Fourth Grade
Mathematics Curriculum Resource
for the Maryland College and Career Ready Standards
2014-2015
Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Fourth Grade Overview
Operations and Algebraic Thinking (OA)

Use the four operations with whole numbers to solve problems.

Gain familiarity with factors and multiples.

Generate and analyze patterns.
Number and Operations in Base Ten (NBT)

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 (NF)

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.
Measurement and Data (MD)

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Represent and interpret data.

Geometric measurement: understand concepts of angle and measure angles.
Geometry (G)
 Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Major Cluster
Grade 4
Supporting Cluster
Wicomico County Public Schools Revised 2014-2015
Additional Cluster
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Standards for Mathematical Practice
Standards
Explanations and Examples
1. Make sense of
problems and
persevere in solving
them.
In fourth grade, students know that doing mathematics involves solving problems and discussing how they solved them.
Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete
objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves,
“Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another
method to check their answers.
Fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols
and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of
quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write
simple expressions, record calculations with numbers, and represent or round numbers using place value concepts.
In fourth grade, students may construct arguments using concrete referents, such as objects, pictures, and drawings. They
explain their thinking and make connections between models and equations. They refine their mathematical communication
skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?”
They explain their thinking to others and respond to others’ thinking.
Students experiment with representing problem situations in multiple ways including numbers, words (mathematical
language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities
to connect the different representations and explain the connections. They should be able to use all of these representations
as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make
sense.
Fourth graders consider the available tools (including estimation) when solving a mathematical problem and decide when
certain tools might be helpful. For instance, they may use graph paper or a number line to represent and compare decimals
and protractors to measure angles. They use other measurement tools to understand the relative size of units within a system
and express measurements given in larger units in terms of smaller units.
As fourth graders develop their mathematical communication skills, they try to use clear and precise language in their
discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning
of the symbols they choose. For instance, they use appropriate labels when creating a line plot.
In fourth grade, students look closely to discover a pattern or structure. For instance, students use properties of operations to
explain calculations (partial products model). They relate representations of counting problems such as tree diagrams and
arrays to the multiplication principal of counting. They generate number or shape patterns that follow a given rule.
Students in fourth grade should notice repetitive actions in computation to make generalizations Students use models to
explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own
algorithms. For example, students use visual fraction models to write equivalent fractions.
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.
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
GRADE 4 COMMON CORE INTRODUCTION
In Grade 4, instructional time should focus on three critical areas: (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; (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.
1. Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their
understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive
property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending
on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency
with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of
operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the
relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon
the context.
2. Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 =
5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built
from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning
of multiplication to multiply a fraction by a whole number.
3. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students
deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Fourth Grade Math At-A-Glance
2014-2015
Unit 1: Applying Place Value Concepts in
Whole Number Addition and Subtraction
(14 days)
Unit 2: Efficiency with Multiplication and Understanding Division
(20 days)
Unit 3: Solving Problems Using Multiplicative Comparison
(10 days)
Unit 4: Understanding & Comparing Fractions
(22 days)
Unit 5: Fraction Operations
(23 days)
Unit 6: Understanding & Comparing Decimals
(13 days)
Important Dates
September 1 Labor Day
September 26 Professional Day
October 17 MSEA Convention
October 21 Interim Assessment #1
This day is not counted as an instructional day.
November 3 Professional Day
November 4 Election Day
November 26-28 Thanksgiving
December 10 Interim Assessment #2
This day is not counted as an instructional day.
December 22-January 2 Winter Holiday
January 19 MLK Day
January 26 Professional Day
Spiral Review
(8 days)
February 13 Professional Day
February 16 President’s Day
February 19 Interim Assessment #3
This day is not counted as an instructional day.
PARCC PBA/MYA Testing Window March 2-27 (2 days within this window)
Unit 7: Measurement Conversions & Problem Solving
April 1-6 Spring Holiday
(12 days)
April 7 Professional Day
Unit 8: Geometry
(16 days)
PARCC EOY Testing Window April 20- May 15 (2 days within this window)
Unit 9: Fluency with Problem Solving
May 25 Memorial Day
Follows EOY PARCC
(32 days or remainder of year)
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Unit One – Applying Place Value Concepts in Whole Number Addition and Subtraction (14 days)
The focus of this unit is to provide students time to develop and practice efficient addition and subtraction of multi-digit whole numbers while developing
place value concepts.
Unit One Standards
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. This standard
will be revisited in unit 7 connected to conversions within the metric system of measurement.
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. This standard will be revisited in unit 3 with multiplication
and division as a context.
4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. This standard will be revisited in unit 7 and finalized in
unit 9 for fluency in addition and subtraction of multi‐digit whole numbers.
Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged
to use these math terms in explanations or justifications.
addend
digits
minuend
algorithm
equation
place value
compare
estimation
rounding
decompose
expanded form
subtrahend
difference
expression
sum
Essential Questions
How does our base-10 number system work?
How does understanding base-10 number system help us add and subtract?
How do digit values change as they are moved around in large numbers?
What determines the value of a digit?
What conclusions can I make about the places within our base ten number system?
What happens to a digit when multiplied and divided by 10?
What effect does the location of a digit have on the value of the digit?
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
How does the value of digits in a number help me compare two numbers?
How can we tell which number among many large numbers is the largest or smallest?
Why is it important for me to be able to compare numbers?
How can we compare large numbers?
What determines the value of a number?
Why is it important for me to be able to compare numbers?
What information is needed in order to round whole numbers to any place?
How are large numbers estimated?
How does understanding place value help me explain my method for rounding a number to any place?
How can I round to help me find a reasonable answer to a problem?
How does estimation keep us from having to count large numbers individually?
How are large numbers estimated?
What information is needed in order to round whole number to any place?
How can rounding help me compute numbers?
What strategies can I use to help me make sense of a written algorithm?
What strategies help me add and subtract multi-digit numbers?
How can I ensure my answer is reasonable?
What is a sensible answer to a real problem?
How does knowing and using algorithms help us to be efficient problem solvers?
Common Misconceptions
NBT.4 - Often students mix up when to “carry” and when to “borrow/regroup”. Also students often do not notice the need of borrowing/regrouping and just
take the smaller digit from the larger one. Emphasize place value and the meaning of the digits.
If students are having difficulty with linking up similar place values in numbers as they are adding and subtracting, it is sometimes helpful to have them write
their calculations on the grid paper. This assists the student with lining up the numbers more accurately.
If students are having a difficult time with a standard addition algorithm, a possible modification to the algorithm might be helpful. Instead of the “shorthand” of
“carrying,” students could add by place value, moving left to right placing the answers down below the “equals” line.
For example:
249
+ 372
500
(Start with 200 + 300 to get the 500
110
then 40 + 70 to get 110
11
and 9 + 2 to get 11.)
621
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit One – Applying Place Value Concepts in Whole Number Addition & Subtraction (14 days)
Connections/Notes
Resources
4.NBT.A.1
Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
Teaching Student-Centered Mathematics
pg. 48 Figure 2.7 What Comes Next Activity 2.8
Students use the structure of the base‐ten system to generalize their strategies and to discuss
reasonableness of their computations and work towards fluency. (MP.6, MP.8).
Lessons:
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Recognize a Digit Represents 10 Times the Value
Generalize place value understanding for multi-digit whole numbers.
as the Digit to Its Right
Students generalize their previous understanding of place value for multi-digit whole numbers
This supports their work in multi-digit multiplication and division, carrying forward into grade 5, when
students will extend place value to decimals.
Students should be familiar with and use place value as they work with numbers. Some activities that will
help students develop understanding of this standard are:


Investigate the product of 10 and any number, then justify why the number now has a 0 at the end.
(7 x 10 = 70 because 70 represents 7 tens and no ones, 10 x 35 = 350 because the 3 in 350
represents 3 hundreds, which is 10 times as much as 3 tens, and the 5 represents 5 tens, which is
10 times as much as 5 ones.) While students can easily see the pattern of adding a 0 at the end of
a number when multiplying by 10, they need to be able to justify why this works.
Investigate the pattern, 6, 60, 600, 6,000, 60,000, and 600,000 by dividing each number by the
previous number.
Activities and Tasks:
Place Value Problems
Place Value Task Cards
Practice/Assessment Sheet
Videos:
Understanding Multi-Digit Whole Number Place
Value Concepts
Use a Place Value Chart and Arrow Cards to
Understand Large Numbers
Model Numbers Using Base Ten Blocks
Understand Relationships Between Digits and Their
Place Value
Example:
Recognize that 700 ÷ 70 = 10 applying concepts of place value and division.
In the number 85,254, how many times greater is the 5 in the thousands place than the 5 in the
tens place?
Multiply by Powers of Ten
Divide by Powers of 10
Online:
Place Value Number Line NLVM
Place Value Calculator
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit One – Applying Place Value Concepts in Whole Number Addition & Subtraction (14 days)
Connections/Notes
Resources
4.NBT.A.1 Continued
Templates and Visuals
Place Value Chart
Place Value Arrow Cards
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 the comparisons.
The expanded form of 275 is 200 + 70 + 5. Students use place value to compare numbers. For example,
in comparing 34,570 and 34,192, a student might say, both numbers have the same value of 10,000s and
the same value of 1000s however, the value in the 100s place is different so that is where I would
compare the two numbers.
Examples:
Which number makes this sentence true?
Which number makes this sentence true?
701 < 717 - x
381 + x > 830
I can rewrite the numbers as (300 + 80 + 1) + x > (800 + 30).
This way I can see how many hundreds, tens, and ones I can add to make the inequality sentence true.
Teaching Student-Centered Mathematics
pgs. 47-51 (Numbers Beyond 1000)
Lessons:
Expand That Number! Illuminations
Read and Write Numbers Using Base Ten
Numerals, Number Names, and Expanded Form
Activities and Tasks:
Place Value Problems
Place Value Triangle
Numeral, Word and Expanded Form
Frayer Model
Ordering 4-Digit Numbers
Place Value QR Code Task Cards
In Between Game
Videos:
Read and Write Numbers in Numeric Form
Connections: 4.NBT.A.1
Read and Write Numbers in Word Form
Creating Numbers Based on Given Conditions by
Comparing Digits
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit One – Applying Place Value Concepts in Whole Number Addition & Subtraction (14 days)
Connections/Notes
Resources
4.NBT.A.2 Continued
Read and Write Numbers in Expanded Form
Templates and Visuals:
Place Value Arrow Cards
4.NBT.A.3
Use place value understanding to round multi-digit whole numbers to any place.
The expectation is that students have a deep understanding of place value and number sense and can
explain and reason about the answers they get when they round. Students should have number
experiences using a number line and hundreds chart as tools to support their work with rounding.
When students are asked to round large numbers, they first need to identify which digit is in the
appropriate place.
Examples:
Round 76,398 to the nearest 1000.

Step 1: Since I need to round to the nearest 1000, then the answer is either 76,000 or 77,000.

Step 2: I know that the halfway point between these two numbers is 76,500.

Step 3: I see that 76,398 is between 76,000 and 76,500.

