Commercial Township Public Schools
Common Core Curriculum
Content Area:
EnVision Math
Grade:
4
Unit Plan Title:
Unit 4
Unit Summary:This unit will cover fraction concepts including subtracting
fractions with like denominators, adding/subtracting fractions on a number line,
decomposing/composing fractions, a re-visit of improper fractions and mixed
numbers from Unit 3, and multiplying fractions by whole numbers; decimal
concepts including relating fractions to decimals, fractions and decimals on a
number line, finding equivalent fractions and decimals, using money to
understand decimals; solving assorted problems of area, perimeter,
measurement, money, and line plots; and problem solving strategies of
drawing a picture, writing and equation, and making a table.
Unit Rationale:
 In this topic students will make connections between numerators,
denominators, and one whole. Students will have the ability to add and
subtract simple fractions to build upon their understanding of mixed
numbers and ready themselves for topic 13. Students will know how to
read a tape measure and follow fractions on a number line for real world
situations.
 In this topic students will make connections between numerators,
denominators, and one whole from topic 12. Students will have a better
understanding of adding and subtracting simple fractions to build upon
their understanding of mixed numbers. Students will know how to read a
tape measure and follow fractions on a number line for real world
situations. This will give students a base understanding for data collection
and presentation in later topics and real world scenarios.
 In this topic students will build upon their prior knowledge of
measurement, fractions, and data collection. Students will present the
information in a way that is organized to prepare them for higher learning
in data collection and presentation.
In this unit plan the following 21st Century themes and skills are addressed
Indicate whether these skills are EEncouraged, T-Taught, or ACheck all that apply.
Assessed in this unit by marking E, T,
A on the line before the appropriate
21st Century Themes
skill.
21st Century Skills
X
Global Awareness
E,T
Environmental Literacy
E,T,A Critical Thinking and
Problem Solving
Health Literacy
Creativity and Innovation
Civic Literacy
E,T
Communication
Financial, Economic, Business,
and Entrepreneurial Literacy
E,T
Collaboration
Primary Interdisciplinary Connections:
Students will need a good reading comprehension strategy to use in Math.
Students will use context clues in order to determine meanings of unfamiliar
words. Students will make real world connections with problem solving and
mathematical problems.
Anchor Standards, Domains, ContentStandard (s)
 Numbers and Operations—Fractions (Domain)
o Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers. (Cluster)
 4.NF.3-Understand a fraction a/b with a>1 as a sum of fractions
1/b. (Standard)
 4.NF.3a-Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
(Standard)
 4.NF.3b-Decompose a fraction into a sum of fractions with the
same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by
using a visual fraction model. Example: 3/8=1/8 + 1/8 + 1/8;
3/8= 1/8 + 2/8. (Standard)
 4.NF.3c-Add and subtract mixed numbers with like
denominators, e.g., by replacing each mixed number with an
equivalent fraction, and/or by using properties of operations and
the relationship between addition and subtraction. (Standard)
 4.NF.3d-Solve word problems involving addition and subtraction
of fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and
equations to represent the problem. (Standard)
o Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers (Cluster)
 4.NF.4-Apply and extend previous understandings of
multiplication to multiply a fraction by a whole number.
(Standard)
 4.NF.4a-Understand a fraction a/b as a multiple of 1/b. For
example, use a visual fraction model to represent 5/4 as the
product 5 x (1/4), recording the conclusion by the equation
5/4=5 x (1/4).(Standard)
 4.NF.4b-Understand a multiple of a/b as a multiple of 1/b, and
use this understanding to multiply a fraction by a whole number.
For example, use a visual fraction model to express 3 x (2/5) as
6 x (1/5), recognizing this product as 6/5. (In general, n x
(a/b)=(n x a)/b). (Standard)
 4.NF.4c-Solve word problems involving multiplication of a
fraction by a whole number, e.g., by using visual fraction models
and equations to represent the problem. For example, if each
person at a party will eat 3/8 of a point of roast beef, and there
will be 5 people at the party, how many points of roast beef will
be needed? Between what two whole numbers does your
answer lie? (Standard)
o Understand decimal notation for fractions, and compare decimal
fractions (Cluster)
 4.NF.5-Express a fraction with denominator 10 as an equivalent
fraction with denominator 100, and use this technique to add
two fraction with respective denominators 10 and 100.
(Standard)
 4.NF.6-Use decimal notation for fractions with denominators 10
and 100. (Standard)
 4.NF.7-Compare two decimals to hundredths by reasoning
about their size. Recognize that comparisons are valid only
when the two decimals refer to the same whole. Record the
results of comparisons with the symbols >, =, or < and justify the
conclusions, e.g., by using a visual model. (Standard)
 Measurement and Data (Domain)
o Solve problems involving measurement and conversion of
measurements from a larger unit to a smaller unit. (Cluster)
 4.MD.1-Know relative sizes of measurement units within one
system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min,
sec. Within a single system of measurement, express
measurements in a larger unit in terms of a smaller unit. Record
measurements equivalents in a two-column table. (Standard)
 4.MD.2-Use the four operations to solve word problems
involving distances, intervals of time, liquid volumes, masses of
objects, and money, including problems involving simple
fractions or decimals, and problems that require expressing
measurements given in a larger unit in terms of a smaller unit.
