East Saint Louis District 189 Math Curriculum Grade 4
Sequence of Grade 4 Modules Aligned with the Standards
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Module 1: Place Value of Whole Numbers
Module 2: Estimation and Number Theory
Module 3: Whole Number Multiplication and Division
Module 4: Tables and Line Graphs
Module 5: Data and Probability
Module 6: Fractions and Mixed Numbers
Module 7: Decimals
Module 8: Adding and Subtracting Decimals
Module 9: Angles
Module 10: Perpendicular and Parallel Line Segments
Module 11: Squares and Rectangles
Module 12: Area and Perimeter
Module 13: Symmetry
Module 14: Tessellations
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8 Days
12 Days (including benchmark assessment)
17 days
13 Days (including benchmark assessment)
14 Days
20 Days (including benchmark assessment)
15 Days
10 Days (including benchmark assessment)
9 Days
9 Days
10 Days (including benchmark assessment)
24 Days
10 Days
2 Days (including benchmark assessment)
Summary of Year
Fourth grade mathematics is about (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of
dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of
fractions with like denominators, and multiplication of fractions by whole numbers; and (3) understanding that geometric figures can be analyzed
and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
Key Areas of Focus for 3-5: Multiplication and division of whole numbers and fractions—concepts, skills, and
problem solving
Required Fluency:
4.NBT.4 Add and subtract within 1,000,000.
Adapted from Math In Focus
Page 1
East Saint Louis District 189 Math Curriculum Grade 4
CCSS Major Emphasis Clusters
Operations and Algebraic Thinking
 Use the four operations with whole numbers to solve problems.
Number and Operations in Base Ten
 Generalize place value understanding for multi-digit whole numbers.
 Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations – Fractions
 Extend understanding of fraction equivalence and ordering.
 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
 Understand decimal notation for fractions, and compare decimal fractions.
Rationale for Module Sequence in Grade 4
Module 1 begins with a study of large numbers. Students are familiar with big units. For example, movies take about a gigabyte (1,000,000,000
bytes) to store on a computer while songs take about a megabyte (1,000,000 bytes). Place-value concepts are reviewed and extended to the ten
thousands place. Students will compare numbers large numbers up to 100,000 and stating which number is greater or less. Students will be
able to order a given set of numbers and identify patterns and relationships within patterns of numbers. Students will state a rule for number
patterns and find missing numbers in the pattern.
Estimation is a critically important skill for students to quickly and accurately assess the reasonableness of their answers. Students will learn
various methods of estimating in Module 2. Students will be introduced to factors, multiples, least common multiples, and greatest common
factor. Students will make lists of factors to find the LCM and GCF. They are introduced to “double division” method by successively dividing
two numbers by any common divisor. This will also help them to determine the LCM and GCF of two numbers.
In earlier grades, students learned their multiplication facts up to 10x10. In Module 2, students will extend their knowledge to multiplying and
dividing multi-digit numbers. The place-value concept is used to facilitate understanding of multiplying with and without regrouping. Students
will be able to multiply and divide in vertical form by the end of the module. Students should be comfortable with using the Commutative
Property of Multiplication. Teachers should encourage the use of precise vocabulary in this chapter and review terms such as product, quotient,
divisor and remainder. Students will apply their work in all four operations to solve real-world problems.
Adapted from Math In Focus
Page 2
East Saint Louis District 189 Math Curriculum Grade 4
In primary grades, students learned to construct and analyze frequency tables, picture graphs, bar graphs, and line plots. They also used four
operations to solve problems based on their graphs. In Module 4, students will continue this work by collecting and organizing data and
interpreting line graphs and tables. Students will compare, analyze and classify data as they look for patterns and trends in the graphs.
Students are introduced to line graphs which have two numerical axes. Students will recognize that data flows continuously from left to right in
preparation for their work with functions in middle school grades.
Students will use a variety of tools in Module 5 to analyze data, such as average, median and probability. Vocabulary will play a key role in
helping students learn the new topics introduced throughout this module. Students will apply their understanding of place value and graphs to
develop and use stem-and-leaf plots to find mean, median, mode and range. Students will learn to describe the possibility of the occurrence of
different outcomes as a fraction. They will be given opportunities to solve real-world problems to check their understanding and ability to make
projections based on the data they are given using different data representations.
In earlier grades, students learned to find equivalent fractions. In Module 6, students will learn how to add and subtract like and unlike fractions
with and without renaming. They will be introduced to the concept of fractions of a set and will learn to apply this to real-world problems.
