GRADE 4 ATHEMATICS CURRICULUM UIDE
Transcript of GRADE 4 ATHEMATICS CURRICULUM UIDE
GRADE 4 MATHEMATICS
CURRICULUM GUIDE
Loudoun County Public Schools
2011-2012 Complete scope, sequence, pacing and resources are available on the LCPS Intranet.
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun
County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other
statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers
concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is the
lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program that remains relatively unchanged
over several student generations. Other documents, called RESOURCES, are updated more frequently. These are published separately but teachers can
combine them with the GUIDE for ease in lesson planning.
Mathematics Internet Safety Procedures
1. Teachers should review all Internet sites and links prior to using it in the classroom.
During this review, teachers need to ensure the appropriateness of the content on the site,
checking for broken links, and paying attention to any
inappropriate pop-ups or solicitation of information.
2. Teachers should circulate throughout the classroom while students are on the
internet checking to make sure the students are on the appropriate site and
are not minimizing other inappropriate sites.
Teachers should periodically check and update any web addresses that they have on their
LCPS web pages.
3. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
4. Teachers should assure that the use of websites correlate with the objectives
of the lesson and provide students with the appropriate challenge.
Grade 4 Mathematics Nine Weeks Overview
1st Quarter 2
nd Quarter 3
rd Quarter 4
th Quarter
Place value 4.1
Add and subtract
whole numbers 4.4 a, b, d
Functions 4.15
Equality 4.16
Multiplication and division
of whole numbers 4.4
Probability 4.13
Graphing 4.14
Fractions 4.5 a, b, d
4.2
Decimals 4.3
4.5 c
Measurement 4.7
4.6
4.8
Geometry 4.10
4.11
4.12
Elapsed time 4.9
Grade 4 Quarter 1 School Year 2011-12
Number of Days
Topics, Essential Questions, and Essential Understandings
(Students should be able to answer essential questions.)
REQUIRED Critical Thinking
Lessons
Standard(s) of Learning Essential Knowledge and Skills
Additional Instructional Resources
ESS: VDOE Enhanced Scope and Sequence
25 days
Working with Whole Numbers 4.1 Essential Questions • Demonstrate and explain the relationship
between each place in a number. • Demonstrate and explain how the place value
system can be used to name and compare large numbers.
• Compare and contrast the appropriateness of using estimation and finding the exact value.
4.1 Essential Understandings • Understand the relationships in the place
value system in which the value of each place is ten times the value of the place to its right.
• Use the patterns in the place value system to read and write numbers.
• Understand that reading place value correctly is essential when comparing numbers.
• Understand that rounding gives a close number to use when exact numbers are not needed for the situation at hand.
• Develop strategies for rounding.
INV: Mathematical Thinking at Grade 4 Investigation 1: “How Many Hundreds”, Sessions 1 – 4 Investigation 3: “Using Number Patterns”, Sessions 1 - 5 INV: Landmarks in the Thousands Investigation 1: “Working with 100”, Sessions 1 – 3 Investigation 2: “Exploring Multiples of 100”, Sessions 1 – 5 Investigation 3: “How Much is 1000”, Sessions 1 – 5 Investigation 4: “Making a 10,000 Chart”, Sessions 1 - 3
SOL 4.1 The student will a) identify orally and in writing the place value for each digit in a whole number expressed through millions; b) compare two whole numbers expressed through millions using symbols (>, <, or =); and c) round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand. 4.1 Essential Knowledge and Skills • Identify and communicate, both orally and
in written form, the placed value for each digit in whole numbers expressed through the one millions place.
• Read whole numbers through the one millions place that are presented in standard format, and select the matching number in written format.
• Write whole numbers through the one millions place in standard format when the numbers are presented orally or in written format.
• Identify and use the symbols for greater than, less than, and equal to.
• Compare two whole numbers expressed through the one millions, using symbols >, <, or =.
• Round whole numbers expressed through
ESS: • Location, Location,
Location • Estimation Game • Modeling Addition and
Subtraction • Multiplying and
Trading • Balance Beams • Weighty Problems
~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4.4 Essential Questions • Demonstrate and explain finding a sum, a
difference. • Demonstrate and explain inverse operations.