Step 4: Therefore, the rounded number would be 76,000.
Round 368 to the nearest hundred. This will be either 300 or 400, since those are the two hundreds before
and after 368. Draw a number line, subdivide it as much as necessary and determine whether 368 is
closer to 300 or 400. Since 368 is closer to 400, this number should be rounded to 400.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Teaching Student-Centered Mathematics
pg. 47, Approximate Numbers & Rounding,
Figure 2.6 (Number line)
Lessons:
Round Numbers to the Thousands Place Using the
Vertical Number Line
Round Numbers to Any Place Using the Vertical
Number Line
Use Place Value Understanding to Round Numbers
to Any Place
Use Place Value to Round Numbers Using Real
World Applications
Activities and Tasks:
Rounding to Nearest Ten Number Line
Rounding
Videos:
Locate Benchmark Numbers on a Number Line
Round Numbers to the Leading Digit Using a
Number Line
Round Numbers to a Specified Place on a Number
Line
Round in Real-Life Situations
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit One – Applying Place Value Concepts in Whole Number Addition & Subtraction (14 days)
Connections/Notes
Resources
4.NBT.A.3 Continued
Templates and Visuals:
Estimating Chart
Hundreds Chart for Rounding
4.NBT.B.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Students build on their understanding of addition and subtraction, their use of place value and their
flexibility with multiple strategies to make sense of the standard algorithm. They continue to use place
value in describing and justifying the processes they use to add and subtract.
When students begin using the standard algorithm their explanation may be quite lengthy. After much
practice with using place value to justify their steps, they will develop fluency with the algorithm. Students
should be able to explain why the algorithm works.
Student explanation for this problem:
3892
+ 1567
1. Two ones plus seven ones is nine ones.
2. Nine tens plus six tens is 15 tens.
3. I am going to write down five tens and think of the10 tens as one more hundred. (notates with
a 1 above the hundreds column)
4. Eight hundreds plus five hundreds plus the extra hundred from adding the tens is 14
hundreds.
5. I am going to write the four hundreds and think of the 10 hundreds as one more 1000. (notates
with a 1 above the thousands column)
6. Three thousands plus one thousand plus the extra thousand from the hundreds is five
thousand.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Teaching Student-Centered Mathematics
pg. 113 Figure 4.7, refer to top bullets
Lessons:
Add with Standard Algorithm
Multi-Step Word Problems with Bar Models
Solve Multi-Step Problems Using the Standard
Addition Algorithm
2-Step Subtraction
Activities and Tasks:
Making Sense of the Algorithm
To Regroup or Not to Regroup
Adding and Subtracting Word Problems
Addition and Subtraction Number Stories
Videos:
Add Using Partial Sums
Add Using an Open Number Line
Add Using the Standard Algorithm
Subtract Using an Open Number Line
Subtract Using the Standard Algorithm
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit One – Applying Place Value Concepts in Whole Number Addition & Subtraction (14 days)
Connections/Notes
Resources
4.NBT.B.4 Continued
4.NBT.B.4 Continued
3546
- 928
Student explanation for this problem:
1. There are not enough ones to take 8 ones from 6 ones so I have to use one ten as 10 ones.
Now I have 3 tens and 16 ones. (Marks through the 4 and notates with a 3 above the 4 and
writes a 1 above the ones column to be represented as 16 ones.)
2. Sixteen ones minus 8 ones is 8 ones. (Writes an 8 in the ones column of answer.)
3. Three tens minus 2 tens is one ten. (Writes a 1 in the tens column of answer.)
4. There are not enough hundreds to take 9 hundreds from 5 hundreds so I have to use one
thousand as 10 hundreds. (Marks through the 3 and notates with a 2 above it. (Writes down a
1 above the hundreds column.)
5. Now I have 2 thousand and 15 hundreds.
6. Fifteen hundreds minus 9 hundreds is 6 hundreds.
7. (Writes a 6 in the hundreds column of the answer).
8. I have 2 thousands left since I did not have to take away any thousands. (Writes 2 in the
thousands place of answer.)
Online:
Circle 99 NLVM
Diffy NLVM
Addition with Base Ten Blocks NLVM
Subtraction with Base Ten Blocks NLVM
Dicey Operations NRICH Math
Students use the structure of the base--‐ten system to generalize their strategies and to discuss
reasonableness of their computations and work towards fluency (MP.6, MP.8).
Note: Students should know that it is mathematically possible to subtract a larger number from a smaller
number but that their work with whole numbers does not allow this as the difference would result in a
negative number.
Connections: 4.NBT.A.2
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Unit Two – Efficiency with Multiplication and Understanding Division (20 days)
In this unit students develop understanding of multiples and factors, applying their understanding of multiplication from the previous year. This
understanding lays a strong foundation for generalizing strategies learned in previous grades to develop, discuss, and use efficient, accurate, and
generalizable computational strategies involving multi--‐digit numbers. These concepts and the terms “prime” and “composite” are new to Grade 4, so
they are introduced early in the year to give students ample time to develop and apply this understanding. Students continue using computational and
problem‐solving strategies, with a focus on building conceptual understanding of multiplication of larger numbers and division with remainders. Area and
perimeter of rectangles provide one context for developing such understanding. Students will continue to evaluate expressions using the conventional
order or operations that was introduced in grade 3.
Unit Two Standards
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.
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.
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.
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.
4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged
to use these math terms in explanations or justifications.
area model
array
associative property
bar model/tape diagram
base ten
commutative property
compatible numbers
composite
decompose
distributive property
divide
dividend
divisor
division (repeated subtraction) equation
estimate
expanded form
expression
factors
inverse operation
measurement division
multiples
multiplier
multiplicand
multiply
number bond
partial product
place value
prime
product
properties
quotient
remainder
represent
symbol
variable
Essential Questions
How do I identify prime numbers?
How do I identify composite numbers?
What is the difference between a prime and a composite number?
How is skip counting related to identifying multiples?
What is the difference between a factor and product?
How do we know if a number is prime or composite?
How are factors and multiples defined?
How will diagrams help us determine and show the products of two-digit numbers?
How can I effectively explain my mathematical thinking and reasoning to others?
What real life situations require the use of multiplication?
What effect does a remainder have on my rounded answer?
How can I mentally compute a division problem?
What are compatible numbers and how do they aid in dividing whole numbers?
How are multiplication and division related to each other?
What patterns of multiplication and division can assist us in problem solving?
What happens in division when there are zeroes in both the divisor and the dividend?
What is the meaning of a remainder in a division problem?
How do multiplication, division, and estimation help us solve real world problems?
How can we organize our work when solving a multi-step word problem?
How can a remainder affect the answer in a division problem?
How are area and perimeter related?
How are the units used to measure perimeter different/alike from the units used to measure area?
How do we find the area/perimeter of a rectangle?
How does the area change as the rectangle’s dimensions change (with a fixed perimeter)?
What is the relationship between area and perimeter when the area is fixed?
What is the relationship between area and perimeter when the perimeter is fixed?
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes
(20 days)
Resources
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.
Students should understand the process of finding factor pairs so they can do this for any number 1 -100.
Teaching Student Centered Mathematics
Divisibility rules can be used as a strategy for determining if a number is prime or composite.
pg. 63, Finding Factors - 2.22
Example:
pg. 64,Factor Patterns -2.23
 Factor pairs for 96: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12.

Multiples can be thought of as the result of skip counting by each of the factors. When skip
counting, students should be able to identify the number of factors counted e.g., 5, 10, 15, 20 (there
are 4 fives in 20).
Example:
 Factors of 24: 1, 2, 3, 4, 6, 8,12, 24
 Multiples
of 1: 1,2,3,4,5…24
of 2: 2,4,6,8,10,12,14,16,18,20,22,24
of 3: 3,6,9,12,15,18,21,24
of 4: 4,8,12,16,20,24
of 5: 8,16,24
of 6: 12,24
of 24: 24
To determine if a number between1-100 is a multiple of a given one-digit number, some helpful hints
include the following:
 all even numbers are multiples of 2
 all even numbers that can be halved twice (with a whole number result) are multiples of 4
 all numbers ending in 0 or 5 are multiples of 5
When listing multiples of numbers, students may not list the number itself. Emphasize that the smallest
multiple is the number itself. Some students may think that larger numbers have more factors. Having
students share all factor pairs and how they found them will clear up this misconception. Some students
may need to start with numbers that only have one pair of factors, then those with two pairs of factors
before finding factors of numbers with several factor pairs.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Lessons:
Times Square Reinforcing Multiplication Skills
Using Factors and Strategy
The Venn Factor
Factor Findings
Find Factor Pairs
Activities and Tasks:
Factor Practice Sheets
Investigating Prime and Composite Numbers
Prime Number PPT
A Remainder of One
How Many Tables?
Finding Multiples
Common Multiples
Prime Number Hunt
Identifying Multiples
Multiples and Factors Fun with QR Codes
Cross the Board Game
Factor Flip Prime/Composite Game
Factor Race Game
Head to One Hundred Game
Factors and Multiples Roll Game
Factors and Multiples Venn Diagram
Least Common Multiples
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
4.OA.B.4 Continued
Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division (20 days)
Connections/Notes
Resources
4.OA.B.4 Continued
Prime vs. Composite:
 A prime number is a number greater than 1 that has only 2 factors, 1 and itself.
 Composite numbers have more than 2 factors.
Students investigate whether numbers are prime or composite by building rectangles (arrays) with
the given area and finding which numbers have more than two rectangles (e.g. 7 can be made into
only 2 rectangles, 1 x 7 and 7 x 1, therefore it is a prime number)
A common misconception is that the number 1 is prime, when in fact; it is neither prime nor composite.
Another common misconception is that all prime numbers are odd numbers. This is not true, since the
number 2 has only 2 factors, 1 and 2, and is also an even number.
The focus of this unit is not necessarily to become fluent in finding all factor pairs, but to use
student’s understanding of the concept and language to discuss the structure of multiples and
factors (MP.3, MP.7).
Videos:
Find All the Factor Pairs of a Number Using Area
Models
Determine Multiples of a Number Using Area
Models
Find All Factor Pairs Using a Rainbow Factor Line
Determine Multiples of a Number Using Number
Bonds
Use Divisibility Rules to Determine Multiples
Use Divisibility Rules to Determine Multiples 2
Online
Factor Trail Game Illuminations
Factorize Illuminations
Factor Game Illuminations
Factor Track NRICH Math
Factor Lines NRICH Math
Interactive Hundred Chart
Factor Tree NLVM
Sieve of Eratosthenes NLVM
100 Board Splat
Templates and Visuals:
Frayer Model
Example/Non-Example Template
Hundred Twenty Chart
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.
Teaching Student-Centered Mathematics
pg. 291 Predict Down The Line - Activity 10.1
Patterns involving numbers or symbols either repeat or grow. Students need multiple opportunities
pg. 293 Grid Patterns Activity & Figure 10.2
creating and extending number and shape patterns. Numerical patterns allow students to reinforce facts
pg. 294 Extend & Explain Activity 10.3 & Predict
and develop fluency with operations.
How Many 10.4
p. 299 What's Next & Why Activity 10.6 & 10.7
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4.OA.C.5 Continued
Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division (20 days)
Connections/Notes
Resources
4.OA.C.5 Continued
Patterns and rules are related. A pattern is a sequence that repeats the same process over and over. A
rule dictates what that process will look like. Students investigate different patterns to find rules, identify
features in the patterns, and justify the reason for those features.
Example:
Lessons:
Patterns on Charts Illuminations
Growing Patterns Illuminations
Polygons, Perimeter, and Patterns Illuminations
Exploring Other Number Patterns Illuminations
Calendar Capers AIMS
A Banquet at Tony’s AIMS
Activities and Tasks:
Numeric Patterns Practice Sheet
Double Plus One
Extending Patterns
Doubling Dimes
Piecing Together Patterns
After students have identified rules and features from patterns, they need to generate a numerical pattern
from a given rule.
Example:
 Rule: Starting at 1, create a pattern that starts at 1 and multiplies each number by 3. Stop when
you have 6 numbers.
Students write 1, 3, 9, 27, 81, 243. Students notice that all the numbers are odd and that the sums of the
digits of the 2 digit numbers are each 9. Some students might investigate this beyond 6 numbers. Another
feature to investigate is the patterns in the differences of the numbers (3 - 1 = 2, 9 - 3 = 6, 27 - 9 = 18, etc.)
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. (1, 4, 7, 10, 13)
While working on 4.OA.C.5, students use manipulatives to determine whether a number is prime or
composite. Although there are shape patterns in arrays, the focus of this unit is number patterns.
4.OA.C.5 is repeated in unit 8, where the focus will be on identifying shape patterns.
Connections: 4.OA.B.4
Grade 4
Wicomico County Public Schools Revised 2014-2015
Videos:
Find the Rule for a Function Machine Using a
Vertical table
Find Missing Elements in Growing Patterns
Determine the Rule in Patterns that Decrease
Generate a Pattern Sequence Using a T-Chart
Chessboard Algebra and Function Machines
On Line:
Number Patterns NLVM
Hundreds Chart NLVM
100 Board Splat
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes
(20 days)
Resources
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.
Focus should NOT be on finding KEY WORDS to indicate the four operations!
Students need many opportunities solving multistep story problems using all four operations.
This is the first time students are expected to interpret remainders based upon the context. All
four operations will be addressed in unit 7, and the standard will be finalized in unit 9.
Example:
 Chris bought clothes for school. She bought 3 shirts for $12 each and a skirt for $15. How much
money did Chris spend on her new school clothes?
3 x $12 + $15 = a
In division problems, the remainder is the whole number left over when as large a multiple of the divisor as
possible has been subtracted.
Example:
 Kim is making candy bags. There will be 5 pieces of candy in each bag. She had 53 pieces of
candy. She ate 14 pieces of candy. How many candy bags can Kim make now?
(7 bags with 4 pieces left over)
 There are 29 students in one class and 28 students in another class going on a field trip. Each car
can hold 5 students. How many cars are needed to get all the students to the field trip?
(12 cars, one possible explanation is 11 cars holding 5 students and the 12th holding the remaining
2 students) 29 + 28 = 11 x 5 + 2
Grade 4
Wicomico County Public Schools Revised 2014-2015
Lessons:
How to Bag It Illuminations
Get the Picture, Get the Story Illuminations
A Squadron of Bugs: Introducing Division with
Remainders Illuminations
Area & Perimeter Multistep Word problems
Activities and Tasks:
Multistep Word Problems
Multistep Problems Add-Subtract
Multistep Problems Add-Multiply
Multistep Mixed Practice
Carnival Tickets
At the Circus
Kickoff Prep Interpreting Remainders
Videos:
Estimate to Assess Whether an Answer is
Reasonable
Solve Word Problems Using Objects
Solve Word Problems by Drawing Pictures
Solve Word Problems by Writing an Equation
Solve Multi-Step Word Problems by Writing an
Equation
Online:
Multi-Step Word Problem Resource
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Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes
(20 days)
Resources
4.OA.A.3 Continued
Estimation skills include identifying when estimation is appropriate, determining the level of accuracy
needed, selecting the appropriate method of estimation, and verifying solutions or determining the
reasonableness of situations using various estimation strategies. Estimation strategies include, but are
not limited to:
 front-end estimation with adjusting (using the highest place value and estimating from the front
end, making adjustments to the estimate by taking into account the remaining amounts)
 clustering around an average (when the values are close together an average value is selected
and multiplied by the number of values to determine an estimate)
 rounding and adjusting (students round down or round up and then adjust their estimate
depending on how much the rounding affected the original values)
 using friendly or compatible numbers such as factors (students seek to fit numbers together-e.g.,
rounding to factors and grouping numbers together that have round sums like 100 or 1,000)
 using benchmark numbers that are easy to compute (students select close whole numbers for
fractions or decimals to determine an estimate)
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.
The focus of instruction should be on strategies other than the algorithm.
Teaching Student-Centered Mathematics
pg. 113-118, Figures 4.8, 4.10, 4.11, 4.12, pg.
Students who develop flexibility in breaking numbers apart have a better understanding of the importance
129 Expanded Area Lesson
of place value and the distributive property in multi-digit multiplication. Students use base ten blocks, area
models, partitioning, compensation strategies, etc. when multiplying whole numbers and use words and
Lessons:
diagrams to explain their thinking. They use the terms factor and product when communicating their
Multiply and Conquer
reasoning. Multiple strategies enable students to develop fluency with multiplication and transfer that
Number Line Dancing
th
understanding to division. Use of the standard algorithm for multiplication is an expectation in the 5
All About Multiplication: Modeling Multiplication with
grade.
Streets and Avenues
Connect Area Models and Partial Products
Frame Filling AIMS
 Base Ten Blocks and Drawings:
Multiplying with Tens AIMS
To illustrate 154 x 6 students use base 10 blocks or use drawings to show 154 six times. Seeing 154 six
Multiplication Stretch AIMS
times will lead them to understand the distributive property,
154 x 6 = (100 + 50 + 4) x 6 = (100 x 6) + (50 x 6) + (4 x 6) = 600 + 300 + 24 = 924
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Fourth Grade Mathematics Curriculum Guide for the
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4.NBT.B.5 Continued

