Course Description
Open to: Grade 8 One Year Course
Prerequisite: Instructor/Counselor Approval/Accelerated Mathematics 7
Content: Students will study the structure of the real number system and will
apply it to steps involved in solving algebra problems. Equations and inequalities
will be solved using math axioms. Graphic and algebraic analysis of equations,
inequalities, and systems of equations will be studied. Emphasis will be placed
upon factoring, algebraic fractions, radicals, and problem solving.
Adopted Materials
Title: Algebra-Structure and Method Book 1
Edition: 2000
Publisher McDougal Littell
ISBN: 0-395-97722-3
Resource Materials:
Textbook:
Brown,
Dolciani, Sorgenfrey, and Cole. Algebra I. Structure
and Method Book 1 McDougal Littel, Houghton Mifflin
Company 2000. (PH)
Additional
Resources:
Taylor, Harold and Loretta. Developing Skills in Algebra I Book A. Palo
Alto, Ca. Dale Seymour. 1984. (DS-A)
Taylor, Harold and Loretta. Developing Skills in Algebra I Book B. Palo
Alto, Ca. Dale Seymour. 1984. (DS-B)
Taylor, Harold and Loretta. Developing Skills in Algebra I Book C. Palo
Alto, Ca. Dale Seymour. 1984. (DS-C)
Taylor, Harold and Loretta. Developing Skills in Algebra I Book D. Palo
Alto, Ca. Dale Seymour. 1984. (DS-C)
Marcy, Steve and Janis. Middle School Math with Pizazz C revised. Chicago.
Creative Publications, 1996. (CP-C)
Marcy, Steve and Janis. Middle School Math with Pizazz D revised. Chicago.
Creative Publications,1996. (CP-D)
Marcy, Steve and Janis. Middle School Math with Pizazz E revised. Chicago.
Creative Publications,1996. (CP-E)
Marcy, Steve and Janis. Algebra with Pizazz revised. Chicago. Creative
Publications, 1996. (CP-A)
Mathematics Curriculum
Map
Course overview, activities, vocabulary, supplemental materials in pdf format.
Copyright
Resources
Course Scope
| Unit 0 |
Preparation and Review |
|
| Unit 1 |
Introduction to Algebra |
2 Weeks |
| Unit 2 |
Working with Real Numbers |
2 Weeks |
| Unit 3 |
Solving Equations and Problems |
3 Weeks |
| Unit 4 |
Polynomials |
3 Weeks |
| Unit
5 |
Exponents and Polynomials |
5 Weeks |
| Unit 6 |
Fractions (through 6.3 in Semester 1, then from
6.4 on 2nd Semester |
2 Weeks |
| Unit 7 |
Applying Fractions |
2 Weeks |
| Unit 8 |
Introduction to Functions |
2 Weeks |
| Unit 9 |
Systems of Linear Equations |
2 Weeks |
| Unit 10 |
Inequalities |
2 Weeks |
| Unit 11 |
Rational and Irrational Numbers |
2 Weeks |
| Unit 12 |
Quadratic Functions |
1 Week |
| Unit Various |
Selected Topics |
|
Assessment
Correlation acronyms key
Mathematics Curriculum Matrix K-12 pdf or Word
document
|
Unit
0 |
Preparation and Review |
1 week |
|
Instructional Objective
0813.01 Review arithmetic skill prerequisites
from previous years. |
Standard Reference
AI.1.1.1, AI.1.2.1, AI.5.2.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Demonstrate proficiency at performing basic
arithmetic skills using fractions and decimals. |
Text p. 43, p. 92
(Maint. Skills end of Chap) |
TMA |
|
Instructional Objective
0813.02 Understand and use procedures for
operating on algebraic expressions. |
Standard Reference
AI.1.1.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Evaluate an algebraic expression using rational
numbers. |
Ch. 1-1, 1-2 |
TMA, EOC |
|
Instructional Objective
0813.03 Use the proper order of operations.
Perform operations with real numbers. |
Standard Reference
AI.1.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Use the order of operations to simplify numerical
expressions. |
Ch. 1-1, 1-2, 1-3 |
TMA, EOC |
|
Instructional Objective
0813.04 Understand and use variables, expressions,
equations, and inequalities. |
Standard Reference
AI.3.2.2 |
|
No.
