lessons
Multiple Resources to Teach Fractions
Resources/Sites for Multiplying Fractions
Site for Generating Practice Sheets with
Fractions
Map Scale Activities
3. Use this interactive site to practice
multiplying fractions by whole numbers.
4-5a. Watch this video lesson explaining how
to find the area of a rectangle with fractional
side lengths by tiling.
4-5b. Follow this lesson plan to teach
multiplying fractions using area models.
4-5c. Use this interactive site to practice
modeling fraction multiplication with area
models. Practice examples are included.
4-5d. Watch this video to explain how to
model multiplication of fractions.
6. Make a map using scale.
6-7. Use this site to teach and give a
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Mathematics
5th Grade Math Standard 1.4
demonstration on multiplication as scaling.
7. Practice estimating products of fractions
using this site.
8a. Use these lesson plans to teach equivalent
fractions.
8b. Use this interactive site to teach equivalent
fractions.
8c. Watch this step-by-step explanation of how
to find equivalent fractions.
9. Use this interactive site to allow students to
practice solving word problems involving
multiplying fractions.
10a. Use this lesson and explanation to teach
dividing fractions by whole numbers.
10b. Practice dividing fractions by whole
numbers using this interactive site.
10c. Watch this video on how to model
dividing fractions by whole numbers.
11a. Watch this video on how to divide whole
numbers by fractions. The video demonstrates
how to draw models to represent the answer.
12a. Practice dividing fractions and whole
numbers using this interactive site.
12b. Use recipe fractional quantities to solve
real world problems. Divide the class into four
groups. Give each group a copy of the recipe.
The students must HALF the recipe. They
should work together and compare answers.
When finished, they will actually follow the
directions to make the cookies. The teacher can
work with the lunchroom to have the cookies
baked or store the cookie dough in the
refrigerator and take them home to bake. This
activity also involves measuring. It is a great
culmination to a unit on multiplying and
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Mathematics
5th Grade Math Standard 1.4
dividing fractions.
1-12. Use this fraction unit for multiple
fraction concepts. The unit includes
performance tasks and suggestions for
differentiation.
1. Relating Fractions to Division
2. Division with Fractional Remainders
3. Multiplying Fractions by Whole Numbers
Interactive Site
4-5a. Area of a Rectangle with Fractional
Sides Video
4-5b. Explanation/Practice of Multiplying
Fractional Sides
4-5c. Practice Modeling Multiplying Fractions
4-5d. Multiplying Fractions Video
6. Make a Map
6-7. Multiplication as Scaling
7. Practice Estimating the Size of Products
8a. Lesson Plans for Teaching Equivalent
Fractions
8b. Equivalent Fractions Interactive Site
8c. Study Jams Video on Equivalent Fractions
9. Word Problems Multiplying Fractions
10a. Dividing Fractions by Whole Numbers
10b. Dividing Fractions by Whole Numbers
Interactive Site
10c. Video on Dividing Fractions by Whole
Numbers
10-11. Fraction Division Lesson
11a. Video on Dividing Whole Numbers by
Unit Fractions
11b. Dividing Whole Numbers by Fractions
12a. Word Problems on Dividing Fractions by
Whole Numbers
12b. Cookie Recipe
1-12. Fractions Unit
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Mathematics
5th Grade Math Standard 2.1
5.Math.2.1 Number patterns are based on operations and relationships
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Generate two numerical patterns using given
1. How can you generate two numerical
rules.
patterns given rules?
2. Identify apparent relationships between
corresponding terms.
2. How can you identify the relationship
between corresponding terms?
3. Form ordered pairs consisting of
3. How can you form and graph ordered pairs
corresponding terms from the two patterns, and
graphs the ordered pairs on a coordinate plane.
consisting of corresponding terms from two
patterns?
4. Explain informally relationships between
corresponding terms in the patterns.
4. How can you explain the relationship
between corresponding terms in a pattern?
5. Explain, extend, and use patterns and
relationships in solving problems, including
5. How can patterns be used to help you solve
those involving saving and checking accounts
real world problems?
such as understanding that spending more
means saving less.
