GRADE 6 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.
3. Teachers should periodically check and update any web addresses that they have on their
LCPS web pages.
4. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
5. Teachers should assure that the use of websites correlate with the objectives
of the lesson and provide students with the appropriate challenge.
Grade 6 Mathematics Nine Weeks Overview
1st Quarter 2
nd Quarter 3
rd Quarter 4
th Quarter
Properties of Real Numbers 6.19
Rational Numbers 6.2
Sequences 6.17
Number 6.5
6.3
6.11
6.8
Equations and
Inequalities 6.20
Fractions 6.6 b
6.4
6.6
Benchmark
Decimals 6.7
Ratios 6.1
Rational Number
Relationships 6.2 c
Measurement 6.9
Geometry 6.13
6.12
6.10 c
Circles 6.10 a, b
Volume and Surface
Area 6.10 d
Probability and
Statistics 6.16
6.15
6.14
Grade 6 Quarter 1 School Year 2011-12
Number of
Blocks
Topics, Essential Questions, and Essential
Understandings
(Students should be able to answer essential
questions.)
Standard(s) of Learning
Essential Knowledge and Skills
Additional Instructional Resources
ESS: Grade 6 Enhanced
Scope and Sequence
Properties of Real Numbers
Introduce properties of real numbers in order to use
properties all year.
6.19 Essential Questions
What is the result of multiplying any real number
by zero?
Do all real numbers have a multiplicative inverse?
Compare and contrast the identity properties for
multiplication and addition.
How are the identity properties for multiplication
and addition the same? Different?
Create a real number equation and identify the
property of operations used to solve it.
6.19 Essential Understandings
How are the identity properties for
multiplication and addition the same?
Different? For each operation the
identity elements are numbers that combine
with other numbers without changing the
value of the other numbers. The additive
identity is zero (0). The multiplicative
identity is one (1).
What is the result of multiplying any real
number by zero? The product is always
zero.
Do all real numbers have a multiplicative
inverse? No. Zero has no multiplicative
inverse because there is no real number that
can be multiplied by zero resulting in a
product of one.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Rational Numbers
Introduction to rational numbers in decimal format
6.2 Essential Questions
Create and justify representations in decimal format.
SOL 6.19 The student will investigate and recognize
a) the identity properties for addition and multiplication;
b) the multiplicative property of zero; and
c) the inverse property for multiplication.
6.19 Essential Knowledge and Skills
Identify a real number equation that represents each property of
operations with real numbers, when given several real number
equations.
Test the validity of properties by using examples of the properties
of operations on real numbers.
Identify the property of operations with real numbers that is
illustrated by a real number equation.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Review material to prepare for SOL 6.2
SOL 6.2 The student will
a) investigate and describe fractions, decimals, and percents as
ratios;
Grade 6 Quarter 1 School Year 2011-12
Demonstrate and explain how benchmarks can be
used to compare and order decimals.
Prove a sequence of values in decimal format using
two different strategies.
Compare and contrast addition and subtraction of
whole numbers and decimals.
Compare and contrast multiplication and division of
whole numbers and decimals.
What is the role of estimation in solving problems?
How can the distributive property help with
computation involving decimals?
Prove that using the distributive property does not
change the value of an equation.
6.2 Essential Understandings
What is the relationship among fractions, decimals
and percents?
Fractions, decimals, and percents are three different
ways to express the same number. A ratio can be
written using fraction form ( 2
3 ), a colon (2:3), or the
word to (2 to 3). Any number that can be written as a
fraction can be expressed as a terminating or
repeating decimal or a percent.
b) identify a given fraction, decimal, or percent from
representations;
c) demonstrate equivalent relationships between fractions,
decimals, and percents; and
d) compare and order fractions, decimals, and percents.
6.2 Essential Knowledge and Skills
Identify the decimal and percent equivalents for numbers
written in fraction form including repeating decimals.
Represent fractions, decimals, and percents on a number line.
Describe orally and in writing the equivalent relationships
among decimals, percents, and fractions.
Represent, by shading a grid, a fraction, decimal, and percent.
Represent rational numbers in fraction, decimal, and percent
form a given shaded region of a grid.
Compare two decimals using manipulatives, pictorial
representations, number lines, and symbols (<, ,, >, =).