Concrete materials are used extensively to illustrate the addition and subtraction of fractions. Students will learn correct vocabulary such as
numerator and denominator to refer to their work with fractions. Students will learn to convert from improper fractions to mixed numbers and
vice versa. Students will apply their knowledge of finding common factors and multiples to add and subtract unlike but related fractions. Bar
models will be used to illustrate adding and subtracting real-world problems to help students visualize the problems they are solving.
In Module 7, students will learn to recognize, compare and round decimals in tenths and hundredths with the use of a number line. Students
will be introduced to the meaning and concept of a decimal point and that the digits to the right represent fractional parts of a whole. Students
will apply their knowledge of equivalent fractions to decimals through models and number lines. Students will develop an understanding of the
rule to describe a sequence of decimals and complete sequences by studying number patterns.
Students will add and subtract decimals up to two places in Module 8. They will learn that the same algorithms for adding and subtracting whole
numbers can be applied to decimal numbers. Students will review place value concepts of decimals to aid in working with regrouping in addition
and subtraction of decimals. Bar models are a good way to translate the words in a problem into a visual picture from which students can
decide what strategy to adopt to solve that problem. Students will extend that skill to drawing bar models for real-world problems with twostep decimal problems.
Students learn that angles can be seen everywhere around them. In Grade 3, students estimated the size of angles by comparing them to right
angles. In Module 9, students learn how to estimate angle measures and measure angles with a protractor. They will learn to draw angles up to
180° using a protractor. Another important concept is turns and their relation to angle measure. Students will use the work from Grade 3
(congruence, slides, flips and turns) to relate right angles to fractions of a turn.
Adapted from Math In Focus
Page 3
East Saint Louis District 189 Math Curriculum Grade 4
In Module 10, students extend their knowledge of line segments and continue to explore parallel and perpendicular line segments. Students will
learn to use a protractor or drawing triangle to draw perpendicular line segments when a grid is not provided. Students will also learn how to
draw parallel line segments using a drawing triangle. Students will identify horizontal and vertical lines.
Students will learn the properties of squares and rectangles in Module 11. They will identify and define squares and rectangles based on their
knowledge of angles and perpendicular and parallel line segments. Students will also learn to decompose shapes made up of square and
rectangles. Students will learn to find the measures of adjacent angels of a right angle in a square or rectangle. They will also learn to find the
side lengths of composite figures by using the properties of a square and rectangle.
In earlier grades, students learned to count grid squares to find the area of a figure. This is extended in Module 12 to find the area of a rectangle
by using the formula. Students connect this model to the area model for multiplication. Students have previously learned to add the lengths of
all the sides of a figure to find its perimeter. Students will apply what they have learned to find the perimeter of composite figures. They will
also learn to find one side of a rectangle or square when given its perimeter or area. Students will be required to apply their knowledge of area
and perimeter to solve real-world problems.
In Module 13, students learn to identify lines of symmetry of figures and to make symmetric shapes and patterns. This is a continuation of
previous chapters on drawing, analyzing, comparing and classifying two-dimensional shapes based on attributes and properties. Students will
solve problems involving congruence and symmetry. Students should be given many opportunities to experiment with making their own
symmetrical shapes and identifying the line of symmetry. Students also learn to identify figures with rotational symmetry through hands-on
activities.
Module 14 can be done if there is time. This is not a major focus of the Common Core Standards. Two days will be used for assessment for end
of year. Those items on the assessment can be ignored or whited out.
Adapted from Math In Focus
Page 4
East Saint Louis District 189 Math Curriculum Grade 4
Alignment Chart
Module and
Approximate
Number of
Instructional
Days
Module 1:
Place Value of
Whole Numbers
(8 days)
Do not forget
Common Core
Lesson 1.2a Page
276A and 1.2b from
Page 276B
M.P. 1
M.P. 4
M.P. 6
M.P. 7
Common Core Learning Standards Addressed in
Grade 4 Modules
Generalize place value understanding for
multi-digit whole numbers.
4.NBT.A.1 Recognize that in a multi-digit whole number,
a digit in one place represents ten times what it
represents in the place to its right. For example,
recognize that 700 ÷ 70 = 10 by applying concepts of
place value and division.
4.NBT.A.2 Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form. Compare two multi-digit numbers based
on meanings of the digits in each place, using >, =, and
< symbols to record the results of comparisons.
Use place value understanding and
properties of operations to perform multidigit arithmetic.
4.NBT.B.4 Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
Generate and analyze patterns.