Academic Vocabulary:
Assessment:
1a-b. Complete number patterns as assessment
for Activities 1 and/or 2.
numerical pattern
generate
4. Complete an in/out chart accurately as
ordered pairs
assessment when playing the "Guess my Rule"
coordinate plane
Game.
corresponding terms
1-5. Use the "Pea Soup" Performance Task
Rubric.
1-5. Use assessments in the
Geometry/Coordinate Plane Unit.
Suggested Activities/Strategies:
1b. Input/Output Game Board
2. Number Patterns Assessment
2. Number Patterns Assessment 2
1-5a. Pea Soup Performance Task Rubric
1-5b. Geometry and the Coordinate Plane Unit
Resources/Technology:
Number Patterns Task Bank
1a. Use the PowerPoint Game for practice
finding numerical patterns.
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Mathematics
5th Grade Math Standard 2.1
1b. Use in/out charts to illustrate the
relationship between sets of numbers. Play
the game to practice finding the missing
number in a chart and seeing the corresponding
graph.
2. Use the Number Patterns Performance
Tasks. See the site for a variety of tasks in
which students can extend patterns.
4. Play the "Guess My Rule" Game to practice
finding number patterns.
1-5. Complete the Pea Soup Performance Task
which incorporates all standards.
1-5. Use the Geometry/Coordinate Plane Unit
Activities.
1a. Number Patterns PowerPoint
1b. Input/Output Game
2. Number Patterns Tasks
4. Guess My Rule Game and Patterns
1-5a. Pea Soup Performance Task
1-5b. Geometry and the Coordinate Plane Unit
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Mathematics
5th Grade Math Standard 3.1
5.Math.3.1
Visual displays are used to interpret data
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Make a line plot to display a data set of
1. How can you make a line plot to display a
measurements in fractions of a unit (1/2, 1/4,
set of fractional measurements?
1/8).
2. How do you use your knowledge of
fractions to solve problems from information
presented in a line plot?
Academic Vocabulary:
data
represent
fraction
line plot
Suggested Activities/Strategies:
2. Use operations on fractions for this grade to
solve problems involving information
presented in line plots.
Assessment:
1. Use completed line plots for assessment.
2. Collect the index cards from the students
and create an assessment based upon the
questions the class formulated. Students will
answer the questions for a grade.
Resources/Technology:
1a. Complete the line plot task. This can be
adapted to measuring to the nearest 1/8 inch.
1b. Have students measure various items in
the classroom to the nearest 1/8 inch
(e.g., length of pencils, library books, shoes.)
Collect the data and construct a collaborative
line plot.
2. Then have students formulate questions
from the line plot, write these on an index
card, and answer on the back of the card.
Sample questions might include, What is the
combined length of the two longest
objects? What is the difference in length
between the longest and the shortest objects?
1a. Line Plot Task
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Mathematics
5th Grade Math Standard 4.1
5.Math.4.1 Properties of multiplication and addition provide the foundation for volume an
attribute of solids
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Model the volume of a right rectangular
1. How can you use cubes to find the volume
prism with whole-number side lengths by
of a rectangular prism? Why must you use
packing it with unit cubes.
cubic units?
2. Show that the volume is the same as would
2. How can you use modeling with cubes to
be found by multiplying the edge lengths,
justify the volume formula for rectangular
equivalently by multiplying the height by the
prisms?
area of the base.
3. How can you use the associative property of
multiplication to help find the volume of
rectangular prisms?
3. Represent threefold whole-number products
as volumes to represent the associative
property of multiplication.
4. How can you find the volume of a figure by
counting cubes?
4. Measure volumes by counting unit cubes,
using cubic cm, cubic in, cubic ft, and
improvised units.
5. What are the different ways to write the
volume formula for rectangular prisms?
6. How can you find the volume of a solid
figure by adding the volumes of its parts?
Academic Vocabulary:
volume
length
width
height
associative property
length of base (b)
area of the base (B)
cubic unit (cubic cm, cubic in., cubic ft.)
