UNIT 1
Whole Numbers
Total Number of Days: 17




ESSENTIAL QUESTIONS
How can you write whole numbers in different forms?
How does the position of a digit affect its value?
What symbolic expressions can be used to compare and
round numbers?
Why is place value important when comparing and
rounding numbers?
PACING
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of place value
concepts from fourth grade
3 days
SKILLS
1. Write numbers in
the ten thousands
place in word form,
standard form and
expanded form.
2. Identify the value
of each digit in a
number up to the ten
thousands place.
Grade/Course: 5/Math
ENDURING UNDERSTANDINGS
 Numbers can be written in standard form, word form, and
expanded form.
 The value of a number is determined by the place of its digits.
 Numbers can be compared and ordered according to the place
value of their digits.
 Number lines and place value can be used to round numbers to a
specific place value.
RESOURCES
LEARNING
STANDARD
ACTIVITIES/ASSESSMENTS
OTHER
S
(All lessons should begin
Math in
(e.g.,
(CCCS/MP)
with a Do-Now and end
Focus
tech)
with an Exit Ticket)
4.NBT.A.1
Assessmen
ts:
pp. 4-6
TE 5-A:
pp. 1-4
Pre-Assessment:
Chapter 1 Test Prep
Assessment
Assessment Book pp. 4-6
Chapter Opener- TE pp. 1-4
Quick Check TE pp. 4
Core:
SE 5-A:
pp. 1-4
3. Compare numbers
using a place value
chart.
1
4. Round numbers
using a number line.
1.1 Numbers to 10,000,00
1. Count by ten
thousands and
hundred thousands
to 10,000,000.
2. Use place-value
charts to show
numbers to
10,000,000.
3 Days
MP:
MP 1
MP 3
MP 4
MP5
3. Read and write
numbers to
10,000,000 in
standard form and in
word form.
1.2 Place Value
3 days
CCCS:
5.NBT.A.1
1. Identify the place
value of any digit in
numbers to
10,000,000.
2.Recognize that in a
multi-digit number, a
TE-5A:
pp.5-15
Blackline
Master
TR01
Core:
SB-5A:
pp. 5-15
WKBK-5A:
pp. 1-6
ExtraP-5A:
pp.1-4
Place
Value
Chart
(TR01)
CCCS:
5.NBT.A.1
MP:
MP 4
Core:

Place
Value
Chips
White
Board (1
per
student)
Basic
Reteach5A:
pp.1-4
Advanced:
Enrich-5A:
pp.1-8
TE-5A:
pp.16-19
Blackline
Master
TR01

5-Minute Warm Up TE
pp. 5
Math Discussion TE pp. 713
o Whiteboards
o After discussing
each Learn activity
of the chapter,
have several
students
formulate
questions about
what they learned
and call on other
students to
answer the
questions

Let’s Practice TE pp. 14
Place
Value
Chart
(TR01)

Place
Value

5-Minute Warm Up TE
pp. 16
Learn Zillions VideoPlace Value
o Base Ten Blocks
Math Discussion TE pp.
16-18

2
digit in one place
represents 10 times
as much as it
represents in the
place to its right and
1/10 of what it
represents to its left.
SB-5A:
pp. 16-19
WKBK-5A:
pp. 7-10
ExtraP-5A:
pp.5-8
Basic
Reteach5A:
pp.5-8
3. Read and write
numbers to
10,000,000 in
expanded form
1.3 Comparing Numbers to
10,000,000
2 days
1. Compare and
order numbers to
10,000,000.
2. Identify and
complete a number
pattern.
3. Find a rule for a
number pattern.
Advanced:
Enrich-5A:
pp.1-8
CCCS:
5.NBT.A.1
MP:
MP 4
MP7
Chips
Base-Ten
Blocks
White
Board (1
per
student)
Learn
Zillions
Video
http://lea 
rnzillion.c
om/lesso
ns/424identifythe-valueof-a-digitbylookingat-itsplace
TE-5A:
pp.20-24
Blackline
Master
TR01
White
Board (1
per
student)
Core:
SB-5A:
pp. 20-24
WKBK-5A:
Place
Value
Chart
(TR01)


o Whiteboards
o Place Value Chips
o Have students
make their own
place-value chart
and use the chart
to identify the
values of digits
until they master
the order and
names of the
places
Let’s Practice TE pp. 19
5-Minute Warm Up TE
pp. 20
Math Discussion TE pp.
20-22
o Whiteboards
o Place Value Chart
o To help students
find a rule to
complete a
number pattern,
3
have them write
the first two
numbers in the
pattern, one below
the other, and
compare each
digit one place at a
time to analyze
more readily how
the numbers
change.
ExtraP-5A:
pp. 11-14
Basic
Reteach5A:
pp. 9-14
Advanced:
Enrich-5A:
pp.1-8
1.4 Rounding and
Estimating
3 days
1. Round numbers to
the nearest
thousand.
CCCS:
5.NBT.A.4
MP:
2. Locate numbers on MP1
a number line.
MP2
MP4
3. Use rounding to
MP8
estimate or check
sums, differences,
and products.
4. Use related
multiplication facts
to estimate
quotients.
TE-5A:
pp. 25-35
Blackline
Master
TR02
Core:
SB-5A:
pp. 25-35
WKBK-5A:
pp. 15-24
ExtraP-5A:
pp. 11-14
Basic
Reteach5A:
pp.15-26
Advanced:
Enrich-5A:

Number
Lines
(TR02)
White
Board (1
per
student)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/52
3-locatebenchma
rknumbers
-on-a-



Let’s Practice TE pp. 2324
5-Minute Warm Up TE
pp. 25
Learn Zillions VideoRounding on a Number
Line
o Number Line
Math Discussion TE pp.
25-34
o Whiteboards
o Number Line

Let’s Practice TE pp. 3435

Math Critical Thinking
and Problem Solving TE
pp. 35
4
pp.1-8
Chapter Wrap Up
Chapter Assessment
1. Reinforce and
consolidate chapter
skills and concepts.
3 days
CCCS:
5.NBT.A.1
5.NBT. A.4
MP:
MP1
MP3
MP6
TE-5A:
pp. 36-40
Assessmen
t Book
pp. 5-7
Core:
SB-5A:
pp. 36-40
numberline
Chapter Wrap Up Study
Guide TE pp.36-37
Chapter Review TE pp.38-39
Unit 1 Assessment
(Assessments 5 pp. 5-7)

INSTRUCTIONAL FOCUS OF UNIT
o Students extend their understanding of place value to numbers through millions in various contexts.
o Students use place-value charts to show greater numbers and write these numbers in standard form, word form, and expanded
form.
o Students extend their knowledge of comparing numbers to greater numbers and apply this knowledge in completing number
patterns.
o Students extend their rounding and estimating skills to greater place values. Students adopt strategies such as number lines
and front-end estimation with adjustment to estimate numbers or results of operations in an efficient manner.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 1 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 1

Example of Key Advances from Grade 4 to Grade 5
o In grade 5, students will integrate decimal fractions more fully into the place value system (5.NBT.1-4). By thinking about
decimals as sums of multiples of base-ten units, students begin to extend algorithms for multidigit operations to decimals
5
(5.NBT.7).
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Whole Numbers
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on whole numbers for unit 1. Apply
skills and knowledge learned on whole numbers to real world
scenarios given in the menu. Complete at least 15 points out of the
20 points available (80% and higher).
Critical Thinking:
Math Journal
 How can you write whole numbers in different forms?
 How does the position of a digit affect its value?
 What symbolic expressions can be used to compare and round
numbers?
 Why is place value important when comparing and rounding
numbers?
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to the number
system. Evaluate real world problems through the application of
whole number concepts by completing various critical thinking
activities with at least 85% accuracy.
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
6
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Patterns R Us
activity (pdf pp.44-49
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit1FrameworkSE.pdf)

Students work
collaboratively to discover patterns created when numbers
are multiplied by powers of 10.
Communication – Power points/Presentations
TLWBAT: Identify, describe, and explain any patterns they notice
when multiplying numbers by powers of 10 such as 1,000, 100
and 10 with at least 80% accuracy
MODIFICATIONS/ACCOMMODATIONS


Whiteboards (1 per student)
Additional Support (ELL, Struggling Learners) TE 5A pp. 1B
APPENDIX
(Teacher resource extensions)
CCCS:
5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its
right and 1/10 of what it represents in the place to its left.
5.NBT.A.4 Use place value understanding to round decimals to any place
Mathematical Practice: (MP)
1.Make sense of problems and persevere in solving them.
2.Reason abstractly and quantitatively.
3.Construct viable arguments and critique the reasoning of others.
4.Model with mathematics.
5.Use appropriate tools strategically
6.Attend to precision
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Unpacking the Standards (Examples and Rationales)
Lesson 2.2, 2.3, 2.4, 2.5, 2.6
7
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
8
UNIT 2
Whole Number Multiplication and Division
Total Number of Days: 25 Grade/Course: 5/Math





ESSENTIAL QUESTIONS
Why is it important to follow an order of operations?
How can I write an expression that demonstrates a
situation or context?
How does multiplying a whole number by a power of
ten affect the product?
What strategies can we use to efficiently solve
multiplication problems?
What strategies can we use to efficiently solve division
problems?
PACING
3 days
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of place value
concepts from fourth grade
SKILLS
1. Write numbers
word form and
expanded form.
2. Use bar models to
show the four
operations.
ENDURING UNDERSTANDINGS

Multiplication may be represented by rectangular arrays/area
models. There are two common situations where division may be
used: fair sharing (given the total amount and the number of equal
groups, determine how many/much in each group) and
measurement (given the total amount and the amount in a group,
determine how many groups of the same size can be created)

Some division situations will produce a remainder, but the
remainder will always be less than the divisor. If the remainder is
greater than the divisor, that means at least one more can be given
to each group (fair sharing) or at least one more group of the given
size (the dividend) may be created.
 The properties of multiplication and division help us solve
computation problems easily and provide reasoning for choices we
make in problem solving.
RESOURCES
LEARNING
STANDARD
ACTIVITIES/ASSESSMENTS
OTHER
S
(All lessons should begin
Math in
(e.g.,
(CCCS/MP)
with a Do-Now and end
Focus
tech)
with an Exit Ticket)
5.NBT.A.1
Assessmen
ts:
pp. 13-16
TE 5-A:
pp. 41-46
Pre-Assessment:
Chapter 2 Test Prep
Assessment
Assessment Book TE pp. 1316
Chapter Opener- TE pp. 419
Core:
SE 5-A:
pp. 41-46
3. Rounding to the
nearest thousand.
46
Quick Check TE pp. 44
4. Estimating
products by
rounding.
5. Estimate quotients
by using related
multiplication facts.
2.1 Using a Calculator
1 day
1. Use a calculator to
add, subtract,
multiply, and divide
whole numbers.
CCCS:
5.NBT.B.5
5.NBT.B.6
MP:
MP 4
MP 5
MP 6
TE-5A:
pp.47-50
Blackline
Master
TR03
Core:
SB-5A:
pp. 47-50
WKBK-5A:
pp. 27-28
ExtraP-5A:
pp.17-18
Basic
Reteach5A:
pp. 27-30
Advanced:
Enrichmen
Calculato 
r Keypad
(for

teacher
only)
(TR03)
Calculato
r per
student
5-Minute Warm Up TE
pp. 47
Math Discussion TE pp.
47-50
o Calculators
o To help check that
they have not
made careless
mistakes in
entering operation
signs on their
calculators, have
students estimate
whether their
answer will be
greater than or
less than the first
number they
enter. For
addition and
multiplication
problems, the
10
t 5A:
pp.9-19

2.2 Multiplying by Tens,
Hundreds, or Thousands
4 days
1. Multiply numbers
by 10, 100, or 1,000
using patterns.
2. Multiply numbers
up to 4 digits by
multiples of 10, 100,
or 1,000.
3. Use rounding to
estimate products.
4. Multiply whole
CCCS:
5.NBT.A.1
5.NBT.A.2
5.NBT.B.5
5.OA.A.1
5.OA.B.3
MP:
MP 4
MP 5
MP 6
MP 8
TE-5A:
pp.51-63
Blackline
Master
TR01,
TR04,
TR05,
TR06,
TR07
Common
Core
Lessons
and
Place
Value
Chart
(TR01)
Place
Value
Chips
Table of
Multiplic
ation 1
(TR04)



answer will be
greater; for
subtraction and
division problems,
the answer will be
less.
Hands-On Activity: (work
in pairs)
o Practice entering
numbers on a
calculator (TE
pp.47)
o Find sums and
differences using a
calculator (TE
pp.49)
o Find products and
quotients using a
calculator (TE pp.
50)
5-Minute Warm Up TE
pp. 51
Learn Zillions VideoPowers of Ten
Math Discussion TE pp.
51-63
o Whiteboards
o After learning to
multiply by 10,
100, and 1,000
and their
multiples, help
students see the
11
numbers by 10
squared or 10 cubed.
Ex.
36x10=36x101=360
•36x10x10=36x102=
3600
•36x10x10x10=36x1
03=36,000
Activities
E-Book
2.2A
(thinkcent
ral.com)
Core:
SB-5A:
pp. 51-63
WKBK-5A:
pp. 29-36
ExtraP-5A:
pp. 19-22
Basic
Reteach5A:
pp. 31-38
relationship
among the
multiples. Have
them complete
patterns such as:
12 x 3= 36; 12 x
30=360; 12 x ? =
3,600; 12 x 3,000=
?
Table of
Multiplic
ation
(TR05)
Table of
Multiplic
ation 3
(TR06)
Table of
Multiplic
ation 4
(TR07)

Calculato
r per
student
Advanced:
Enrichmen White
t 5A:
Board (1
pp.9-19
per
student)
Learn
Zillions
Video

http://le
arnzillio
n.com/le
ssons/43
4multiplywhole-
Hands-On Activity (Pairs)
o Use Place Value to
Find a Rule
(Multiples of 10)
TE pp. 53
o Break Apart
Factors (Multiples
of 10) TE pp. 55
o Use Place Value to
Find a Rule
(Multiples of 100,
1,000) TE pp. 58
o Break Apart
Factors (Multiples
of 100, 1,000) TE
pp. 60
Let’s Practice TE pp. 63
12
numbers
-bypowersof-ten
2.3 Multiplying by 2-digit
Numbers
1. Multiply a 2-, 3-,
or 4-digit number by
a 2-digit number
CCCS:
5.NBT.B.5
5.OA.A.1
MP:
MP 2
3 days
TE-5A:
pp.64-69
Core:
SB-5A:
pp. 64-69
WKBK-5A:
pp. 37-42
White
Board (1
per
student)
Learn
Zillion
Videos
ExtraP-5A: http://le
pp. 23-24
arnzillio
n.com/le
Basic
ssons/52
Reteach85A:
multiplypp. 39-46
multidigi
tAdvanced: numbers
Enrichmen -usingt 5A:
an-areapp.9-19
model



5-Minute Warm Up TE
pp. 64
Learn Zillions Video Area
Model Multiplication
Math Discussion TE pp.
64-69
o Whiteboards
o Throughout this
lesson, students
learn to multiply
multi-digit
numbers and use
estimation to
check that their
answers are
reasonable. For
some of the
computations,
have students
estimate first to
give them an idea
of what their
answers should
be, and then use
the estimate they
already made to
check the
reasonableness of
13
their answers.
2.4 Dividing by Tens,
Hundreds, or Thousands
4 days
1. Divide numbers by
10, 100, or 1,000
using patterns.
CCCS:
5.NBT.A.1
5.NBT.A.2
5.NBT.B.6
2. Divide numbers up 5.OA.A.1
to 4 digits by
5.OA.B.3
multiples of 10, 100,
1,000.
MP:
MP 1
3. Use rounding and
MP 3
related
MP 4
multiplication facts
MP 5
to estimate quotients MP 6
MP 8
TE-5A:
pp. 70-81
Blackline
Master
TR01,
TR08,
TR09,
TR10,
TR11
Core:
SB-5A:
pp. 70-81
WKBK-5A:
pp. 43-48
ExtraP-5A:
pp. 25-28
Basic
Reteach5A:
pp.47-52
Place
Value
Chart
(TR01)
Place
Value
Chips

Let’s Practice TE pp. 69

5-Minute Warm Up TE
pp. 70
Learn Zillions VideoPowers of Ten
Math Discussion TE pp.
70-81
o Whiteboards
o After learning to
divide by 10, 100,
and 1,000 and
their multiples,
help students to
see the
relationship
among the
divisors. Have
them complete
patterns such as:
12  3 = 4; 120 
30 = 4; 1,200  ? =;
12,000  3,000 = ?