4.OA.C.5 Generate a number or shape pattern that
follows a given rule. Identify apparent features of the
pattern that were not explicit in the rule itself. For
example, given the rule “Add 3” and the starting number
1, generate terms in the resulting sequence and observe
that the terms appear to alternate between odd and
even numbers. Explain informally why the numbers will
continue to alternate in this way
Adapted from Math In Focus
Vocabulary
Number Talks and
Instructional Strategies
Ten thousand,
Hundred
thousand,
Standard form,
Word form,
Expanded
form,
Greater than >,
Less than <,
More than,
Greatest,
Least,
Order,
Visuals; place value charts,
place value disks; place value
chart, number line
Number lines help show the
value of the numbers. Place
value chart shows how to
organize the digits – use place
value chart to line numbers up
vertically is a strategy to order
several numbers. Place value
strips are another tool to use.
Use skip counting by 10, 100,
1000 from any given number
forward and backward.
Write number sequences start with 4 digit number and
show 5 terms in the sequence
- increase by 10's, decrease by
100's, etc. Ask questions find
the number that is 100 less
than 20,000? 23,400 is how
much more than 22,400?
89,341 is how much less than
99, 341? Find the number that
is 10 less than 10,200.
Key in on place value patterns,
appropriate wording.
Performance
Based Tasks/
Assessments
Page 5
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Module 2:
Estimation and
Number Theory
(12 days—includes
1 day for
benchmark
assessment.)
M.P. 1
M.P. 2
M.P. 3
M.P. 6
Common Core Learning Standards Addressed in
Grade 4 Modules
Generalize place value understanding for
multi-digit whole numbers.
4.NBT.A.1 Recognize that in a multi-digit whole number,
a digit in one place represents ten times what it
represents in the place to its right. For example,
recognize that 700 ÷ 70 = 10 by applying concepts of
place value and division.
4.NBT.A.2 Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form. Compare two multi-digit numbers based
on meanings of the digits in each place, using >, =, and
< symbols to record the results of comparisons.
4.NBT.A.3 Use place value understanding to round
multi-digit whole numbers to any place.
Use place value understanding and
properties of operations to perform multidigit arithmetic.
4.NBT.B.4 Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
Use the four operations with whole
numbers to solve problems.
4.OA.A.3 Solve multistep word problems posed with
whole numbers and having whole-number answers
using the four operations, including problems in which
remainders must be interpreted. Represent these
problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of
answers using mental computation and estimation
Adapted from Math In Focus
Vocabulary
Number Talks and
Instructional Strategies
Estimate,
Reasonable,
Front-end
estimation,
Rounding,
Product,
Quotient,
Factor,
Common
factor,
Greatest
common
factor,
Prime number,
Composite
number,
Multiple,
Common
multiple,
Least common
multiple
Place value disks are a
valuable tool for showing
relationships of the place
values for 4.NBT.A.1.
Find LCM and GCF of two
numbers by making lists of
multiples or factors.
Then "double division"
method - successively dividing
both numbers by any common
divisor, repeating processes,
find all the common divisors
(factors) of two numbers.
Products of these common
divisors is the GCF of 2
numbers. LCM of numbers is
the product of the common
divisors and the two numbers
that remain.
Extend the act hands-on
activity.
Students can use a laminated
hundred grid with counters or
markers. They can find the
numbers that have a factor of
two. With another color, find
factors of 4. Are all numbers a
factor of both 2 and 4? What
patterns do you see? A
Performance
Based Tasks/
Assessments
Page 6
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
strategies including rounding.
Gain familiarity with factors and multiples.
4.OA.B.4 Find all factor pairs for a whole number in the
range 1–100. Recognize that a whole number is a
multiple of each of its factors. Determine whether a
given whole number in the range 1–100 is a multiple of
a given one-digit number. Determine whether a given
whole number in the range 1–100 is prime or composite
Module 3:
Whole Number
Multiplication
and Division
(17 days)
Additional Common
Core Lessons for
Chapter 3:
Lesson 3.0 Pg. 276D
Lesson 3.1a Pg.
276E
Lesson 3.5a Pg.
276F
M.P. 4
M.P. 5
M.P. 6
M.P. 7
Generalize place value understanding for
multi-digit whole numbers.
4.NBT.A.1 Recognize that in a multi-digit whole number,
a digit in one place represents ten times what it
represents in the place to its right. For example,
recognize that 700 ÷ 70 = 10 by applying concepts of
place value and division.
4.NBT.A.2 Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form. Compare two multi-digit numbers based
on meanings of the digits in each place, using >, =, and
< symbols to record the results of comparisons.
4.NBT.A.3 Use place value understanding to round
multi-digit whole numbers to any place.
Use place value understanding and
properties of operations to perform multidigit arithmetic.
4.NBT.B.4 Fluently add and subtract multi-digit whole
Adapted from Math In Focus
Round,
Estimate,
Product,
Regroup,
Rename,
Quotient,
Divisor,
Dividend,
Remainder
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
strategy for finding a number
that ends in 4 is choose a
number, subtract 20 until you
get a number that is divisible
by 4. Then that number is
divisible by 4.