4.4 Essential Understandings • Develop and use strategies to estimate whole
number sums and differences and to judge the reasonableness of such results.
• Understand that addition and subtraction are inverse operations.
• Understand how to solve single-step and multistep problems using whole number operations.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 4.15 Essential Questions • Create and justify numerical patterns using
words, tables, graphs, and/or symbols. • Analyze and extend numerical patterns using
various methods. 4.15 Essential Understandings Understand that patterns and functions can be
represented in many ways and described using words, tables, graphs, and symbols.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
the one millions place to the nearest thousand, ten thousand, and hundred-thousand place.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.4 The student will a) estimate sums, differences, …; b) add, subtract, and multiply whole numbers; d) solve single-step and multistep addition, subtractions, …problems with whole numbers. 4.4 Essential Knowledge and Skills • Estimate whole number sums, differences. • Refine estimates by adjusting the final
amount, using terms such as closer to, between, and a little more than.
• Determine the sum or difference of two whole numbers, each 999,999 or less, in vertical and horizontal form with or without regrouping, using paper and pencil, and using a calculator.
• Solve single-step and multistep problems using whole number operations.
• Verify the reasonableness of sums, differences … of whole numbers using estimation.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.15 The student will recognize, create, and extend numerical and geometric patterns. 4.15 Essential Knowledge and Skills • Describe geometric and numerical
patterns, using tables, symbols, or words. • Create geometric and numerical patterns,
using concrete materials, number lines, tables, and words.
• Extend geometric and numerical patterns, using concrete materials, number lines, tables, and words.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SOL 4.16 The student will
~~~~~~~~~~~~~~~~~~~~ Grade 4 ESS: • This Fruit is a Mass! • Kiddy Pool Grade 5 ESS: • Measurement Mania
Smart Measurement Site http://smartmeasurement.wikispaces.com/ ~~~~~~~~~~~~~~~~~~ Exploration of a Balance
20 days
4.16 Essential Questions • What is an equation? • Demonstrate and explain the associative
property. • How are the associative properties for
addition and multiplication alike? • Demonstrate and explain the commutative
property. • How are the commutative properties for
addition and multiplication alike? • Compare and contrast the associative
properties for addition and multiplication. 4.16 Essential Understandings • Understand that mathematical relationships
can be expressed using equations. • Understand that quantities on both sides of an
equation must be equal. • Understand that the associative property for
addition means you can change the groupings of three or more addends without changing the sum.
• Understand that the associative property for multiplication means you can change the groupings of three or more factors without changing the product.
a) recognize and demonstrate the meaning of equality in an equation; and b) investigate and describe the associative property for addition and multiplication. 4.16 Essential Knowledge and Skills • Recognize and demonstrate that the equals
sign (=) relates equivalent quantities in an equation.
• Write an equation to represent equivalent mathematical relationships (e.g., 4 × 3 = 2 × 6).
• Recognize and demonstrate appropriate use of the equals sign in an equation.
• Investigate and describe the associative property for addition as (6 + 2) + 3= 6 + (2 + 3).
• Investigate and describe the associative property for multiplication as (3 x 2) x 4 = 3 x (2 x 4).
(Lesson 2)
3 days Enrichment, Assessment, and Remediation
Grade 4 Quarter 2 School Year 2011-12
Page 1
Number
of Days
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
REQUIRED
Critical
Thinking
Lessons
Standards of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
ESS: VDOE
Enhanced Scope
and Sequence
Lessons
20 days
Working with Whole Numbers
4.4 Essential Questions
There are many methods for
determining a product. What are the
criteria considered when choosing a
strategy?
What are inverse relationships?
What does it mean to divide?
What does multiplication mean?
What effect does multiplication have
on a number?
What does the divisor represent in a
real life application? Dividend?
Quotient? How are each of these
represented using the three division
models?
What is the similarity between
multiplication and addition?
What is the similarity between
division and subtraction?