Partial Products:

Rectangular Array:
Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division (20 days)
Connections/Notes
Resources
4.NBT.B.5 Continued
Activities and Tasks:
Multiplication Using the Area Model Teaching Pkt.
Partial Products Template
Multiplication Area Model PPT
Area Model for Multiplication Problems
Multiply 2-digit x 2-digit Practice
Multiplication Strategy: Partial Products 1
Multiplication Strategy: Partial Products 2
Multiplication Strategy: Doubling & Halving
Make the Smallest Product
Make the Largest Product
Multiplication Bump
French Fries
Closest to One Thousand
Target 300 Game
Breaking Apart a Factor
Videos:

Use an Array to Multiply a Two-Digit Number by a
One-Digit Number
Use Area Models to Show Multiplication of Whole
Numbers
Use Place Value Understanding to Multiply Three
and Four Digit Numbers
Use an Area Model for Multiplication of Two-Digit
Numbers
Use an Area Model to Multiply a Three Digit Number
Ready for Two Steps?
Bar Model
Online:
Rectangle Measurement: Virtual Manipulative
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes

(20 days)
Resources
Area Models:
14 x 16 = 224
Using the area model, students first
verbalize their understanding:
 10 x 10 is 100
 4 x 10 is 40
 10 x 6 is 60, and
 4 x 6 is 24.
They use different strategies to record
this type of thinking.
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Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes

Area Models Continued:

Place Value Disks:
(20 days)
Resources
Connections:
4.OA.A.2; 4.OA.A.3; 4.NBT.A.1
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes
(20 days)
Resources
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.
The focus of instruction should be on strategies and models before the algorithm.
In fourth grade, students build on their third grade work with division within 100. Students need
opportunities to develop their understandings by using problems in and out of context.
Examples:
A 4th grade teacher bought 4 new pencil boxes. She has 260 pencils. She wants
to put the pencils in the boxes so that each box has the same number of pencils.
How many pencils will there be in each box?
Using Base 10 Blocks: Students build 260 with base 10 blocks and distribute them into 4 equal groups.
Some students may need to trade the 2 hundreds for tens but others may easily recognize that 200
divided by 4 is 50.
Using Place Value: 260 ÷ 4 = (200 ÷ 4) + (60 ÷ 4)
Using Multiplication:
4 x 50 = 200, 4 x 10 = 40, 4 x 5 = 20; 50 + 10 + 5 = 65; so 260 ÷ 4 = 65
Using an Open Array or Area Model:
After developing an understanding of using arrays to divide, students begin to use a more abstract
model for division. This model connects to a recording process that will be formalized in the 5 th
grade.
1: 150 ÷ 6
Students make a rectangle and write 6 on one of its sides. They
express their understanding that they need to think of the rectangle
as representing a total of 150.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Teaching Student-Centered Mathematics
pg. 93 How Close Can You Get? Activity 3.10,
pg. 121-124, pg. 121 Figure 4.16, pg. 124 Figure
4.17
Lessons:
Pack 10 Trading AIMS
Leftovers with 100
Division Requiring Decomposing a Remainder
Division with remainders Using Arrays and Area
Models
Division Word Problems with Remainders
Explain Remainders Using Place Value
Understanding
Whole Number Quotients and Remainders
Two-Digit Dividends with Number Disks
Solve Division Problems Without Remainders Using
Area Models
Solve Division Problems With Remainders Using
Area Models
Activities and Tasks:
Division Using the Area Model Teacher Packet
Division of the Day
Division Strategy: Partial Quotients 1
Division Strategy: Partial Quotients 2
Division Strategy: Partition the Dividend
Estimate the Quotient
Group Activity for Division
Remainders Game
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Fourth Grade Mathematics Curriculum Guide for the
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4.NBT.B.6 Continued
Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division (20 days)
Connections/Notes
Resources
4.NBT.B.6 Continued
1.
Students think, 6 times what number is a number close to 150? They recognize that 6 x 10 is 60 so
they record 10 as a factor and partition the rectangle into 2 rectangles and label the area aligned to
the factor of 10 with 60. They express that they have only used 60 of the 150 so they have 90 left.
2. Recognizing that there is another 60 in what is left they repeat the process above. They express
that they have used 120 of the 150 so they have 30 left.
3. Knowing that 6 x 5 is 30. They write 30 in the bottom area of the rectangle and record 5 as a factor.
4. Students express their calculations in various ways:
Example 1:
Videos:
Divide Two-Digit Dividends Using Friendly Multiples
Report Remainders as Fractions
Report Remainders as Whole Numbers by Drawing
Pictures to Decide Whether to Round Up or Down
Divide Three-Digit Dividends
Divide Four-Digit Dividends
Online:
The Quotient Cafe Illuminations
Remainders Count
Models for Division Video from Math Playground
Time for Remainders Video from Math Playground
Area Model Division with Single Digit Divisors
Video form YouTube
Rectangle Division NLVM
Templates and Visuals:
Division Anchor Chart Samples
Example 2:
1,917 ÷ 9
A student’s description of his or her thinking may be:
I need to find out how many 9s are in 1917. I know that 200 x 9 is 1800.
So if I use 1800 of the 1917, I have 117 left. I know that 9 x 10 is 90.
So if I have 10 more 9s, I will have 27 left. I can make 3 more 9s.
I have 200 nines, 10 nines and 3 nines. So I made 213 nines. 1917 ÷ 9 = 213
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Two - Efficiency with Multiplication and Understanding Division
Connections/Notes
(20 days)
Resources
4.MD.A.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Students developed understanding of area and perimeter in 3rd grade by using visual models.
While students are expected to use formulas to calculate area and perimeter of rectangles, they need to
understand and be able to communicate their understanding of why the formulas work.
The formula for area is I x w and the answer will always be in square units.
The formula for perimeter can be 2 l + 2 w or 2 (l + w) and the answer will be in linear units.
This standard provides the context of area and perimeter of rectangles to use for problem solving.
Students are first introduced to formulas in this unit and make sense of the formulas using their
prior work with area and perimeter.
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.
Teaching Student-Centered Mathematics
Pg. 265 Fixed Perimeters & Areas Activities 9.7 &
9.8 pg. 288-289 Fixed Areas Expanded Lesson
Lessons:
What's My Area? Illuminations
Chairs Illuminations
Figuring Areas Math Solutions
Area in Metric (Unit)
Conversions (Unit)
Activities and Tasks:
Area & Perimeter Word Problems
Area and Perimeter of Shapes
Using Equations to Find Area of Shapes
Finding Area of Rod Designs
Area with Cuisenaire Rods
Determining the Missing Side with Perimeter
Area and Perimeter with Cheese Crackers
Designing a Zoo Enclosure (Area)
Fencing a Garden (Perimeter)
Sammy’s Sport Complex Area Practice
Going to the Dogs
Horsing Around
How Many Tables
Perimeter and Area Practice
Videos:
Use Area Models to Find the Area of Rectangles
Find Missing Side Lengths Using the Formula for
Area
Find Perimeter Using the Standard Formula
Find Missing Side Lengths Using the Formula for
Perimeter
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Unit Three – Solving Problems Using Multiplicative Comparison (10 days)
In this unit students are introduced to multiplicative compare problems, extending their conceptual work with multiplicative comparison. For students to
develop this concept, they must be provided rich problem situations that encourage them to make sense of the relationships among the quantities
involved, model the situation, and check their solution using a different method. These problems are new to Grade 4 students.
The comparison is based on one set being a particular multiplier of the other. In an additive comparison problem, the underlying question is what amount
would be added to one quantity in order to result in the other. The underlying question for multiplicative comparison problems is what factor would multiply
one quantity in order to result in the other.
It is important to introduce multiplicative comparison problems to our grade 4 students as these problems can be extended in later years to include
multiplication and division of fractions. Thus, including these problems with whole numbers in grade 4 lays the groundwork for developing an understanding of
multiplication and division of fractions and decimals in later grades.
Multiplicative comparison problems involve a comparison of two quantities in which one is described as a multiple of the other. The relation between
quantities is described in terms of how many times larger one is than the other. The number quantifying this relationship is not an identifiable quantity. In the
following problem, the animals’ weights are measurable quantities, but the other quantity (three times as much) simply describes the relationship between the
measurable quantities:
The first grade class has a hamster and a gerbil. The hamster weighs 3 times as much as the gerbil. The gerbil weighs 9 ounces. How much does the
hamster weigh?
The table on the following page is an important resource for writing multiplicative comparison problems.
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Multiplicative Comparison problems can also be constructed for any of the three basic problem types, as seen below. Multiplicative compare problems appear
first in the CCSSM in fourth grade, with whole number values. In Grade 5, unit fractions language such as “one third as much” may be used.
Multiplicative
Comparison
4th Grade
4.OA.2
5th Grade
Smaller Unknown:
Larger Unknown:
The giraffe is 18 feet tall. She is 3 times
as tall as the kangaroo. How tall is the
kangaroo?
The giraffe in the zoo is 3 times as tall
as the kangaroo. The kangaroo is 6 feet
tall. How tall is the giraffe?
Measurement Example:
A rubber band is stretched to be 18
centimeters long and that is 3 times as
long as it was at first. How long was the
rubber band at first?
Measurement Example:
A rubber band is 6 centimeters long.
How long will the rubber band be when
it is stretched to be 3 times as long?
The giraffe is 18 feet tall. The kangaroo
is 1/3 as tall as the giraffe. How tall is
the kangaroo?
The kangaroo is 6 feet tall. She is 1/3
as tall as the giraffe. How tall is the
giraffe?
Multiplier Unknown:
The giraffe is 18 feet tall. The
kangaroo is 6 feet tall. The giraffe is
how many times taller than the
kangaroo?
Measurement Example:
A rubber band was 6 centimeters long
at first. Now it is stretched to be 18
centimeters long. How many times as
long is the rubber band now as it was at
first?
The giraffe is 18 feet tall. The
kangaroo is 6 feet tall. What fraction
of the height of the giraffe is the
height of the kangaroo?
Unit Three Standards
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.
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.
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Fourth Grade Mathematics Curriculum Guide for the
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Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use
these math terms in explanations or justifications.
additive comparison
area model
associative property
bar model/tape diagram
base ten
commutative property
compatible numbers
composite
decompose
distributive property
equation
estimate
expanded form
expression
factors
inverse operation
multiplicand
multiplier
multiples
multiplicative comparison
multiply
number bond
partial product
place value
prime
product
properties
represent
symbol
variable
Essential Questions
How can multiplication be used to answer questions?
How do you express a multiplication comparison equation as a written statement?
What is the difference between a multiplicative comparison and an additive comparison?
How do we solve multiplication word problems involving multiplicative comparison using drawings and equations?
Common Misconceptions
Use of Key Words
1. Key words are misleading. Some key words typically mean addition or subtraction. This is not always true. Consider: There were 4 jackets left on the
playground on Monday and 5 jackets left on the playground on Tuesday. How many jackets were left on the playground? "Left" in this problem does not mean
subtract.
2. Many problems have no key words. Example: How many legs do 7 elephants have? There is no key word. However, any 1st grader should be able to
solve the problem by thinking and drawing a picture or building a model.
3. It sends a bad message. The most important strategy when solving a problem is to make sense of the problem and to think. Key words encourage
students to ignore meaning and look for a formula. Mathematics is about meaning (Van de Walle, 2012).
Avoid Key Words
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Three - Solving Problems Using Multiplicative Comparison (10 days)
Connections/Notes
Resources
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.
A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to
get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and
verbalize which quantity is being multiplied and which number tells how many times.
In multiplicative comparison problems, there are two different sets being compared. The first set
contains a certain number of items. The second set contains multiple copies of the first set. Any two
factors and their product can be read as a comparison. Let’s look at a basic multiplication equation:
4 x 2 = 8.
Teaching Student-Centered Mathematics:
pg. 63 Figure 2.15, pg. 65 The broken
Multiplication Key Activity 2.25
Lessons:
Multiplicative Comparison (Unit)
Activities and Tasks:
Representing Multiplicative Comparison Problems
Comparing Growth Variation1
Comparing Growth Variation 2
Task Cards Multiplication as a Comparison
Measuring Mammals
Interpreting Multiplicative Comparison
Interpreting Multiplicative Comparison 2
multiplicative comparisons.
Videos:
Comparing Numbers Using Bar Models
See Multiplication As a Comparison Using Number
Sentences
Example:
5 x 8 = 40.
Sally is five years old. Her mom is eight times older. How old is Sally’s Mom?
Online:
Multiplicative Comparison Samples
Students should be given opportunities to write and identify equations and statements for
5 x 5 = 25
Sally has five times as many pencils as Mary. If Sally has 5 pencils, how many does Mary
have?
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Three - Solving Problems Using Multiplicative Comparison (10 days)
Connections/Notes
Resources
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.
Students need many opportunities to solve contextual problems.
A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat
cost?
In solving this problem, the student should identify $6 as the quantity that is being multiplied by 3. The
student should write the problem using a symbol to represent the unknown. ($6 x 3 =
)
A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the
blue hat?
In solving this problem, the student should identify $18 as the quantity being divided into shares of $6.
The student should write the problem using a symbol to represent the unknown. ($18 ÷ $6 =
)
When distinguishing multiplicative comparison from additive comparison, students should note that:
 Additive comparisons focus on the difference between two quantities (e.g., Deb has 3 apples
and Karen has 5 apples. How many more apples does Karen have?) A simple way to
remember this is, “How many more?”
Multiplicative comparisons focus on comparing two quantities by showing that one quantity is a
specified number of times larger or smaller than the other. (e.g., Deb ran 3 miles. Karen ran 5 times
as many miles as Deb. How many miles did Karen run?) A simple way to remember this is “How
many times as much?” or “How many times as many?”
Grade 4
Teaching Student Centered Mathematics
pg.304 - 307, Story Translations - Activity 10.10
Lessons:
Multiply and Conquer
Multiplicative Comparison Word Problems
2-Step Multiplicative Comparison
Multiplicative Comparison (Unit)
Activities and Tasks:
Representing Multiplicative Comparison Problems
Multiplicative Comparison Problems
Comparing Money Raised
At the Circus
Multiplication Story Structures Fall Themed PPT
Practice Task
Multiplicative Comparison Task Cards
Multiplicative Comparison Word Problems Within 100
Multiplicative Comparison Word Problems 2
Task Cards Multiplication as a Comparison
Online:
Thinking Blocks (virtual manipulatives)
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Three - Solving Problems Using Multiplicative Comparison (10 days)
Connections/Notes
Resources
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.
Work should be specifically with word problems using multiplicative comparison with distances, time,
money, and measurements.
Grade 4
Activities and Tasks:
Word Problems
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Unit 4 – Understanding and Comparing Fractions (22 days)
In this unit students extend their prior knowledge of unit fractions with denominators of 2, 3, 4, 6, and 8 from Grade 3 to include denominators of 5, 10,
12, and 100. In Grade 4, they use their understanding of partitioning to find unit fractions to compose and decompose fractions in order to add
fractions with like denominators. This is foundational for other work with fractions, such as comparing fractions and multiplying fractions by a whole
number. Students will also develop an understanding of fraction equivalence and various methods for comparing fractions. Students should
understand that when comparing fractions, it is not always necessary to generate equivalent fractions. Other methods, such as comparing fractions to
a benchmark, can be used to discuss relative sizes. The justification of comparing or generating equivalent fractions using visual models is an
emphasis of this unit.
Unit Four Standards
4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. 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.
4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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 principal 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 ½. 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.
Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use
these math terms in explanations or justifications.
benchmark fractions
equivalent fractions
number line
visual fraction model
Grade 4
compare
fraction
numerator
whole
decompose
increment
parts
whole number
denominator
mixed number
partition
Wicomico County Public Schools Revised 2014-2015
equation
multiple
unit fraction
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Essential Questions
What is a fraction and how can it be represented?
How can equivalent fractions be identified?
How can we find equivalent fractions?
How can a fraction represent parts of a set?
What do the parts of a fraction tell about its numerator and denominator?
What is a fraction and how can it be represented?
What is a fraction and what does it represent?
What is a mixed number and how can it be represented?
What is an improper fraction and how can it be represented?
What is the relationship between a mixed number and an improper fraction?
Why is it important to identify, label, and compare fractions (halves, thirds, fourths, sixths, eighths, tenths) as representations of equal parts of a whole or set?
In what ways can we model equivalent fractions?
How can identifying factors and multiples of denominators help to identify equivalent fractions?
How can we find equivalent fractions?
In what ways can we model equivalent fractions?
How can we find equivalent fractions and simplify fractions?
How can benchmark fractions be used to compare fractions?
What are benchmark fractions?
How are benchmark fractions helpful when comparing fractions?
How do we know fractional parts are equivalent?
What happens to the value of a fraction when the numerator and denominator are multiplied or divided by the same number?
How are equivalent fractions related?
How can you compare and order fractions?
How are benchmark fractions helpful when comparing fractions?
How do I compare fractions with unlike denominators?
How do you know fractions are equivalent?
What can you do to decide whether your answer is reasonable?
How can identifying factors and multiples of denominators help to identify equivalent fractions?
How do we represent a fraction that is greater than one?
How do we locate fractions on a number line?
How do we make a line plot to display a data set?
How do we apply our understanding of fractions in everyday life?
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Four – Understanding & Comparing Fractions (22 days)
Connections/Notes
4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Resources
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation.
Justify decompositions, e.g., by using a visual fraction model.
A fraction with a numerator of one is called a unit fraction.
When students investigate fractions other than unit fractions, such as 2/3, they should be able to
decompose the non-unit fraction into a combination of several unit fractions.
Fraction Example 1:
Being able to visualize this decomposition into unit fractions helps students when adding or subtracting
fractions. Students need multiple opportunities to work with mixed numbers and be able to decompose
them in more than one way. Students may use visual models to help develop this understanding.
Grade 4
Teaching Student Centered Mathematics
pg. 150 First Estimates Activity 5.13
Lessons:
Decompose Fractions as a Sum of Unit Fractions 1
Decompose Fractions as a Sum of Unit Fractions 2
Decompose Fractions Using Tape Diagrams
Decompose Fractions into Sums of Smaller Fractions
Activities and Tasks:
Adding Fractions Using Pattern Blocks
Pizza Share
Picture Pie
Decomposing Fractions
Comparing Sums of Unit Fractions
Making 22 Seventeenths in Different Ways
Plastic Building Blocks
Writing a Mixed Number as an Equivalent Fraction
Adding and Subtracting Like Fractions
Fraction Field Event
Fraction Missing Addends
Pizza Parlor
Chocolate Bar Problem
Sense or Nonsense
Sense or Nonsense 2
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Four – Understanding & Comparing Fractions (22 days)
Connections/Notes
4.NF.B.3 Continued
Resources
4.NF.B.3 Continued
Fraction Example 2:
Videos:
Add Fractions by Joining Parts
Online:
Number Line Bars - Fractions NLVM
Word Problem Example 1:
Mary and Lacey decide to share a pizza. Mary ate 3/6 and Lacey ate 2/6 of the pizza. How
much of the pizza did the girls eat together?
Solution: The amount of pizza Mary ate can be thought of a 3/6 or 1/6 and 1/6 and 1/6. The
amount of pizza Lacey ate can be thought of a 1/6 and 1/6. The total amount of pizza they ate
is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 or 5/6 of the whole pizza.
Suggested manipulatives to develop this
concept: fraction strips, Cuisenaire rods, fraction
towers, fraction fringes (AIMS), fraction squares,
fraction circles, and pattern blocks.
Visual fraction models include tape diagrams,
area models, number line diagrams, set diagrams
(See Van de Walle pgs.162-166).
4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x 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 principal to recognize and generate equivalent fractions.
Teaching Student-Centered Mathematics:
pgs. 144-146 Activities 5.7, 5.8, and 5.9
This standard extends the work in third grade by using additional denominators (5, 10, 12, and 100).
pgs. 151-156 Activities 5.14 - 5.19, Figure 5.20
Students can use visual models or applets to generate equivalent fractions.
pgs. 140-141 activities 5.4 and 5.5
Lessons:
MSDE Unit: Equivalent Fractions
Investigating Fractions with Pattern Blocks
Investigating Equivalent Fractions with Relationship
Rods
Grade 4
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Four – Understanding & Comparing Fractions (22 days)
Connections/Notes
4.NF.A.1 Continued
Resources
4.NF.A.1 Continued
Lessons Continued :
Eggsactly Equivalent
Fraction Clothesline
Black Wholes AIMS
Fraction Fringe AIMS
Fractions with Pattern Blocks AIMS
Fraction Time AIMS
Fraction Dominoes
Picture Parts AIMS
Same Name Frame AIMS
Shady Fractions AIMS
Fraction Equivalence Using a Tape Diagram
Half Track AIMS
All the models above show 1/2. The second model shows 2/4 but also shows that 1/2 and 2/4 are
equivalent fractions because their areas are equivalent. When a horizontal line is drawn through the
center of the model, the number of equal parts doubles and size of the parts is halved.
Students will begin to notice connections between the models and fractions in the way both the parts
and wholes are counted and begin to generate a rule for writing equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12
and 100.
Grade 4
Activities and Tasks:
Equal Fractions PPT
Geoboard Activity 1
One-Color Rod Trains
Creating Equivalent Fractions
Money in the Piggy Bank
Explaining Fraction Equivalence with Pictures
Equal Fraction Pairs with Cuisenaire Rods
Fraction Wall Game
Pattern Block Puzzles
Using Benchmarks to Compare Fractions
Choose a Denominator
MSDE Unit Equivalent Fractions
Running Laps Task
Sugar in Six Cans of Soda Task
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Four – Understanding & Comparing Fractions (22 days)
Connections/Notes
Resources
4.NF.A.1 Continued
Videos:
Recognize Equivalent Fractions Using Area Models
Online:
Fraction Bars Virtual Manipulative NLVM
Equivalent Fractions Virtual Manipulative NLVM
12 Fraction Activity Tools
Fraction Models Tool Illuminations
Equivalent Fractions Illuminations
Templates and Visuals:
Fraction Squares
Equivalent Fraction Cards
Equivalent Fractions Display
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 ½. 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.
Benchmark fractions include common fractions between 0 and 1 such as halves, thirds,
fourths, fifths, sixths, eighths, tenths, twelfths, and hundredths.
Teaching Student Centered Mathematics
pgs. 144-146 Activities 5.7, 5.8, and 5.9
pgs. 146-148 Activities 5.10, 5.11, and 5.12
Fractions can be compared using benchmarks, common denominators, or common numerators.
Symbols used to describe comparisons include <, >, =.
Fractions may be compared using
Grade 4
1
as a benchmark.
2
Lessons:
Fractional Clothesline Illuminations
Benchmark Fractions
Fraction Sort
Half Track AIMS
Using Benchmarks to Compare Fractions
Extend Understanding of Fraction Equivalence and
Ordering
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Four – Understanding & Comparing Fractions (22 days)
Connections/Notes
4.NF.A.2 Continued
4.NF.A.2 Continued
Possible student thinking by using benchmarks:
1
1
is smaller than
because when
8
2
o
1 whole is cut into 8 pieces, the pieces
are much smaller than when 1 whole
is cut into 2 pieces.
Possible student thinking by creating common denominators:
o
5 1
3 1
5 3
>
because
=
and
>
6 2
6 2
6 6
Fractions with common denominators may be compared using the numerators as a guide.
o
2 3 5
<
<
6 6 6
Fractions with common numerators may be compared and ordered using the denominators as a
guide.
o
3
3 3
<
<
10 8 4
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8,
10, 12, and 100.
Grade 4
Resources
Activities and Tasks:
Birthday Fractions
Spin to Win Game
Pattern Block Fractions
Who Ate More?
Which is Larger?
How to Find a Fraction on a Number Line PPT
Snack Time
Determining Fraction Value on a Number Line
Fraction Card Games
Fraction Compare
Listing Fractions in Increasing Size
Compare Fraction Strategies
Write About Fractions
Fraction Card Games
Between 0 and 1 Fair Pairs AIMS
Videos:
Compare Fractions Using the Benchmark Fraction 1/2
Compare Fractions to a Benchmark of One Half Using
Number Lines
Online:
Fun with Fractions Illuminations Lessons
Playing Fraction Tracks NCTM Game
Locating & Ordering Equivalent Fractions on a Number
Line PBIS Lesson
Fraction Monkeys Game
Fraction Models Tool Illuminations
Templates and Visuals:
Fraction Squares
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Unit Five – Fraction Operations (23 days)
In this unit students will use their understanding of adding and subtracting fractions and generating equivalent fractions to solve problems involving
fractions and mixed numbers. Students rely on their previous work with whole numbers as fractions to compose and decompose whole numbers into
fractional quantities. Data is used in this unit to support students’ understanding of fractional quantities both smaller and larger than 1. Students
also apply their understanding of composing and decomposing fractions to develop a conceptual understanding of multiplication of a fraction by a
whole number. Students use and extend their previous understandings of operations with whole numbers and relate that understanding to fractions.
Unit Five Standards
4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
c. 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.
d. 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.
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.
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.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. 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).
b. 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.)
c. 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.
Grade 4
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use
these math terms in explanations or justifications.
benchmark fractions
equivalent fractions
multiple
partition
compare
fraction
multiplicative comparison
unit fraction
decompose
increment
number line
visual fraction model
denominator
line plot
numerator
whole
equation
mixed number
parts
Essential Questions
How are fractions used in problem-solving situations?
How can I find equivalent fractions?
How can I represent fractions in different ways?
How can improper fractions and mixed numbers be used interchangeably?
How can I add and subtract fractions of a given set?
How can you use fractions to solve addition and subtraction problems?
How do we add fractions with like denominators?
What happens to the denominator when I add fractions with like denominators?
Why does the denominator remain the same when I add fractions with like denominators?
How can I be sure fractional parts are equal in size?
How can I model the multiplication of a whole number by a fraction?
How can I multiply a set by a fraction?
How can I multiply a whole number by a fraction?
How can I represent multiplication of a whole number?
How can we model answers to fraction problems?
How can we use fractions to help us solve problems?
How can we write equations to represent our answers when solving word problems?
How do we determine a fractional value when given the whole number?
How do we determine the whole amount when given a fractional value of the whole?
How does the number of equal pieces affect the fraction name?
How is multiplication of fractions similar to division of whole numbers?
How is multiplication of fractions similar to repeated addition of fraction?
What does it mean to take a fractional portion of a whole number?
What is the relationship between multiplication by a fraction and division?
What is the relationship between the size of the denominator and the size of each fractional piece (i.e. the numerator)?
What strategies can be used for finding products when multiplying a whole number by a fraction?
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Five – Fraction Operations (23 days)
Connections/Notes
4.NF.B.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
Resources
c. 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.
d. 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.
Mixed numbers are introduced for the first time in 4 grade. Students should have ample experience
subtracting and adding mixed numbers where they work with mixed numbers or convert mixed numbers to
improper fractions.
A separate algorithm for mixed numbers in addition and subtraction is not necessary. Students will tend to add
or subtract the whole numbers first and then work with the fractions using the same strategies they have
applied to problems that contained only fractions.
Students use visual and concrete models to represent a fractional situation in order to add and subtract
fractions (MP.4).
Word Problem Example:
 Susan and Maria need 8 3/8 feet of ribbon to package gift baskets. Susan has 3 1/8 feet of ribbon and
Maria has 5 3/8 feet of ribbon. How much ribbon do they have altogether? Will it be enough to
complete the project? Explain why or why not.
The student thinks: I can add the ribbon Susan has to the ribbon Maria has to find out how much
ribbon they have altogether. Susan has 3 1/8 feet of ribbon and Maria has 5 3/8 feet of ribbon. I can
write this as 3 1/8 + 5 3/8. I know they have 8 feet of ribbon by adding the 3 and 5. They also have
1/8 and 3/8 which makes a total of 4/8 more. Altogether they have 8 4/8 feet of ribbon. 8 4/8 is larger
than 8 3/8 so they will have enough ribbon to complete the project. They will even have a little extra
ribbon left, 1/8 foot.
Additional Example:

Grade 4
Trevor has 4 1/8 pizzas left over from his soccer party. After giving some pizza to his friend, he has 2
4/8 of a pizza left. How much pizza did Trevor give to his friend?
Wicomico County Public Schools Revised 2014-2015
Lessons:
Add Mixed Numbers
Subtract Mixed Numbers
Add a Mixed Number and a Fraction
Subtract a Fraction from a Mixed Number
Subtract a Mixed Number from a Mixed Number
Estimate Sums and Differences of Fractions
Add and Subtract Fractions (Unit)
Adding Fractions on a Number Line (Unit)
Lesson Use Visual Models to Add and Subtract
Two Fractions with the Same Units
Lesson Use Visual Models to Add Two Fractions
with Related Units
Activities and Tasks:
Adding Mixed Numbers
Adding Fractions Using Pattern Blocks
Adding and Subtracting Like Fractions
Geoboard Add Like Denominators
Making Granola
Mixed Number Word Problems
Sense or Nonsense
Sense or Nonsense 2
The Chocolate Bar Problem
I Have…Who Has Fraction Game
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Five – Fraction Operations (23 days)
Connections/Notes
Resources
4.NF.B.3 Continued
4.NF.B.3 Continued
Solution: Trevor had 4 1/8 pizzas to start. This is 33/8 of a pizza. The x’s show the pizza he has left
which is 2 4/8 pizzas or 20/8 pizzas. The shaded rectangles without the x’s are the pizza he gave to
his friend which is 13/8 or 1 5/8 pizzas.
Activities and Tasks Continued:
Writing a Mixed Number as an Equivalent
Fraction Word Problems
Choose a Denominator
Making 22 Seventeenths in Different Ways
Who Has Fraction Game
Subtracting Fractions Using a Number Line
Videos:
Adding Mixed Numbers by Creating Equivalent
Fractions
Add Fractions with Like Denominators by
Decomposing Into Unit Fractions
A cake recipe calls for you to use ¾ cup milk, ¼ cup of oil, and 2/4 cup of water. How much liquid is needed to
make the cake?
𝟔
𝟒
𝟒
𝟒
Online:
Adding Fractions e-tool NLVM
Fraction Models Tool Illuminations
Thinking Blocks - Fractions
𝟐
𝟒
Often students think that it does not matter which model to use when finding the sum or difference of fractions.
They may represent one fraction with a rectangle and the other fraction with a circle. They need to know that
the models need to represent the same whole. In addition students have a tendency to add both the
numerator and denominator when using different operations with fractions as opposed to just adding
numerators.
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Five – Fraction Operations (23 days)
Connections/Notes
Resources
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.
Teaching Student Centered Mathematics
Example:
pg. 333
Ten students in Room 31 measured their pencils at the end of the day. They recorded their results on the line
Lessons:
plot below.
Line Plots
Measurement in Fraction Units
Measurement and Data Line Plots (Unit)
Fraction Line Plot Word Problems
Fraction Word Problems with Line Plots
Line Plot Lesson
4.MD.B.4 extends students’ work from Grade 3 with simple fractions on a line plot (3.MD.B.4) to include
eighths and to now solve addition and subtraction problems using the data.
Students reason about fractions by using abstract models to represent both the data and the fractional
quantities (MP.2, MP.4).
Activities and Tasks:
Measuring & Showing
Length of Ants
Objects in My Desk
Pulling a Few Strings
Measurement Line Plots
Measure in Fractional Units Word Problems
Videos:
Create a Line Plot Using a Data Set of
Fractional Measures
Create a Line Plot Using Fractions
Online:
Ruler Game
Templates and Visuals:
Line Plot Template
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Five – Fraction Operations (23 days)
Connections/Notes
Resources
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.
Lessons:
Solve Multiplicative Comparison Word Problems
4.OA.A.1 is readdressed in this unit to include multiplication of fractions and apply the understanding of
Involving Fractions
“times as much” (i.e. multiplication as comparison) to multiplying a fraction by a whole number.
4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. 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).
b. 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.)
c. 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.
Students need many opportunities to work with problems in context to understand the connections between
Teaching Student Centered Mathematics
models and corresponding equations. Contexts involving a whole number times a fraction lend themselves to
pg. 167 - 169 Figure 6.6 (left side)
modeling and examining patterns.
Examples:
 3 x (2/5) = 6 x (1/5) = 6/5