Compare two fractions using manipulatives, pictorial
representations, number lines, and symbols (<, ,, >, =).
Compare two percents using pictorial representations and
symbols (<, ,, >, =).
Order fractions, decimals, and percents in ascending or
descending order.
Sequences
Geometric and Arithmetic Sequences
6.17 Essential Questions and Understandings
What is the difference between an arithmetic and a
geometric sequence?
Compare and contrast arithmetic and geometric
sequences.
How can numerical or algebraic symbols represent
change in a pattern? (Based on a pattern, a prediction
can be made of the nth
term.)
Create and explain the strategies used to recognize
and describe the change between terms in arithmetic
patterns.
Create and explain the strategies used to recognize
and describe geometric patterns.
Continue to discuss sequences in the context of
exponents and square root.
SOL 6.17 The student will identify and extend geometric and
arithmetic sequences.
6.17 Essential Knowledge and Skills
Investigate and apply strategies to recognize and describe the
change between terms in arithmetic patterns.
Investigate and apply strategies to recognize and describe
geometric patterns.
Describe verbally and in writing the relationships between
consecutive terms in an arithmetic or geometric sequence.
Extend and apply arithmetic and geometric sequences to similar
situations.
Extend arithmetic and geometric sequences in a table by using a
given rule or mathematical relationship.
Compare and contrast arithmetic and geometric sequences.
Identify the common difference for a given arithmetic sequence.
Grade 6 Quarter 1 School Year 2011-12
Identify the common ratio for a given geometric sequence.
Number and Number Sense
Exponents, perfect squares, square roots, scientific
notation
6.5 Essential Questions and Understandings
What does exponential form represent?
Recognize and describe patterns in exponents and
perfect squares.
Prove the value of a perfect square using
representation.
What is the relationship between perfect squares and
a geometric square?
SOL 6.5 The student will investigate and describe concepts of
positive exponents and perfect squares.
6.5 Essential Knowledge and Skills
Recognize and describe patterns with exponents that are natural
numbers, by using a calculator.
Recognize and describe patterns of perfect squares not to exceed
202
, by using grid paper, square tiles, tables, and calculators.
Recognize powers of ten by examining patterns in a place value
chart: 104 = 10,000, 10
3 = 1000, 10
2 = 100, 10
1 = 10, 10
0=1.
ESS
http://www.doe.virginia.gov/testing/sol/
standards_docs/mathematics/index.sht
ml
Squares and Square Roots
Order of Operations
6.8 Essential Question and Understanding
What is the significance of the order of operations?
SOL 6.8 The student will evaluate whole number numerical
expressions, using the order of operations.
Simplify expressions by using the order of operations in a
demonstrated step-by-step approach. The expressions should be
limited to positive values and not include braces { } or absolute
value | |.
Find the value of numerical expressions, using order of operations,
mental mathematics, and appropriate tools. Exponents are limited
to positive values.
Interpret numerical expressions at a level necessary to calculate
their value using a calculator or spreadsheet. For expressions with
variables, use and interpret conventions of algebraic notion, such
as y/2 is y ÷ 2 or ½ × y; (3± y) ÷ 5 or 1/5 × (3± y); is a × a, a3 is a
× a × a, a2b is a × a × b
ESS
http://www.doe.virginia.gov/testing/sol/
standards_docs/mathematics/index.sht
ml
Toothpick Patterns
Integers
6.3 Essential Questions and Understandings
Represent and explain the value of an integer using a
number line.
Compare and justify order of a set of integers using a
number line.
Create, model, and solve a real life problem
situations using integers.
SOL 6.3 The student will
a) identify and represent integers;
b) order and compare integers; and
c) identify and describe absolute value of integers.
6.3 Essential Knowledge and Skills
Identify an integer represented by a point on a number line.
ESS
http://www.doe.virginia.gov/testing/s
ol/standards_docs/mathematics/index.
shtml
Investigating Integers
Grade 6 Quarter 1 School Year 2011-12
What role do negative integers play in practical
situations?
How does the absolute value of an integer compare
to the absolute value of its opposite?
Represent integers on a number line.
Order and compare integers using a number line.
Compare integers, using mathematical symbols
(<, >, =).