4.4 Essential Understandings
All students should:
Develop and use strategies to
estimate whole number sums and
Packages and
Groups
Investigation 2:
Double Digit
Multiplication,
Sessions 1 – 3
Investigation 3:
Multiplication
and Division
Choices,
Sessions 1 - 10
SOL 4.4 The student will
a) a) estimate … products, and quotients
of whole numbers;
b) …multiply whole numbers;
c) c) divide whole numbers, finding
quotients with and without remainders;
and
d) d) solve single-step and multistep …
multiplication problems with whole
numbers.
4.4 Essential Knowledge and Skills
Estimate whole number …
products, and quotients.
Refine estimates by adjusting the
final amount, using terms such as
closer to, between, and a little more
than.
Estimate and find the products of
two whole numbers ….
Estimate and find the quotient of
two whole numbers….
Solve single-step and multipstep
problems using whole number
operations.
Verify the reasonableness of sums,
ESS:
http://www.doe.vir
ginia.gov/testing/s
ol/standards_docs/
mathematics/index
.shtml
Grade 4 Quarter 2 School Year 2011-12
Page 2
differences and to judge the
reasonableness of such results.
Understand that addition and
subtraction are inverse operations.
Understand that division is the
operation of making equal groups or
equal shares. When the original
amount and the number of shares are
known, divide to find the size of each
share. When the original amount and
the size of each share are known,
divide to find the number of shares.
Understand that multiplication and
division are inverse operations.
Understand various representations of
division and the terms used in
division are dividend, divisor, and
quotient.
dividend divisor = quotient
quotient divisor dividend
Understand how to solve single-step
and multistep problems using whole
number operations.
differences, products, and quotients
of whole numbers using estimation.
5 days
Outcomes and Data
4.13 Essential Questions
Between what 2 numbers do probability
values lie? Why?
Explain how the outcome of a simple
SOL 4.13 The student will
a) predict the likelihood of an outcome of
a simple event; and
b) represent probability as a number
between 0 and 1, inclusive.
Grade 4 Quarter 2 School Year 2011-12
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event relates to the numbers of 0 and 1.
Identify the likelihood of an event
occurring and relate it to its rational
representation.
Provide a real life example of something
that has a probability of 1. 0. ½ and
others in between.
Represent the probability of an event as a
common fraction.
4.13 Essential Understandings
Understand and apply basic concepts of
probability.
Describe events as likely or unlikely and
discuss the degree of likelihood, using
the terms certain, likely, equally likely,
unlikely, and impossible.
Predict the likelihood of an outcome of
a simple event and test the prediction.
Understand that the measure of the
probability of an event can be
represented by a number between 0 and
1, inclusive.
4.13 Essential Knowledge and Skills
Model and determine all possible
outcomes of a given simple event
where there are no more than 24
possible outcomes, using a variety of
manipulatives, such as coins, number
cubes, and spinners.
Write the probability of a given
simple event as a fraction, where the
total number of possible outcomes is
24 or fewer.
Identify the likelihood of an event
occurring and relate it to its fractional
representation (e.g., impossible/0;
equally likely/1
2 ; certain/1).
Determine the outcome of an event
that is least likely to occur (less than
half) or most likely to occur (greater
than half) when the number of
possible outcomes is 24 or less.
Represent probability as a point
between 0 and 1, inclusively, on a
number line.
10 days
4.14 Essential Questions
Collect, organize, display, and interpret data
from a variety of graphs.
Compare and contrast line, bar, picture,
circle graphs, and line plots.
4.14 Essential Understandings
Understand the difference between
representing categorical data and
representing numerical data.
Understand that line graphs show
INV: The Shape of
Data
Investigation 1:
Introduction to
Data Analysis,
Sessions 1 – 3
Investigation 2:
Landmarks in the
Data, Sessions 1 –
7
SOL 4.14 The student will collect,
organize, display, and interpret data from a
variety of graphs.
4.14 Essential Knowledge and Skills
Collect data, using, for example,
observations, measurement, surveys,
scientific experiments, polls, or
questionnaires.
Organize data into a chart or table.
Construct and display data in bar
ESS
http://www.doe.virg
inia.gov/testing/sol/s
tandards_docs/math
ematics/index.shtml
Lucky Sums?
Looking for a Pet!
How Certain Are
You?