If each person at a party eats 3/8 of a pound of roast beef, and there are 5 people at the party, how
many pounds of roast beef are needed? Between what two whole numbers does your answer lie?
A student may build a fraction model to represent this problem.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Lessons:
Introducing Multiplication of Fractions
Product of Whole Number and a Mixed Number
Multiplying Fractions
Multiply Fraction by Whole Number (Unit)
Activities and Tasks:
Fraction of a Whole Number QR Code Activity
Models for Fraction Multiplication
Whole Number by Fraction Word Problems
Visual Fractions by Whole Numbers
Fraction as a Multiple of One Game
A Bowl of Beans
Birthday Cake
Fractions and Whole Numbers in Words
Products of Fractions and Whole Numbers
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Grade 4 Unit Five – Fraction Operations (23 days)
Connections/Notes
4.NF.B.4 Continued
Resources
4.NF.B.4 Continued
Animal Shelter
Multiplying a Whole Number by a Fraction
Tadpoles and Frogs
Grade 4
Wicomico County Public Schools Revised 2014-2015
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Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Unit Six – Understanding & Comparing Decimals (13 days)
In this unit of study students use their previous work with fractions to represent special fractions in a new way. Students use their understanding of
equivalent fractions to begin to use decimal notation, however, it is not the intent at this grade level to connect this notation to the base--‐ten system.
The focus is on solving word problems involving simple fractions or decimals. Work with money can support this work with decimal fractions.
Unit Six Standards
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.
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.
Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged
to use these math terms in explanations or justifications.
base ten system
equivalent
tenths
Grade 4
decimal
hundredths
unit fraction
decimal fraction
increment
visual models
decimal point
number line
whole number
Wicomico County Public Schools Revised 2014-2015
denominator
numerator
46
Fourth Grade Mathematics Curriculum Guide for the
Maryland College and Career Ready Standards
Essential Questions
How are decimal fractions written using decimal notation?
How are decimal numbers and decimal fractions related?
How are decimals and fractions related?
How can I combine the decimal length of objects I measure?
How can I model decimals and fractions using the base-ten and place value system?
What are the benefits and drawbacks of each of these models?
How can I write a decimal to represent a part of a group?
How does the metric system of measurement show decimals?
What are the characteristics of a decimal fraction?
What is a decimal fraction and how can it be represented?
What models can be used to represent decimals?
What patterns occur on a number line made up of decimal fractions?
What role does the decimal point play in our base-ten system?
When can tenths and hundredths be used interchangeably?
When is it appropriate to use decimal fractions?
When you compare two decimals, how can you determine which one has the greater value?
Why is the number 10 important in our number system?
Common Misconceptions
NF.5, 6 & 7 - Students treat decimals as whole numbers when making comparison of two decimals. They think the longer the number, the greater the value.
For example, they think that .03 is greater than 0.3. Furthermore, students do not understand how the places in decimal notation have the same
correspondence (places to the left are 10 times greater than the places to their immediate right) as the places in whole numbers.
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Grade 4 Unit Six – Understanding & Comparing Decimals (13 days)
Connections/Notes
Resources
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.
Teaching Student Centered Mathematics
pg. 182 Base-Ten Fraction Models, figure 7.1
Students can use base ten blocks, graph paper, and other place value models to explore the relationship
between fractions with denominators of 10 and denominators of 100.
Lessons:
What's the (Decimal) Point?
Fraction Decimal Equivalence on Place Value
Students may represent 3/10 with 3 longs and may also write the fraction as 30/100 with the whole in this case
Chart
being the flat (the flat represents one hundred units with each unit equal to one hundredth). Students begin to
make connections to the place value chart as shown in 4.NF.6.
Activities and Tasks:
This work in fourth grade lays the foundation for performing operations with decimal numbers in fifth grade.
Students’ work with decimals (4.NF.5–7) depends to some extent on concepts of fraction equivalence and
elements of fraction arithmetic. Students express fractions with a denominator of 10 as an equivalent fraction
with a denominator of 100;
Example:
Express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Sums of One
Equivalent Fractions with Denominators of 100
Adding Tenths and Hundredths
Expanded Fractions and Decimals
How Many Tenths and Hundredths
PARCC Sample Item
Introduction of Decimals with Base Ten
Fractions and Decimal Number Line
Denominators of Tenths and Hundredths
Show What You Know About Decimals
Videos:
Use a Number Line to Show How Fractions with
Denominators of 10 and 100 Are Equivalent
Templates and Visuals:
Decimal Fraction Cards
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Grade 4 Unit Six – Understanding & Comparing Decimals (13 days)
Connections/Notes
Resources
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.
Teaching Student Centered Mathematics
pg. 183 Multiple Names & Formats
Students make connections between fractions with denominators of 10 and 100 and the place value chart. By
pg. 186 Activity7.2 Base Ten Fractions to
reading fraction names, students say 32/100 as thirty-two hundredths and rewrite this as 0.32 or represent it
Decimals
on a place value model as shown below.
pg. 187 Activity 7.3 Calculator Decimal
Hundreds
Tens
Ones
Tenths
Hundredths