5. Apply the formulas V = l × w × h and V = B
× h for rectangular prisms to find volumes of
right rectangular prisms with whole-number
edge lengths.
6. Use the additive nature of volume to find
volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding
the volumes of the non-overlapping parts.
Assessment:
1-6a,b,c. Use these differentiated attachments
to assess finding volume.
6. Use this assessment for volume of
composite figures.
1-5a. Volume Assessment for Advanced
Learners
1-5b. Volume Assessment for Learners
Needing Additional Assist
1-6c. Volume Assessment Using Counting
Cubes
6. Volume of Composite Figures
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Mathematics
5th Grade Math Standard 4.1
Suggested Activities/Strategies:
1-5a. Introduce volume by watching this
video on what volume is, why we use cubic
units, and the formulas for finding volume.
Resources/Technology:
1-5b. Watch this StudyJams video to explain
volume.
1. Students will use manipulatives to calculate
the volume of three-dimensional shapes before
and after a dimension is changed (e.g., If a
rectangular prism is 7 x 3 x 6, what will be the
change in its volume if the height is halved?)
2. Students will estimate the number of
chickpeas it takes to fill their classroom.
3. Practice finding the volume of rectangular
prisms using this interactive site.
3-4. Use this worksheet as guided practice for
finding volume.
5. Given the length, width, and height of a box
(rectangular prism), students find the volume
of the shape by using LxWxH=Volume.
1-6a. Follow this lesson plan to teach volume.
1-6b. Follow this comprehensive volume
unit. Many hands-on activities are included, as
well as performance tasks.
1-5a. Volume Video
1-5b. Study Jams Volume Video
2. Estimating Chickpeas Video
3. Interactive Site to Practice Calculating
Volume
3-4. Volume Guided Practice Sheet
5. Basic Volume
1-6a. Volume Lesson Plan
1-6b. Volume Unit
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
5th Grade Math Standard 4.2
5.Math.4.2 Geometric figures can be described by their attributes and specific locations in the
plane
Essential Questions - 21st Century Skills
Evidence Outcomes:
and Readiness Competencies:
1. Represent real world and mathematical
1. How can you use graphing coordinates to
problems by graphing points in the first
help solve real world problems?
quadrant of the coordinate plane and interpret
coordinate values of points in the context of
the situation.
2. How can you classify two-dimensional
shapes based on their properties?
2. Classify two-dimensional figures into
categories based on their properties.
3. How can you classify two dimensional
shapes into a hierarchy based on their
attributes?
3. Classify two-dimensional figures in a
hierarchy based on properties. Explain that
attributes belonging to a category of twodimensional figures also belong to all
subcategories of that category.
Academic Vocabulary:
Assessment:
1a. Use the attached rubric to assess.
graphing
2. Use the assessment included in the Lesson
coordinates
Plan.
coordinate plane
classify
2-3. Use tasks and assessments included in the
two-dimensional
unit as assessment. Multiple types of activities
attributes
are included, even ways to differentiate
properties
instruction.
sides
vertices
angles
1a. Rubric
hierarchy
2. Geometric Shapes Assessment
2-3. Geometry Unit
Suggested Activities/Strategies:
Resources/Technology:
1. Graph ordered pairs using a variety of
activities. This site includes games and art
activities involving graphing.
1a. Using large graph paper, students will
construct a map of a fictitious town. Plot ten
common locations in the town, including
a home, library, school, post office, grocery
store, park, community center, friend’s house,
Copyright © 2013 South Central Board of Cooperative Educational Services and Education Designs.
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Mathematics
5th Grade Math Standard 4.2
and grandma's house. List locations and paired
coordinates. Place plotted locations using
symbols.
2. Follow the lesson plan for classifying twodimensional shapes. (Omit the activities
involving 3-D shapes. The plan was designed
for 4th grade, but can be applied to 5th.)
2-3. Use the Geometry Unit which contains
multiple tasks for teaching the classification
of polygons (including using a hierarchy.)
1. Graphing Coordinates Activities
2. Lesson Plans for Classifying 2-D Figures
2-3. Geometry Unit
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