|
Performance Objective
|
Resource Reference |
Assessment Correlation |
|
01 |
Translate an English phrase or sentence into
an algebraic expression and vice versa. |
Ch 1-4, 1-5 |
TMA, EOC |
|
Instructional Objective
0813.05 Use a variety of methods, including
common mathematical formulas, to solve problems
drawn from daily life. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective
|
Resource Reference |
Assessment Correlation |
|
01 |
Use a problem-solving model to develop and apply
problem-solving strategies. (e.g., guess and
check, draw a diagram, make a list, work backwards,
and identify a simpler problem.) |
Ch. 1-6, 1-7 |
TMA, EOC |
|
Instructional Objective
0813.06 Understand properties of the real
number system. |
Standard Reference
AI.1.3.1 |
|
No.
|
PerforAzmance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Recognize and use a property of real numbers
(associative, commutative, distributive, and
equality) in an algebraic expression. |
Ch. 2-1 |
TMA, EOC |
|
02 |
Identify and use identity and inverse properties
in algebraic expressions. |
Ch. 2-2 |
TMA, EOC |
|
Instructional Objective
0813.07 Understand and use positive and negative
numbers, fractions, decimals, percentages,
and scientific notation. |
Standard Reference
AI.1.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Understand and perform basic operations on positive
and negative numbers. |
Ch. 2-2, 2-3, 2-4, 2-5, 2-6, 2-8, 2-9 |
TMA, EOC |
|
Instructional Objective
0813.08 Use a variety of methods, including
common mathematical formulas, to solve problems
drawn from daily life. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective
|
Resource Reference |
Assessment Correlation |
|
01 |
Use a problem-solving model to develop and apply
problem-solving strategies. (e.g., guess and
check, draw a diagram, make a list, work backwards,
and identify a simpler problem.) |
Ch. 2-7 |
TMA, EOC |
|
Instructional Objective
0813.09 Make and evaluate logical arguments. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Make and evaluate logical arguments (e.g. explain
why it is not possible to divide by zero.) |
Ch. 2.9 |
EOC |
|
Back to Top |
|
Unit
3 |
Solving Equations and
Problems |
3 weeks |
|
Instructional Objective
0813.10 Understand and use appropriate procedures
to solve linear equations and inequalities
such as:
3x – 4 = 2
or
3x – 4 > 2 |
Standard Reference
AI.3.1.1, AI.3.2.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve linear equations with one variable for
computational or word problems. |
Ch. 3-1, 3-2, 3-3, 3-4, 3-5 |
TMA, EOC |
|
Instructional Objective
0813.11 Use a variety of methods, including
common mathematical formulas, to solve problems
drawn from daily life. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective
|
Resource Reference |
Assessment Correlation |
|
01 |
Use a problem-solving model to develop and apply
problem-solving strategies. (e.g., guess and
check, draw a diagram, make a list, work backwards,
and identify a simpler problem.) |
Ch. 3-4, 3-6, 3-7 |
TMA, EOC |
|
Instructional Objective
0813.12 Solve problems that involve varying
quantities with variables, expressions, equations,
inequalities, and absolute values. |
Standard Reference
AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve problems that involve varying quantities