Counting, figure 7.7

3
2
Students use the representations explored in 4.NF.5 to understand 32/100 can be expanded to 3/10 and
2/100.
Students represent values such as 0.32 or 32/100 on a number line. 32/100 is more than 30/100 (or 3/10) and
less than 40/100 (or 4/10). It is closer to 30/100 so it would be placed on the number line near that value.
Lessons:
Clued Into Decimals AIMS
Decimal Detectives AIMS
Express Money Amounts as Decimal Numbers
Model Equivalence of Tenths and Hundredths
Activities and Tasks:
Decimal Fraction Dominoes
Equivalence Dominoes
Decimal Scavenger Hunt
Decimals in Money
Representing Decimals with Base 10 Blocks
Decimal Match
Decimal Match Set 2
Decimal Model Matching Cards
Flag Fractions
Videos:
Convert Decimals to Fractions to the Tenths
Understand decimal notation for fractions, and compare decimal fractions. Extending fraction equivalence to
the general case is necessary to extend arithmetic from whole numbers to fractions and decimals.
Grade 4
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Online:
Decimal Squares
Templates and Visuals:
Decimals Visual
Decimal Squares Set
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Grade 4 Unit Six – Understanding & Comparing Decimals (13 days)
Connections/Notes
Resources
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.
Students build area and other models to compare decimals. Through these experiences and their work with
fraction models, they build the understanding that comparisons between decimals or fractions are only valid
when the whole is the same for both cases.
Each of the models below shows 3/10 but the whole on the right is much bigger than the whole on the left.
They are both 3/10 but the model on the right is a much larger quantity than the model on the left.
When the wholes are the same, the decimals or fractions can be compared.
Draw a model to show that 0.3 < 0.5. (Students would sketch two models of approximately the same size to
show the area that represents three-tenths is smaller than the area that represents five-tenths.
Teaching Student Centered Mathematics
pg. 191 Activity 7.9 Line 'Em Up, Figure 7.11
pg. 202-203 Expanded Lesson Friendly
Fractions to Decimals
Lessons:
Compare Decimals
Use Place Value Chart and Metric Measurement
to Compare Decimals
Dueling Decimals AIMS
Activities and Tasks:
Compare & Order Decimal PPT
Ordering Decimals
Comparing Decimals
Decimal Sort
Trash Can Basketball
Decimal Path Game
Expanding Decimals with Money
Dismissal Duty
Using Place Value
Decimal Activities
Create Your Own Decimal Number Line
Online:
Decimal Squares
Templates and Visuals:
Decimal Ruler
Decimal Cards for Comparing and Ordering
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Grade 4 Unit Six – Understanding & Comparing Decimals (13 days)
Connections/Notes
Resources
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.
Examples:
Lessons:
Solve Word Problems with Measurements in
4.MD.A.2 was addressed in unit 3. It is important to note that students are not expected to do
Decimal Form
computations with quantities in decimal notation. Students can use visual fraction models to solve
Solve
Word Problems Involving Money
problems involving simple fractions or decimals.
Example:
.3 + .6 =
Grade 4
𝟑
𝟏𝟎
Activities and Tasks:
Margie Buys Apples
Money Word Problems
Decimal Place Value Mat
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Unit Seven –Measurement Conversions & Problem Solving (12 days)
In this unit students build a conceptual understanding of the relative sizes of units of measure within a single system of measurement. Measurement
conversions are used to reinforce multiplication as a comparison. In this unit students combine competencies from different domains to solve
measurement problems using the four operations. Measurement, in this unit, provides a context for problem solving. All of the problem types in the
Common Core State Standards for Mathematics Situations Tables, on pages 52 and 53, must be addressed in this unit using larger numbers than
those in the table.
Unit Seven Standards
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.NBT.A.1 Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
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.
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.
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.
Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged
to use these math terms in explanations or justifications.
capacity
ounces
liquid volume
metric
quart (qt)
yard (yd)
Grade 4
centimeter(cm)
foot (ft)
liter (L)
mile (mi)
relative size
conversion
gallon (gal)
mass
milliliter (mL)
ton
cup (c)
gram (g)
measure
ounce (oz)
unit
Wicomico County Public Schools Revised 2014-2015
customary
kilogram (kg)
equivalents
pint (pt)
volume
equivalents fluid
kilometer (km)
meter (m)
pound (lb)
weight
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Essential Questions
About how heavy is a kilogram?
Can different size containers have the same capacity?
Does volume change when you change the measurement material? Why or why not?
How are fluid ounces, cups, pints, quarts, and gallons related?
How are grams and kilograms related?
How are the units of linear measurement within a standard system related?
How are units in the same system of measurement related?
How can fluid ounces, cups, pints, quarts, and gallons be used to measure capacity?
How can we estimate and measure capacity?
How do we compare customary measures of fluid ounces, cups, pints, quarts, and gallons?
How do we compare metric measures of milliliters and liters?
How do we measure volume?
How do we use weight measurement?
How heavy does one pound feel?
What around us weighs about a gram?
What around us weights about a kilogram?
What connection can you make between the volumes of geometric solids?
What do you do if a unit is too heavy to measure an item?
What happens to a measurement when we change units?
What is a unit?
What is the difference between a gram and a kilogram?
What is weight?
What material is the best to use when measuring capacity?
What material is the best to use when measuring volume?
What should you do if a unit is too heavy to measure an item?
What units are appropriate to measure weight?
When do we use conversion of units?
When should we measure with grams? Kilograms?
Why are standard units important?
Why are units important in measurement?
Why do we measure weight?
Why do we need to be able to convert between capacity units of measurement?
Why is it important to be able to measure weight?
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Common Misconceptions
4.MD.1 & 2 - Student believe that larger units will give larger measures. Students should be given multiple opportunities to measure the same object with
different measuring units. For example, have the students measure the length of a room with one-inch tiles, with one-foot rulers, and with yard sticks.
Students should notice that it takes fewer yard sticks to measure the room than the number of rulers of tiles needed.
4.MD.4 - Students use whole-number names when counting fractional parts on a number line. The fraction name should be used instead. For example, if twofourths is represented on the line plot three times, then there would be six-fourths.
Specific strategies may include:
Create number lines with the same denominator without using the equivalent form of a fraction. For example, on a number line using eighths, use 48 instead
of 12. This will help students later when they are adding or subtracting fractions with unlike denominators. When representations have unlike denominators,
students ignore the denominators and add the numerators only.
Have students create stories to solve addition or subtraction problems with fractions to use with student created fraction bars/strips.
4.MD.5 - Students are confused as to which number to use when determining the measure of an angle using a protractor because most protractors have a
double set of numbers. Students should decide first if the angle appears to be an angle that is less than the measure of a right angle (90°) or greater than the
measure of a right angle (90°). If the angle appears to be less than 90°, it is an acute angle and its measure ranges from 0° to 89°. If the angle appears to be
an angle that is greater than 90°, it is an obtuse angle and its measures range from 91° to 179°. Ask questions about the appearance of the angle to help
students in deciding which number to use.
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Fourth Grade Mathematics Curriculum Guide for the
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Grade 4 Unit Seven – Measurement Conversions & Problem Solving (12 days)
Connections/Notes
Resources
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.
This standard was addressed in unit 3, in which the focus was on basic facts. In this unit,
measurement will be the focus of the word problems.
Lessons:
Multiplicative Comparison Using Measurement
Activities and Tasks:
Multiplicative Comparison Problems
Multiplicative Comparison Problems 2
4.NBT.A.1
Recognize that a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
This standard was addressed in unit 3, in which the focus was on addition and subtraction. In this unit,
metric measurement provides an opportunity to deepen the students’ understanding of place value in
relation to multiples of 10.
Lessons:
Relate Metric Units to Place Value Units
Activities and Tasks:
Metric Relationships
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.
The units of measure that have not been addressed in prior years are pounds, ounces, kilometers, milliliters,
and seconds. Students’ prior experiences were limited to measuring length, mass, liquid volume, and
elapsed time. Students did not convert measurements. Students need ample opportunities to become
familiar with these new units of measure.
Grade 4
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Teaching Student Centered Mathematics
pg. 275 About One Unit Activity 9.13
pg. 276 Activities 9.14, 9.15
pg. 277 Activity 9.16
pg. 280 Activities 9.18 & 9.19
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Grade 4 Unit Seven – Measurement Conversions & Problem Solving (12 days)
Connections/Notes
4.MD.A.1 Continued
Students may use a two-column chart to convert from larger to smaller units and record equivalent
measurements. They make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches
because there are 3 groups of 12.
Example:
kg
g
ft
in
lb
oz
1
1000
1
12
1
16
2
2000
2
24
2
32
3
3000
3
36
3
48
Resources
4.MD.A.1 Continued
Lessons:
Counting Crocodiles Math Solutions
Create Conversion Tables for Measurement and
Use Tables to Solve Problems
Activities and Tasks:
Equivalent Capacities
Capacity Creature
Time Equivalents
Measurement Conversion Problems
Making a Kilogram
Estimating Weight
Measurement Concentration
Relative Sizes of Measurement Units
Equivalent Measure Tables
Capacity Equivalents Flipbook
Metric Relationships
Fruit Roll Up Measurement
Customary Measurement Foldable
Videos:
Compare and Convert Customary Units of Length
Online:
Measurement Games
Templates and Visuals:
Equivalent Graphic
Measurement Signs
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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.
4.OA.A.3 is repeated here to include all four operations and will be finalized in Unit 14. Repeating
these standards throughout the year provides students multiple opportunities to develop these skills—
which are major areas of focus for this grade level.
Lessons:
Ready to take the Plunge
(omit % problems or have students solve with a
calculator)
Multi-Step Word Problems Mixed Number
Measurements to Single Units
Solve Multi-Step Measurement Word Problems
Use Addition and Subtraction to Solve Multi-Step
Word Problems Involving Length, Mass, and
Capacity
Activities and Tasks:
Multi-Step Word Problems with Measurement
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.
Examples:

Division/fractions: Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends so
each friend gets the same amount. How much ribbon will each friend get?
Students may record their solutions using fractions or inches. (The answer would be 2/3 of a foot or
8 inches. Students are able to express the answer in inches because they understand that 1/3 of a
foot is 4 inches and 2/3 of a foot is 2 groups of 1/3.)

Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40
minutes on Wednesday. What was the total number of minutes Mason ran?
Grade 4
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Lessons:
Found Pounds Illuminations
Using a Timeline to Determine Elapsed Time
Illuminations
It’s the Last Straw AIMS
Fuel Filling Figures AIMS
Mix-Ups & Mysteries AIMS
Word Problems with Weight
Create Conversion Tables for Time and Use
Tables to Solve Problems
Solve Problems Using Mixed Units of Time
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4.MD.A.2 Continued
4.MD.A.2 Continued

Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she gave
the clerk a $5.00 bill, how much change will she get back?

Multiplication: Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters,
Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did
the boys have?
Number line diagrams that feature a measurement scale can represent measurement quantities. Examples
include: ruler, diagram marking off distance along a road with cities at various points, a timetable showing
hours throughout the day, or a volume measure on the side of a container.
At 7 a.m., Candace wakes up to go to school. It takes her 8 minutes to shower, 9 minutes to get dressed,
and 17 minutes to eat breakfast. How many minutes does she have until the bus comes at 8 a.m.? Use the
number line to help solve the problem.
Lessons Continued:
Addition and Subtraction Word Problems Involving
Metric Length
Word Problems Involving Metric Mass
Word Problems Involving Metric Capacity
Activities and Tasks:
Elapsed Time PPT/TPT
Measurement Word Problems
Elapsed Time Practice Sheets(3)
Elapsed Time Warm-Ups
And the Winner Is…
As the Clock Ticks
Tournament Time
Metric System Problems
Videos:
Convert Measurements to Solve Distance
Problems
Represent Fractional Distance Measurement
Quantities Using Diagrams
Online:
Orange Drink
Some parts of this standard could be met earlier in the year (such as using whole-number multiplication to
express measurements given in a larger unit in terms of a smaller unit —see also 4.MD.1), while others
might be met only by the end of the year (such as word problems involving addition and subtraction of
fractions or multiplication of a fraction by a whole number—see also 4.NF.3d and 4.NF.4c.
Grade 4
Wicomico County Public Schools Revised 2014-2015
NRICH Math
Templates and Visuals:
Elapsed Time Ruler 1
Elapsed Time Ruler 2
24 Hour Number Line
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Unit Eight – Geometry (16 days)
This unit is an introduction to angles and angle measurement. Students start this unit drawing and naming points, lines, segments, rays and angles
since it is foundational to the other standards in this unit. Students use their understanding of equal partitioning and unit measurement to understand
angle and turn measure. Students also develop their spatial reasoning skills by using a wide variety of attributes to talk about 2-dimensional shapes.
Students analyze geometric figures based on angle measurement, parallel and perpendicular lines, and symmetry.
Unit Eight Standards
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.
a. 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.
b. 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 a specified measure.
4.G.A.1
figures.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional
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.
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.
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.
4.G.A.3 Recognize a line of symmetry for a two-dimensional 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.
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Math Language
The terms below are for teacher reference. Although these do not need to be memorized by the students, students should be encouraged to use
these math terms in explanations or justifications.
acute angle
degree
line
one-degree angle
polygon
reflex angle
square
trapezoid
angle
equiangular triangle
line segment
parallel lines
protractor
rhombus
straight angle
vertex (of a 2-D figure)
arc
equilateral triangle
line of symmetry
parallelogram
quadrilateral
right angle
supplementary angle
circle
intersect
measure
perpendicular lines
ray
scalene triangle
symmetry
complimentary angle
isosceles triangle
obtuse angle
plane figure
rectangle
side
triangle
Essential Questions
What is an angle?
How are a circle and an angle related?
Why do we need a standard unit with which to measure angles?
How are the angles of a triangle related?
How can angles be combined to create other angles?
How can we measure angles using wedges of a circle?
How can we use angle measures to draw reflex angles?
How can we use the relationship of angle measures of a triangle to solve problems?
How do we measure an angle using a protractor?
How does a circle help with measurement?
How does a turn relate to an angle
How is a circle like a ruler?
What are benchmark angles and how can they be useful in estimating angle measures?
What do we actually measure when we measure an angle?
What do we know about the measurement of angles in a triangle?
What does half rotation and full rotation mean?
How are geometric objects different from one another?
How are quadrilaterals alike and different?
How are symmetrical figures created?
How are symmetrical figures used in artwork?
How are triangles alike and different?
How can angle and side measures help us to create and classify triangles?
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How can shapes be classified by their angles and lines?
How can the types of sides be used to classify quadrilaterals?
How can triangles be classified by the measure of their angles?
How can we sort two-dimensional figures by their angles?
How can you create different types of quadrilaterals?
How can you create different types of triangles?
How can you determine the lines of symmetry in a figure?
How can you use only a right angle to classify all angles?
How do you determine lines of symmetry? What do they tell us?
How is symmetry used in areas such as architecture and art? In what areas is symmetry important?
What are the geometric objects that make up figures?
What are the mathematical conventions and symbols for the geometric objects that make up certain figures?
What are the properties of quadrilaterals?
What are the properties of triangles?
What are triangles?
What is a quadrilateral?
What is symmetry?
What makes an angle a right angle?
What properties do geometric objects have in common?
Where is geometry found in your everyday world?
Which letters of the alphabet are symmetrical?
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Grade 4 Unit Eight – Geometry (16 days)
Connections/Notes
Resources
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.
a. 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 “onedegree angle,” and can be used to measure angles.
b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
The diagram below will help students understand that an angle measurement is not related to an
area since the area between the 2 rays is different for both circles yet the angle measure is the
same.
Teaching Student Centered Mathematics
pg. 272 A Unit Angle Activity 9.12, Figure 9.13
Lessons:
Use a Circular Protractor to Understand a OneDegree Angle
Circles and Angles (Unit)
Activities and Tasks:
Angles PPT
Angles on the Geoboard
Angles as Parts of a Circle
Angle Explorer Tool
Angle Web
Student Angle Explorer
Angle Flipbook
Templates and Visuals:
7 x 7 Geoboard Paper
Online:
Angle Explorer
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4.MD.C.6
Measure angles in whole-number degrees using a protractor. Sketch angles of a specified measure.
Teaching Student Centered Mathematics
Before students begin measuring angles with protractors, they need to have some experiences with pgs. 272-274
benchmark angles. They transfer their understanding that a 360º rotation about a point makes a
Lessons:
complete circle to recognize and sketch angles that measure approximately 90º and 180º. They
extend this understanding and recognize and sketch angles that measure approximately 45º and
Flagging Down Angles AIMS
30º. They use appropriate terminology (acute, right, and obtuse) to describe angles and rays
Flight Paths AIMS
(perpendicular).
Using Protractors
Circles and Angles (Unit)
Activities and Tasks:
Angle Flip Cards
Using a Protractor
Angles in Triangles
Angles in Quadrilaterals
Predicting and Measuring Angles
Angles
Angle Barrier Game
Angles PPT
Determining 90° Angles
Measuring Angles
Measuring Angles 2
Measuring Angles Using a Protractor
I Have…Who Has…Angles
Angles in Names
Types of Angles
Types of Angles 2
Comparing Angles
Angle Explorer Tool
Student Angle Explorer
Protractor Golf
What is the measure of angle m?
Ask the student to estimate the measure of the
angle. Then, measure the angle with a protractor
with paying close attention to the double labeling
of the protractor.
Grade 4
Videos:
Read a Protractor
Angle & Protractor Video
Angle & Protractor Activities
Types of Angles
Online:
Angle Explorer
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Maryland College and Career Ready Standards
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.
Examples of points, line segments, lines, angles, parallelism, and perpendicularity can be seen
daily. Students do not easily identify lines and rays because they are more abstract.
Students select and use a protractor to measure
angles and represent the angles with drawings
(MP.4, MP.5).
Students might explore line segments, lengths,
perpendicularity, and parallelism on different types
of grids, such as rectangular and triangular
(isometric) grids.
Can you find a rectangle on a triangular grid? Can
you find a non-rectangular parallelogram on a
rectangular grid?
Given a segment on a rectangular grid that is not
parallel to a grid line, draw a parallel segment of the
same length with a given endpoint.
Teaching Student Centered Mathematics
pg. 217 Can You Make It? Activity 8.5
Lessons:
Line Segments on the Geoboard Math Solutions
Parallel Lines
Points, Lines, Segments, Rays and Angles
Lines, Segments, Rays Unit
Types of Lines (Unit)
Activities and Tasks:
Line Flip Book
Types of Lines PPT
Identifying Lines
Comparing Angles
Alphabet Lines
Line Segments on the Geoboard
QR Code Scavenger Hunt
Parallel and Perpendicular Pictures with Questions
Getting Gym Equipment in Line
The Race Is On
Videos:
Draw Points, Lines, Segments
Draw Parallel and Perpendicular Lines
Label and Name Points, Lines, Rays and Angles
Using Math Notation
Templates and Visuals:
Geoboard Recording Paper
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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.
In this unit, 4.OA.C.5 includes repeated and growing shape patterns.
The concepts in this unit lend themselves to using technology applications (MP.5).
Teaching Student Centered Mathematics
pg. 291 Predict Down The Line - Activity 10.1
pg. 293 Grid Patterns Activity & Figure 10.2
pg. 294 Extend & Explain Activity 10.3 & Predict
How Many 10.4
p. 299 What's Next & Why Activity 10.6 & 10.7
Patterns involving numbers or symbols either repeat or grow. Students need multiple opportunities
creating and extending number and shape patterns.
Patterns and rules are related. A pattern is a sequence that repeats the same process over and
over. A rule dictates what that process will look like.
Students investigate different patterns to find rules, identify features in the patterns, and justify the
reason for those features.
After students have identified rules and features from patterns, they need to generate a numerical or
shape pattern from a given rule.
Lessons:
Looking Back and Moving Forward Illuminations
What's Next? Illuminations
Growing Patterns Illuminations
Shape Patterns Math Solutions
Activities and Tasks:
Shape Patterns Practice Sheets
Square Numbers
Triangular Numbers
Videos:
Generating Number/Shape Patterns That Follow a
Given Rule and Identifying Pattern Features
Find the 9th Shape for a Geometric Pattern Using
a Table
Online:
Color Patterns NLVM
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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.
Examples:
 If the two rays are perpendicular, what is the value of m?

