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+Georgia Performance Standards Mathematics Revisions
On July 13, 2006, the Georgia State Board of Education approved the following revisions to the Mathematics Georgia Performance Standards.
Changes K-5
Kindergarten
MKN2. Students will use representations to model addition and subtraction.
a. Use counting strategies to find out how many items are in two sets when they are combined, separated, or compared.
c. Use objects, pictures, numbers, or words to create, solve and explain story problems (combining, separating, or comparing) for two numbers that are each less than 10.
MKM1. Students will group objects according to common properties such as color, shape, texture, or number. longer/shorter, more/less, taller/shorter, and heavier/lighter.
MKM3. Students will tell time as it relates to a daily schedule.
b. Tell the time when daily events occur, such as lunch, to the nearest hour. morning, afternoon, and night.
MKG1. Students will correctly name simple two and three-dimensional figures, and recognize them in the environment.
a. Recognize and name the following basic two-dimensional shapes figures: triangles, rectangles, squares, and circles.
b. Recognize and name the following three-dimensional shapes figures: spheres (balls), and cubes.
MKG2. Students will understand basic positional spatial relationships.
MKG3. Students will identify, create, extend, and transfer patterns from one representation to another using actions, objects, and geometric shapes.
b. Extend a given pattern, and recognize similarities (such as color, shape, texture, or number) in different patterns.
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
MKP1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
MKP2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
MKP3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
MKP4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
MKP5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Grade 1
Concepts/Skill to Maintain
Positional words Spatial relationships positional words
Calendar time and daily schedule
Measurement comparing and ordering
M1N1. Students will estimate, model, compare, order, and represent whole numbers up to 100.
c. Compare small sets using the terms greater than, less than, and equal to (<,
>, =). (>, <, =)
M1N2. Understand place value notation for the numbers between 1 and 100.
(Discussions may allude to 3-digit numbers to assist in understanding place value.)
a. Determine to which multiple of ten a given number is nearest (rounding) using tools such as a sequential number line or hundreds chart to assist in estimating.
b. Represent collections of less than 30 objects with 2-digit numbers and understand the meaning of place value. (Make sure that students, when given a number like 27 initially describe it as 2 tens and 7 ones, and only later use standard language, twenty-seven, when talking about the number.)
c. Decompose numbers between 11 and 19 as one ten and the appropriate number of ones.
M1N3. Students will add and subtract numbers less than 100 as well as understand and use the inverse relationship between addition and subtraction.
c. Compose/decompose numbers up to 10 --break numbers apart, e.g., 8 is represented as 4 + 4, 3 + 5, 5 + 2 + 1, and 10-2). Decompose numbers between 11 and 19 as one ten and the appropriate number of ones.
g. Apply addition and subtraction to 2 digit numbers without regrouping (e.g.
15 + 4, 80-60, 56 + 10, 100-30, 58 + 5 52 + 5).
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
M1P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M1P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M1P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M1P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M1P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Grade 2
Concepts/Skill to Maintain
Telling time
Measurement estimating, comparing, and ordering
Basic geometric figures and spatial relationsips
M2N1. Students will understand the place value use multiple representation of whole numbers through four digits. to connect symbols to quantities.
M2N4. Students will understand and compare common fractions with small denominators.
M2N5. Students will represent and interpret quantities and relationships using mathematical expressions including equality and inequality signs (=, <, > , >, <).
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
M2P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M2P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M2P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M2P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M2P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Terms/Symbols:
Perimeter
Grade 3
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
M3P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M3P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M3P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking throughcommunication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M3P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M3P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Grade 4
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
M4P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M4P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M4P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M4P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M4P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Grade 5
Process Standards
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.
M5P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
M5P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
M5P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
M5P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
M5P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Changes 8 - 12
M8A1. Students will use algebra to represent, analyze, and solve problems.
d. Interpret solutions in problem contexts. Solve equations involving several variables for one variable in terms of the others.
e. Interpret solutions in problem contexts.
M8A4. Students will graph and analyze graphs of linear equations and inequalities.
e. Graph the solution set of a linear inequality, identifying whether the solution
set is an open or a closed half-plane.
e. f. Determine the equation of a line given a graph, numerical information that
defines the line, or a context involving a linear relationship.
f. g. Solve problems involving linear relationships.
M8A5. Students will understand systems of linear equations and inequalities and use them to solve problems.
a. Given a problem context, write an appropriate system of linear equations or
inequalities.
c. Graph the solution set of a system of linear inequalities in two variables.
c. d. Interpret solutions in problem contexts.
MM1A2. Students will simplify and operate with radical expressions, polynomials,
and rational expressions.
d. Expand binomials using the Binomial Theorem.
d. e. Add, subtract, multiply, and divide rational expressions.
e. f. Factor expressions by greatest common factor, grouping, trial and error, and
special products limited to the formulas below.
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
(x + y)(x - y) = x2 - y2
(x + a)(x + b) = x2 + (a + b)x + ab
(x + y)3 = x3 + 3 x2y + 3xy2 + y3
(x - y)3 = x3 - 3x2y + 3xy2 - y3
f. g. Use area and volume models for polynomial arithmetic.
Note: The terms definition, axiom, and theorem were added to the terms and symbols section of Mathematics 1. The word conjectures was changed to the singular, conjecture.
MM2D1. Using sample data, students will make informal inferences about
population means and standard deviations.
d. Compare the means and standard deviations of random samples with the
corresponding population parameters, including those population parameters
for normal distributions. Observe that the different sample
means vary from one sample to the next. Observe that the distribution of the
sample means has less variability than the population distribution.
MM2D2. Students will determine an algebraic model to quantify the association
between two quantitative variables.
d. Investigate issues that arise when using data to explore the relationship
between two variables, including confusion between correlation and
causation.
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