Sandwich Data
Grade 4 Quarter 2 School Year 2011-12
Page 4
change over time (numerical data).
Understand that bar graphs should be
used to compare counts of different
categories (categorical data).
Understand how data displayed in bar
and line graphs can be interpreted so
that informed decisions can be made.
Understand that the title and labels of the
graph provide the foundation for
interpreting the data.
graphs, labeling one axis with equal
whole number increments of 1 or
more (numerical data) (e.g., 2, 5, 10,
or 100) and the other axis with
categories related to the title of the
graph (categorical data) (e.g.,
swimming, fishing, boating, and water
skiing as the categories of “Favorite
Summer Sports”).
Construct and display data in line
graphs, labeling the vertical axis with
equal whole number increments of 1
or more and the horizontal axis with
continuous data commonly related to
time (e.g., hours, days, months, years,
and age). Line graphs will have no
more than 10 identified points along a
continuum for continuous data. For
example, growth charts showing age
versus height place age on the
horizontal axis (e.g., 1 month, 2
months, 3 months, and 4 months).
Title or identify the title in a given
graph and label or identify the axes.
Interpret data from simple line and bar
graphs by describing the
characteristics of the data and the data
as a whole (e.g., the category with the
greatest/least, categories with the
same number of responses,
similarities and differences, the total
number). Data points will be limited
to 30 and categories to 8.
Interpret the data to answer the
question posed, and compare the
answer to the prediction (e.g., “The
Say, “Here!”
Spinning Colors
Grade 4 Quarter 2 School Year 2011-12
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summer sport preferred by most is
swimming, which is what I predicted
before collecting the data.”).
Write at least one sentence to describe
the analysis and interpretation of the
data, identifying parts of the data that
have special characteristics, including
categories with the greatest, the least,
or the same.
6 days Assessment, Enrichment, and
Remediation
Grade 4 Quarter 3 School Year 2011-12
Page 1
Number
of Days
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer
essential questions.)
REQUIRED
Critical
Thinking
Lessons
Standards of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
ESS: VDOE
Enhanced Scope
and Sequence
Lessons
22 days
Working with Rational Numbers
Fractions
4.5 a, b, d Essential Questions
Compare and contrast whole number
operations with fraction operations.
Explain why least common multiples
and least common denominators are
used when computing the sums and
differences of fractions.
Give an example of a practical
problem using fractions.
Give an example of a practical
problem using decimals.
4.5 a, b, d Essential Understandings Understand and use common multiples
and common factors for simplifying
fractions.
Develop and use strategies to estimate
addition and subtraction involving
fractions ….
Use visual models to add and subtract
with fractions and decimals.
INV: Different
Shapes, Equal
Pieces
Investigation 3:
Ordering
Fractions,
Sessions 1 – 9
INV: Three Out
of Four Like
Spaghetti
Investigation 1:
Using Fractions
to Describe Data,
Sessions 1 – 4
SOL 4.5 a, b, d The student will a) determine common multiples and
factors, including least common multiple
and greatest common factor;
b) add and subtract fractions having like
and unlike denominators that are limited to
2, 3, 4, 5, 6, 8, 10, and 12, and simplify the
resulting fractions, using common
multiples and factors;
4.5 a, b, d Essential Knowledge and
Skills Find common multiples and common
factors of numbers.
Determine the least common multiple
and greatest common factor of
numbers.
Use least common multiple and/or
greatest common factor to find a
common denominator for fractions.
Add and subtract with fractions
having like denominators whose
denominators are limited to 2, 3, 4, 5,
6, 8, 10, and 12, and simplify the
resulting fraction using common
multiples and factors.
Add and subtract with fractions having
ESS
http://www.doe.vir
ginia.gov/testing/s
ol/standards_docs/
mathematics/index
.shtml
Fraction Grids
Register Tape
Fractions
Circle Fractions
Fraction Strips
Egg Carton
Fractions
Pattern Block
Fractions
Build the Whole
Pattern Block
Fraction Game
Comparing
Fractions
Which is Closer?
Fraction Strip
Addition
Fraction Riddles
Fraction Bar Kit
Grade 4 Quarter 3 School Year 2011-12
Page 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.2 a, b, c Essential Questions
Demonstrate and explain patterns
within equivalent fractions.