Find patterns of multiple and
factors on the hundred board
with 3, 6, 9, etc.
Multiplication as scaling is the
big idea (not repeated
addition). A key strategy is to
make estimates for the
problems first to build number
sense before beginning any
paper/pencil computation.
Round to compatible numbers
(related facts) or largest place
value for students.
Compatible numbers are
especially important during
the division section. Use the
place value disks to begin all
the operations. Keep working
on number talks –
multiplication and division
with multiplication strings and
one digit by 2 digit numbers.
Page 7
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
numbers using the standard algorithm.
4.NBT.B.5 Multiply a whole number of up to four digits
by a one-digit whole number, and multiply two two-digit
numbers, using strategies based on place value and the
properties of operations. Illustrate and explain the
calculation by using equations, rectangular arrays,
and/or area models.
4.NBT.B.6 Find whole-number quotients and
remainders with up to four-digit dividends and one-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.
Use the four operations with whole
numbers to solve problems.
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
Continue number talks that
have students estimate these
types of problems for the
remainder of the year. You
can also give students one or
two problems a day to do
paper and pencil to continue
to practice.
Mastery of multi-digit
multiplication and division is
not an expected mastery until
5th and 6th grades. However,
addition and subtraction of
multi-digit numbers is an
expected mastery.
4.OA.A.1 Interpret a multiplication equation as a
comparison, e.g., interpret 35 = 5 × 7 as a statement
that 35 is 5 times as many as 7 and 7 times as many as
5. Represent verbal statements of multiplicative
comparisons as multiplication equations.
4.OA.A.2 Multiply or divide to solve word problems
involving multiplicative comparison, e.g., by using
drawings and equations with a symbol for the unknown
number to represent the problem, distinguishing
multiplicative comparison from additive comparison.
Adapted from Math In Focus
Page 8
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Module 4:
Tables and
Graphs
(13 days--includes 2
days for benchmark
assessment)
Common Core Learning Standards Addressed in
Grade 4 Modules
Build fractions from unit fractions.
4.NF.B.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.
Represent and interpret data.
M.P. 1
M.P. 3
M.P. 6
M.P. 7
Module 5:
Data and
Probability
(14 days)
M.P. 1
M.P. 3
M.P. 4
M.P. 6
4.MD.B.4 Make a line plot to display a data set of
measurements in fractions of a unit (1/2, 1/4, 1/8). Solve
problems involving addition and subtraction of fractions
by using information presented in line plots. For
example, from a line plot find and interpret the difference
in length between the longest and shortest specimens in
an insect collection.
Extend understanding of fraction
equivalence and ordering.
4.NF.A.1 Explain why a fraction a/b is equivalent to a
fraction (n × a)/(n × b) by using visual fraction models,
with attention to how the number and size of the parts
differ even though the two fractions themselves are the
same size. Use this principle to recognize and generate
equivalent fractions.
Use the four operations with whole
numbers to solve problems.
4.OA.A.3 Solve multistep word problems posed with
whole numbers and having whole-number answers
using the four operations, including problems in which
Adapted from Math In Focus
Vocabulary
Number Talks and
Instructional Strategies
Data, Table,
Tally chart,
Row,
Column,
Intersection,
Line graph,
Horizontal
axis,
Vertical axis
This units is missing an
important piece with line plots
and fractions.
Average,
Mean,
Median,
Mode,
Range,
Line plot,
Stem and leaf
plot,
Outlier,
Outcome,
Certain,
More likely,
Equally likely,
Less likely,
Even though probability and
measures of central tendency
are not specifically stated in
the CCSS for mathematics, the
lessons give practical
application for operations
with numbers. The unit
connects measurements,
fractions, and scaling. Do not
extend this unit. .
Performance
Based Tasks/
Assessments
http://www.mathworkshee
tsland.com/4/26measfrac/g
uided.pdf has a good lesson.
Replace the Put on Your
Thinking Cap with this activity.
This will not affect your end of
module assessment.
Page 9
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
remainders must be interpreted. Represent these
problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of
answers using mental computation and estimation
strategies including rounding.
Module 6:
Fractions and
Mixed Numbers
(20 days—includes
2 days for
benchmark
assessment)
Additional Common
Core Lessons for
Chapter 6:
Lesson 6.0 Pg. 276H
Lesson 6.7a Pg.
276I
Lesson 6.8a Pg.
276J
M.P. 2
M.P. 3
M.P. 4
M.P. 6
Extend understanding of fraction equivalence
and ordering.
