Math sol common core overview

CRIN E07: Elementary Math Curriculum and Instruction
Dr. Margie Mason/Ms. Rachael Cofer
November 7, 2011

Mathematics SOLs/Common Core State Standards

Overview for Grades 6—8

Complied by
Sharon Antal, Ericca Dent, Courtney Mann,
Rob Schupbach, and Holly Stainback

November 7, 2011
SOL/Common Core Overview

a) They both stress application to real-life situations. Both focus on using
calculators and appropriate technology (computers and spreadsheets)

b) The SOLs focus on problem solving and is a major part of the math program
at every grade level, but the Common Core does not mention this.

The SOLs encourage students to apply information to science and other disciplines
they are studying and the common does not mention this.

The Common Core mentions that students should be able to develop their own
arguments and reasoning and critique the reasoning of others and the SOLs do not
mention this.

The SOLS focus using concrete materials for all age levels where the Common
Core suggest their use only for younger children.

c) SOL Focus

6th Grade
Focuses on transitioning from whole number arithmetic to foundations of algebra

7th Grade
Focuses on continued emphasis of foundations of algebra

8th Grade
Focuses on reviewing concepts and skills learned in previous grades and giving
new content that prepares students for algebra and geometry

d) Common Core Focus Grades 6 - 8

In Grade 6, instructional time should focus on four critical areas: (1) connecting
ratio and rate to whole number multiplication and division and using concepts of
ratio and rate to solve problems; (2) completing understanding of division of
fractions and extending the notion of number to the system of rational numbers,

November 7, 2011
which includes negative numbers; (3) writing, interpreting, and using expressions
and equations; and (4) developing understanding of statistical thinking.

In Grade 7, instructional time should focus on four critical areas: (1) developing
understanding of and applying proportional relationships; (2) developing
understanding of operations with rational numbers and working with expressions
and linear equations; (3) solving problems involving scale drawings and informal
geometric constructions, and working with two- and three-dimensional shapes to
solve problems involving area, surface area, and volume; and (4) drawing
inferences about populations based on samples.

In Grade 8, instructional time should focus on three critical areas: (1) formulating
and reasoning about expressions and equations, including modeling an association
in bivariate data with a linear equation, and solving linear equations and systems of
linear equations; (2) grasping the concept of a function and using functions to
describe quantitative relationships; (3) analyzing two- and three-dimensional space
and figures using distance, angle, similarity, and congruence, and understanding
and applying the Pythagorean Theorem.

e) Overall, I think the core is a little too specifiic, even when the full scope and
sequence of the SOLs are considered. The core seems to talk a good game
about abstract reasoning, but I don’t see any proof that there standards are
really guaranteeing that this is happening. It’s not exactly there with the
SOLs either, but I think there is more of a conceptual definition for certain
standards, rather than just formulas (perhaps by design) and as such it seems
like at least due to to what form its creator have chosen to write it, a teacher
might be able to fit true problem-solving in more easily. However, the
specificity with which the Core is written and its insistence on maintaining
certain concepts throughout (rational numbers seem to be throughout the
grade band and not just put in with a vengeance in 8th grade) the Core might
make students really focus on certain concepts and might make teachers
better aware of what they should be stressing. Clarity can be really good.

From Education Week, September 2011:

November 7, 2011
Fresh Perspective
The common standards represent such a big change that states shouldn't even try to find
commonalities between them and their old state standards, but view them "as something
completely new," said Ken Krehbiel, the associate executive director of communications for the
National Council of Teachers of Mathematics.

That way, he said, educators are more likely to find fresh ways to design lessons based on the
"mathematical practices" that form the core of the standards, emphasizing skills such as problem-
solving and mathematical modeling.

NCTM and others are working to build a library of sample tasks that reflect those practices and
are making them available to educators as they are assembled, Mr. Krehbiel said.