Joey knows that when a clock’s hands are exactly on 12 and 1,
the angle formed by the clock’s hands measures 30°. What is the
measure of the angle formed when a clock’s hands are exactly on the 12 and 4?

The five sections in the diagram are the exact same size.
Write an equation that will help you find the measure of the indicated angle.
Find the angle measurement.
Lessons:
Supplementary Angles Math is Fun Mini-Lesson
Complementary Angles Math is Fun Mini-Lesson
Decompose Angles Using Pattern Blocks
Activities and Tasks:
How Many Degrees?
Unknown Angle Word Problems
Finding an Unknown Angle
Pattern Block Angles
Angles in a Right Triangle
Additive Angles
Additive Angles #2
Additive Angles #3
Additive Angle Practice
Videos:
Understand that Angle Measure is Additive by
Decomposing
Compose and Decompose Angles
Find Unknown Angles Using Angle Properties
Online:
Banana Hunt Angle Game
Decomposing Angles
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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.
Teaching Student Centered Mathematics
A trapezoid is a quadrilateral with at least one pair of parallel sides.
pg. 212 Shape Sorts Activity 8.1
pg. 213 What's my Shape Activity 8.2
Two-dimensional figures may be classified using different characteristics such as, parallel or
pg. 225 Triangle Sort BLM #29
perpendicular lines or by angle measurement.
Parallel or Perpendicular Lines:
Students should become familiar with the concept of parallel and perpendicular lines. Two lines are
parallel if they never intersect and are always equidistant. Two lines are perpendicular if they
intersect in right angles (90°).
Students may use transparencies with lines to arrange two lines in different ways to determine that
the 2 lines might intersect in one point or may never intersect. Further investigations may be
initiated using geometry software. These types of explorations may lead to a discussion on angles.
Parallel and perpendicular lines are shown here:

Example:
Identify which of these shapes have perpendicular or parallel sides and justify your
selection.
A possible justification that students might give is:
The square has perpendicular lines because the sides
meet at a corner, forming right angles.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Lessons:
Rectangles and Parallelograms
What's So Special About Triangles, Anyway?
Trying Out Tangrams
Polygon Capture
Analyze and Classify Triangles
Classify Triangles
Quadrilateral Unit
Triangles and Quadrilaterals (Unit)
Activities and Tasks:
Triangles on the Geoboard
Classifying Triangles 1
Classifying Triangles 2
Triangle Pack for Classifying
Right Triangles on the Geoboard
Isosceles Triangles on the Geoboard
Constructing Quadrilaterals
Are These Right?
Quadrilateral Criteria
Classifying 2-Dimensional Figures
Classifying Quadrilaterals
Quadrilateral Word Problems
Quadrilateral Mini-Lesson Power Point
Special Quadrilateral Reference Sheet
Monster Munch Identifying Triangles
Videos:
Know Your Quadrilaterals
Classify Various Quadrilaterals by Describing Their
Properties
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4.G.A.2 Continued
4.G.A.2 Continued
Angle Measurement:
Classify Two-Dimensional Figures by Examining
Their Properties
This expectation is closely connected to 4.MD.5, 4.MD.6, and 4.G.1. Students’ experiences with
drawing and identifying right, acute, and obtuse angles support them in classifying two-dimensional
figures based on specified angle measurements. They use the benchmark angles of 90°, 180°, and
360° to approximate the measurement of angles.
Triangle Classification:
Right triangles can be a category for classification. A right triangle has one right angle. There are
different types of right triangles. An isosceles right triangle has two or more congruent sides and a
scalene right triangle has no congruent sides
Students will use side length to classify triangles as equilateral, equiangular, isosceles, or scalene;
and can use angle size to classify them as acute, right, or obtuse. They then learn to cross-classify,
for example, naming a shape as a right isosceles triangle.
Classify Triangles by Examining Their Properties
Online:
Quadrilateral Quest
Virtual Pinboard Create & Identify 2-Dimensional
Figures
Templates and Visuals:
Geoboard Recording Paper
Frayer Model 2-D Shapes
*IRC has die cuts for: squares, rectangles,
octagon, hexagon, pentagon, trapezoid, triangle,
and rhombus. One piece of construction paper will
produce 4 of each 2D figure for students to use in
sorting activities. Ordering multiple figures will
allow you to modify the 2D shapes. Example: Cut
one trapezoid to make it a right trapezoid.
4.G.A.3
Recognize a line of symmetry for a two-dimensional 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.
Students need experiences with figures which are symmetrical and non-symmetrical. Figures
include both regular and non-regular polygons. Folding cut-out figures will help students determine
whether a figure has one or more lines of symmetry.

Recognize a line of symmetry for a two-dimensional 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.

Given a half of a figure and a line of symmetry, accurately draw the other half to create a
symmetric figure.
Grade 4
Wicomico County Public Schools Revised 2014-2015
Teaching Student Centered Mathematics
pg. 234 Pattern Block Mirror Symmetry Activity
8.15
pg. 235 Dot Grid Line Symmetry Activity 8.16
Lessons:
Finding Lines of Symmetry
Recognize Lines of Symmetry
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4.G.A.3 Continued
Polygons with an odd number of sides have lines of symmetry that go from a midpoint of a side
through a vertex.
4.G.A.3 Continued
Activities and Tasks:
Determining Symmetry
Symmetry in Shapes
Symmetry on the Geoboard
Symmetry in Regular Polygons
Symmetrical Coin Designs
Symmetrical Coin Designs 2
Lines of Symmetry for Triangles
Lines of Symmetry for Quadrilaterals
Lines of Symmetry for Circles
Pattern Block Symmetry
Videos:
Identify Line Symmetry in Regular Polygons
Identify Line Symmetry in Irregular Polygons
Identify Line Symmetry in a Geometric Figure
Using Imagery to Find Lines of Symmetry
Online:
Symmetry Game
Symmetry Sort
Virtual Geoboard
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Unit Nine – Fluency with Problem Solving (32 days or remainder of year)
This is a culminating unit in which students focus on problem solving in order to demonstrate fluency with the standard algorithms in addition and
subtraction. They demonstrate computational fluency with all problem types. All standards in this unit have been addressed in prior units. These
concepts require greater emphasis due to the depth of the ideas, the time they take to master, and/or their importance to future mathematics.
Students should experience rich problem solving across the standards. The problem solving should not be skill isolated. In demonstrating fluency,
students explain and flexibly use properties of operations and place value to solve problems, looking for shortcuts and applying generalized strategies
(MP.2, MP.8).
This unit is designed for application and review of the problem types for which your students show the least fluency. Review back to the previous
units for comments, clarification, examples, and resources according to the needs of your students.
Unit Nine Standards
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.
4.NBT.B.4
Fluently add and subtract multi-digit whole 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.
4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
d. 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.
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4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
c. 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.
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.
4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
Mixed Problem Solving Resources:
Lessons:
Building a Business Illuminations
Exploring with Math Trails Illuminations
Super Bowl Scores Illuminations
Activities and Tasks:
Fraction Word Problems Mixed
Karl’s Garden
Multi-Step Word Problems QR Code Task Cards
Measurement Distance, Time, Liquid Volume Word Problems
Saving Money 1 & 2
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