4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction
(n × a)/(n × b) by using visual fraction models, with attention to
how the number and size of the parts differ even though the
two fractions themselves are the same size. Use this principle
to recognize and generate equivalent fractions.
4.NF.A.2 Compare two fractions with different numerators and
different denominators, e.g., by creating common
denominators or numerators, or by comparing to a benchmark
fraction such as 1/2. Recognize that comparisons are valid
only when the two fractions refer to the same whole. Record
the results of comparisons with symbols >, =, or <, and justify
the conclusions, e.g., by using a visual fraction model .
Build fractions from unit fractions.
4.NF.B.3a Understand addition and subtraction of fractions as
joining and separating parts referring to the same whole.
4.NF.B.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. Examples: 3/8 = 1/8 + 1/8 + 1/8 ;
3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NF.B.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
Adapted from Math In Focus
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
Impossible,
Favorable
outcome,
Probability
Numerator,
Denominator,
Equivalent
fraction,
Unlike
fraction,
Mixed
number,
Simplest form,
Improper
fraction
Fraction bar,
Division rule,
Multiplication
rule
Understanding fractions as a
number is very important, not
just as a part to a whole. Fraction
is number of parts out of a total
number of equal parts.
Denominator represents ordinal
numbers. Fractions are numbers,
represent quantity amounts, can
be shown on a number line, and
can be used to perform
operations.
Estimation of fraction operations
is important. Rely on the
benchmark fractions students
should master, 0, 1, ½, ¼, ¾.
To reinforce that the fractions
need like denominators, write
addition of fractions as
1 2
1+2
3
+ =
=
6 6
6
6
Simplifying the fractions can be
done, but credit should be given
if they have the appropriate
fraction. Equivalent fractions are
created by multiplying or dividing
by another representation of 1.
Page 10
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
and the relationship between addition and subtraction.
4.NF.B.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 × (1/4), recording the conclusion by the equation 5/4
= 5 × (1/4).
4.NF.B.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
× (2/5) as 6 × (1/5), recognizing this product as 6/5. (In
general, n × (a/b) = (n × a)/b.)
4.NF.B.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 pound of roast beef,
and there will be 5 people at the party, how many pounds of
roast beef will be needed? Between what two whole numbers
does your answer lie?
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
Remember to compose and
decompose fractions just as you
whole numbers, and using the
fraction strips.
Remember, in comparing
fractions, a strategy can be to
convert to the same numerator
to help, i.e. 2/5 and 1/3. You can
create an equivalent fraction for
1/3 which is 2/6. So you have 2/5
and 2/6. Which is bigger? Have
students focus on the size of the
unit fraction. Which is bigger 1/5
or 1/6?
The standards give good
examples of fraction operations.
Solve problems involving measurement and
conversion of measurements.
4.MD.A.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 measurement equivalents in a two-column table. For
example, know that 1 ft is 12 times as long as 1 in. Express
the length of a 4 ft snake as 48 in. Generate a conversion
table for feet and inches listing the number pairs (1, 12), (2,
24), (3, 36), ...
4.MD.A.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.
Adapted from Math In Focus
Page 11
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Tenth,
Decimal form,
Decimal point,
Expanded
form,
Hundredth,
Placeholder
Students need lots of practice
with verbally reading the
decimals numbers. Reinforce
2.3 as two and 3 tenths. Do
not say point.
As you work with renaming
fractions and decimals, ask
Performance
Based Tasks/
Assessments
Represent measurement quantities using diagrams such as
number line diagrams that feature a measurement scale.
Represent and interpret data.
4.MD.B.4 Make a line plot to display a data set of
measurements in fractions of a unit (1/2, 1/4, 1/8). Solve
problems involving addition and subtraction of fractions by
using information presented in line plots. For example, from a
line plot find and interpret the difference in length between the
longest and shortest specimens in an insect collection.
Use the four operations with whole numbers to
solve problems.
4.OA.A.2 Multiply or divide to solve word problems involving
multiplicative comparison, e.g., by using drawings and
equations with a symbol for the unknown number to represent
the problem, distinguishing multiplicative comparison from
additive comparison.
4.OA.A.3 Solve multistep word problems posed with whole
numbers and having whole-number answers using the four
operations, including problems in which remainders must be
interpreted. Represent these problems using equations with a
letter standing for the unknown quantity. Assess the
reasonableness of answers using mental computation and
estimation strategies including rounding.
Module 7:
Decimals
(15 days)
M.P. 1
M.P. 4
Solve problems involving measurement
and conversion of measurements.