Represent measurement quantities using diagrams such as
number line diagrams that feature a measurement scale.
(Standard)
 4.MD.3-Apply the area and perimeter formulas for rectangles in
real world and mathematical problems. (Standard)
o Represent and interpret data. (Cluster)
 4.MD.4-Make a line plot to display a data set of measurements
in fractions of a unit (1/2, ¼, 1/8). Solve problems involving
addition and subtraction of fractions by using information
presented in line plots. (Standard)
Technology Standards
8.1.4.A.1: Demonstrate effective input of text and data using an input device
8.1.4.E.2: Evaluate the accuracy of, relevance to, and appropriateness of using
print and non-print electronic information sources to complete a variety of tasks
8.1.4.F.1: Select and apply digital tools to collect, organize, and analyze data that
support a scientific finding.
Essential Questions
Enduring Understandings
 12-3How can models be used to
 12-3: A model can be used to
subtract fractions with like
subtract two or more fractions.
denominators?
 12-4: When subtracting fractions
 12-4 How will computational procedures
with like denominators, you are
be sued to subtract fractions with like
subtracting portions of the same
denominators and solve problems?
size. So you can subtract the
numerators without changing the
denominator.
 12-5 How will the number line be used
to add and subtract fractions with like
 12-5: Positive fractions can be
denominators?
added or subtracted by locating a
fraction on the number line and then
moving to the right to add or to the
left to subtract.
 12-6 How can students identify and
write mixed numbers as improper
 12-6: Fractional amounts greater
fractions and improper fractions as
than 1 can be represented using a
mixed numbers?
whole number and a fraction.
Whole number amounts can be
represented as fractions. When the
numerator and denominator are
equal, the fraction equals 1.
 12-7 How will models be used to add
and subtract mixed numbers?
 12-7: Models can be used to show
different ways of adding and
 12-8 How will models and
subtracting mixed numbers.
computational procedures be used to
add mixed numbers?
 12-8: One way to subtract mixed
numbers is to subtract the fractional
parts and then subtract the whole
number parts. Sometimes whole
 12-9 How will models and
numbers or fractions need to be
computational procedures be used to
renamed.
subtract mixed numbers?
 12-9: One way to subtract mixed
numbers is to subtract the fractional
parts and then subtract the whole
 12-10 How will students decompose
number parts. Sometimes whole
fractions and represent them as
numbers or fractions need to be
compositions of fractions in a variety of
removed.
ways?
 12-10: A fractional amount can be
 12-11 How will drawing and writing an
decomposed into a sum of fractions
equation help solve a problem?
in more than one way.
 12-11: Information in a problem can
 13-1 How can unit fractions and
multiplication be used to describe
fractions that are multiples of the unit
fraction?
 13-2 How can models be used to
multiply a fraction by a whole number?
 13-3 How can students multiply a whole
number and a fraction to solve
problems?
 13-4 How can students write fractions
as decimals and decimals as fractions?
 13-5 How can students learn to locate
and name fractions and decimals on a
number line?
 13-6 How can students use equivalent
fractions to write fractions as decimals?
often be shown using a diagram and
used to solve the problem. Some
problems can be solved by writing
and completing a number sentence
or equation.
 13-1: Physical representations and
symbols can be used to develop the
𝑎
1
understanding that 𝑏 = 𝑎 x 𝑏.
 13-2: Models can be used to find
the product of a whole number and
a fraction.
 13-3: To multiply a fraction by a
whole number, one must multiply
the whole number by the numerator
of the fraction and then divide the
product by the denominator of the
fraction.
 13-4: A decimal is another name for
a fraction.
 13-5: Each fraction, mixed number,
and decimal can be associated with
a unique point on the number line.
 13-6: Every fraction can be
represented by an infinite number of
equivalent fractions, but each
fraction is represented by the same
decimal or an equivalent form.
 15-1 How can formulas for the
 13-9: Relationships among dollars,
perimeter and area of rectangles be
dimes, and pennies are a good
used to solve real-world problems?
model for decimal numeration.
 13-10: Information in a problem can
 15-2 How can diagrams be used to
often be shown with a picture or
show data and analyze how the
diagram and used to understand
quantities are related to solve real-world
and solve the problem.
measurement problems?
 15-1: Some problems can be solved
 15-3 How can students solve real-world
by applying the formula for the
problems that involve money and giving
perimeter of a rectangle or the
change by counting?
formula for the area of a rectangle
 15-2: Some measurement problems
 15-4 How can constructing a line plot
can be represented and solved
be used to give data and a line plot
using models.
used to answer questions about the
data set?