Identify and describe the absolute value of an integer.
Grade 6 Quarter 1 School Year 2011-12
Equations and Inequalities
6.18 Essential Questions
What is a variable?
Compare and contrast expressions and equations.
When solving an equation, why is it necessary to perform
the same operation on both sides of an equal sign?
Create and explain a one-step linear equation using two
strategies.
6.18 Essential Understandings
6.20 Essential Understandings
In an inequality, does the order of the elements matter?
Yes, the order does matter. For example, x > 5 is not the
same relationship as 5 > x. However, x > 5 is the same
relationship as 5 < x.
SOL 6.18 -The student will solve one-step linear equations in one
variable….
Understand that an expression records operations with numbers or
with letters standing for numbers.
Describe the structure and elements of simple expressions using
correct terminology (sum, term, product, factor, quotient,
coefficient); describe an expression by viewing one or more of its
parts as a single entity.
Understand and generate equivalent expressions:
o Understand that two expressions are equivalent if they name the
same number regardless of which numbers the variables in them
stand for.
o Understand that applying the laws of arithmetic to an expression
results in an equivalent expression
o Generate equivalent expressions to reinterpret the meaning of an
expression.
Understand that an equation is a statement that two expressions are
equal, and a solution to an equation is a replacement value of the
variables (or replacement values for all the variables if there is more
than one) that makes the equation true.
Using the idea of maintaining equality between both sides of the
equation, solve equations of the form x + p = q and px = q for cases in
which, p, q, and x are all nonnegative rational numbers.
SOL 6.20 The student will graph inequalities on a number line.
6.20 Essential Knowledge and Skills
o Given a simple inequality with integers, graph the relationship on
a number line.
Given the graph of a simple inequality with integers, represent the
inequality two different ways using symbols (<, >, <, >).
Hands-on Equations: Book
1
5th
Grade ESS
http://www.doe.virginia.g
ov/testing/sol/standards_d
ocs/mathematics/index.sh
tml
Writing Algebraic
Expressions
Variables in Open
Sentences
Algebra Balance Scales:
http://nlvm.usu.edu/en/nav/
frames_asid_201_g_4_t_2.
html?open=instructions&fr
om=category_g_4_t_2.html
Assessment, Enrichment, and Remediation
Grade 6 Quarter 2 School Year 2011-2012
Number of
Blocks
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer essential
questions.)
Standard(s) of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
ESS: VDOE
Enhanced
Scope and Sequence
Fractions
Add and Subtract Fractions in Practical Problems
6.6 b Essential Questions
Justify the use of estimation with rational numbers in
fraction format?
Compare and contrast addition and subtraction of fractions
and addition and subtraction of whole numbers?
Why are common denominators required to add or subtract
fractions?
Justify that the sum or difference is in simplest form.
6.6 b Essential Understandings
What is the role of estimation in solving problems?
o Estimation helps determine the reasonableness of
answers.
SOL 6.6 b Estimate solutions and then solve single-step
and multistep practical problems involving addition,
subtraction, multiplication, and division of fractions.
6.6 b Essential Knowledge and Skills
Solve single-step and multistep practical problems that
involve addition and subtraction with fractions and
mixed numbers, with and without regrouping, that
include like and unlike denominators of 12 or less.
Answers are expressed in simplest form.
Grade 6 Quarter 2 School Year 2011-2012
Multiplication and Division of Fractions
6.4 Essential Questions
What is the role of estimation in solving problems?
Justify multiple representations of multiplication and
division of fractions.
Create, demonstrate, and explain a model using
multiplication and/or division of fractions.
Justify that a fraction is in simplest form.
6.4 Essential Understandings
When multiplying fractions, what is the meaning of the
operation?
o When multiplying a whole by a fraction such as 3 x 1
2 ,
the meaning is the same as with multiplication of whole
numbers: 3 groups the size of 1
2 of the whole.
o When multiplying a fraction by a fraction such as2 3
3 4,
we are asking for part of a part.
o When multiplying a fraction by a whole number such as
1
2 x 6, we are trying to find a part of the whole.