Table of
Division
1 (TR08)
Table of
Division
(TR09)
Table of
Division
3 (TR10)
Table of
Division 
Advanced: 4 and
Enrichmen 5(TR11)
t 5A:
pp.9-19
Calculato
r per
student
Hands-On Activity
o Use Place Value to
Find a Rule
(Divide by 10) TE
pp. 72
o Break Apart
Divisors (Divide
by 10) TE pp. 73
14
White
Board (1
per
student)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/43
6-dividea-wholenumberby-apowerof-ten
2.5 Dividing by 2-Digit
Numbers
3 days
1. Divide a 2-, 3-, or
4-digit number by a
2-digit number.
CCCS:
5.NBT.B.6
MP:
Example: 9984 ÷ 64
MP 2
An area model for
division is shown
below. As the
student uses the area
model, s/he keeps
track of how much of
TE-5A:
pp. 82-89
Blackline
Master
TR02
White
Board (1
per
student)
Core:
SB-5A:
pp. 82-89
WKBK-5A:
pp. 49-54
Learn
Zillions
Video
http://le
arnzillio
o Use Place Value to
Find a Rule
(Divide by 100,
1,000) TE pp. 76
o Break Apart
Divisors (Divide
by 100, 1,000) TE
pp. 78
o Find Divisors of a
Given Whole
Number TE pp. 80

Let’s Explore (Work in
Pairs) TE pp. 81
o Use a place value
chart to divide
whole numbers
that are not
multiples of 10.

Let’s Practice TE pp. 81

5-Minute Warm Up TE
pp. 82
Learn Zillions Video-Area
Model Division
Math Discussion TE pp.
82-89
o Whiteboards
o Use pictorial
examples or
models to help
students
15


the 9984 is left to
divide.
2.6 Order of Operations
2 days
1. Use order of
operations to
simplify a numeric
expression.
2. Evaluate
numerical
expressions with
parentheses,
brackets, and braces.
Ex: 3{2 + 6 [5 + (2 x
10)]+ 3}
Ex: Write an
expression for the
steps “double six and
then add 28.”
ExtraP-5A:
pp. 29-30
n.com/le
ssons/55
2-divideBasic
4digitReteachdividend
5A:
s-bypp.53-62
2digitdivisorsAdvanced: by-usingEnrichmen an-area- 
t 5A:
model
pp.9-19

CCCS:
5.NBT.B.5
5.NBT.B.6
5.OA.A.1
5.OA.A.2
MP:
MP 1
MP 3
MP 6
MP 7
TE-5A:
pp. 96-108
Blackline
Master
TR12,
TR13
Common
Core
Lessons
and
Activities
E-Book
2.6.A
(thinkcent
ral.com)
Core:
SB-5A:
Number/ 
Symbol
Cards
(TR12)

(per
pair)

Table of
Numeric
Expressi
ons
(TR13)
(per
pair)
Calculato
r per
student
understand the
procedure for
dividing a 2-digit
number by a 2digit number,
rather than having
them memorize
the steps
Let’s Practice TE pp. 89
Math Journal TE pp. 89
o Students reflect on
the multi-step
division procedure
5-Minute Warm Up TE
pp. 90
You Tube Video-Writing
Simple Expressions
Math Discussion TE pp.
90-108; Common Core
Lessons and Activities EBook 2.6.A
(ThinkCentral.com)
o Whiteboards
o To encourage
students to check
which operations
are in an
expression before
they begin their
16
(2x6)+28
pp. 96-108
WKBK-5A:
pp. 63-74
ExtraP-5A:
pp. 33-40
White
Board (1
per
student)
Basic
Reteach5A:
pp. 71-78
You Tube
Video
(Writing
simple
expressi
Advanced: ons)
Enrichmen http://w
t 5A:
ww.yout
pp.9-19
ube.com
/watch?v 
=OCP0DJ
LiE2M
calculations, have
them circle the
first pair of
numbers they will
simplify. To do
this, they will have
to look at the
entire expression
to see if it includes
parentheses,
multiplication, or
division before
they begin to
simplify.
Hands-On Activity (work
in pairs) TE pp. 94
o Form Expressions
with Two or More
Operations and
Simplify
o Number/Symbol
Cards (TR12)

Let’s Explore (work in
pairs) TE pp. 95
o Students explore
the meaning of
“left to right” in
the order of
operations (TR13)

Let’s Practice TE pp. 95
17
2.7 Real-Word Problems:
Multiplication and Division
1. Use efficient
strategies to solve
multi-step problems
involving
multiplication and
division.
CCCS:
5.NBT.B.5
5.NBT.B.6
5.OA.A.1
5.OA.A.2
MP:
2. Express and
MP 1
interpret the product MP 2
or quotient
MP 4
appropriately.
MP 5
MP 7
MP 8
3 days
TE-5A:
pp. 96-108
Core:
SB-5A:
pp. 96-108
WKBK-5A:
pp. 63-74
ExtraP-5A:
pp. 33-40
Calculato 
r per
pair

Basic
Reteach5A:
pp. 71-78
Advanced:
Enrichmen
t 5A pp. 919
5-Minute Warm Up TE
pp. 96
Math Discussion TE pp.
96-108
o Whiteboards
o Student
Notebook/Journal
o For additional
practice in solving
real-world
problems, after
completing
targeted guided
practice exercises,
have volunteers
replace the
numbers in a
problem with new
numbers, and then
solve the new
problem following
the same
procedure.

Let’s Practice TE pp. 102,
107-108

Math Critical Thinking
and Problem Solving TE
pp. 109
18
Chapter Wrap Up
Chapter Assessment
1. Reinforce and
consolidate chapter
skills and concepts.
2 days
CCCS:
5.NBT.A.1
5.NBT. A.2
5.NBT.B.5
5.NBT.B.6
5.OA.A.1
5.OA.A.2
5.OA.B.3
MP:
MP.1
MP.2
TE-5A:
pp. 110113
Assessmen
t Book
pp. 13-16
Core:
SB-5A:
pp. 110113
Chapter Wrap Up Study
Guide TE pp. 110-111
Chapter Review TE pp. 112113
Unit 2 Assessment
(Assessments 5 pp. 13-16)

INSTRUCTIONAL FOCUS OF UNIT
Students use a calculator to perform the four operations on whole numbers.
Students multiply numbers by 10, 100, or 1,000 using patterns and multiply numbers up to 4 digits by 2-digit numbers using
conventional algorithms.
Students round numbers to estimate products and use them to check the reasonableness of their answers.
Students divide numbers by 10, 100, or 1,000 using patterns and divide numbers up to 4 digits by 2-digit numbers using
conventional algorithms. The inverse relationship between multiplication and division is pointed out as needed.
Students simplify numeric expressions using the order of operations and solve real-world multiplication and division problems
using tools and strategies including bar models and organized lists.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 2 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 2





19

Example of Key Advances from Grade 4 to Grade 5
o Students extend their grade 4 work in finding whole-number quotients and remainders to the case of two-digit divisors
(5.NBT.6).
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Multiplication and Division of
Whole Numbers
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on multiplication and division of whole
numbers for unit 2. Apply skills and knowledge learned on
multiplication and division of whole numbers to real world
scenarios given in the menu. Complete at least 15 points out of the
20 points available (80% and higher).
Critical Thinking:
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to the
multiplication and division. Evaluate real world problems
through the application of whole number concepts by completing
various critical thinking activities with at least 85% accuracy.
Math Journal
 Explain why, when using place value and regrouping to
multiply a 3-digit number by a 2-digit number, the second
partial product is always greater than the first.
 In your own words, describe a pattern that you can use
with the dividend and quotient when dividing the
expressions 32  8, 320  8, 3,200  8, and 32,000  8.
 When you divide, one way to check your answer is to
compare it to your estimate. When should an estimate not
be used to check your answer?
 Explain the different ways that you can use multiplication
to estimate and solve division problems.
20

Explain and give two examples to show how using
parenthesis, brackets, and braces can change the order in
which operations are performed in an expression.
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Hogwarts House
Cup (pp. 25-29
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit1FrameworkSE.pdf)

Task can be broken
up into 3 parts.
TLWBAT: Explore writing expressions and equations as well as
simplifying expression in the context of points earned at Hogwarts
with at least 80% accuracy
Communication – Power points/Presentations
MODIFICATIONS/ACCOMMODATIONS


Whiteboards (1 per student)
Additional Support (ELL, Struggling Learners) TE 5A pp. 41B
21
APPENDIX
(Teacher resource extensions)
CCCS:
5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its
right and 1/10 of what it represents in the place to its left.
5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote
powers of 10.
5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.B.6 Find whole number quotients of whole numbers with up to four digit dividends and two digit divisors, using strategies
based on place value, the properties of operations and/or the relationship between multiplication and division. Illustrate and explain
the calculation by using equations, rectangular arrays, and/or area models.
5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating
them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three
times as large as 18932 + 921, without having to calculate the indicated sum or product.
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Online Resources
Lesson 2.2; 2.4
Powers of Ten Worksheets
http://www.math-drills.com/powersoften.shtml
Lesson 2.6
Brainpop Video Order of Operations
http://www.brainpop.com/math/numbersandoperations/orderofoperations/
Order of Operations Game (IXL)
22
http://www.ixl.com/math/grade-5/simplify-expressions-using-order-of-operations-and-parentheses
Unpacking the Standards (Examples and Rationales)
Lesson 2.2, 2.3, 2.4, 2.5, 2.6
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
23
UNIT 3
Fractions and Mixed Numbers
Total Number of Days:25 Grade/Course: 5/Math





ESSENTIAL QUESTIONS
How can decomposing fractions or mixed numbers help
us model fraction multiplication?
How can fractions with different denominators be
added together?
How can making equivalent fractions and using models
help us solve problems?
What do equivalent fractions have to do with adding and
subtracting fractions?
What strategies can we use for adding and subtracting
fractions with different denominators?





ENDURING UNDERSTANDINGS
Fractions are relations – the size or amount of the whole matters.
Equivalent fractions represent the same value.
With unit fractions, the greater the denominator, the smaller the
piece is.
Pieces don’t have to be congruent to be equivalent.
Fractions and decimals are different representations for the
same amounts and can be used interchangeably
RESOURCES
PACING
3 days
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of fractions
from fourth grade
SKILLS
STANDARD
S
(CCCS/MP)
1. Find equivalent
5.NF.A.1
fractions and express
fractions in simplest
form
2. Represent
fractions on a
number line.
3. Identify prime and
composite numbers
Math in
Focus
Assessmen
ts:
pp. 13-16
TE 5-A:
pp. 114121
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
Pre-Assessment:
Chapter 3 Test Prep
Assessment
Assessment Book 5 pp. 21-24
Chapter Opener- TE pp. 114121
Quick Check TE pp. 121
Core:
24
3. 1 Adding Unlike
Fractions
4. Add and subtract
fractions with like
and unlike
denominators.
5. Express fractions
and decimals.
1. Add two unlike
fractions where one
denominator is not a
multiple of the other.
2. Estimate sums of
fractions.
2 day
SE 5-A:
pp. 114121
CCCS:
5.NF.A.1
5.NF.A.2
MP:
MP 1
MP 2
MP 3
MP 6
TE-5A:
pp.122126
Blackline
Master
TR14
Core:
SB-5A:
pp. 122126
WKBK-5A:
pp. 93-98
ExtraP-5A:
pp.47-48
Basic
Reteach5A:
pp. 79-78
Fraction
Circles
(TR14)
for the
teacher



White
Board (1
per
student)
Fraction
Tiles
(Math In
Focus
Manipula
tive Kit)
Learn
Zillions
Video
Advanced: http://le
Enrichmen arnzillio
t 5A:
n.com/le
pp. 20-29
ssons/97
3-addfractions
-withdifferent

5-Minute Warm Up TE
pp. 122
Learn Zillions Video: Add
Unlike Fractions
Math Discussion TE pp.
122-126
o White Boards
o Fraction Tiles
o Have students
compare the
numerators and
denominators in
fractions that are
closer to 0 and
those that are
closer to 1. Have
them generalize
their observations.
Guide students to
see that lesser
numerators are
closer to 0. A
fraction with
numerator and
denominator of
about the same
value close to 1.
Hands-On Activity: (work
in pairs) TE pp. 123
25
denomin
atorsusingfractionbars
3.2 Subtracting Unlike
Fractions
2 days
1. Subtract two
unlike fractions
where one
denominator is not a
multiple of the other.
2. Estimate
differences of
fractions.
CCCS:
5.NF.A.1
5.NF.A.2
MP:
MP 1
MP 2
MP 3
MP 6
MP 8
TE-5A:
pp. 127130
Blackline
Master
TR14
Core:
SB-5A:
pp. 127130
WKBK-5A:
pp. 99-102
ExtraP-5A:
pp. 49-50
Fraction
Circles
(TR14)
for
teacher
White
Board (1
per
student)
Fraction
Tiles
(Math In
Focus

o Model Adding
Unlike Fractions
Using a Computer
Let’s Explore: TE pp. 125
o Estimate sums of
fractions using
benchmark

Math Journal TE pp. 125
o Students reflect on
the models
showing the
addition of
fractions and
recognize the
common mistakes
made when
drawing models.