variables, expressions, equations, inequalities,
and absolute values. |
Ch. 3-4, 3-5 |
TMA, EOC |
|
Instructional Objective
0813.13 Use the proper order of operations.
Perform operations with real numbers. |
Standard Reference
AI.1.1.2,AI.1.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Use the order of operations to simplify numerical
expressions. |
Ch. 4-1 |
TMA, EOC |
|
Instructional Objective
0813.14 Understand and use procedures for
operating on algebraic expressions. |
Standard Reference
AI.1.1.1, AI.1.2.1, AI.1.3.3 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Evaluate an expression using exponents. |
Ch. 4-1 through 4-4 |
TMA, EOC |
|
02 |
Simplify expressions involving exponents. |
Ch. 4-5 through 4-7 |
TMA, EOC |
|
Instructional Objective
0813.15 Use a variety of methods, including
common mathematical formulas, to solve problems
drawn from daily life. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective
|
Resource Reference |
Assessment Correlation |
|
01 |
Use a problem-solving model to develop and apply
problem-solving strategies. (e.g., guess and
check, draw a diagram, make a list, work backwards,
identify a simpler problem.) |
Ch. 4-8 through 4-10 |
TMA, EOC |
|
Instructional Objective
0813.16 Use number theory concepts (divisibility
rules, factors, multiples, primes) to solve
problems. |
Standard Reference
AI.1.3.1, AI.1.3.3 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Apply definitions of prime and composite numbers
to solve mathematical problems. |
Ch. 5-1, 5-2, 5-3 |
TMA, EOC |
|
Instructional Objective
0813.17 Make and evaluate logical arguments. |
Standard Reference
|
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Make and evaluate logical arguments (e.g., explain
why it is not possible to divide by zero.) |
Ch. 5-2 |
EOC |
|
Instructional Objective
0813.18 Use appropriate procedures to simplify
and solve polynomial equations and inequalities
such as:
x2 + 3x = 7
or
x2 + 3x < 7
|
Standard Reference
AI.1.3.1, AI.1.3.3 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Factor simple polynomials. |
Ch. 5-3, 5-5, 5-6, 5-7, 5-8, 5-9, 5-10, 5-11 |
TMA, EOC |
|
02 |
Factor the difference of two squares or perfect
square trinomials. |
Ch. 5-5, 5-6 |
TMA, EOC |
|
03 |
Solve polynomial word problems with or without
factoring. |
Ch. 5-12, 5-13 |
TMA, EOC |
|
Instructional Objective
0813.19 Understand and use procedures for
operating on algebraic expressions. |
Standard Reference
AI.1.1.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Evaluate an algebraic expression using rational
numbers. |
Ch. 6-1, 6-2, 6-3 |
TMA, EOC |
|
Instructional Objective
0813.20 Model real-world phenomena using polynomial,
rational, and basic exponential functions,
noting restricted domains. |
Standard Reference
AI.1.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Model real-world phenomena using polynomial,
rational, and basic exponential functions. |
Ch. 6-2, 6-3, 6-5, 6-6, 6-7 |
TMA, EOC |
|
Instructional Objective
0813.21 Understand and use procedures for
operating on algebraic expressions. |
Standard Reference
AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Evaluate an algebraic expression using rational
numbers. |
Ch. 7-1 through 7-3 |
TMA, EOC |
|
Instructional Objective
0813.22 Understand and use proportions, ratios,
and scaling. |
Standard Reference
AI.3.3.1, AI.2.1.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Calculate the solutions to number problems using
ratio, proportion, and percent. |
Ch. 7-1, 7-2, 7-5, 7-6 |
TMA, EOC |
|
Instructional Objective
0813.23 Understand and use appropriate procedures
to solve linear equations and inequalities
such as:
3x – 4 = 2
or
3x – 4 > 2 |
Standard Reference
AI.3.2.2AI.3.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve fractional equations |
Ch. 7-3, 7-4 |
TMA, EOC |
|
Instructional Objective
0813.24 Make and evaluate logical arguments. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Make and evaluate logical arguments (e.g., explain
why it is not possible to divide by zero.) |
Ch. 7-4 |
EOC |
|
Instructional Objective
0813.25 Understand and use positive and negative
numbers, fractions, decimals, percentages,
and scientific notation. |
Standard Reference
AI.1.2.1, AI.1.3.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Convert decimals (terminating and repeating),