 15-3: Making change is often
 15-5 How can breaking a problem into
easiest by counting up from the
smaller, more manageable pieces help
 13-9 How can place-value charts be
used to read, write, and compare
decimals in tenths and hundredths
using money?
 13-10 How can the strategy “Draw a
Picture” be used to solve problems?
find a pattern to fit?
smaller amount to the larger
amount.
 15-4: Some data can be
represented using a line plot and
the line plot can be used to answer
certain questions about the data.
 15-5: Some problems can be solved
by breaking apart or changing the
problem into simpler ones, solving
simpler ones, and using these
solutions to solve the original
problem. Recording information in a
table can help students understand
and solve some problems.
Learning Targets/Objectives
12-3 :Students will use models to subtract fractions with like denominators.
12-4 :Students will use computational procedures to subtract fractions with like
denominators and solve problems.
12-5 :Students will use the number line to add and subtract fractions with like
denominators.
12-6 :Students will identify and write mixed numbers as improper fractions and
improper fractions as mixed numbers.
12-7 :Students will use models to add and subtract mixed numbers.
12-8 :Students will use models and computational procedures to add mixed
numbers.
12-9 :Students will use models and computational procedures to subtract mixed
numbers.
12-10 :Students decompose fractions and represent them as compositions of
fractions in a variety of ways.
12-11 :Students will draw a picture and write an equation to solve a problem.
13-1 :Students will use unit fractions and multiplication to describe fractions that
are multiples of the unit fractions.
13-2 :Students will use multiply a fraction by a whole number using models.
13-3 :Students will multiply a whole number and a fraction to solve problems.
13-4 :Students will understand how to write fractions as decimals and decimals
as fractions.
13-5 :Students will learn to locate and name fractions and decimals on a number
line.
13-6 :Students will understand how to use equivalent fractions to write fractions
as decimals.
13-7 :Students will use models and place-value charts to represent decimals to
hundredths. They will read and write decimals in expanded, standard, and word
form.
13-8 :Students will use models and place-value charts to compare decimals to
hundredths. They will use greater-than and less-than symbols to order decimal
numbers.
13-9 :Students will use place-value charts to read, write, and compare decimals
in tenths and hundredths using money.
13-10 :Students will solve problems using the strategy “Draw a Picture”.
15-1 :Students will use the formulas for the perimeter and area of rectangles to
solve real-world problems.
15-2 :Students will use diagrams to show data and analyze how the quantities
are related to solve real-world measurement problems.
15-3 :Students will solve real-world problems that involve money and giving
change by counting.
15-4 :Students will construct line plots using given data and use the line plot to
answer questions about the data set.
15-5 :Students will break a problem into smaller, more manageable pieces and
find a pattern to fit.
Evidence of learning
Summative Assessment:
 Topic 12 Test
 Topic 13 Test
 Topic 15 Test
 Unit 4 RAC Assessment
Formative Assessments:
*Any or all of these may be used to informally assess students.
 Daily Common Core Review (www.pearsonsuccessnet.com)
 Quick Check (www.pearsonsuccessnet.com)
 enVision Practice Workbooks
 Teacher Observation
 Multiplication Timed Tests
 Teacher Created Materials
 Center Activities
 Sweep Scores
 Index Card with Summaries
 Hand Signals
 Student Conference
 3-minute pause
 Self-Assessment
 Exit Card
 Portfolio Check
 Choral Response
 Debriefing
 One Sentence Summary
 Think-Pair-Share
 Turn to Your Partner
 Oral Questioning
Lesson Plans
Lesson
Timeframe
Lessons 12-3 and 12-4
One 80-90 min. lesson
Lessons12-5 and 12-6
Lesson 12-7 and RAC Review #1-6
Lessons 12-8 and 12-9
Lessons 12-10 and 12-11
Topic 12 Test
Lessons 13-1 and 13-2
Lesson 13-3
Lessons 13-4 and 13-5
Lesson 13-6 and Review of
Fractions/Decimals
Lessons 13-9 ; 13-10 ; and Review
RAC # 7-14
Topic 13 Test
Lesson 15-1
Common Core Coach Review and
Supplemental Material of Area and
Perimeter
Lesson 15-2 and RAC Review #15-17
Lesson 15-3
Lesson 15-4
Common Core Coach and
Supplemental Review of Line Plots
Common Core Coach and
Supplemental Review of Line Plots
Review and Math Project Day
Lesson 15-5 and RAC Review #18-19
Topic 15 Test
Common Core Coach and
Supplemental Materials: Variables;
Word Problems; RAC #20-22
Common Core Coach and
Supplemental Materials: Measurement
Common Core Coach and
Supplemental Materials: Measurement
and RAC #23-25
RAC Review of Unit 4 Material
Unit 4 RAC Assessment
Resources
 enVision Materials
 Protractors
 SmartBoard Measurement Tools
 (www.pearsonsuccessnet.com)
 Unit 4 RAC Assessment
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
One 80-90 min. lesson
Three 80-90 min. lessons
One 80-90 min. lesson