Let’s Practice: TE pp.126
5-Minute Warm Up TE
pp. 127
Learn Zillions VideoSubtract Unlike Fractions
Math Discussion TE pp.
127-130
o Whiteboards
o Fraction Tiles
o Have students
compare the form
of the number line
here to the one on
page 124. Point
out that if you


26
Basic
Reteach5A:
pp. 89-94
Manipula
tive Kit)
Learn
Zillions
Video
Advanced: http://lea
Enrichmen rnzillion.c
t 5A:
om/lesso
pp. 20-29
ns/974subtractfractionswithdifferent- 
denomina
torsusingfractionbars

3.3 Fractions, Mixed
Numbers, and Division
Expressions
2 days
1. Understand and
apply the
relationship between
fractions, mixed
numbers, and
division expressions.
CCCS:
5.NF.A.2
5.NF.B.3
MP:
MP 2
MP 4
MP 5
MP 6
TE-5A:
pp.131136
Blackline
Master
TR15
Core:
SB-5A:
White
Board (1
per
student)
Fraction
Tiles
(Math In




were to a draw a
number line that
shows both 8/9
and 4/10, you
would need a
number line with
90 intervals.
Explain that
instead, you can
draw two number
lines one for each
fraction.
Hands-On Activity TE pp.
128
o Model subtracting
unlike fractions
using a computer.
Let’s Explore: TE pp. 129
o Estimate
differences
between fractions
using benchmarks.
Let’s Practice TE pp. 130
5-Minute Warm Up TE
pp. 131
Learn Zillions: Writing
Improper Fractions
Math Discussion TE pp.
131-136
o Whiteboards
o Fraction Tiles
27
MP 8
pp. 131136
WKBK-5A:
pp. 103106
ExtraP-5A:
pp. 49-50
Basic
Reteach5A:
pp. 89-94
Focus
Manipula
tive Kit)
Strips of
Paper
(TR15)
per
group
Learn
Zillions
Video
Advanced: http://le
Enrichmen arnzillio
t 5A:
n.com/le
pp. 20-29
ssons/92
-writeimprope
rfractions


o Help students
make
generalizations
about the
relationships
between division
expressions and
mixed numbers.
Student should
understand that
the division
expression for
mixed numbers
and improper
fractions always
has a divisor less
than the dividend.
For the fractions,
the divisor is
always greater
than the dividend.
Hands on Activity (TR15)
o Write division
expressions and
fractions. TE pp.
133
o Write division
expressions,
improper
fractions, and
mixed numbers.
TE pp. 135
Let’s Practice TE pp. 136
28
3.4 Expressing Fractions,
Division Expressions, and
Mixed Numbers as
Decimals
1. Express fractions,
division expressions,
and mixed numbers
as decimals.
CCCS:
5.NF.2
5.NF.3
MP:
MP 6
TE-5A:
pp. 137139
Blackline
Master
TR16
Core:
SB-5A:
pp. 137139
WKBK-5A:
pp. 107108
ExtraP-5A:
pp. 53-54
3 days
Decimal
Models
(TR16)
for the
teacher


White
Board (1
per
student)
5-Minute Warm Up TE
pp. 137 TR16
Math Discussion TE pp.
137-139
o Whiteboards
o Provide practice
on finding factors
students can use
to make products
of 10 and 100.

Let’s Practice TE pp. 139

5-Minute Warm Up TE
pp. 140
Learn Zillions VideoAdding Mixed Numbers
Math Discussion TE pp.
140-144
o Whiteboards
o Fraction Tiles
29
Basic
Reteach5A:
pp.101104
3.5 Adding Mixed Numbers
3 days
1. Add mixed
numbers with or
without renaming.
2. Estimate sums of
mixed numbers
CCCS:
5.NF.A.1
5.NF.A.2
MP:
MP 1
MP3
MP6
Advanced:
Enrichmen
t 5A:
pp.20-29
TE-5A:
pp. 140White
144
Board (1
per
Core:
student)
SB-5A:
pp. 140Fraction
144
Tiles


WKBK-5A:
pp. 109112
ExtraP-5A:
pp. 55-56
(Math In
Focus
Manipula
tive Kit)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/11
Advanced: 9-addEnrichmen andt 5A:
subtractpp.20-29
mixednumbers
-bygrouping
-andrenamin
g
o Discuss
similarities and
differences
between adding
fractions and
adding mixed
numbers.
Encourage
students to apply
what they know
about adding
fractions to adding
mixed numbers.
Students should
realize that adding
the fractional
parts of mixed
numbers is the
same as adding
fractions.
Basic
Reteach5A:
pp.105108
3.6 Subtracting Mixed
Numbers
3 days
1. Subtract mixed
numbers with or
without renaming.
CCCS:
5.NF.A.1
5.NF.A.2
TE-5A:
pp. 145149
2. Estimate
differences between
mixed numbers.
MP:
MP 4
MP 6
Core:
SB-5A:
pp. 145149
White
Board (1
per
student)
Fraction
Tiles
(Math In

Let’s Explore: TE pp. 143
o Estimate sums of
mixed numbers
using benchmarks.


Let’s Practice TE pp. 144
5-Minute Warm Up TE
pp. 145
Learn Zillions VideoSubtracting Mixed
Numbers
Math Discussion TE pp.
145-149
o Whiteboards
30


WKBK-5A:
pp. 113116
ExtraP-5A:
pp. 57-58
Focus
Manipula
tive Kit)
Learn
Zillions
Basic
Video
Reteachhttp://le
5A:
arnzillio
pp. 109n.com/le
112
ssons/11
7Advanced: subtractEnrichmen mixedt 5A: pp.
numbers
20-29
decompo
singwholes
3.7 Real-Word Problems:
Fractions and Mixed
Numbers
4 days
1. Solve real-world
problems involving
fractions and mixed
numbers.
CCCS:
5.NF.A.1
5.NF.A.2
5.NF.B.3
MP:
MP 1
MP 7
MP 8
TE-5A:
pp. 150155
Blackline
Master TR
17
Core:
SB-5A:

Calculato 
r per
pair

o Fraction Tiles
o Discuss the
similarities and
differences
between
subtracting
fractions and
subtracting mixed
numbers.
Encourage
students to apply
what they know
about subtracting
fractions to
subtracting mixed
numbers.
Students should
realize that
subtracting the
fractional parts of
mixed numbers is
the same as
subtracting
fractions.
Let’s Practice TE pp. 95
5-Minute Warm Up TE
pp. 150
Math Discussion TE pp.
150-153
o Calculator
o Student
Notebook/Journal
o Display a poster
31
pp. 150155
WKBK-5A:
pp. 117130
ExtraP-5A:
pp. 59-64
Basic
Reteach5A:
pp. 113116
showing key
phrases that serve
as clues when to
add, subtract, or
use division
expression to
solve problems in
this lesson.


Let’s Practice TE pp. 153
Math Journal: TE pp. 154
o Students reflect on
adding unlike
fractions and
recognize the
common mistakes
made when
adding unlike
fractions.

Math Critical Thinking
and Problem Solving TE
pp. 155
Advanced:
Enrichmen
t 5A pp.
20-29
Chapter Wrap Up
Chapter Assessment
3 days
1. Reinforce and
consolidate chapter
skills and concepts.
CCCS:
5.NF.A.1
5.NF.A.2
5NF.B.3
MP:
MP.1
MP.2
TE-5A:
pp. 156159
Assessmen
t Book
pp. 21-24
Core:
SB-5A:
pp. 156-
Chapter Wrap Up Study
Guide TE pp. 156-157
Chapter Review TE pp. 158159
Unit 3 Assessment
(Assessments 5 pp. 21-24)
32
159




INSTRUCTIONAL FOCUS OF UNIT
Students add and subtract unlike fractions by rewriting the fractions as like fractions using the concept of least common
denominator and equivalent fractions. This is an extension of what students have learned about adding and subtracting fractions.
Students explore the relationships and equivalences among fractions, mixed numbers, division expressions, and decimals, before
they add and subtract mixed numbers.
Having mastered fraction skills, students translate real-world problems into division expressions and solve them.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 3 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 3
o Sara and Harry are putting together a puzzle. Sara put together 7/12 of the puzzle pieces. Harry put together 7/24of the
puzzle pieces. What fraction of the total number of puzzle pieces has NOT been used?
o Tom makes a cake for a class party. The recipe calls for 5/8 cup of orange juice and 5/12 cup of water. Can Tom use a onecup container to hold both the orange juice and water at the same time? Explain your thinking.
o Maria had 9 liters of lemonade. She poured all of the lemonade into 6 pitchers so that there was an equal amount in each
pitcher. How many liters of lemonade did Maria pour into each pitcher?

Example of Key Advances from Grade 4 to Grade 5
o Students use their understanding of fraction equivalence and their skill in generating equivalent fractions as a strategy to
add and subtract fractions, including fractions with unlike denominators.
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Adding and Subtracting Unlike
Fractions.
 Point percentage Menu where students will pick any
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on addition and subtractions of unlike
fractions for unit 3. Apply skills and knowledge learned on
addition and subtraction of fractions to real world scenarios given
33
activity in order to reach a certain amount of points for the
project.
Critical Thinking:
Math Journal
 Give an example of an instance where you might want to
find an estimate for fraction sums or differences rather
than an exact answer.
 Draw and explain how you can use a number line to
rename a fraction greater than 1 as a mixed number.
 Describe how adding and subtracting mixed numbers can
help you with recipes.
 Explain when you know you need to rename a mixed
number to subtract.
in the menu. Complete at least 15 points out of the 20 points
available (80% and higher).
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to the addition
and subtraction of fractions. Evaluate real world problems
through the application of fraction concepts by completing
various critical thinking activities with at least 85% accuracy.
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Up and Down the
Number Line (pp.78-83
https://www.georgiastandards.org/Common-
TLWBAT: Use their fractional understandings to add and subtract
fractions and look for relationships between certain fractions with at
least 80% accuracy
34

Core/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit4FrameworkSE.pdf)
In this task students
spin a spinner to move their counters up and/or down the
number line. The first to move to their side of the number line
wins the game. This game will allow students to use their
fractional understandings to add and subtract fractions, look
for relationships between certain fractions, and as their
fractional computation strategies develop, logical thinking and
problem solving skills will begin to develop their game
playing strategies.
Communication – Power points/Presentations
MODIFICATIONS/ACCOMMODATIONS



Whiteboards
Fraction Tiles
Additional Support (ELL, Struggling Learners) TE 5A pp. 114B
APPENDIX
(Teacher resource extensions)
CCCS:
5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with
equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3
+ 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike
denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense
of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7,
by observing that 3/7 < 1/2.
5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving the
division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g. by using visual fraction models or
equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3
and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50 pound sack
of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
35
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Online Resources
Learn Zillions Video (Estimating with Benchmarks)
http://learnzillion.com/lessons/1049-estimate-the-addition-of-fractions-with-unlike-denominators-using-a-benchmarkfraction
Additional Hands-On Activity
https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit4FrameworkSE.pdf
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
36
UNIT 4
Multiplying and Dividing Fractions and Mixed Numbers
Total Number of Days: 24 Grade/Course: 5/Math





ESSENTIAL QUESTIONS
How can decomposing fractions or mixed numbers help
us multiply fractions?
How can fractions be used to describe fair shares?
How can modeling an area help us with multiplying
fractions?
How can we model dividing a unit fraction by a whole
number with manipulatives and diagrams?
How can we tell if a fraction is greater than, less than, or
equal to one whole






ENDURING UNDERSTANDINGS
A fraction is another representation for division
Fractions are relations – the size or amount of the whole matters.
Equivalent fractions represent the same value.
With unit fractions, the greater the denominator, the smaller the
piece is.
Pieces don’t have to be congruent to be equivalent.
Fractions and decimals are different representations for the
same amounts and can be used interchangeably
RESOURCES
PACING
3 days
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of fractions
from fourth grade
SKILLS
1.Express fractions
as decimals.
2. Multiply fractions
by a whole number.
3. Find the number
of units to solve a
problem.
4. Draw a model to
represent a problem.
STANDARD
S
(CCCS/MP)
5.NF.B.4
5.NF.B.5
Math in
Focus
Assessmen
ts: pp. 2932
TE 5-A:
pp. 160164
Core:
SE 5-A:
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
Pre-Assessment:
Chapter 4 Test Prep
Assessment
Assessment Book 5 pp. 29-32
Chapter Opener- TE pp. 160164
Quick Check TE pp. 164
37
4.1 Multiply Proper
Fractions
1. Multiply proper
fractions
CCCS:
5.NF.B.4.a
5.NF.B.4.b
5.NF.B.5.a
5.NF.B.5.b
5.NF.B.6
MP:
MP 3
MP 4
MP 5
MP 6
2 day
pp. 160164
TE-5A:
pp.165168
Blackline
Master
TR18
Core:
SB-5A:
pp. 165168
WKBK-5A:
pp. 131132
ExtraP-5A:
pp.69-70
Basic
Reteach5A:
pp. 117122
Grid
Paper
(TR18)
per pair

1 yellow
and 1
blue
crayon
per pair


White
Board (1
per
student)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
Advanced: ssons/12
Enrichmen 8t 5A:
multiplypp. 30-38
fractions
-byfractions
-using-a- 
sequence
-ofoperatio
5-Minute Warm Up TE
pp. 165
Learn Zillions Video:
Multiply fractions by
fractions
Math Discussion TE pp.
165-168
o White Boards
o This lesson
presents two
methods for
multiplying
proper fractions
(with or without
models). Some
students may
prefer one method
to the other.
Encourage
students to use
whichever method
that works best
for them. Have
them share their
reasons for
preferring that
method with
classmates.
Hands-On Activity: (work
in pairs) TE pp. 167
(TR18)
o Make area models
38
ns
4.2 Real-World Problems:
Multiplying with proper
fractions.
2 days
1. Solve real-world
problems involving
multiplication of
proper fractions.
CCCS:
5.NF.B.4.a
5.NF.B.6
MP:
MP 1
TE-5A:
pp. 169174
Blackline
Master
TR17
Core:
SB-5A:
pp. 169174
WKBK-5A:
pp. 133138
ExtraP-5A:
pp. 71-76
Basic
Table of
Measure
s (TR17)
as
needed
White
Board (1
per
student)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
to multiply two
fractions
(commutative
property)

Let’s Explore: TE pp. 168
o Explore the
difference
between
multiplying two
whole numbers
and multiplying
two proper
fractions.