4.MD.A.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 measurement
Adapted from Math In Focus
Page 12
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
M.P. 6
M.P. 7
Common Core Learning Standards Addressed in
Grade 4 Modules
equivalents in a two-column table. For example, know
that 1 ft is 12 times as long as 1 in. Express the length
of a 4 ft snake as 48 in. Generate a conversion table for
feet and inches listing the number pairs (1, 12), (2, 24),
(3, 36), ...
Generalize place value understanding for
multi-digit whole numbers.
4.NBT.A.1 Recognize that in a multi-digit whole number,
a digit in one place represents ten times what it
represents in the place to its right. For example,
recognize that 700 ÷ 70 = 10 by applying concepts of
place value and division.
4.NBT.A.2 Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form. Compare two multi-digit numbers based
on meanings of the digits in each place, using >, =, and
< symbols to record the results of comparisons.
Extend understanding of fraction
equivalence and ordering.
4.NF.A.1 Explain why a fraction a/b is equivalent to a
fraction (n × a)/(n × b) by using visual fraction models,
with attention to how the number and size of the parts
differ even though the two fractions themselves are the
same size. Use this principle to recognize and generate
equivalent fractions.
Build fractions from unit fractions.
Vocabulary
Number Talks and
Instructional Strategies
zero,
More than,
Less than,
Greater than,
Least,
Greatest,
Order,
Round,
Equivalent
fraction
How many tenths are there in
0.4?
How many tenths are there in
1?
How many tenths are there in
1.4?
How many tenths are there in
4?
What is the decimal number
for 42 tenths?
Do the same types of
questions as you move to
hundredths.
Continue with number talks
with decimals and key on the
students’ familiarity with
money. Have students break
up numbers into the different
place values and write it in
different representations. As,
6
60
4.6; 4 ; 4.60; 4
.
10
Performance
Based Tasks/
Assessments
100
Remember that the same
strategies we used to make
100 will be used with decimals
to make 1.
4.NF.B.3a Understand addition and subtraction of
fractions as joining and separating parts referring to the
Adapted from Math In Focus
Page 13
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
same whole.
Understand decimal notation for fractions,
and compare decimal fractions.
4.NF.C.5 Express a fraction with denominator 10 as an
equivalent fraction with denominator 100, and use this
technique to add two fractions with respective
denominators 10 and 100.2 For example, express 3/10
as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.C.6 Use decimal notation for fractions with
denominators 10 or 100. For example, rewrite 0.62 as
62/100; describe a length as 0.62 meters; locate 0.62 on
a number line diagram.
4.NF.C.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.
Generate and analyze patterns.
4.OA.C.5 Generate a number or shape pattern that
follows a given rule. Identify apparent features of the
pattern that were not explicit in the rule itself. For
example, given the rule “Add 3” and the starting number
1, generate terms in the resulting sequence and observe
that the terms appear to alternate between odd and
even numbers. Explain informally why the numbers will
continue to alternate in this way.
Module 8:
Adding and
Generalize place value understanding for
Adapted from Math In Focus
There is a decimal game on
page 30 that can be played
Page 14
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Subtracting
Decimals
Common Core Learning Standards Addressed in
Grade 4 Modules
multi-digit whole numbers.
(10 days—includes
1 day for
benchmark
assessment)
4.NBT.A.1 Recognize that in a multi-digit whole number,
a digit in one place represents ten times what it
represents in the place to its right. For example,
recognize that 700 ÷ 70 = 10 by applying concepts of
place value and division.
M.P. 1
M.P. 4
M.P. 7
M.P. 8
4.NBT.A.2 Read and write multi-digit whole numbers
using base-ten numerals, number names, and
expanded form. Compare two multi-digit numbers based
on meanings of the digits in each place, using >, =, and
< symbols to record the results of comparisons.
Use place value understanding and
properties of operations to perform multidigit arithmetic.
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
throughout the unit. Change
the rules to have students
draw two cards and get the
sum. Students can check on a
calculator to see if they are
correct.
Number talks can include
adding and subtracting with
tenths and hundredths, as in
the examples in the standards,
i.e. 4/10 + 4/100.
Practice in writing and saying
the numbers can be included
in this chapter also.
4.NBT.B.4 Fluently add and subtract multi-digit whole
numbers using the standard algorithm.
Understand decimal notation for fractions,
and compare decimal fractions.
4.NF.C.5 Express a fraction with denominator 10 as an
equivalent fraction with denominator 100, and use this
technique to add two fractions with respective
denominators 10 and 100.2 For example, express 3/10
as 30/100, and add 3/10 + 4/100 = 34/100.
Use the four operations with whole
numbers to solve problems.