Given more than one fraction,
how do you determine which
fraction is smallest?
Identify the division statement
that represents a fraction.
Explain the strategy of using
landmark ¼, ½, ¾ help you in
comparing and ordering fractions.
Explain how a fraction can
represent a relationship as well as
a division operation.
Justify how a fractional number
describes part of a set.
Explain how to determine a
fraction is in simplest form.
Demonstrate and explain that
multiple representations of
unlike denominators whose
denominators are limited to 2, 3, 4, 5,
6, 8, 10, and 12, and simplify the
resulting fraction using common
multiples and factors.
Solve problems that involve adding
and subtracting with fractions having
like and unlike denominators whose
denominators are limited to 2, 3, 4, 5,
6, 8, 10, and 12, and simplify the
resulting fraction using common
multiples and factors.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.2 a, b, c The student will
a) compare and order fractions and mixed
numbers;
b) represent equivalent fractions; and
c) identify the division statement that
represents a fraction.
4.2 Essential Knowledge and Skills Compare and order fractions having
denominators of 12 or less, using
manipulative models and drawings,
such as
region/area models.
Compare and order fractions with like
denominators by comparing number
of parts (numerators) (e.g., 1
5 <
3
5 ).
Compare and order fractions with like
numerators and unlike denominators
by comparing the size of the parts
INV: Different
Shapes, Equal
Pieces
Investigation 1:
Parts of Squares:
Halves, Fourths,
and Eighths,
Sessions 1 – 5
Investigation 2:
Parts of
Rectangles:
Thirds, Sixths, and
Twelfths,
Sessions 1 – 4
Grade 4 Quarter 3 School Year 2011-12
Page 3
answers are equivalent. (For
example, ½ and 2/4 are the same.)
Explain equivalent fractions through
multiple representations.
4.2 a, b, c Essential Understandings
Two fractions are equivalent
(represent the same number) when both
fractions correspond to the same point on
the number line.
Recognize and generate
equivalent fractions with denominators of
2, 3, 4, and 6 (e.g., ½ =2/4, 4/6=2/3), and
explain the reasoning.
Fractions apply to situations
where a whole is decomposed into equal
parts; use fractions to describe parts of
wholes. For example, to show 1/3 of a
length, decompose the length into 3 equal
parts and show one of the parts
Develop an understanding of fractions
as parts of unit wholes, as parts of a
collection, and as locations on a number
line. Understand that a mixed number is a
fraction that has two parts: a whole
number and a proper fraction. The
mixed number is the sum of these two
parts.
Use models, benchmarks, and
equivalent forms to judge the size of
fractions.
(e.g., 3
9 <
3
5 ).
Compare and order fractions having
unlike denominators of 12 or less by
comparing the fractions to
benchmarks
(e.g., 0, 1
2 or 1) to determine their
relationships to the benchmarks or by
finding a common denominator.
Compare and order mixed numbers
having denominators of 12 or less.
Use the symbols >, <, and = to
compare the numerical value of
fractions and mixed numbers having
denominators of 12 or less.
Represent equivalent fractions
through twelfths, using region/area
models, set models, and measurement
models.
Identify the division statement that
represents a fraction (e.g., 3
5 means
the same as 3 divided by 5).
Grade 4 Quarter 3 School Year 2011-12
Page 4
~~~~~~~~
22 days
Recognize that a whole divided into
nine equal parts has smaller parts than if
the whole had been divided into five
equal parts.
Recognize and generate equivalent
forms of commonly used fractions and
decimals.
Understand the division statement that
represents a fraction.
Understand that the more parts the
whole is divided into, the smaller the
parts (e.g.,
1
5 <
1
3 ).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Decimals
4.3 a, b, c, d Essential Questions
Prove how a fraction and a decimal can
represent the same value.
Explain the difference between reading a
number with a decimal compared to
reading a number without a decimal.
Describe the differences between saying,
reading, and/or writing one hundred and
one hundredths? (also do tens vs. tenths.
. . and thousands vs. thousandths)
Explain how the place value system is
used to name and compare decimal
numbers smaller than 1.