Let’s Practice: TE pp.168
5-Minute Warm Up TE
pp. 169
Learn Zillions VideoMultiply fractions
Math Discussion TE pp.
169-174
o Whiteboards
o Many of the
problems in this
lesson involve
subtracting
fractions. You
may wish to
review converting
unlike fractions to
like fractions, and
subtracting a
fraction from a
39


Reteach5A:
pp. 123128
4.3 Multiplying Improper
Fractions by Fractions
1. Multiply improper
fractions by proper
or improper
fractions.
CCCS:
5.NF.B.4.a
5.NF.B.4.b
5.NF.B.5.b
MP:
MP 2
MP 4
MP 5
MP 6
MP 8
1 days
ssons/12
4multiplyfractions
-byAdvanced: whole
Enrichmen numbers
t 5A:
pp. 30-38
describin
g-theproblem
TE-5A:

pp.175White
176
Board (1 
per
Core:
student)
SB-5A:
pp. 175176
WKBK-5A:
pp. 139142
ExtraP-5A:
pp. 77-76
Basic
Reteach5A:
pp. 123128
Advanced:
Enrichmen
t 5A:
pp. 30-38
whole number
before beginning
this lesson.
Let’s Practice TE pp. 174
5-Minute Warm Up TE
pp. 175
Math Discussion TE pp.
175-176
o Whiteboards
o After explaining
the two methods,
discuss the
similarities and
differences
between
multiplying
proper fractions
and multiplying a
proper and
improper fractions
with students.
Students should
understand that
the procedure is
the same-only the
factors are
different.
40
4.0 Multiplying Whole
Numbers and Proper
Fractions
1. Compare the size
of the product to the
size of its factors.
CCCS:
5.NF.B.5.a
MP:
MP 3
MP7
MP8
1 day
Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent
ral.com)
Chapter 4
Lesson 4.0
White
Board (1
per
student)

Let’s Practice TE pp. 176

Math Discussion
(thinkcentral.comcommon core focus
lesson 4.0)
o Whiteboards
Let’s Explore
o Explore the
differences
between
multiplying with
whole numbers
and proper
fractions.


4.4 Multiplying Mixed
Numbers and Whole
Numbers
2 days
1. Multiply a mixed
number by a whole
number.
CCCS:
5.NF.B.4.a
5.NF.B.5.b
5.NF.6
MP:
MP 1
MP3
MP5
MP6
TE-5A:
pp. 177180
Core:
SB-5A:
pp. 177180
WKBK-5A:
pp. 143146
ExtraP-5A:
pp. 79-80
White
Board (1
per
student)
4 sheets
of blank
paper
per
student
Learn
Zillions



Let’s Practice-common
core focus lesson 4.0
5-Minute Warm Up TE
pp. 177
Learn Zillions VideoMultiplying Mixed
Numbers
Math Discussion TE pp.
177-180
o Whiteboards
o Have students
work in pairs or
small groups to
complete the
Hands-On Activity.
Be sure each
41
Basic
Reteach5A:
pp. 129130
Video
http://le
arnzillio
n.com/le
ssons/12
9Advanced: multiplyEnrichmen mixedt 5A: pp.
numbers
30-38
-usingpictures 

4.5 Real-World Problems:
Multiplying with Mixed
Numbers
2 days
1. Solve real-world
problems involving
multiplication of
whole numbers and
mixed numbers.
CCCS:
5.NF.B.4.a
5.NF.B.6
TE-5A:
pp. 181184
MP:
MP 1
MP 7
Core:
SB-5A:
pp. 181184
WKBK-5A:
pp. 147148
ExtraP-5A:
White
Board (1
per
student)



group has at least
14 pieces of paper
to complete the
first activity. Then
encourage
students to use
their paper
models to
complete the Let’s
Explore section.
Hands-On Activity-TE
179
o Make a model to
multiply a mixed
number and a
whole number.
Let’s Explore: TE pp. 179
o Use models to
break apart mixed
numbers as
products
Let’s Practice TE pp. 180
5-Minute Warm Up TE
pp. 181
Math Discussion TE pp.
145-149
o Whiteboards
o Review the
procedures for
changing a
fraction to a
decimal on page
162 of the student
book. You may
42
pp. 81-82
Basic
Reteach5A:
pp. 135136
Advanced:
Enrichmen
t 5A: pp.
30-38
4.6 Dividing a Fraction by a
Whole Number
2 days
1. Divide a fraction
by a whole number.
CCCS:
5.NF.B.7.a
5.NF.B.7.c
TE-5A:
pp. 185189
MP:
MP 1
MP 4
MP 5
MP 6
Core:
SB-5A:
pp. 185189
WKBK-5A:
pp. 149152
ExtraP-5A:
pp. 83-86
Basic
Reteach5A:
pp. 137140
Whitebo
ard (1
per
student)




2 sheets
of blank
paper
per
student
1 colored
pencil
per pair
Learn
Zillion
Video
http://le
Advanced: arnzillio
Enrichmen n.com/le

want to make a list
of common
fractions and their
decimal
equivalents, for
example: 1/5=0.2;
¼=0.25; ½=0.5;
¾= 0.75. Students
can use this list as
a reference for this
chapter as
necessary.
Let’s Practice TE pp.184
5-Minute Warm Up TE
pp. 185
Learn Zillion VideoDividing Fractions
Math Discussion TE pp.
185-189
o Whiteboard
o This lesson
presents three
methods for
dividing a fraction
by a whole
number. Have
students explain
which method
they prefer and
why.
Hands-On Activity-TE pp.
188
o Make a model to
divide a fraction
43
t 5A pp.
30-38
4.6.a Dividing a Whole
Number by a Unit Fraction
1. Divide a whole
number by a unit
fraction.
CCCS:
5.NF.B.7.b
1. Solve real-world
problems involving
multiplication and
division in fractions.
CCCS:
5.NF.B.7.a
5.NF.B.7.c
TE-5A:
pp. 190198
MP:
MP 1
MP 2
MP 7
MP 8
Core:
SB-5A:
pp. 190198
WKBK-5A:
pp. 153158
MP:
MP 4
MP 7
1 day
4.7 Real-World Problems:
Multiplying and Dividing
with Fractions
3 days
Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent
ral.com)
Chapter 4
Lesson
4.6.a
ssons/13
0-divideunitfractions
drawingpictures
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/13
4-dividewholenumbers
-byfractions
-usinginverserelations
by a whole
number

Let’s Practice TE pp. 189

Math Discussion
(thinkcentral.comcommon core focus
lesson 4.6.a)
o Whiteboards
Let’s Practice-common
core focus lesson 4.6.a

5-Minute Warm Up TE
pp. 190
Math Discussion TE pp.
190-194

o Student
Notebook/Journal
o This lesson
presents several
types of realworld problems
44
ExtraP-5A:
pp. 87-92
Basic
Reteach5A:
pp. 141142
Advanced:
Enrichmen
t 5A pp.
30-38



with three
methods of solving
them. After each
Learn example,
have students
make up their own
word problems
using those in the
Learn examples as
a model. Students
can then solve the
problem using one
of the three
methods. Have
students share
and compare
problems and
solutions before
moving on to the
next Learn
example.
Let’s Practice TE pp. 197
Math Journal: TE pp. 198
o Students reinforce
their
understanding of
dividing fractions
by whole
numbers, and
multiplying
proper fractions.
Critical Thinking and
Problem Solving-TE pp.
199
o These activities
45
require students
to apply strategies
of looking for
patterns and
drawing a model
to solve problems.
4.7.a Real-World Problems: 1. Solve real-world
Dividing a Whole Number
problems involving
by a Unit Fraction
division of a whole
number by a unit
fraction.
1 day
Chapter Wrap Up
Chapter Assessment
3 days

1. Reinforce and
consolidate chapter
skills and concepts.
CCCS:
5.NF.B.7.c
MP:
MP 2
MP 4
CCCS:
5.NF.B.4
5.NF.B.5
5NF.B.6
5.NF.B.7
MP:
MP.1
MP.2
Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent
ral.com)
Chapter 4
Lesson
4.7.a
TE-5A:
pp. 200203
Assessmen
t Book
pp. 29-32
Core:
SB-5A:
pp. 200203
Whitebo
ards (1
per
student)


Math Discussion
(thinkcentral.comcommon core focus
lesson 4.7.a)
o Whiteboards
Let’s Practice-common
core focus lesson 4.7.a
Chapter Wrap Up Study
Guide TE pp. 200-201
Chapter Review TE pp. 202203
Unit 4 Assessment
(Assessments 5 pp. 29-32)
INSTRUCTIONAL FOCUS OF UNIT
Students multiply proper fractions using models and then apply what they have learned to solve real-world problems.
46


Students multiply an improper fraction by an improper or proper fraction, a mixed number by a whole number, and apply what
they have learned to solve real-world problems.
Students divide a fraction by a whole number and apply what they have learned to solve real-world problems.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 4 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 4

47

Example of Key Advances from Grade 4 to Grade 5
o Students apply and extend their previous understanding of multiplication to multiply a fraction or whole number by a
fraction (5.NF.4). They also learn the relationship between fractions and division, allowing them to divide any whole number
by any nonzero whole number and express the answer in the form of a fraction or mixed number (5.NF.3). And they apply
and extend their previous understanding of multiplication and division to divide a unit fraction by a whole number or a
whole number by a unit fraction.
o Students able to multiply fractions in general can develop strategies to divide fractions in general by reasoning about the
relationship between multiplication and division. But the division of a fraction by a fraction is not a requirement in this
grade.
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Multiplying and Dividing Fractions.
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
Critical Thinking:
Math Journal
 How can decomposing fractions or mixed numbers help us
model fraction multiplication?
 How can we describe how much someone gets in a fair-share
situation if the fair share is less than 1?
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on multiplication and division of
fractions for unit 4. Apply skills and knowledge learned on
multiplication and division of fractions to real world scenarios
given in the menu. Complete at least 15 points out of the 20 points
available (80% and higher).
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to the
multiplication and division of fractions. Evaluate real world
problems through the application of fraction concepts by
completing various critical thinking activities with at least 85%
48

How can we model dividing a unit fraction by a whole number
with manipulatives and diagrams?
accuracy.
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Comparing MP3’s
(pp.90-101 https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit4FrameworkSE.pdf)

This task was
developed to give students a real world application of
multiplying fractions that would be engaging. It also allows
students to take the concept of arrays, which they should have
worked with extensively in their study of multiplication, and
apply this familiar concept to another area of multiplication –
fractions. The relationships between factor sizes and products
can be discovered and generalized as students study partial
products.
Communication – Power points/Presentations
TLWBAT: Extend their knowledge of whole numbers multiplication
to fraction multiplication by using concepts of arrays and distributive
property to compare the dimensions of MP3 players with 80%
accuracy.
49
MODIFICATIONS/ACCOMMODATIONS


Whiteboards
Additional Support (ELL, Struggling Learners) TE 5A pp. 160B
APPENDIX
(Teacher resource extensions)
CCCS:
5.NF.B.4.a Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of
operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3 and create a story context for this equation. Do the
same with (2/3) x (4/5) = 8/15. (In general (a/b) x (c/d) = ac/bd.)
5.NF.B.4.b 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 it would be found by multiplying the side lengths. Multiply fractional side lengths to find
areas of rectangles, and represent fraction products as rectangular areas.
5.NF.B.5.a Interpret multiplication as scaling (resizing) by comparing 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.
5.NF.B.5.b Interpret multiplication as scaling (resizing) by explaining why multiplying a given number by a fraction greater than 1
results in a product greater than the given number (recognizing multiplication by whole numbers as a familiar case); explaining why
multiplying a given number less than 1 results in a product smaller than the given number; and relating the principle of fraction
equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.
5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g. by using visual fraction models or
equations to represent the problem.
5.NF.B.7.a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story
context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to
explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.
5.NF.B.7.b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for
4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷
(1/5) = 20 because 20 x (1/5) = 4.
5.NF.B.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by
50
unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each
person get if 3 people share ½ pound of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Online Resources
Learn Zillions Video
5.NF.4.
http://learnzillion.com/lessons?utf8=✓&query=5.nf.4&commit=Go
5.NF.6
http://learnzillion.com/lessons?utf8=✓&filters%5Bsubject%5D=math&query=5.nf.6
5.NF.7
http://learnzillion.com/lessons?utf8=✓&query=5.nf.7&filters%5Bsubject%5D=math&commit=Go
Additional Hands-On Resources
https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit4FrameworkSE.pdf
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
51
UNIT 5
Algebra (6.EE.A.1)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 6.
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
UNIT 6
Area of a Triangle (6.G.A.1)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 6.
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
UNIT 7
Ratios (6.RP.A.1)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 6.
52
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
53
UNIT 8
Decimals
Total Number of Days:13 Grade/Course: 5/Math






ESSENTIAL QUESTIONS
What is the relationship between decimals and
fractions?
How can we read, write, and represent decimal values?
How are decimal numbers placed on a number line?
How can rounding decimal numbers be helpful?
How do we compare decimals?
What strategies can I use to add and subtract decimals?
PACING
3 days
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of decimals
from fourth grade
SKILLS
ENDURING UNDERSTANDINGS

Like whole numbers, the location of a digit in decimal numbers
determines the value of the digit.

Rounding decimals should be “sensible” for the context of the
problem.

Decimal numbers can be represented with models.