What does it mean to divide with fractions?
o For measurement division, the divisor is the number of
groups and the quotient will be the number of groups in
the dividend. Division of fractions can be explained as
how many of a given divisor are needed to equal the
given dividend. In other words, for 1 2
4 3 the question
is, “How many 2
3 make
1
4?”
o For partition division the divisor is the size of the group,
so the quotient answers the question, “How much is the
whole?” or “How much for one?”
SOL 6.4 The student will demonstrate multiple representations of multiplication and division of fractions.
6.4 Essential Knowledge and Skills
Demonstrate multiplication and division of fractions using
multiple representations.
Model algorithms for multiplying and dividing with
fractions using appropriate representations.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Area Model of
Multiplication
Dividing Fractions,
Using Pattern Blocks
Decimal Division
Estimation Strategies
Estimation in
Problem Solving
Grade 6 Quarter 2 School Year 2011-2012
Multiplication and Division of Fractions in Practical
Situations
6.6 Essential Questions
Justify that product or quotient is in simplest form.
How are multiplication and division of fractions and
multiplication and division of whole numbers alike?
Create and solve a practical problems using estimation of
fractions.
How could the distributive property be used in computation
strategies for fractions?
Prove that the use of the distributive property does not
change the value of the product.
Create and explain single-step practical problems using
fractions.
Create and explain multistep practical problems using
fractions.
6.6 Essential Understandings
How are multiplication and division of fractions and
multiplication and division of whole numbers alike?
o Fraction computation can be approached in the same
way as whole number computation, applying those
concepts to fractional parts.
What is the role of estimation in solving problems?
o Estimation helps determine the reasonableness of
answers.
SOL 6.6 The student will
a) multiply and divide fractions and mixed numbers;
and
b) estimate solutions and then solve single-step and
multistep practical problems involving addition,
subtraction, multiplication, and division of fractions.
Essential Knowledge and Skills Multiply and divide with fractions and mixed numbers.
Answers are expressed in simplest form.
Solve single-step and multistep practical problems that
involve multiplication and division with fractions and
mixed numbers that include denominators of 12 or less.
Answers are expressed in simplest form.
Decimals
Solve multi-step problems involving decimals
6.7 Essential Questions
What is the role of estimation in solving problems?
Create and solve a practical problem using estimation of
decimals.
Justify estimation strategies for the sum, difference,
product, or quotient of two quantities.
How could the distributive property be used in computation
strategies for decimals?
Prove that the use of the distributive property does not
SOL 6.7 The student will solve single-step and multistep
practical problems involving addition, subtraction,
multiplication, and division of decimals.
6.7 Essential Knowledge and Skills
Solve single-step and multistep practical problems
involving addition, subtraction, multiplication and division
with decimals expressed to thousandths with no more than
two operations.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Pizza Your Way
Getting the Most for
Your Money!
Grade 6 Quarter 2 School Year 2011-2012
change the value of the product.
Create and explain single-step practical problems using
decimals.
Create and explain multistep practical problems using
decimals.
6.7 Essential Understandings
What is the role of estimation in solving problems?
o Estimation gives a reasonable solution to a problem
when an exact answer is not required. If an exact
answer is required, estimation allows you to know if
the calculated answer is reasonable.
Ratios
6.1 Essential Questions
Create real life problem situations comparing data using a
variety of ratios relationships.
Justify the relationship between the two values in a ratio?
6.1 Essential Understandings
What is a ratio?
o A ratio is a comparison of any two quantities. A ratio is
used to represent relationships within a set and between
two sets. A ratio can be written using fraction form
( 2
3 ), a colon (2:3), or the word to (2 to 3).
SOL 6.1 The student will describe and compare data,
using ratios, and will use appropriate notations, such
as a
b , a to b, and a:b.
6.1 Essential Knowledge and Skills
Describe a relationship within a set by comparing part of
the set to the entire set.
Describe a relationship between two sets by comparing
part of one set to a corresponding part of the other set.
Describe a relationship between two sets by comparing
all of one set to all of the other set.
Describe a relationship within a set by comparing one
part of the set to another part of the same set.
Represent a relationship in words that makes a
comparison by using the notations a
b, a:b, and a to b.
Create a relationship in words for a given ratio expressed
symbolically.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Exploring Ratio
Paper Chains and
Countries
Assessment, Enrichment, and Remediation
Grade 6 Quarter 3 School Year 2011-2012
Number of
Blocks
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer essential
questions.)