Justify how the magnitude of a base-10
model represents decimals.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.3 The student will a) read, write, represent, and identify
decimals expressed through thousandths;
b) round decimals to the nearest whole
number, tenth, and hundredth;
c) compare and order decimals; and
d) given a model, write the decimal and
fraction equivalents.
4.3 Essential Knowledge and Skills Investigate the ten-to-one place value
relationship for decimals through
thousandths, using Base-10
manipulatives (e.g., place value
mats/charts, decimal squares, Base-10
blocks, money).
Represent and identify decimals
~~~~~~~~~~~~~~~~
ESS
http://www.doe.vir
ginia.gov/testing/s
ol/standards_docs/
mathematics/index
.shtml
Comparing
Decimals
Rounding
Decimals
Decimal Rings
Reading and
Writing Decimals
Grade 4 Quarter 3 School Year 2011-12
Page 5
Demonstrate and prove fraction and
decimal equivalents.
Compare and prove decimal values using
>, <. =.
Explain when it would be appropriate to
round a number to a whole number,
tenths, or hundredths.
4.3 a, b, c, d Essential Understandings Understand the place value structure of
decimals and use this structure to read,
write, and compare decimals.
Understand that decimal numbers can
be rounded to an estimate when exact
numbers are not needed for the situation
at hand.
Understand that decimals are rounded in
a way that is similar to the way whole
numbers are rounded.
Understand that decimals and fractions
represent the same relationship;
however, they are presented in two
different formats.
Understand that models are used to
show decimal and fraction equivalents.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.5 c Essential Questions
Compare and contrast adding and
subtracting fractions and decimals.
Compare and contrast whole number
operations with decimal operations.
4.5 c Essential Understandings Develop and use strategies to estimate
expressed through thousandths, using
Base-10 manipulatives, pictorial
representations, and numerical
symbols (e.g., relate the appropriate
drawing to 0.05).
Identify and communicate, both orally
and in written form, the position and
value of a decimal through
thousandths. For example, in 0.385,
the 8 is in the hundredths place and
has a value of 0.08.
Read and write decimals expressed
through thousandths, using Base-10
manipulatives, drawings, and
numerical symbols.
Round decimals to the nearest whole
number, tenth, and hundredth.
Compare decimals, using the symbols
>, <, =.
Order a set of decimals from least to
greatest or greatest to least.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.5 c The student will c) add and subtract with decimals; and….
4.5 c Essential Knowledge and Skills Find common multiples and common
factors of numbers.
Determine the least common multiple
and greatest common factor of
Grade 4 Quarter 3 School Year 2011-12
Page 6
addition and subtraction involving
fractions ….
Use visual models to add and subtract
with …decimals.
numbers.
Use least common multiple and/or
greatest common factor to find a
common denominator for fractions.
Add and subtract with fractions
having like denominators whose
denominators are limited to 2, 3, 4, 5,
6, 8, 10, and 12, and simplify the
resulting fraction using common
multiples and factors.
Add and subtract with fractions
having unlike denominators whose
denominators are limited to 2, 3, 4, 5,
6, 8, 10, and 12, and simplify the
resulting fraction using common
multiples and factors.
Solve problems that involve adding
and subtracting with fractions having
like and unlike denominators whose
denominators are limited to 2, 3, 4, 5,
6, 8, 10, and 12, and simplify the
resulting fraction using common
multiples and factors.
.
4 days Enrichment, Assessment, and
Remediation
Grade 4 Quarter 4
School Year 2011-12
Number
of Days
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer essential
questions.)
REQUIRED
Critical Thinking
Lessons
Standard(s) of Learning
Essential Knowledge and Skills
Additional Instructional
Resources
ESS: VDOE Enhanced
Scope and Sequence
15 days
Measurement
4.7 Essential Questions
Length/Distance
Give a real life example of what you would
measure in inches, feet, yards, miles,
millimeters, centimeters, meters, and
kilometers.
Why are there two different units of
measurement?
What is an appropriate tool to measure in
inches, feet, yards, millimeters, centimeters,
meters, and kilometers?
4.7 Essential Understandings
All students should:
Use benchmarks to estimate and measure
length.