Addition and subtraction with decimals are based on the
fundamental concept of adding and subtracting the numbers in like
position values.
RESOURCES
LEARNING
STANDARD
ACTIVITIES/ASSESSMENTS
OTHER
S
(All lessons should begin
Math in
(e.g.,
(CCCS/MP)
with a Do-Now and end
Focus
tech)
with an Exit Ticket)
1.Understanding
4.NF.C.5
tenths and
4.NF.C.6
hundredths.
4.NF.C.7
2. Rounding and
comparing decimals.
3.Expressing
fractions as decimals.
4. Expressing mixed
numbers as
decimals.
Assessmen
ts: pp. 2932
TE 5B:
pp. 1-6
Core:
SE 5B:
pp. 1-6
Pre-Assessment:
Chapter 8 Test Prep
Assessment
Assessment Book 5 pp. 71-73
Chapter Opener- TE B pp. 1-4
Quick Check TE B pp. 5-6
54
8.1 Understanding
Thousandths
3 days
1. Read and write
thousandths in
decimal and
fractional forms.
2. Represent and
interpret
thousandths in
models or in placevalue charts.
3. Write a fraction
with denominator
1,000 as a decimal.
CCCS:
5.NBT.A.1
5.NBT. A.3.a
5.NBT.B.7
MP:
MP 2
MP 3
MP 4
MP 5
MP 6
MP 7
MP 8
TE-5B:
pp. 7-17
Blackline
Master
TR02,
TR29,
TR30,
TR31
Core:
SB-5B:
pp. 7-17
WKBK-5B:
pp. 1-4
ExtraP-5B:
pp.1-4
Base-ten
blocks
for the
teacher
Placevalue
chips for
the
teachers
Number
Lines 1
(TR02)
for the
teacher



PlaceBasic
Value
ReteachChart 1
5B:
(TR29)
pp. 1-8
for the
teacher
Advanced: and 2
Enrichmen copies
t 5B:
per
pp. 1-7
student
Thousan
dths
Models
(TR30)
per
student
Number

5-Minute Warm Up TE B
pp. 7
Learn Zillions Video:
Decimals
Math Discussion TE B pp.
7-17
o White Boards
o To help students
visualize the 1,000
units that the
model on page 7
represents,
demonstrate
stacking 10
hundred-squares.
This will show
that although the
picture only shows
the faces of the
model, each layer
has 100 units.
There are 10
layers, so the
model represents
1,000 units. Point
out that this is
why each unit
stands for 1/1000.
Hands-On Activity: (work
in pairs) TE B pp. 14
(note cards)
o Write a decimal in
different ways
55
Lines 2
(TR31)
per
student

Let’s Practice: TE B
pp.15-17
8 note
cards per
pair
White
Board (1
per
student)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/42
3understa
nd-thatthevalue-ofa-digitin-oneplace-is110-thevalue-ofthe-digitto-theleft56
usingdecimals
8.2 Comparing and
Rounding Decimals
2 days
1. Compare and
order decimals to 3
decimal places.
2. Round decimals to
the nearest
hundredth.
CCCS:
5.NBT.A.1
5.NBT.A.3.b
5.NBT.A.4
MP:
MP 4
MP 7
TE-5B:
pp. 18-22
Blackline
Master
TR02,
TR32
Core:
SB-5B:
pp. 18-22
WKBK-5B:
pp. 5-8
ExtraP-5B:
pp.5-8
Basic
Reteach5B:
pp. 9-10
Connecti
ng cubes
for the
teacher
(7)
PlaceValue
Chart 2
(TR32)
per
student
Number
Lines 1
(TR02)
per
student
White
Board (1
Advanced: per
Enrichmen student)
t 5B:
pp. 1-7
Learn
Zillions
Video
http://le
arnzillio
n.com/le



5-Minute Warm Up TE B
pp. 18
Learn Zillions VideoCompare Decimals
Math Discussion TE pp.
18-22
o Whiteboards
o To help students
draw their
number lines,
demonstrate how
to decide on the
hundredths to
write at the first
and last tick marks
of the number line.
Point out that in
the example, the
hundredth at the
first tick mark
(0.12) is the
hundredth in the
given decimal
(0.123) and the
hundredth at the
last tick mark
(0.13) is one
hundredth more
than the
hundredth in the
57
ssons/56
3compare
decimals
-using-anumberline
8.3 Rewriting Decimals as
Fractions and Mixed
Numbers
2 days
1. Rewrite decimals
as fractions and
mixed numbers in
simplest form.
CCCS:
5.NBT.A.1
5.NBT.A.3.a
MP:
MP 1
MP 2
MP 4
TE-5B:
pp. 23-25
Core:
SB-5B:
pp. 23-25
WKBK-5B:
pp. 9-12
ExtraP-5B:
pp. 9-10
Basic
Reteach5B:
pp. 17-18
Advanced:
Enrichmen
t 5B:
pp. 1-7
White
Board (1
per
student)
given decimal
(0.01 more than
0.12 is 0.13)

Let’s Practice TE B pp.
21-22

5-Minute Warm Up TE B
pp. 23
Math Discussion TE B pp.
23-25
o Whiteboards
o When rewriting
decimals as
fractions, go over
the process stepby-step. For
example, to write
0.08 as decimal,
write the
denominator
based on the
number of decimal
places. 0.08 is a
hundredths
decimal, so the
denominator is
100. Write the
digits that make
up the decimal as
the numerator.
The digit in 0.08 is
58

Chapter Wrap Up
Chapter Assessment
3 days
1. Reinforce and
consolidate chapter
skills and concepts.
CCCS:
5.NBT.A.1
5.NBT.A.3.a
5.NBT.A.3.b
5.NBT.A.4
5.NBT.B.7
MP:
MP.1
MP.2


TE-5B:
pp. 26-29
Assessmen
t Book
pp. 71-73
Core:
SB-5B:
pp. 26-29
8. Write 8/100.
Write the fraction
in simplest form
by dividing the
numerator and
denominator by 4.
Write 2/25.
 Let’s Practice TE B pp. 25
 Critical Thinking and
Problem Solving-TE B pp.
25
o This activity
requires students
to reverse the
process of
rounding.
Chapter Wrap Up Study
Guide TE B pp. 26-27
Chapter Review TE B pp. 2829
Unit 8 Assessment
(Assessments 5 pp. 71-73)
INSTRUCTIONAL FOCUS OF UNIT
Students recognize the relationship between ones, tenths, hundredths, and thousandths. These relationships are reinforced by
using models such as number lines, base-ten blocks, and place-value charts.
Students express fractions or mixed numbers with denominators of 1,000 as decimals. They also express decimals as fractions and
mixed numbers in simplest form.
PARCC FRAMEWORK/ASSESSMENT
59

Online assessment Unit 8 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 4
60

Example of Key Advances from Grade 4 to Grade 5
o In grade 5, students will integrate decimal fractions more fully into the place value system (5.NBT.1-4). By thinking about
decimals as sums of multiples of base-ten units, students begin to extend algorithms for multidigit operations to decimals
(5.NBT.7).
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Decimals.
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on decimals for unit 8. Apply skills and
knowledge learned on decimals to real world scenarios given in
the menu. Complete at least 15 points out of the 20 points
available (80% and higher).
Critical Thinking:
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to decimals
place value. Evaluate real world problems through the application
of decimal concepts by completing various critical thinking
61
Math Journal
 Write four decimal values with the digit 4 in a different
place in each – ones, tenths, hundredths, and thousandths.
Then write a statement that compares the value of the 4 in
the different decimals.
 What is the relationship between decimals and fractions?
activities with at least 85% accuracy.
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

In the Paper (pp.3135 https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit2FrameworkSE.pdf)

In this task, students
will explore the characteristics of words in a 100 word passage
of a newspaper article. They will report their findings in
fraction and decimal forms and order decimals from smallest
to largest.

LAL cross-curricular
activity
Communication – Power points/Presentations
TLWBAT: Write and model numbers smaller than one as decimal
fractions and decimal number and order decimals from smallest to
largest with at least 90% accuracy.
MODIFICATIONS/ACCOMMODATIONS

Whiteboards
62





Base-Ten Blocks
Number Lines
Place-Value Charts
Place-Value Chips
Additional Support (ELL, Struggling Learners) TE 5B pp. 1B
APPENDIX
(Teacher resource extensions)
CCCS:
5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its
right and 1/10 of what it represents in the place to its left.
5.NBT.A.3 Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 =
3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to
record the results of comparisons.
5.NBT.A.4 Use place value understanding to round decimals to any place.
5.NBT.A.7 Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place
value, the properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method
and explain the reasoning used.
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Online Resources
63
Learn Zillions Video Decimals
http://learnzillion.com/lessons/433-round-decimals-to-the-nearest-hundredth-using-a-number-line
http://learnzillion.com/lessons?utf8=✓&query=compare+decimals&commit=Go
http://learnzillion.com/lessons?utf8=✓&filters%5Bsubject%5D=math&query=decimals&filters%5Bgrade%5D%5B%5D=5
&filters%5Bdomain%5D=&filters%5Bstandard%5D=
Additional Hands-On Activities:
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit2FrameworkSE.pdf
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
64
UNIT 9
MUTIPLYING AND DIVIDING DECIMALS
Total Number of Days: 23 Grade/Course: 5/Math





ESSENTIAL QUESTIONS
How does multiplying or dividing by a power of ten
affect the product?
How can we use models to help us multiply and divide
decimals? How do the rules of multiplying whole numbers
relate to multiplying decimals?
What are some patterns that occur when multiplying
and dividing by decimals?
How can we efficiently solve multiplication and division
problems with decimals?
How can we check for errors in multiplication or
division of decimals?



ENDURING UNDERSTANDINGS
Multiplying or dividing a number by 10 or a multiple of 10
determines the placement of the decimal.
Multiplication and division are inverse operations of each other.
Rules for multiplication and division of whole numbers also
apply to decimals.
RESOURCES
PACING
3 days
CONTENT
SKILLS
Recall Prior Knowledge:
Review of previous
knowledge of decimals
from fourth grade and
whole number applications
from Unit 1 and 2.
1.Multiply and divide
numbers by tens,
hundreds, and
thousands.
2.Estimate quotients
and products.
3. Add and subtract
STANDARD
S
(CCCS/MP)
5.NBT.1
Math in
Focus
Assessmen
ts: pp. 7780
TE 5B:
pp. 30-35
Core:
SE 5B:
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
Pre-Assessment:
Chapter 9 Test Prep
Assessment
Assessment Book 5 pp. 77-80
Chapter Opener- TE B pp. 3034
Quick Check TE B pp. 35
65
decimals.
9.1 Multiplying Decimals
1. Multiply tenths
and hundredths by a
1-digit whole
number.
pp. 30-35
CCCS:
5.NBT.A.1
5.NF.B.5.b
5.NBT.B.7
MP:
MP 4
3 days
TE-5B:
pp. 36-42
Blackline
Master
TR33,
TR34,
TR35,
TR36
Core:
SB-5B:
pp. 36-42
WKBK-5B:
pp. 15-20
ExtraP-5B:
pp.13-14
Basic
Reteach5B:
pp. 19-30
Placevalue
chips for
the
teachers
Number
Lines 3
(TR033)
for the
teacher
PlaceValue
Chart 3
(TR34)
for the
teacher
(2)
PlaceValue
Advanced: Charts 4
Enrichmen (TR35)
t 5B:
per
pp. 8-16
student
PlaceValue
Chart 5
(TR36)
for the



5-Minute Warm Up TE B
pp. 36 (TR34)
Learn Zillions Video:
Multiply Decimals using
Area Models
Math Discussion TE B pp.
36-42
o White Boards
o As you present the
methods for
multiplying tenths
by a whole
number, you may
wish to point out
the similarities
and differences
between
multiplying whole
numbers and
decimals.
Students should
realize that in both
procedures, they
multiply one place
at a time. The
main difference is
that when
multiplying
decimals they
need to place the
decimal point
correctly in the
66
teacher
product.
White
Board (1
per

student)
Let’s Practice: TE B pp.42
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/55
6multiplydecimals
-bywholenumbers
-byusing-anareamodel
9.2 Multiplying by Tens,
Hundreds, and Thousands
3 days
1. Multiply tenths
and hundredths by
10, 100, and 1,000.
2. Multiply tenths
and hundredths by
multiples of 10, 100,
CCCS:
5.NBT.A.1
5.NBT.A.2
5.NBT.B.7
5.NF.B.5.b
TE-5B:
pp. 43-50
Blackline
Master
TR37,
TR38,
PlaceValue
chips for
the
teacher
and per



5-Minute Warm Up TE B
pp. 43
Learn Zillions Video:
Multiply Decimals by
Powers of 10
Math Discussion TE B pp.
67
and 1,000
MP:
MP 4
MP 5
MP 6
TR39,
TR40
Core:
SB-5B:
pp. 43-50
WKBK-5B:
pp. 21-24
ExtraP-5B:
pp.13-14
Basic
Reteach5B:
pp. 19-30
Advanced:
Enrichmen
t 5B:
pp. 8-16
pair
43-50
o Whiteboards
o You may wish to
provide visuals to
show how to move
the decimal point
to the right when
multiplying
decimals by 100
and 1,000.
Ruler
and
measuri
ng per
pair
(4)
PlaceValue
Chart 6
(TR37)
for the
teacher

Hands-On Activity:
o Use place-value
charts to show
multiplication of
decimals by 10TE B pp. 44
o Use place-value
charts to show
multiplication of
decimals by 100
and 1,000- TE B
pp.47
o Measure lengths in
decimal form and
multiply the
measurement by
10, 100, 1,000- TE
B pp.49 (ruler and
measuring tape
per pair)

Let’s Practice TE B pp. 50
(2)
PlaceValue
Chart 6
(TR37)
per pair
Table of
Multiplic
ation 1
(TR38)
per pair
Table of
Multiplic
ation 2
(TR39)
per pair
68
Table
Multiplic
ation 3
(TR40)
per
student
White
Board (1
per
student)
9.2.a Multiplying Decimals
by Powers of 10
1 day
1. Multiply decimals
by 10 squared or 10
cubed.
CCCS:
5.NBT.A.2
MP:
MP 8
Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent
ral.com)
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/43
5multiplydecimalnumbers
-by-apowerof-ten
Learn

Zillions
Video
Math Discussion
(thinkcentral.comcommon core focus
lesson 9.2.a)
o Whiteboards
Let’s Practice-common
core focus lesson 9.2.a
69
Chapter 9
Lesson
9.2.a
9.3 Dividing Decimals
3 days
1. Divide tenths and
hundredths by a 1digit whole number.
2. Round quotients to
the nearest tenth or
hundredth.
CCCS:
5.NBT.A.1
5.NBT.A.4
5.NBT.B.7
MP:
MP 1
MP 4
TE-5B:
pp. 51-59
Blackline
Master
TR34,
TR35,
TR36,
TR41,
TR42,
TR43
White
Board (1
per
student)
Core:
SB-5B:
pp. 51-59
WKBK-5B:
pp. 21-24
ExtraP-5B:
pp. 15-16
PlaceValue
Chart 3
(TR34)
for the
teacher
Basic
Reteach5B:
pp. 31-38


PlaceValue
Chips for
the
teacher
PlaceValue
Chart 4
(TR35)
for the
teacher
Advanced:
Enrichmen Placet 5B:
Value
pp. 8-16
(TR36)
for the
teacher
and per