Standard(s) of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
ESS: VDOE
Enhanced
Scope and Sequence
Rational Number Relationships
6.2 Essential Questions
What is the relationship among fractions, decimals,
and percents?
Justify that fractions, decimals, and percents are ratios.
Compare and prove order of a set of fractions,
decimals, and percents using two strategies.
Compare and contrast fractions, decimals, and
percents.
6.2 Essential Understanding
What is the relationship among fractions, decimals
and percents?
o Fractions, decimals, and percents are three
different ways to express the same number. A
ratio can be written using fraction form ( 2
3 ), a
colon (2:3), or the word to (2 to 3). Any number
that can be written as a fraction can be expressed
as a terminating or repeating decimal or a percent.
SOL 6.2 The student will a) investigate and describe fractions, decimals and percents
as ratios;
b) identify a given fraction, decimal or percent from a
representation;
c) demonstrate equivalent relationships among fractions,
decimals, and percents; and
d) compare and order fractions, decimals, and percents. 6.2 Essential Knowledge and Skills
Identify the decimal and percent equivalents for numbers
written in fraction form including repeating decimals.
Represent fractions, decimals, and percents on a number line.
Describe orally and in writing the equivalent relationships
among decimals, percents, and fractions that have
denominators that are factors of 100.
Represent, by shading a grid, a fraction, decimal, and percent.
Represent in fraction, decimal, and percent form a given
shaded region of a grid.
Compare two decimals through thousandths using
manipulatives, pictorial representations, number lines, and
symbols (<, ,, >, =).
Compare two fractions with denominators of 12 or less using
manipulatives, pictorial representations, number lines, and
symbols (<, ,, >, =).
Compare two percents using pictorial representations and
symbols (<, ,, >, =).
Order no more than 3 fractions, decimals, and percents
(decimals through thousandths, fractions with denominators of
12 or less), in ascending or descending order.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Percent Grid Patterns
Who Has 100
Things?
Grade 6 Quarter 3 School Year 2011-2012
Measurement
Comparisons between metric and U.S. Customary
systems
6.9 Essential Questions and Understandings
Why are there two different measurement
systems?
How do you determine which units to use at
different times?
Create scenarios and justify the unit of
measurement used to solve each problem.
Compare and justify measurements in U.S.
Customary with ballpark measurements in the
metric systems.
Compare and justify measurements in the metric
system with ballpark measurements in U.S.
Customary system.
Compare and contrast ballpark measurements
between U.S. Customary and metric systems.
Create scenarios in which benchmark
measurements are justified. Compare and contrast weight and mass.
SOL 6.9 The student will make ballpark comparisons between
measurements in the U.S. Customary System of measurement
and measurements in the metric system.
6.9 Essential Knowledge and Skills
Estimate the conversion of units of length, weight/mass,
volume, and temperature between the U.S. Customary
system and the metric system by using ballpark
comparisons. Ex: 1 L 1qt. Ex: 4L 4 qts.
Estimate measurements by comparing the object to be
measured against a benchmark.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Measuring Mania
Geometry
Classify Quadrilaterals
6.13 Essential Questions and Understandings
Compare and contrast characteristics of
quadrilaterals.
Justify how a quadrilateral can belong to more
than one subset.
Prove the sum of the angles of any quadrilateral
using two strategies.
SOL 6.13 The student will describe and identify properties of
quadrilaterals.
6.13 Essential Knowledge and Skills
Understand that properties belonging to a category of
quadrilaterals also belong to all subcategories of that
category.
Classify quadrilaterals in a hierarchy based on properties.
o Quadrilaterals include quadrilaterals, parallelograms,
rectangles, trapezoids, kites, rhombi, and squares.
o Properties include number of parallel sides, angle
measures and number of congruent sides.
Identify the sum of the measures of the angles of a
quadrilateral as 360°.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Exploring
Quadrilaterals
Quadrilaterals
Grade 6 Quarter 3 School Year 2011-2012
Congruence
6.12 Essential Questions and Understandings
Create and justify congruent and noncongruent
segments, angles, and polygons using two
strategies.
Given two congruent figures, what inferences can
be drawn about how the figures are related?