Mathematics Standards of Learning for Virginia Public Schools

Grade Six
The sixth-grade standards are a transition from the emphasis placed on whole number arithmetic
in the elementary grades to foundations of algebra. The standards emphasize rational numbers.
Students will use ratios to compare data sets; recognize decimals, fractions, and percents as
ratios; solve single-step and multistep problems, using rational numbers; and gain a foundation in
the understanding of integers. Students will solve linear equations and use algebraic terminology.
Students will solve problems involving area, perimeter, and surface area, work with π (pi), and
focus on the relationships among the properties of quadrilaterals. In addition, students will focus
on applications of probability and statistics.
While learning mathematics, students will be actively engaged, using concrete materials and
appropriate technology such as calculators, computers, and spreadsheets. However, facility in the
use of technology shall not be regarded as a substitute for a student’s understanding of
quantitative concepts and relationships or for proficiency in basic computations. Students will
also identify real-life applications of the mathematical principles they are learning and apply
these to science and other disciplines they are studying.
Mathematics has its own language, and the acquisition of specialized vocabulary and language
patterns is crucial to a student’s understanding and appreciation of the subject. Students should
be encouraged to use correctly the concepts, skills, symbols, and vocabulary identified in the
following set of standards.
Problem solving has been integrated throughout the six content strands. The development of
problem-solving skills should be a major goal of the mathematics program at every grade level.
Instruction in the process of problem solving will need to be integrated early and continuously
into each student’s mathematics education. Students must be helped to develop a wide range of
skills and strategies for solving a variety of problem types.

November 7, 2011
Number and Number Sense

Focus: Relationships among Fractions, Decimals, and Percents
6.1 The student will describe and compare data, using ratios, and will use appropriate
a
notations, such as , a to b, and a:b.
b
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.
a) identify and represent integers;
b) order and compare integers; and
c) identify and describe absolute value of integers.
6.4 The student will demonstrate multiple representations of multiplication and division of
fractions.
6.5 The student will investigate and describe concepts of positive exponents and perfect
squares.

Computation and Estimation

Focus: Applications of Operations with Rational Numbers
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.
6.7 The student will solve single-step and multistep practical problems involving addition,
subtraction, multiplication, and division of decimals.
6.8 The student will evaluate whole number numerical expressions, using the order of
operations.

Measurement

Focus: Problem Solving with Area, Perimeter, Volume, and Surface Area
6.9 The student will make ballpark comparisons between measurements in the U.S.
Customary System of measurement and measurements in the metric system.
a) define π (pi) as the ratio of the circumference of a circle to its diameter;

November 7, 2011
b) solve practical problems involving circumference and area of a circle, given the
diameter or radius;
c) solve practical problems involving area and perimeter; and
d) describe and determine the volume and surface area of a rectangular prism.

Geometry

Focus: Properties and Relationships
a) identify the coordinates of a point in a coordinate plane; and
b) graph ordered pairs in a coordinate plane.
6.12 The student will determine congruence of segments, angles, and polygons.
6.13 The student will describe and identify properties of quadrilaterals.

Probability and Statistics

Focus: Practical Applications of Statistics
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.
a) describe mean as balance point; and
b) decide which measure of center is appropriate for a given purpose.
a) compare and contrast dependent and independent events; and
b) determine probabilities for dependent and independent events.

Patterns, Functions, and Algebra

Focus: Variable Equations and Properties
6.17 The student will identify and extend geometric and arithmetic sequences.
6.18 The student will solve one-step linear equations in one variable involving whole
number coefficients and positive rational solutions.
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.
6.20 The student will graph inequalities on a number line.

November 7, 2011

Grade Seven
The seventh-grade standards continue to emphasize the foundations of algebra. Students who
successfully complete the seventh-grade standards should be prepared to study Algebra I in
grade eight. Topics in grade seven include proportional reasoning, integer computation, solving
two-step linear equations, and recognizing different representations for relationships. Students
will apply the properties of real numbers in solving equations, solve inequalities, and use data
analysis techniques to make inferences, conjectures, and predictions.
appropriate technology such as calculators, computers, and spreadsheets. However, facility in the
use of technology shall not be regarded as a substitute for a student’s understanding of
quantitative concepts and relationships or for proficiency in basic computations. Students will
also identify real-life applications of the mathematical principles they are learning and apply
these to science and other disciplines they are studying.


Focus: Proportional Reasoning
a) investigate and describe the concept of negative exponents for powers of ten;
b) determine scientific notation for numbers greater than zero;
c) compare and order fractions, decimals, percents, and numbers written in scientific
notation;
d) determine square roots; and
e) identify and describe absolute value for rational numbers.
7.2 The student will describe and represent arithmetic and geometric sequences, using
variable expressions.