4.OA.A.3 Solve multistep word problems posed with
whole numbers and having whole-number answers
using the four operations, including problems in which
Adapted from Math In Focus
Page 15
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Ray,
Vertex,
Protractor,
Degrees,
Vocabulary journals will be
very important in this module.
You may need to play some
vocabulary games each day, as
Performance
Based Tasks/
Assessments
remainders must be interpreted. Represent these
problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of
answers using mental computation and estimation
strategies including rounding.
Solve problems involving measurement
and conversion of measurements.
4.MD.A.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 measurement
equivalents in a two-column table. For example, know
that 1 ft is 12 times as long as 1 in. Express the length
of a 4 ft snake as 48 in. Generate a conversion table for
feet and inches listing the number pairs (1, 12), (2, 24),
(3, 36), ...
4.MD.A.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.
Module 9:
Angles
(9 days)
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.
Adapted from Math In Focus
Page 16
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Additional
Common Core
Lessons for
Chapter 9:
Lesson 9.3a Pg.
242A
Lesson 9.3b Pg.
242B
M.P. 2
M.P. 3
M.P. 5
M.P. 6
Common Core Learning Standards Addressed in
Grade 4 Modules
4.G.A.1 Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
Geometric measurement: understand
concepts of angle and measure angles.
4.MD.C.5 Recognize angles as geometric shapes that
are formed wherever two rays share a common
endpoint, and understand concepts of angle
measurement:
4.MD.C.5a An angle is measured with reference to a
circle with its center at the common endpoint of the rays,
by considering the fraction of the circular arc between
the points where the two rays intersect the circle. An
angle that turns through 1/360 of a circle is called a
“one-degree angle,” and can be used to measure
angles.
Vocabulary
Number Talks and
Instructional Strategies
Inner scale,
Outer scale,
Acute angle,
Obtuse angle,
Straight angle,
Turn,
Additive
riddles, guess my word, word
wall categories, etc.
The circle is a very important
concept – having 360 degrees.
The Babylonians may have
decided on 360 since there
was 360 days in their year.
360 is easily divisible by many
factors which makes it easy to
work with.
Students should be able to
measure to the nearest
degree. Always have them
look at an angle to estimate
first, knowing it is obtuse,
acute, right, etc.
Performance
Based Tasks/
Assessments
4.MD.C.5b An angle that turns through n one-degree
angles is said to have an angle measure of n degrees.
4.MD.C.6 Measure angles in whole-number degrees
using a protractor. Sketch angles of specified measure.
4.MD.C.7 Recognize angle measure as additive. When
an angle is decomposed into non-overlapping parts, the
angle measure of the whole is the sum of the angle
measures of the parts. Solve addition and subtraction
problems to find unknown angles on a diagram in real
world and mathematical problems, e.g., by using an
equation with a symbol for the unknown angle measure.
Adapted from Math In Focus
Page 17
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Module 10:
Perpendicular and
Parallel Line
Segments
(9 days)
M.P. 1
M.P. 3
M.P. 5
M.P. 6
Module 11:
Squares and
Rectangles
(10 days—includes
2 days for
benchmark
assessment)
M.P. 3
M.P. 5
M.P. 6
M.P. 7
Common Core Learning Standards Addressed in
Grade 4 Modules
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.
4.G.A.1 Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
4.G.A.2 Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular lines,
or the presence or absence of angles of a specified size.
Recognize right triangles as a category, and identify
right triangles
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.
4.G.A.2 Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular lines,
or the presence or absence of angles of a specified size.
Recognize right triangles as a category, and identify
right triangles.
Vocabulary
Number Talks and
Instructional Strategies
Perpendicular
line segments,
Drawing
triangle,
Parallel line
segments,
Base,
Horizontal
lines,
Vertical lines
Having a real life picture from
the internet of a railroad
center, city, park, etc. where
students can identify parallel
and perpendicular lines is
motivating for students Keep
reinforcing the vocabulary
from previous module.
Number talks that use angles
and lines will help students
keep strategies for whole
number operations.
This module should embed
previous 2 modules
understandings and
reasoning. Students should
master appropriate notation
of geometric shapes, angles,
segments, etc..
Square,
Rectangle,
Right angle,
Parallel,
Performance
Based Tasks/
Assessments
Solve problems involving measurement
and conversion of measurements.
4.MD.A.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 measurement
equivalents in a two-column table. For example, know
Adapted from Math In Focus
Page 18
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
that 1 ft is 12 times as long as 1 in. Express the length
of a 4 ft snake as 48 in. Generate a conversion table for
feet and inches listing the number pairs (1, 12), (2, 24),
(3, 36), ...
4.MD.A.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.
Geometric measurement: understand
concepts of angle and measure angles.