Given two congruent polygons, what inferences
can be drawn about how the polygons are related?
SOL 6.12 The student will determine congruence of segments,
angles, and polygons.
6.12 Essential Knowledge and Skills
Characterize polygons as congruent and noncongruent
according to the measures of their sides and angles.
Determine the congruence of segments, angles, and
polygons given their attributes.
Draw polygons in the coordinate plane given coordinates for
the vertices; use coordinates to find the length of a side joining
points with the same first coordinate or the same second
coordinate. Apply these techniques in the context of solving
practical and mathematical problems.†
ESS
http://www.doe.virgini
a.gov/testing/sol/stand
ards_docs/mathematics
/index.shtml
Congruence
Perimeter and Area in Practical Problems
6.10 c Essential Questions and Understandings
Why is area expressed in square units?
Compare and contrast perimeter and area.
How is perimeter used?
How might the distributive property help to find
perimeter?
Create and explain a practical problem involving
area and/or perimeter.
SOL 6.10 c The student will …
c) solve practical problems involving area and perimeter;
and ….
Understand that plane figures can be decomposed,
reassembled, and completed into new figures.
Apply formulas to solve practical problems involving
area and perimeter of triangles and rectangles.
Determine if a problem situation involving polygons of
four or fewer sides represents the application of
perimeter or area.
ESS
http://www.doe.virgi
nia.gov/testing/sol/sta
ndards_docs/mathem
atics/index.shtml
Measuring Mania
Areas with
Pentominoes/
Graph Paper/
Geoboards
Assessment, Enrichment, and Remediation
Grade 6 Quarter 4 School Year 2011-2012
Number
of
Blocks
Topics, Essential Questions, and
Essential Understandings
(Students should be able to answer essential
questions.)
Standard(s) of Learning
Essential Knowledge and Skills
Additional
Instructional
Resources
ESS: VDOE Enhanced
Scope and Sequence
Geometry
Circles
6.10 a, b Essential Questions and Understandings
Create and solve problems that involve finding the
circumference and area of a circle when given the diameter
or radius.
SOL 6.10 a, b The student will
a) define pi (π) as the ratio of the circumference of a circle
to its diameter;
b) solve practical problems involving circumference and
area of a circle, given the diameter or radius; ….
6.10 a, b Essential Knowledge and Skills
Derive an approximation for pi (3.14 or 22
7 ) by
gathering data and comparing the circumference to the diameter
of various circles, using concrete materials or computer models.
Find the circumference of a circle by substituting a
value for the diameter or the radius into the formula C = d or
C = 2 r.
Find the area of a circle by using the formula
A = r2.
Create and solve problems that involve finding the
circumference and area of a circle when given the diameter or
radius.
Geometry
Volume and Surface area of a Rectangular Prism
6.10 d Essential Questions and Understandings
Why is volume expressed in cubic units?
Prove volume of a three-dimensional figure using
multiple strategies.
Compare and contrast surface area and volume.
What is the relationship between area and surface
area?
SOL 6.10 d The student will …
d) describe and determine the volume and surface area of a
rectangular prism.
6.10 d Essential Knowledge and Skills
Understand concepts of volume measurement:
The volume of a right rectangular prism with whole-unit side
lengths can be found by packing it with unit cubes and using
Grade 6 Quarter 4 School Year 2011-2012
multiplication to count their number.
Decompose right rectangular prisms into layers of arrays of
cubes; determine and compare volumes or right rectangular
prisms, and objects well described as right rectangular prisms,
by counting cubic units.
Understand that three-dimensional figures can be formed by
joining rectangles and triangles along their edges to enclose a
solid region with no gaps or overlaps. The surface area is the
sum of the areas of the enclosing rectangles and triangles.
Find the surface area of cubes, prisms and pyramids (include
the use of nets to represent these figures.)
Solve problems that require finding the surface area of a
rectangular prism, given a diagram of the prism with the
necessary dimensions labeled.
Solve problems that require finding the volume of a rectangular
prism given a diagram of the prism with the necessary
dimensions labeled.
Probability
6.16 b Essential Questions and Understandings
Compare and contrast experimental or theoretical
probability to predict an outcome in an event.
Determine the probability of two dependent events.
Determine the probability of two independent
events.
Determine whether two events are dependent or
independent.