Focus: Integer Operations and Proportional Reasoning

November 7, 2011
a) model addition, subtraction, multiplication, and division of integers; and
b) add, subtract, multiply, and divide integers.
7.4 The student will solve single-step and multistep practical problems, using proportional
reasoning.

Measurement

Focus: Proportional Reasoning
a) describe volume and surface area of cylinders;
b) solve practical problems involving the volume and surface area of rectangular
prisms and cylinders; and
c) describe how changing one measured attribute of a rectangular prism affects its
volume and surface area.
7.6 The student will determine whether plane figures—quadrilaterals and triangles—are
similar and write proportions to express the relationships between corresponding sides
of similar figures.

Geometry

Focus: Relationships between Figures
7.7 The student will compare and contrast the following quadrilaterals based on properties:
parallelogram, rectangle, square, rhombus, and trapezoid.
7.8 The student, given a polygon in the coordinate plane, will represent transformations
(reflections, dilations, rotations, and translations) by graphing in the coordinate plane.


Focus: Applications of Statistics and Probability
7.9 The student will investigate and describe the difference between the experimental
probability and theoretical probability of an event.
7.10 The student will determine the probability of compound events, using the Fundamental
(Basic) Counting Principle.
7.11 The student, given data for a practical situation, will
a) construct and analyze histograms; and
b) compare and contrast histograms with other types of graphs presenting information
from the same data set.

November 7, 2011

Focus: Linear Equations
7.12 The student will represent relationships with tables, graphs, rules, and words.
a) write verbal expressions as algebraic expressions and sentences as equations and
vice versa; and
b) evaluate algebraic expressions for given replacement values of the variables.
a) solve one- and two-step linear equations in one variable; and
b) solve practical problems requiring the solution of one- and two-step linear
equations.
a) solve one-step inequalities in one variable; and
b) graph solutions to inequalities on the number line.
7.16 The student will apply the following properties of operations with real numbers:
a) the commutative and associative properties for addition and multiplication;
b) the distributive property;
c) the additive and multiplicative identity properties;
d) the additive and multiplicative inverse properties; and
e) the multiplicative property of zero.

Grade Eight
The eighth-grade standards are intended to serve two purposes. First, the standards contain
content that reviews or extends concepts and skills learned in previous grades. Second, they
contain new content that prepares students for more abstract concepts in algebra and geometry.
The eighth-grade standards provide students additional instruction and time to acquire the
concepts and skills necessary for success in Algebra I. Students will gain proficiency in
computation with rational numbers and will use proportions to solve a variety of problems. New
concepts include solving multistep equations and inequalities, graphing linear equations,
visualizing three-dimensional shapes represented in two-dimensional drawings, and applying
transformations to geometric shapes in the coordinate plane. Students will verify and apply the
Pythagorean Theorem and represent relations and functions, using tables, graphs, and rules. The
eighth-grade standards provide a more solid foundation in Algebra I for those students not ready
for Algebra I in grade eight.
appropriate technologies. However, facility in the use of technology shall not be regarded as a
substitute for a student’s understanding of quantitative concepts and relationships or for
proficiency in basic computations. Students will also identify real-life applications of the
mathematical principles they are learning that can be applied to science and other disciplines
they are studying.

November 7, 2011


Focus: Relationships within the Real Number System
a) simplify numerical expressions involving positive exponents, using rational
numbers, order of operations, and properties of operations with real numbers; and
b) compare and order decimals, fractions, percents, and numbers written in scientific
notation.
8.2 The student will describe orally and in writing the relationships between the subsets of
the real number system.


Focus: Practical Applications of Operations with Real Numbers
a) solve practical problems involving rational numbers, percents, ratios, and
proportions; and
b) determine the percent increase or decrease for a given situation.
8.4 The student will apply the order of operations to evaluate algebraic expressions for
given replacement values of the variables.
a) determine whether a given number is a perfect square; and
b) find the two consecutive whole numbers between which a square root lies.