4.MD.C.7 Recognize angle measure as additive. When
an angle is decomposed into non-overlapping parts, the
angle measure of the whole is the sum of the angle
measures of the parts. Solve addition and subtraction
problems to find unknown angles on a diagram in real
world and mathematical problems, e.g., by using an
equation with a symbol for the unknown angle measure.
Use the four operations with whole
numbers to solve problems.
4.OA.A.3 Solve multistep word problems posed with
whole numbers and having whole-number answers
using the four operations, including problems in which
remainders must be interpreted. Represent these
problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of
Adapted from Math In Focus
Page 19
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Length,
Width,
Composite
figure,
Area,
Perimeter
Students need to memorize
the area and perimeter
formulas for a rectangle. This
module embeds both metric
and customary units. This
materials should be mastered
at this grade level.
Performance
Based Tasks/
Assessments
answers using mental computation and estimation
strategies including rounding.
Module 12:
Area and
Perimeter Measurement
Solve problems involving measurement
and conversion of measurements.
Additional Common
Core Lessons for
Chapter 12:
4.MD.A.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 measurement
equivalents in a two-column table. For example, know
that 1 ft is 12 times as long as 1 in. Express the length
of a 4 ft snake as 48 in. Generate a conversion table for
feet and inches listing the number pairs (1, 12), (2, 24),
(3, 36), ...
Lesson 12.0a Pg.
242D
Lesson 12.0b Pg.
242G
Lesson 12.0c Pg.
242I
Lesson 12.0 d Pg.
242K
4.MD.A.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.
M.P. 2
M.P. 4
M.P. 5
M.P. 6
M.P. 8
4.MD.A.3 Apply the area and perimeter formulas for
rectangles in real world and mathematical problems. For
example, find the width of a rectangular room given the
area of the flooring and the length, by viewing the area
formula as a multiplication equation with an unknown
factor.
(24 days—includes
2 days for
benchmark
assessment)
Adapted from Math In Focus
Page 20
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Line of
symmetry,
Symmetric
figure,
Rotation,
Rotational
symmetry,
Center of
rotation,
Clockwise,
Counterclockwise,
Embed the properties of
lines and angles that was
studied in early modules.
The students should be
fluent with using the
vocabulary to describe the
symmetry.
Performance
Based Tasks/
Assessments
Use the four operations with whole
numbers to solve problems.
4.OA.A.3 Solve multistep word problems posed with
whole numbers and having whole-number answers
using the four operations, including problems in which
remainders must be interpreted. Represent these
problems using equations with a letter standing for the
unknown quantity. Assess the reasonableness of
answers using mental computation and estimation
strategies including rounding.
Module 13:
Symmetry
(10 days)
M.P. 1
M.P. 3
M.P. 6
M.P. 7
Draw and identify lines and angles, and
classify shapes by properties of their lines
and angles.
4.G.A.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such that
the figure can be folded along the line into matching
parts. Identify line-symmetric figures and draw lines of
symmetry.
Generate and analyze patterns.
4.OA.C.5 Generate a number or shape pattern that
follows a given rule. Identify apparent features of the
pattern that were not explicit in the rule itself. For
example, given the rule “Add 3” and the starting number
1, generate terms in the resulting sequence and observe
that the terms appear to alternate between odd and
even numbers. Explain informally why the numbers will
continue to alternate in this way.
Adapted from Math In Focus
Page 21
East Saint Louis District 189 Math Curriculum Grade 4
Module and
Approximate
Number of
Instructional
Days
Module 14:
Tessellations (2
Common Core Learning Standards Addressed in
Grade 4 Modules
Vocabulary
Number Talks and
Instructional Strategies
Performance
Based Tasks/
Assessments
If time permits, three websites could
be useful.
http://www.shodor.org/interacti
vate/activities/FloorTiles/ and
http://www.shodor.org/interacti
vate/activities/Tessellate/ and
http://nlvm.usu.edu/en/nav/fra
mes_asid_163_g_2_t_3.html?op
en=activities&from=category_g_
2_t_3.html.
days for
assessment)
The sites have instructor ideas for
lessons.
Key:
Major Clusters;
Supporting Clusters;
Additional Clusters
Examples of Linking Supporting Clusters to the Major Work of the Grade

Gain familiarity with factors and multiples: Work in this cluster supports students’ work with multi-digit arithmetic as well as their work with fraction
equivalence.

Represent and interpret data: The standard in this cluster requires students to use a line plot to display measurements in fractions of a unit and to
solve problems involving addition and subtraction of fractions, connecting it directly to the Number and Operations — Fractions clusters.
Adapted from Math In Focus
Page 22