Compare and contrast dependent and independent
events.
Determine the probability of two dependent
events.
Determine the probability of two independent events.
SOL 6.16 b The student will …
b) determine probabilities for dependent and independent
events.
6.16 b Essential Knowledge and Skills
Determine the probability of two dependent events.
Determine the probability of two independent events.
ESS
http://www.doe.virgini
a.gov/testing/sol/standa
rds_docs/mathematics/i
ndex.shtml
Fair or Not Fair
Statistics
Measures of Center
6.15 Essential Questions and Understandings
What does the phrase “measure of center” mean?
This is a collective term for the 3 types of averages for a
SOL 6.15 The student will
a) describe mean as balance point; and
b) decide which measure of center is appropriate for a
given purpose.
6.15 Essential Knowledge and Skills
ESS
http://www.doe.virgini
a.gov/testing/sol/standa
rds_docs/mathematics/i
ndex.shtml
Measures of Central
Grade 6 Quarter 4 School Year 2011-2012
set of data – mean, median, and mode.
Compare and contrast the measures of center.
What is meant by mean as balance point?
Mean can be defined as the point on a number line where
the data distribution is balanced. This means that the sum
of the distances from the mean of all the points above the
mean is equal to the sum of the distances of all the data
points below the mean. This is the concept of mean as the
balance point.
Create and explain a scenario depicting mean as a balance
point.
Find the mean for a set of data.
Describe the three measures of center and a situation in which
each would best represent a set of data.
Identify and draw a number line that demonstrates the concept
of mean as balance point for a set of data.
Tendency
Circle Graphs
6.14 Essential Questions and Understandings
What types of data are best presented in a circle graph?
Circle graphs are best used for data showing a relationship
of the parts to the whole.
Predict and draw conclusions based on data presented in a
graph.
Create and explain a circle graph based on a problem
situation.
Compare and contrast data presented in a circle graph
with the same data represented in other graphical forms.
SOL 6.14 The student, given a problem situation, will
a) construct circle graphs;
b) draw conclusions and make predictions, using circle graphs;
and
c) compare and contrast graphs that present information from
the same data set.
6.14 Essential Knowledge and Skills
Collect, organize and display data in circle graphs by depicting
information as fractional.
Draw conclusions and make predictions about data presented in
a circle graph.
Compare and contrast data presented in a circle graph with the
same data represented in other graphical forms.
ESS
http://www.doe.virgini
a.gov/testing/sol/standa
rds_docs/mathematics/i
ndex.shtml
Movie Data
Circle Graphs
The Coordinate System
6.11 Essential Questions and Understandings
Can any given point be represented by more than one
ordered pair?
The coordinates of a point define its unique location in a
coordinate plane. Any given point is defined by only one
ordered pair.
In naming a point in the plane, does the order of the two
coordinates matter?
Yes. The first coordinate tells the location of the point to
the left or right of the y-axis and the second point tells
the location of the point above or below the x-axis. Point
(0, 0) is at the origin.
SOL 6.11 The student will
a) identify the coordinates of a point in a coordinate plane; and
b) graph ordered pairs in a coordinate plane.
6.11 Essential Knowledge and Skills
A given point in the plane can be located by using an ordered
pair of numbers, called its coordinates. The first number
indicates how far to travel from the origin in the direction of
one axis, the second number indicates how far to travel in the
direction of the second axis.
Identify and label the axes of a coordinate plane.
Identify and label the quadrants of a coordinate plane.
Identify the quadrant or the axis on which a point is positioned
by examining the coordinates (ordered pair) of the point.
Grade 6 Quarter 4 School Year 2011-2012
Justify ordered pairs represented by points in the four
quadrants and on the axes of the coordinate plane.
Create and interpret the coordinate values in the context
of a problem situation.
Graph ordered pairs in the four quadrants and on the axes of a
coordinate plane.
Identify ordered pairs represented by points in the four
quadrants and on the axes of the coordinate plane.
Where ordered pairs arise in a problem situation, interpret the
coordinate values in the context of the situation.
Make tables of equivalent ratios relating quantities with whole-
number measurements, finding missing values in the tables,
and plot the pairs of a values on the coordinate plane.
Enrichment, Assessment, and Remediation