Understand how to convert units of length
between the U.S. Customary and metric
systems, using ballpark comparisons.
Understand the relationship between U.S.
Customary units and the relationship between
metric units.
Measurement
Benchmarks
(from 5th grade
Investigations)
Investigation 1:
Measures of Length
and Distance,
Sessions 1 – 6
Investigation 2:
Measures of Weight
and Liquid Volume,
Sessions 1 - 6
SOL 4.7 The student will
a) estimate and measure length, and describe
the result in both metric and U.S.
Customary units; and
b) identify equivalent measurements between
units within the U.S. Customary system
(inches and feet; feet and yards; inches and
yards; yards and miles) and between units
within the metric system (millimeters and
centimeters; centimeters and meters; and
millimeters and meters).
4.7 Essential Knowledge and Skills
Determine an appropriate unit of measure
(e.g., inch, foot, yard, mile, millimeter,
centimeter, and meter) to use when
measuring everyday objects in both metric
and U.S. Customary units.
Estimate the length of everyday objects
(e.g., books, windows, tables) in both
metric and U.S. Customary units of
measure.
Measure the length of objects in both
metric and U.S. Customary units,
measuring to the nearest inch (1
2 ,
1
4 ,
1
8 ),
foot, yard, mile, millimeter, centimeter, or
meter, and record the length including the
appropriate unit of measure (e.g., 24
inches).
http://illuminations.nctm.or
g/LessonDetail.aspx?id=L1
84
How Long? How Tall?
How Wide? How Deep?
http://illuminations.nctm.or
g/LessonDetail.aspx?id=L6
35
Grade 4 Quarter 4
School Year 2011-12
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4.6 Essential Questions
Weight/Mass
What is the difference between weight and mass?
Give a real life example of what you would
measure in ounces, pounds, tons, grams, and
kilograms.
4.6 Essential Understandings
Use benchmarks to estimate and measure
weight/mass.
Identify equivalent measures between units
within the U.S. Customary and between units
within the metric measurements.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.8 Essential Questions
Liquid Volume
Compare estimates of the length of
objects with the actual measurement of
the length of objects.
Identify equivalent measures of length
between units within the U.S. Customary
measurements and between units within
the metric measurements.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.6 The student will
a) a) estimate and measure weight/mass and
describe the results in U.S. Customary and
metric units as appropriate; and
b) b) identify equivalent measurements between
units within the U.S. Customary system
(ounces, pounds, and tons) and between units
within the metric system (grams and
kilograms).
4.6 Essential Knowledge and Skills
Determine an appropriate unit of measure
(e.g., ounce, pound, ton, gram, kilogram)
to use when measuring everyday objects
in both metric and U.S. Customary units.
Measure objects in both metric and U.S.
Customary units (e.g., ounce, pound, ton,
gram, or kilogram) to the nearest
appropriate measure, using a variety of
measuring instruments.
Record the mass of an object including the
appropriate unit of measure (e.g., 24
grams).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.8 The student will
a) estimate and measure liquid volume and
describe the results in U.S. Customary units;
Grade 4 Quarter 4
School Year 2011-12
Give a real life example of what you would
measure in cups, pints, quarts, and gallons.
4.8 Essential Understandings
All students should:
Use benchmarks to estimate and measure
volume.
Identify equivalent measurements between
units within the U.S. Customary system.
and
b) identify equivalent measurements between
units within the U.S. Customary system (cups,
pints, quarts, and gallons).
4.8 Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations to
Determine an appropriate unit of measure
(cups, pints, quarts, gallons) to use when
measuring liquid volume in U.S.
Customary units.
Estimate the liquid volume of containers
in U.S. Customary units of measure to the
nearest cup, pint, quart, and gallon.
Measure the liquid volume of everyday
objects in U.S. Customary units, including
cups, pints, quarts, and gallons, and record
the volume including the appropriate unit
of measure (e.g., 24 gallons).
Identify equivalent measures of volume
between units within the U.S. Customary
system.
20 days
Geometry
Plane Figures
4.10 Essential Questions
Compare and contrast a line, line segment,
angle and ray.