5-Minute Warm Up TE B
pp. 51
Math Discussion TE B pp.
51-59
o Whiteboards
o Use the example
on page 59 to
explain what unit
price means. Note
that these unit
pricing exercises
are an application
of ratio-related
problems.
Hands-On Activity:
o Before discussing
the charts and
steps, have groups
act out the
scenario using
bills and coins cutouts. Have
students work in
groups of 5. Give
each group two
copies of TR41
and TR42 and
three copies of
TR43. Have
groups try to
70
student
(2)
Dollar
Bills CutOuts
(TR41)
per
group
(2)
Dimes
Cut-Outs
(TR42)
per
group

divide 7 dollar
bills, 7 dimes, and
5 pennies equally
among
themselves.
Encourage them to
exchange bills for
coins as they work
through dividing
the money equally.
Have groups share
their methods and
results.
Let’s Practice TE B pp. 58
(3)
Pennies
Cut-Outs
(TR43)
per
group
9.4 Dividing by Tens,
Hundredths, and
Thousandths
3 days
1. Divide tenths and
hundredths by 10,
100, and 1,000.
2. Divide tenths and
hundredths by
multiples of 10, 100,
1,000.
CCCS:
5.NBT.A.1
5.NBT.A.2
5.NBT.B.7
MP:
MP 1
MP 3
MP 4
TE-5B:
pp. 60-67
Blackline
Master
TR37,
TR44,
TR45,
TR46,
TR47
White
Board (1
per
student)
PlaceValue
Chips for
the


5-Minute Warm Up TE B
pp. 60
Math Discussion TE B pp.
60-67
o Whiteboards
o You may wish to
provide visuals to
show how to move
the decimal point
71
MP 5
MP 6
Core:
SB-5B:
pp. 60-67
WKBK-5B:
pp. 33-36
ExtraP-5B:
pp. 19-22
Basic
Reteach5B:
pp. 57-62
teacher
and per
pair
Table of
Measure
s (TR44)
per
student
(4)
PlaceValue
Charts 6
Advanced: (TR37)
Enrichmen for the
t 5B:
teacher
pp. 8-16
(2)
PlaceValue
Charts 6
(TR37)
for the
teacher



to the left when
dividing decimals
by 100 and 1,000.
Hands-On Activity:
o Use place-value
charts to show
division of
numbers by 10. TE B pp. 61 (TR37
TR45)
o Use place-value
charts to show
division of
numbers by 100
and 1,000. – TE B
pp. 64
Let’s Explore: TE B pp. 66
o Use product of
whole numbers to
find the product of
decimals and
whole numbers
mentally.
Let’s Practice TE B pp. 66
Table of
Division
1 (TR45)
per pair
Table of
Division
2 (TR46)
per pair
72
Table of
Division
3 (TR47)
per
student
9.5 Estimating Decimals
2 days
1. Estimate decimal
sums, differences,
products, and
quotients.
CCCS:
5.NBT.A.4
5.NBT.B.7
MP:
MP 1
MP 2
TE-5B:
pp. 68-74
Core:
SB-5B:
pp. 68-74
WKBK-5B:
pp. 37-40
ExtraP-5B:
pp. 23-24
White
Board (1
per
student)
Learn
Zillion
Videos:
http://le
arnzillio
n.com/le
Basic
ssons/43
Reteach1-round5B:
decimals
pp. 63-68
-to-thenearestAdvanced: wholeEnrichmen numbert 5B:
using-app. 8-16
numberline




5-Minute Warm Up TE B
pp. 68
Learn Zillion Video:
Estimating Decimals
Math Discussion TE B pp.
68-74
o Whiteboards
o Comparing
estimates and
actual sums help
students see the
range of answers
that may be
considered
“reasonable”.
Emphasize,
however, that in
real-world
contexts the goal
is to find a quick
way to check
reasonableness,
rather than to find
a close estimate.
Let’s Practice TE B pp.
73
73-74
9.6 Real-World Problems:
Decimals
2 days
1. Solve real-world
problems involving
decimals.
CCCS:
5.NBT.A.4
5.NBT.B.7
MP:
MP 1
MP 6
MP 7
MP 8
TE-5B:
pp. 75-81
Core:
SB-5B:
pp. 75-81
WKBK-5B:
pp. 41-54
ExtraP-5B:
pp. 25-40
Basic
Reteach5B:
pp. 69-72
White
Board (1
per
student)


3-inch
long
strip of
paper
per
student
Newspap 
er
advertise
ment for
Advanced: food
Enrichmen items
t 5B:
per pair

pp. 8-16


5-Minute Warm Up TE B
pp. 75
Math Discussion TE B pp.
75-81
o Whiteboards
o Use guided
questions to help
students
understand and
explain the steps
to solve two-step
problems.
Hands-On Activity: TE B
pp. 79
o Use grocery
circulars to apply
decimal
multiplication.
Let’s Explore: TE B pp. 79
o Find the number
of quarters and
dimes that make
up a sum of
money.
Let’s Practice TE B pp. 80
Critical Thinking and
Problem Solving-TE B pp.
81
o This activity
requires students
74
Chapter Wrap Up
Chapter Assessment
1. Reinforce and
consolidate chapter
skills and concepts.
3 days
CCCS:
5.NBT.A.1
5.NBT.A.2
5.NBT.A.4
5.NBT.B.7
5.NF.B.5.b
MP:
MP.1
MP.2
TE-5B:
pp. 82-84
Assessmen
t Book
pp. 77-80
Core:
SB-5B:
pp. 82-84
to use the guess
and check and
make a systematic
list strategies to
solve problems.
Chapter Wrap Up Study
Guide TE B pp. 82
Chapter Review TE B pp. 8384
Unit 9 Assessment
(Assessments 5 pp. 77-80)

INSTRUCTIONAL FOCUS OF UNIT
Students multiply and divide decimals by 1-digit whole numbers and by tens, hundreds, and thousands. This is similar to the
multiplication of whole numbers.
Students estimate sums, differences, products, and quotients for calculations involving decimals and use these estimates to check
the reasonableness of answers.
Students solve one- and two-step real-world problems involving multiplication and division of decimals.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 9 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 9



75
76

Example of Key Advances from Grade 4 to Grade 5
o In grade 5, students will integrate decimal fractions more fully into the place value system (5.NBT.1-4). By thinking about
decimals as sums of multiples of base-ten units, students begin to extend algorithms for multidigit operations to decimals
(5.NBT.7).
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Decimals.
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on decimals for unit 9. Apply skills and
knowledge learned on decimals to real world scenarios given in
the menu. Complete at least 15 points out of the 20 points
available (80% and higher).
Critical Thinking:
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to multiplying
and dividing decimals. Evaluate real world problems through the
application of decimal concepts by completing various critical
thinking activities with at least 85% accuracy.
Math Journal
 How can we efficiently solve multiplication and division
problems with decimals?
 How can we multiply and divide decimals fluently?
 What strategies are effective for finding a missing factor or
divisor?
 How can we use estimation to assist in solving problems with
decimal operations
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
77
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Place the point (pp.
43-46 https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit3FrameworkSE.pdf)

Students should be
given many opportunities to calculate decimals mentally. The
emphasis shifts from getting exact answers from paper-andpencil calculations to arriving at estimates and being able to
explain why they are reasonable.
Communication – Power points/Presentations
TLWBAT: Explore the place value system by using estimation to
determine where to place the decimal point in several quotients with at
least 90% accuracy.
MODIFICATIONS/ACCOMMODATIONS




Whiteboards
Place-Value Charts
Place-Value Chips
Additional Support (ELL, Struggling Learners) TE 5B pp. 30B
APPENDIX
(Teacher resource extensions)
CCCS:
5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its
right and 1/10 of what it represents in the place to its left.
5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in
the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote
powers of 10.
5.NBT.A.4 Use place value understanding to round decimals to any place.
78
5.NBT.A.7 Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place
value, the properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method
and explain the reasoning used.
5.NF.B.5b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number
(recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a
fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n ×
a)/(n × b) to the effect of multiplying a/b by 1.
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Online Resources
Learn Zillions Video Decimals
http://learnzillion.com/lessons/433-round-decimals-to-the-nearest-hundredth-using-a-number-line
http://learnzillion.com/lessons?utf8=✓&filters%5Bsubject%5D=math&query=5.nbt.2
http://learnzillion.com/lessons?utf8=✓&filters%5Bsubject%5D=math&query=5.nbt.7
Additional WorksheetsPowers of Ten
http://www.math-drills.com/powersoften.shtml
Multiplying and Dividing Decimals
http://www.math-drills.com/decimal.shtml
Additional Hands-On Activities and Games
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit3FrameworkSE.pdf
79
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
80
UNIT 10
Percent (6.RP.A.3.c)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 6. * Can be taught at the end of school year.
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
UNIT 11
Graphs and Probability (7.SP.C.5)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 7. * Lesson 11.2 (only lesson in Unit 11
that is part of 5th grade Common Core Standard) will be included in Measurement and Data (5.MD) Unit.
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
81
UNIT 12
Angles (4.MD.C.5, 6, 7)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 4.
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
82
UNIT 13
Properties of Triangles and Four-sided Figures
Total Number of Days: 13 Grade/Course: 5/Math






ESSENTIAL QUESTIONS
How can plane figures be categorized and classified?
What are the properties of quadrilaterals?
How can you classify different types of quadrilaterals?
How can angle and side measures help us to create and
classify triangles?
Why are some quadrilaterals classified as
parallelograms?
What are ways to classify triangles?



ENDURING UNDERSTANDINGS
Two-Dimensional figures are classified by their properties.
Two-Dimensional figures can fit into more than one category.
Identify and describe properties of two-dimensional figures
more precisely
RESOURCES
PACING
3 days
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of twodimensional figures from
fourth grade.
SKILLS
1.Classify polygons.
2. Finding measures
of angles on a line.
STANDARD
S
(CCCS/MP)
4.G.A.1
4.G.A.2
Math in
Focus
Assessmen
ts: pp. 125130
TE 5B:
pp. 182185
Core:
SE 5B:
pp. 182185
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
Pre-Assessment:
Chapter 13 Test Prep
Assessment
Assessment Book 5 pp. 125130
Chapter Opener- TE B pp.
182-184
Quick Check TE B pp. 184
83
13.1 Classify Triangles
2 days
1. Classify triangles
by the lengths of
their side lengths,
and angle measure.
CCCS:
5.G.B.3
5.G.B.4
MP:
MP 1
TE-5B:
pp. 186190
Blackline
Master
TR56
Core:
SB-5B:
pp. 186190
WKBK-5B:
pp. 121122
ExtraP-5B:
pp.87-88
Basic
Reteach5B:
pp. 129132
Centimet
er ruler
per
student
Protract
or per
student



Table for
Classifyi
ng
Triangle
s (TR56)
per
student
White
Board (1
per
student) 
Advanced:

Enrichmen YouTube
t 5B:
Video
pp. 45-51
http://w
ww.youtu
be.com/w
atch?v=v
nWbxjT5
5Dw

5-Minute Warm Up TE B
pp. 186
YouTube Video:
Classifying Triangles
Math Discussion TE B pg.
186-190
o White Boards
o Protractors
o Be sure students
understand that
obtuse, acute, and
right triangles are
classified based on
their angle
measures, while
isosceles,
equilateral, and
scalene triangles
are classified
based on side
lengths.
Hands-On Activity:
Sorting Triangles online
gamehttp://www.crick
web.co.uk/ks2nu
meracy-shapeandweight.html#trian
gles
Let’s Practice: TE B pp.
190
84
13.2 Measure of Angles of a
Triangle
* Omit this lesson. Not
part of 5th grade Common
Core Standards.
13.3 Right, Isosceles, and
Equilateral Triangles
4 days
1. Understand and
apply the properties
of right, isosceles,
and equilateral
triangles.
CCCS:
5.G.B.3
5.G.B.4
MP:
MP 1
MP 2
MP 3
MP 6
MP 7
MP 8
TE-5B:
pp. 195204
Blackline
Master
TR58
TR18
Core:
SB-5B:
pp. 195204
WKBK-5B:
pp. 125132
ExtraP-5B:
pp.91-94
Basic
Reteach5B:
pp. 139142
Protract
or per
student
Isosceles
Triangle
ABC CutOut
(TR58)
per
student
Grid
Paper
(TR18)
per
student
Pair of
scissors
per
student
White
Advanced: Board (1
Enrichmen per



5-Minute Warm Up TE B
pp. 195 (protractors)
Math Discussion TE B pp.
36-42
o White Boards
Hands-On Activity:
o Draw Right
Triangles on the
Computer-TE B
pp.196
o My Many
Triangles gameThis task requires
students to sort
triangles
according to
common
attributes and
then create
triangles
according to two
properties.
o All resources
located on the
85
t 5B:
pp. 45-51
student)



following PDFhttps://www.geor
giastandards.org/
CommonCore/Common%2
0Core%20Framew
orks/CCGPS_Math
_5_Unit6Framewo
rkSE.pdf
Let’s Explore: TE B pp.
197, 203
o Identify sets of
angles of a right
triangle.
o Draw a classify
triangles
Math Journal: TE B pp.
203
o Provides and
opportunity for
students to
express their
understanding of
the properties of
triangles.
Let’s Practice: TE B
pp.204
13.4 Triangle Inequalities
* Omit this lesson. Not
part of 5th grade Common
Core Standards.
86
13.5 Parallelogram,
Rhombus, and Trapezoid
4 days
1. Understand and
apply the properties
of parallelogram,
rhombus, and
trapezoid
CCCS:
5.G.B.3
5.G.B.4
MP:
MP 1
MP 2
MP 4
MP 5
MP 6
MP7
TE-5B:
pp. 211223
Blackline
Master
TR59,
TR60,
TR61,
TR62,
TR63
Core:
SB-5B:
pp. 211223
WKBK-5B:
pp. 137144
ExtraP-5B:
pp. 99-106
White
Board (1
per
student)

Ruler
per
student



Drawing
triangle
per
student
Parallelo
gram
ABCD
Cut-Outs
(TR59)
per pair
Basic
Reteach5B:
pp. 147152
Trapezoi
d ABCD
Cut-Outs
(TR60)
per pair
Advanced:
Enrichmen
t 5B:
pp. 45-51
Trapezoi
d ABCD
Cut-Out
(TR61)
per pair
Table for
Compari



5-Minute Warm Up TE B
pp. 211
Learn Zillions Video:
Attributes of
Quadrilaterals
Math Discussion TE B pp.
211-223
Hands-On Activity: TE B
pp. 212-214
o Properties of the
sides of
parallelogram
(TR59)
o Angle properties
of a parallelogram
(TR60)
o Angle properties
of a trapezoid (TR
61)
Math Journal: TE B pp.
222
o Provides
opportunity for
students to
compare pairs of
four-sided figures
by listing their
similarities and
differences.
Let’s Practice TE B pp.
222
Critical Thinking and
Problem Solving: TE B pp.
223
87
ng FourSided
Figures
(TR62)
per
group
Table of
FourSided
Figures
(TR63)
per
group
o These problem
solving exercises
enable students to
apply their
knowledge of the
properties of
triangles to find
unknown angle
measures.
Pair of
scissors
per
student
Learn
Zillions
Video
http://le
arnzillio
n.com/le
ssons/17
08identifyquadrilat
eralsbasedonattribute
s
88
Chapter Wrap Up
Chapter Assessment
1. Reinforce and
consolidate chapter
skills and concepts.
3 days
CCCS:
5.G.B.3
5.G.B.4
MP:
MP.1
MP.2
TE-5B:
pp. 224228
Assessmen
t Book
pp. 125130
Core:
SB-5B:
pp. 224228
Chapter Wrap Up Study
Guide TE B pp. 224-225
Chapter Review TE B pp.
226-227
Unit 13 Assessment
(Assessments 5 pp. 125-130)
Please omit questions from
lesson