Measurement

Focus: Problem Solving
a) verify by measuring and describe the relationships among vertical angles, adjacent
angles, supplementary angles, and complementary angles; and

November 7, 2011
b) measure angles of less than 360°.
a) investigate and solve practical problems involving volume and surface area of
prisms, cylinders, cones, and pyramids; and
b) describe how changing one measured attribute of a figure affects the volume and
surface area.

Geometry

Focus: Problem Solving with 2- and 3-Dimensional Figures
a) apply transformations to plane figures; and
b) identify applications of transformations.
8.9 The student will construct a three-dimensional model, given the top or bottom, side,
and front views.
a) verify the Pythagorean Theorem; and
b) apply the Pythagorean Theorem.
8.11 The student will solve practical area and perimeter problems involving composite plane
figures.


Focus: Statistical Analysis of Graphs and Problem Situations
8.12 The student will determine the probability of independent and dependent events with
and without replacement.
a) make comparisons, predictions, and inferences, using information displayed in
graphs; and
b) construct and analyze scatterplots.


Focus: Linear Relationships
8.14 The student will make connections between any two representations (tables, graphs,
words, and rules) of a given relationship.
a) solve multistep linear equations in one variable with the variable on one and two
sides of the equation;

November 7, 2011
b) solve two-step linear inequalities and graph the results on a number line; and
c) identify properties of operations used to solve an equation.
8.16 The student will graph a linear equation in two variables.
8.17 The student will identify the domain, range, independent variable, or dependent
variable in a given situation.

The Common Core Standards for Mathematics

http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

The Common Core Standards
Key Points in Mathematics

● The K-5 standards provide students with a solid foundation in whole numbers, addition,
subtraction, multiplication, division, fractions and decimals—which help young students
build the foundation to successfully apply more demanding math concepts and procedures,
and move into applications.
● In kindergarten, the standards follow successful international models and recommendations
from the National Research Council’s Early Math Panel report, by focusing kindergarten
work on the number core: learning how numbers correspond to quantities, and learning how
to put numbers together and take them apart (the beginnings of addition and subtraction).
● The K-5 standards build on the best state standards to provide detailed guidance to teachers
on how to navigate their way through knotty topics such as fractions, negative numbers, and
geometry, and do so by maintaining a continuous progression from grade to grade.
● The standards stress not only procedural skill but also conceptual understanding, to make
sure students are learning and absorbing the critical information they need to succeed at
higher levels - rather than the current practices by which many students learn enough to get
by on the next test, but forget it shortly thereafter, only to review again the following year.
● Having built a strong foundation K-5, students can do hands on learning in geometry, algebra
and probability and statistics. Students who have completed 7th grade and mastered the
content and skills through the 7th grade will be well-prepared for algebra in grade 8.
● The middle school standards are robust and provide a coherent and rich preparation for high
school mathematics.
● The high school standards call on students to practice applying mathematical ways of
thinking to real world issues and challenges; they prepare students to think and reason
mathematically.

November 7, 2011
● The high school standards set a rigorous definition of college and career readiness, by
helping students develop a depth of understanding and ability to apply mathematics to novel
situations, as college students and employees regularly do.
● The high school standards emphasize mathematical modeling, the use of mathematics and
statistics to analyze empirical situations, understand them better, and improve decisions. For
example, the draft standards state: “Modeling links classroom mathematics and statistics to
everyday life, work, and decision-making. It is the process of choosing and using appropriate
mathematics and statistics to analyze empirical situations, to understand them better, and to
improve decisions. Quantities and their relationships in physical, economic, public policy,
social and everyday situations can be modeled using mathematical and statistical methods.
When making mathematical models, technology is valuable for varying assumptions,
exploring consequences, and comparing predictions with data.”

Resources

Gewertz, C. (2011). Experts: Educators can't separate common core state

standards. Education Week, 30(36), 24.

Kepner Jr., H.S. (2010). A math perspective on the common core standards

initiative. NSTA Reports!, 3-4.

Wiggins, G. (2011). The common-core math standards: They don’t add up.

Education Week, 31 (5), 22-23.

http://www.doe.virginia.gov/VDOE/Superintendent/Sols/home.shtml

http://www.corestandards.org/the-standards

http://www.corestandards.org/about-the-standards/key-points-in-mathematics

Math sol common core overview

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