Create and identify a line, line segment, angle,
and ray.
What is the relationship between a line
segment and an angle?
Explain the relationship between a ray and an
angle.
SOL 4.10 The student will
a) identify and describe representations of
points, lines, line segments, rays, and angles,
including endpoints and vertices; and
b) identify representations of lines that
illustrate intersection, parallelism,
perpendicularity
4.10 Essential Knowledge and Skills
Grade 4 ESS Lessons:
Simple Pictures
Geometry Review
Geometric Figures
Congruent Figures
Coordinate Points
Toothpick, Door and
Staircase Patterns
Investigations:
Mathematical Thinking in
Grade 4 Quarter 4
School Year 2011-12
Identify and justify real life examples of
parallel lines.
Identify and justify real life examples
perpendicular lines.
Compare and contrast characteristics of
intersecting lines and perpendicular lines.
4.10 Essential Understandings
Understand that points, lines, line segments,
rays, and angles, including endpoints and
vertices are fundamental components of
noncircular geometric figures.
Understand that the shortest distance between
two points on a flat surface is a line segment.
Understand that lines in a plane either
intersect or are parallel. Perpendicularity is a
special case of intersection.
Identify practical situations that illustrate
parallel, intersecting, and perpendicular lines.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.11 Essential Questions
Compare and contrast geometric
transformations.
Demonstrate and explain congruency of a
plane figure after a reflection, translation,
and/or rotation.
Demonstrate and justify various strategies for
rotation, reflection, and translation of an
image.
What are real life models of reflection,
translation, and rotation?
Prove the image of a plane figure is congruent
to the original image after a transformation.
Explain what understandings are important
when determining if two figures are
congruent.
Identify and describe representations of
points, lines, line segments, rays, and
angles, including endpoints and vertices.
Understand that lines in a plane can
intersect or are parallel. Perpendicularity
is a special case of intersection.
Identify practical situations that illustrate
parallel, intersecting, and perpendicular
lines.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.11 The student will
a) investigate congruence of plane figures
after geometric transformations, such as
reflection, translation, and rotation, using
mirrors, paper folding, and tracing; and
b) recognize the images of figures resulting
from geometric transformations, such as
translation, reflection, and rotation.
4.11 Essential Knowledge and Skills
Recognize the congruence of plane figures
resulting from geometric transformations such
as translation, reflection, and rotation, using
mirrors, paper folding and tracing.
Grade 4
Investigation 4: “Making
Geometric Patterns”,
Sessions 1 – 6
Grade 4 Quarter 4
School Year 2011-12
4.11 Essential Understandings
Understand the meaning of the term
congruent.
Understand how to identify congruent
figures.
Understand that the orientation of figures
does not affect congruency or
noncongruency.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4.12 Essential Questions
What is a polygon?
Create and identify polygons with ten or
fewer sides.
4.12 Essential Understandings
Identify polygons with 10 or fewer sides in
everyday situations.
Identify polygons with 10 or fewer sides in
multiple orientations (rotations, reflections,
and translations of the polygons)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
SOL 4.12 The student will
a) define polygon; and
b) identify polygons with ten or fewer sides.
4.12 Essential Knowledge and Skills
Define and identify properties of polygons
with 10 or fewer sides.
Identify polygons by name with 10 or
fewer sides in multiple orientations
(rotations, reflections, and translations of
the polygons)
5 days
Elapsed Time
4.9 Essential Questions
What is elapsed time?
How do you determine elapsed time?
Determine elapsed time given between 2
given hours and additional minutes.
Given a beginning and ending time of an
event, use at least two different strategies to
calculate elapsed time.
Provided an ending time and an elapsed time,
determine the start time of the event.
4.9 Essential Understandings
Understand the “counting on” strategy for
determining elapsed time in hour and minute
SOL 4.9 The student will determine elapsed
time in hours and minutes within a 12-hour
period.
Essential Knowledge and Skills
The student will use problem solving,
mathematical communication, mathematical
reasoning, connections, and representations to
Determine the elapsed time in hours and
minutes within a 12-hour period (times
can cross between a.m. and p.m.).
Solve practical problems in relation to
time that has elapsed