INSTRUCTIONAL FOCUS OF UNIT
Students identify and classify different types of triangles: equilateral, isosceles, scalene, right, obtuse, and acute.
Students apply the properties of a parallelogram, a rhombus, and a trapezoid to find unknown angles.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 13 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 13


89

Example of Key Advances from Grade 4 to Grade 5
o For more information visit the PARCC website.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Geometric Properties of 2-D Shapes
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on geometric properties for unit 13.
Apply skills and knowledge learned about properties of triangles
and quadrilaterals to real world scenarios given in the menu.
Complete at least 15 points out of the 20 points available (80%
90
project.
and higher).
Critical Thinking:
Math Journal
 Explain why an isosceles triangle is not a regular polygon.
 All rectangles are parallelograms. Are all parallelograms
rectangles? Explain.
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to triangles and
quadrilaterals. Evaluate real world problems through the
application of geometric concepts by completing various critical
thinking activities with at least 85% accuracy.
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Property List of
Quadrilaterals (pp. 4648https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit6FrameworkSE.pdf)
TLWBAT: Identify the attributes of each quadrilateral, then compare
and contrast the attribute of different quadrilaterals with at least 90%
accuracy.
Communication – Power points/Presentations
91
MODIFICATIONS/ACCOMMODATIONS


Whiteboards
Additional Support (ELL, Struggling Learners) TE 5B pp. 182B
APPENDIX
(Teacher resource extensions)
CCCS:
• 5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that
category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
• 5.G.B.4 Classify two-dimensional figures in a hierarchy based on properties.
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Online Resources
Learn Zillions Video
http://learnzillion.com/lessons?utf8=✓&filters%5Bsubject%5D=math&query=5.g.3
92
Additional Worksheetshttp://www.math-drills.com/geometry.shtml#triangles
Additional Hands-On Activities and Games
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit6FrameworkSE.pdf
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
93
UNIT 14
Three-Dimensional Shapes (6.G.A.4)
Please omit this unit-not part of 5th grade Common Core Standard. Moved to grade 6.
ESSENTIAL QUESTIONS
ENDURING UNDERSTANDINGS
RESOURCES
PACING
CONTENT
SKILLS
STANDARD
S
(CCCS/MP)
Math in
Focus
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
94
UNIT 15
Surface Area and Volume
Total Number of Days: 16 Grade/Course: 5/Math





ESSENTIAL QUESTIONS
How do we measure volume?
How are area and volume alike and different?
How can you find the volume of cubes and rectangular
prisms?
How do you convert volume between units of measure?
Why is volume represented with cubic units and area
represented with square units?




ENDURING UNDERSTANDINGS
Three-dimensional (3-D) figures are described by their faces
(surfaces), edges, and vertices (singular is “vertex”).
Volume can be expressed in both customary and metric units.
Volume is represented in cubic units – cubic inches, cubic
centimeters, cubic feet, etc.
Volume refers to the space taken up by an object itself.
RESOURCES
PACING
3 days
CONTENT
Recall Prior Knowledge:
Review of previous
knowledge of area and
measurements from fourth
grade.
SKILLS
1.Identify
rectangular prisms
and triangular
rectangles.
2. Measure capacity
and volume.
STANDARD
S
(CCCS/MP)
4.MD.A.1
Math in
Focus
Assessmen
ts: pp. 142148
TE 5B:
pp. 256258
Core:
SE 5B:
pp. 256258
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
Pre-Assessment:
Chapter 15 Test Prep
Assessment
Assessment Book 5 pp. 142148 (omit #2, 3, 7, 8)
Chapter Opener- TE B pp.
256-257
Quick Check TE B pp. 258
95
15.1 Building Solids Using
Unit Cubes
1.Build solids using
unit cubes.
CCCS:
5.MD.C.3.a
2. Determine the
MP:
number of unit cubes MP 1
in an irregular solid. MP 3
MP 4
MP 6
2 days
TE-5B:
pp. 259262
Core:
SB-5B:
pp. 259262
WKBK-5B:
pp. 167168
ExtraP-5B:
pp. 115116
Basic
Reteach5B:
pp. 163164
Model of
a cube
for the
teacher
20
connecti
ng cubes
per
student
and for
the
teacher
40
connecti
ng cubes
per pair



Learn
Zillions
Video
Advanced: http://lea
Enrichmen rnzillion.c
t 5B:
om/lesso
pp. 60-69
ns/1590identify
thedifference
-betweena-squareunit-anda-cubicunit

5-Minute Warm Up TE B
pp. 259
Learn Zillions VideoCubic Unit
Math Discussion TE B pg.
259-262
o White Boards
o Connecting cubes
o You may want to
students to
develop a better
understanding of
the relationship
between twodimensional and
three-dimensional
figures. Have
students look at
the solid figures
they build, and
make twodimensional
drawings of the
top, sides, and
front views.
Hands-On Activity: TE B
p. 260
o Use connecting
cubes to build
solids
o 40 connecting
cubes per pair
Let’s Explore: TE B p. 261
o This activity
provides an
96

opportunity for
students to form
different solids
using three or four
unit cubes.
Let’s Practice: TE B p. 262
15.2
* Omit this lesson. Not
part of 5th grade Common
Core Standards.
15.3
Omit this lesson. Not part
of 5th grade Common Core
Standards.
15.4 Understanding and
1. Find the volumes
Measuring Volume
of cubes and
rectangular prisms.
2. Find the volume of
a solid constructed
from unit cubes.
3 days
3. Compare volumes
of cubes, rectangular
prisms, and other
objects.
CCCS:
5.MD.C.3.a
5.MD.C.3.b
5.MD.C.4
5.MD.C.5.a
5.MD.C.5.c
MP:
MP 1
MP 3
MP 4
MP 6
TE-5B:
pp. 275285
Blackline
Master
TR76
Core:
SB-5B:
pp. 275285
WKBK-5B:
pp. 177180
ExtraP-5B:
pp. 127132
Basic
20
connecti
ng cubes
for the
teacher
25
connecti
ng cubes
per pair
Table of
Volumes
of
Rectangu
lar
Prisms
(TR76)
per




5-Minute Warm Up TE B
p. 275
Learn Zillions Video: Find
Volume by Counting
Cubes
Math Discussion TE B pp.
275-285
o White Boards
Hands-On Activity:
o Use a given
number of cubes
to form different
solids-TE B p.282
o How Many Ways
Activity (pdf
pp.22-27)
 All
directions
and
97
Reteach5B:
pp. 173176
student
resources
located on
the
following
PDFhttps://ww
w.georgiast
andards.or
g/Common
Core/Com
mon%20Co
re%20Fra
meworks/C
CGPS_Math
_5_Unit7Fr
ameworkS
E.pdf
White
Board (1
per
student)
Advanced:
Enrichmen
t 5B:
Learn
pp. 60-69
Zillions
Video
http://le
arnzillio
n.com/le
ssons/12
64-findvolumebycounting
-cubes
15.5 Volume of a
Rectangular Prism and
Liquid
3 days
1. Use a formula to
find the volume of a
rectangular prism.
2. Find the capacity
of a rectangular
container.
3. Solve word
CCCS:
5.MD.A.1
5.MD.C.3.a
5.MD.C.3.b
5.MD.C.4
5.MD.C.5.a
5.MD.C.5.b
5.NBT.B.5
TE-5B:
pp. 286297
Blackline
Master
TR44
Core:
SB-5B:
White
Board (1
per
student)
Solid
shapes
for the
teacher

Let’s Explore: TE B p. 283
o Explore a formula
for the volume of a
rectangular prism

Let’s Practice: TE B
pp.284-285
5-Minute Warm Up TE B
pp. 286
Learn Zillions Video: Find
Volume of Solid Figure
Brainpop Video: Metric
System
Math Discussion TE B pp.
211-223




98
problems involving
volume of
rectangular prisms
and liquids.
MP:
MP 1
MP 2
MP 4
MP 5
MP 6
MP7
pp. 286297
WKBK-5B:
pp. 181194
ExtraP-5B:
pp. 133146
Basic
Reteach5B:
pp. 177182
40
connecti
ng cubes
for the
teacher

Cubic
liter
containe
r for the
teacher
Table of
Measure
Advanced: s (TR44)
Enrichmen per
t 5B:
student
pp. 60-69
5 or 6
containe
rs of
various
sizes and
shapes
for the
teacher

Measurin 
g
cylinder
or
pitcher
for the
teacher
Hands-On Activity:
o Rolling
Rectangular
Prisms (pdf pp.3539)
 All
directions
and
resources
located on
the
following
PDFhttps://ww
w.georgiast
andards.or
g/Common
Core/Com
mon%20Co
re%20Fra
meworks/C
CGPS_Math
_5_Unit7Fr
ameworkS
E.pdf
Let’s Practice TE B pp.
294-295
Critical Thinking and
Problem Solving: TE B pp.
296-297
o These problem
solving exercises
reinforce students’
understanding of
99
rectangular
prisms.
Objects
in the
shape of
rectangu
lar
prisms
for the
teacher
Learn
Zillions
Video
http://lea
rnzillion.c
om/lesso
ns/1803find-thevolumeof-asolidfigure-bymultiplyi
ng-v-l-xw-x-h
15.5.a Volume of a
Rectangular Prism
1 day
1. Use a formula to
find the volume of a
rectangular prism
CCCS:
5.MD.C.5.a
MP:
MP 4
MP 6
MP 8
Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent

Math Discussion
(thinkcentral.comcommon core focus
lesson 15.5.a)
o Whiteboards
Let’s Practice-common
core focus lesson 15.5.a
100
ral.com)
Chapter 15
Lesson
15.5.a
15.5.b Volume of Solid
Figures
2. Solve real-world
problems involving
the volume of a solid
figure composed of
two rectangular
prisms.
1 day
Chapter Wrap Up
Chapter Assessment
3 days
1. Find the volume of
a solid figure
composed of two
rectangular prisms.
1. Reinforce and
consolidate chapter
skills and concepts.
CCCS:
5.MD.C.5.c
MP:
MP 4
MP 6
MP 8
CCCS:
5.MD.A.1
5.MD.C.3.a
5.MD.C.3.b
5.MD.C.4
5.MD.C.5.a
5.MD.C.5.b
5.MD.C.5.c
5.NBT.B.5
MP:
MP.1
MP.2

Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent
ral.com)
Chapter
15Lesson
15.5.b

TE-5B:
pp. 298302
Assessmen
t Book
pp. 142148
Chapter Wrap Up Study
Guide TE B pp. 298-299
Core:
SB-5B:
pp. 298302
Math Discussion
(thinkcentral.comcommon core focus
lesson 15.5.b)
o Whiteboards
Let’s Practice-common
core focus lesson 15.5.b
Chapter Review TE B pp.
300-302
Unit 15 Assessment
(Assessments 5 pp. 125-130)
Please omit questions #2, 3,
7, 8
INSTRUCTIONAL FOCUS OF UNIT
Students find the surface areas of prisms from their nets by adding the areas of all the faces on the net.
101


Students express the volumes of cubes and rectangular prisms as the number of cubic units they contain, and relate these volumes
to liquid measures.
PARCC FRAMEWORK/ASSESSMENT
Online assessment Unit 15 (Think Central-Math In Focus Online Assessments)

NJ Model Curriculum Sample Problem for Unit 13
102
103

Example of Key Advances from Grade 4 to Grade 5
o For more information visit the PARCC website
o Students continue their work in geometric measurement by working with volume as an attribute of solid figures and as a
measurement quantity.
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
TLWBAT: Complete a math box choice board by picking any
104
Math Boxes (choice menu) on Volume
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
Critical Thinking:
Math Journal
 How would the surface area of a cube change if you
doubled the length of each side? Give examples to support
you conclusions.
 Write a story problem that involves finding the volume of a
box. Illustrate it and solve it.
activity from the 9 options on volume for unit 15. Apply skills and
knowledge learned about volume to real world scenarios given in
the menu. Complete at least 15 points out of the 20 points
available (80% and higher).
TLWBAT: Refine their mathematical communication skills by
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to volume.
Evaluate real world problems through the application of
measurement concepts by completing various critical thinking
activities with at least 85% accuracy.
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Breakfast For All
(pp. 58- 61 https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
TLWBAT: Design three different sizes of cereal boxes, determine the
dimensions for the original box and then use the appropriate
operations to enlarge or reduce the size of the original box to meet the
specifications of the manufacturer with at least 90% accuracy.
105
Unit7FrameworkSE.pdf)

Task Directions:
Design the packaging for a new breakfast cereal in three
different sized boxes. Draw a design for each box. Label the
dimensions and calculate the volume of each one.
Communication – Power points/Presentations
MODIFICATIONS/ACCOMMODATIONS



Whiteboards
Connecting Cubes
Additional Support (ELL, Struggling Learners) TE 5B pp. 256B
APPENDIX
(Teacher resource extensions)
CCCS:
5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05
m), and use these conversions in solving multi-step, real world problems.
5.MD.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to
measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic
units.
5.MD.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft and improvised units.
5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving
volume.
a. Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes, and show
that the volume is the same as it would be found by multiplying the height by the area of the base. Represent
threefold whole number products as volumes, e.g. to represent the associative property of multiplication.
b. Apply the formula V= l x w x h and V= B x h for rectangular prisms to find volumes of right rectangular prisms with
whole number edge lengths in the context of solving real world and mathematical problems.
c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular
prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
106
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Additional Teaching Strategies
When converting in the metric system, have students extend their prior knowledge of the base- ten system as they multiply or
divide by powers of ten (as referenced in Units 1 and 2). Teaching conversions should focus on the relationship of the
measurements, not merely rote memorization. The questions ask the student to find out the size of each of the subsets. Students
are not expected to know e.g. that there are 5280 feet in a mile. If this is to be used as an assessment task, the conversion factors
should be given to the students. However, in a teaching situation it is worth having them realize that they need that information
rather than giving it to them upfront; having students identify what information they need to have to solve the problem and
knowing where to go to find it allows them to engage in Standard for Mathematical Practice 5, Use appropriate tools
strategically.
Retrieved from Illustrative Mathematics
http://www.illustrativemathematics.org/standards/k8
107
Retrieved from:
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit7FrameworkSE.pdf
Online Resources
Learn Zillions Video
http://learnzillion.com/lessons/1485-identify-and-label-threedimension-figures
Brainpop Video (Metric System)
http://www.brainpop.com/math/numbersandoperations/metricunits/preview.weml
108
Additional Hands-On Activities and Games
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit7FrameworkSE.pdf
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
109
Measurement and Data Unit
*This unit covers Common Core Standards not covered in Math In Focus textbook
Total Number of Days: 13 Grade/Course: 5/Math






ESSENTIAL QUESTIONS
How do coordinate grids help you organize information? 
What relationships can be determined by analyzing two
sets of given rules?

How might a coordinate grid help me understand a
relationship between two numbers?

How can we represent numerical patterns on a
coordinate grid?
How can we use a line plot to show fractional parts of a
whole?
How can the information on the line plot be used to redistribute the items equally?
ENDURING UNDERSTANDINGS
On the coordinate plane, a point represents the two facets of
information associated with an ordered pair.
Graphical representations can be used to make predictions and
interpretations about real world situations.
Given two rules, students can generate two numerical patterns.
Students create line graphs from the pattern. This explains a linear
function and why straight lines are generated from the pattern.
RESOURCES
PACING
2 days
CONTENT
Recall Prior
Knowledge:
Review of
previous
knowledge of
data and
measurements
from fourth
grade.
SKILLS
1.Making and interpreting a bar
graph.
2. Finding the average or mean.
STANDARD
S
(CCCS/MP)
4.MD.A.1
Math in
Focus
Assessmen
ts
*custom
online
assessment
(thinkcentr
al)
TE 5B:
OTHER
(e.g.,
tech)
LEARNING
ACTIVITIES/ASSESSMENTS
(All lessons should begin
with a Do-Now and end
with an Exit Ticket)
Pre-Assessment:
custom online assessment
(thinkcentral)
Chapter Opener- TE B pp.
120-121
Quick Check TE B pp. 122123 #1-5
110
pp. 120121
11.1.a Making
and
Interpreting
Line Plots
1 day
*Math in Focus
Unit 11
Common Core
Focus Lesson
and Activities
E-Book
(Thinkcentral.
com)
1. Make a line plot to represent
data given in fractions of a unit.
CCCS:
5.MD.B.2
2. Use operations on fractions to
solve problems from the
information presented.
MP:
MP 1
MP 2
MP 4
MP 6
MP 7
MP 8
Core:
SE 5B:
pp. 120121
Common
Core Focus
Lesson
and
Activities
E-Book
(thinkcent
ral.com)
Chapter 11
Lesson
11.1.a
White
Boards

Math Discussion
(thinkcentral.comcommon core focus
lesson 11.1.a)
o Whiteboards
Let’s Practice-common
core focus lesson 11.1.a
Hands-On Activity:
o Survival Badge
(pdf pp.48-50)
 All
directions
and
resources
located on
the
following
PDFhttps://ww
w.georgiast
andards.or
g/Common
Core/Com
mon%20Co
re%20Fra
meworks/C
111
CGPS_Math
_5_Unit7Fr
ameworkS
E.pdf
11.2 Graphing
an Equation
1.Read points on a coordinate
grid.
*Math in Focus
Unit 11
2. Plot points on a coordinate
grid.
3. Graph an equation on a
coordinate grid.
2 Days
CCCS:
5.G.A.1
5.G.A.2
5.MD.A.1
5.OA.B.3
MP:
MP 1
MP 3
MP 4
MP 6
TE-5B:
pp. 131138
Blackline
Master
TR52,
TR18, TR
44
Core:
SB-5B:
pp. 131138
WKBK-5B:
pp. 85-88
ExtraP-5B:
pp. 61-64
Ruler for
the
teacher
Basic
Reteach5B:
pp. 103106
Grid
Paper
(TR18)
per pair


Measurin 
g tape
per pair
Coordina
te Grid
(TR52)
for the
teacher
and 3
per
student
Table of
Advanced: Measure
Enrichmen s (TR44)
t 5B:
for the
pp. 28, 33
teacher
Masking
tape for
the

5-Minute Warm Up TE B
pp. 131
Learn Zillions VideoCoordinate Grid
Math Discussion TE B pg.
131-138
o White Boards
o Coordinate Grids
o Relate locating
points in a
coordinate plane
to plotting data in
a line graph.
Students learned
to locate points
using two
numbers and axes
in a line graph.
Guide students to
identify and relate
the similarities
between line
graphs and a
coordinate grid.
Hands-On Activity: TE B
p. 136
o Draw and
interpret a
straight line graph.
112
teacher
o Survival Badge
(pdf pp.42-48)
 All
directions
and
resources
located on
the
following
PDF
https://ww
w.georgiast
andards.or
g/Common
Core/Com
mon%20Co
re%20Fra
meworks/C
CGPS_Math
_5_Unit5Fr
ameworkS
E.pdf
Sticky
labels for
the
teacher
Learn
Zillions
Video
http://lea
rnzillion.c
om/lesso
ns/1700use-amodel-toidentifyparts-ofacoordinat
e-plane

1 Day
9.2 Length
*Go Math
Chapter 9
(thinkcentral.co
m)
1. Measure length to the nearest
unit in the metric and customary
systems.
5.MD.A.1
GO Math
Unit 9
(thinkcent
ral.com)
TE: Unit
9.2
pp. 393396
White
Board
Inch
ruler
Yardstic
k


Let’s Practice: TE B p.
136-138
5-Minute Warm Up TE Go
Math 9.2-p. 393
Math Discussion Go Math
TE 9.2-pp. 393-396
o White Boards
Let’s Practice: Go Math 9.2
TE pp. 395-396
113
Core:
SB 9.2
pp.393396
WKBK-Go
Math
Standards
Practice
9.2
pp. 195
Metric
ruler
Math Journal: Go Math TE
p.396
o How can estimation and
Meterstic
measurement help
k
determine an appropriate
linear unit?
Basic:
Go Math
Reteach
9.2
9.4 Convert
Customary
Length
*Go Math
Chapter 9
(thinkcentral.co
m)
1 day
1. Compare, contrast, and
convert customary linear units
of length.
CCCS:
5.MD.A.1
MP:
MP 1
MP 3
MP 4
MP 6
Advanced:
Go Math
Enrich 9.2
GO Math
Unit 9
(thinkcent
ral.com)
TE: Unit
9.4
pp. 401405
Core:
SB 9.4
pp. 401404
WKBK-Go
Math
White
Board
5-Minute Warm Up TE Go
Math 9.4-p. 401
Math Discussion Go Math TE
9.4-pp. 401-405
o White Boards
Let’s Practice: Go Math 9.4
TE pp. 403-404
Math Journal: Go Math TE p.
404
 Explain how to compare
two lengths that are
measured in different
114
Standards
Practice
9.4
pp. 199
units.
Basic:
Go Math
Reteach
9.4
9.5 Convert
Customary
Capacity
*Go Math
Chapter 9
(thinkcentral.co
m)
1 day
1. Compare, contrast, and
convert customary units of
capacity.
CCCS:
5.MD.A.1
MP:
MP 1
MP 2
MP 4
MP 5
MP 6
MP7
Advanced:
Go Math
Enrich 9.4
GO Math
Unit 9
(thinkcent
ral.com)
TE: Unit
9.5
pp. 407410
Core:
SB 9.5
pp. 407410
WKBK-Go
Math
Standards
Practice
9.5
pp. 201
White
Board (1
per
student)
5-Minute Warm Up TE Go
Math 9.5-p. 407
Math Discussion Go Math TE
9.5-pp. 407-410
o White Boards
Let’s Practice: Go Math 9.5
TE pp. 409-410
Math Journal: Go Math TE p.
410
 Give some examples of
capacities that you would
measure in each of the
units shown in the table
on pg.408
Basic:
Go Math
115
Reteach
9.5
9.6 Convert
Weight
*Go Math
Chapter 9
(thinkcentral.co
m)
1 day
1. Compare, contrast, and
convert customary units of
weight.
CCCS:
5.MD.A.1
MP:
MP 4
MP 6
MP 8
Advanced:
Go Math
Enrich 9.5
GO Math
Unit 9
(thinkcent
ral.com)
TE: Unit
9.6
pp. 411414
Core:
SB 9.6
pp. 411414
WKBK-Go
Math
Standards
Practice
9.6
pp. 203
Math
Boards
5-Minute Warm Up TE Go
Math 9.6-p. 411
Math Discussion Go Math TE
9.5-pp. 411-414
o White Boards
Let’s Practice: Go Math 9.5
TE pp. 413-414
Math Journal: Go Math TE p.
414
Give two examples of items
that weigh less than 1 ounce
and two examples of items
that weigh more than 1 ton.
Basic:
Go Math
Reteach
9.6
Advanced:
Go Math
Enrich 9.6
116
9.7 Convert
Metric
Measures
1. Compare, contrast, and
convert metric units.
CCCS:
5.MD.A.1
MP:
MP 4
MP 6
MP 8
GO Math
Unit 9
(thinkcent
ral.com)
TE: Unit
9.7
pp. 415418
Core:
SB 9.7
pp. 415418
WKBK-Go
Math
Standards
Practic 9.7
pp. 205
1 day
Math
Boards
5-Minute Warm Up TE Go
Math 9.7-p. 415
Math Discussion Go Math TE
9.7-pp. 415-418
o White Boards
Let’s Practice: Go Math 9.7
TE pp. 417-418
Math Journal: Go Math TE p.
418
 Explain the relationship
between multiplying and
dividing by 10, 100, and
1,000 and moving the
decimal point to the right
or to the left.
Basic:
Go Math
Reteach
9.7
3 days
Chapter Wrap
Up
Chapter
Assessment
1. Reinforce and consolidate
chapter skills and concepts.
CCCS:
5.MD.A.1
5.MD.B.2
5.G.A.1
5.G.A.2
5.OA.B.3
Advanced:
Go Math
Enrich 9.7
Custom
Online
Assessmen
t
Thinkcent
ral.com
Unit Assessment-Custom
Online Assessment
(thinkcentral.com)
Core:
117
MP:
MP.1
MP.2
Math In
Focus Unit
11
Go Math
Unit 9

INSTRUCTIONAL FOCUS OF UNIT
Students estimate and measure length to the nearest 1/8 inch and nearest millimeter.
Students read and plot the points on a coordinate grid.
Students plot and interpret straight line graphs from equations in the form of y=nx where n is a whole number.
PARCC FRAMEWORK/ASSESSMENT
Custom Online assessment Unit (Think Central-Math In Focus and Go Math Online Assessments)

NJ Model Curriculum Sample Problem for Unit 13



118
119
120
Example of Key Advances from Grade 4 to Grade 5
o Students build on their previous work with number lines to use two perpendicular number lines to define a coordinate
system.
o For more information visit the PARCC website
 http://www.parcconline.org/mcf/mathematics/examples-key-advances-grade-4-grade-5
21ST CENTURY SKILLS
(4Cs & CTE Standards)
4 Cs
Three part learning objective
Creativity: projects
Math Boxes (choice menu) on Measurement and Data
 Point percentage Menu where students will pick any
activity in order to reach a certain amount of points for the
project.
Critical Thinking:
TLWBAT: Complete a math box choice board by picking any
activity from the 9 options on measurement and data. Apply skills
and knowledge learned about measurement and data to real
world scenarios given in the menu. Complete at least 15 points out
of the 20 points available (80% and higher).
TLWBAT: Refine their mathematical communication skills by
121
Math Journal

Find examples of realworld situations in which you have seen metric units of
mass or capacity used.

Create a table that
shows a pattern. Describe two ways that you could find the
15th entry in the table.

What is a situation in
which you might locate points on a coordinate grid?
Do now

NJASK Extend
Constructed Response review question created by teacher
for common core (3x’s per week)
using clear and precise language in their writing. Develop and
enhance appropriate terminology when referring to measurement
and data. Evaluate real world problems through the application of
geometric and measurement concepts by completing various
critical thinking activities with at least 85% accuracy.
TESTS (Created by teacher or use textbook assessments)

Whole Numbers
Summative assessment
Exit ticket (created by teacher or use thinkcentral.com)

One exit ticket per
lesson
Collaboration: Teams/Groups/Stations
Collaboration Activity:

Earth Day Project
(pp. 31-38 https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_
Unit5FrameworkSE.pdf)
TLWBAT: Use data in a real-world context to determine the pattern
formed by the numbers in the data, extend the pattern in the data, and
use the pattern to make predictions with at least 90% accuracy.
Communication – Power points/Presentations
MODIFICATIONS/ACCOMMODATIONS
122


Whiteboard
Additional Support (ELL, Struggling Learners) TE 5B pp. 119B
APPENDIX
(Teacher resource extensions)
CCCS:
5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05
m), and use these conversions in solving multi-step, real world problems.
5.MD.B.2Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for
this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in
identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally
5.G.A.1Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the
origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called
its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second
number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the
coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and
interpret coordinate values of points in the context of the situation.
5.OA.B.3Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form
ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For
example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the
resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain
informally why this is so.
Mathematical Practice: (MP)
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically
6.
Attend to precision
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Additional Teaching Strategies
When converting in the metric system, have students extend their prior knowledge of the base- ten system as they multiply or
123
divide by powers of ten (as referenced in Units 1 and 2). Teaching conversions should focus on the relationship of the
measurements, not merely rote memorization. The questions ask the student to find out the size of each of the subsets. Students
are not expected to know e.g. that there are 5280 feet in a mile. If this is to be used as an assessment task, the conversion factors
should be given to the students. However, in a teaching situation it is worth having them realize that they need that information
rather than giving it to them upfront; having students identify what information they need to have to solve the problem and
knowing where to go to find it allows them to engage in Standard for Mathematical Practice 5, Use appropriate tools
strategically.
Retrieved from Illustrative Mathematics
http://www.illustrativemathematics.org/standards/k8
Retrieved from:
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit7FrameworkSE.pdf
Online Resources
Learn Zillions Video
http://learnzillion.com/lessons/1485-identify-and-label-threedimension-figures
Brainpop Video (Metric System)
http://www.brainpop.com/math/numbersandoperations/metricunits/preview.weml
http://www.brainpop.com/math/numbersandoperations/metricvscustomary/preview.weml
Additional Hands-On Activities and Games
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit5FrameworkSE.pdf
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_5_Unit7FrameworkSE.pdf
Unpacking the Standards (Examples and Rationales)
http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/5th.pdf
http://www.illustrativemathematics.org/standards/k8
124