fractions, or percents interchangeably. |
Ch. 7-5, 7-6 |
TMA, EOC |
|
02 |
Convert numbers from scientific notation (including
those with negative exponents) to the standard
form and vice versa. |
Ch. 7-10 |
TMA, EOC |
|
Instructional Objective
0813.20 Model real-world phenomena using polynomial,
rational, and basic exponential functions,
noting restricted domains. |
Standard Reference
|
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Model real-world phenomena using polynomial,
rational, and basic exponential functions. |
Ch. 7-4 through 7-8 |
TMA, EOC |
|
Instructional Objective
0813.26 Understand the purpose and capabilities
or appropriate technology. |
Standard Reference
AI.1.3.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Discuss and understand the purpose and capabilities
or appropriate technology. |
Graphing calculator demonstration |
TMA, EOC |
|
Instructional Objective
0813.27 Understand concepts of the Cartesian
Coordinate System. |
Standard Reference
AI.3.1.1, AI.3.1.2, AI.3.4.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Determine the slope of a line using the slope
formula, the equation of the line, or the graph
of the equation. |
Ch. 8-1 through 8-3 |
TMA, EOC |
|
02 |
Determine the linear equation of the line using
the slope, y-intercept, or coordinates and will
compare the slopes of parallel and perpendicular
lines. |
Ch. 8-4, 8-5 |
TMA, EOC |
|
03 |
Determine a linear equation from analyzing the
graph of the equation. |
Ch. 8-4, 8-5 |
TMA, EOC |
|
04 |
Graph a linear equation with two variables. |
Ch. 8-4, 8-5 |
TMA, EOC |
|
Instructional Objective
0813.28 Represent a set of data in a table,
a graph, and as a mathematical relationship. |
Standard Reference
AI.3.1.1, AI.3.2.1, AI.5.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify whether an expression, ordered pair,
or graph does or does not represent a function
and justify the conclusion. |
Ch. 8-6, Vertical Line Test |
TMA, EOC |
|
02 |
Find the range of a function, given its domain. |
Ch. 8-6, 8-7, 8-8 |
TMA, EOC |
|
Instructional Objective
0813.29 Use graphs, matrices, and sequences
to represent and solve problems. |
Standard Reference
AI.3.2.1, AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Use graphs, matrices, and sequences to represent
and solve problems. |
Ch. 9 |
TMA, EOC |
|
Instructional Objective
0813.30 Understand and use appropriate procedures
to solve simple linear systems of equations
and inequalities such as
x + y = 7
2x + 3y = 21
or
x + y < 7
2x + 3y > 21 |
Standard Reference
AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve systems of linear equations in two variables. |
Ch. 9-1, 9-2, 9-3, 9-4, 9-5 |
TMA, EOC |
|
02 |
Graph a linear equation with two variables. |
Ch. 9.1 |
TMA, EOC |
|
Instructional Objective
0813.20 Model real-world phenomena using polynomial,
rational, and basic exponential functions,
noting restricted domains. |
Standard Reference
|
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Model real-world phenomena using polynomial,
rational, and basic exponential functions. |
Ch. 9-6, 9-7 |
TMA, EOC |
|
Instructional Objective
0813.31 Understand and use variables, expressions,
equations, and inequalities. |
Standard Reference
AI.3.2.2 |
|
No.
|
Performance Objective
|
Resource Reference |
Assessment Correlation |
|
01 |
Translate an English phrase or sentence into
an algebraic expression and vice versa. |
Ch. 10-1, 10-3 |
TMA, EOC |
|
Instructional Objective
0813.32 Understand concepts of the Cartesian
Coordinate System. |
Standard Reference
AI.3.1.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Identify inequalities by their representation
on a graph. |
Ch. 10-1, 10-7, 10-8 |
TMA, EOC |
|
02 |
Graph an inequality with one or two variables. |
Ch. 10-1, 10-7, 10-8 |
TMA, EOC |
|
Instructional Objective
0813.33 Understand and use appropriate procedures
to solve linear equations and inequalities
such as:
3x – 4 = 2
or
3x – 4 > 2 |
Standard Reference
AI.3.3.1, AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve absolute value equations. |
Ch. 10-2, 10-3 |
TMA, EOC |
|
02 |
Solve inequalities with one variable in computational
or word problems |
Ch. 10-2, 10-3 |
TMA, EOC |
|
Instructional Objective
0813.34 Understand properties of the real
number system. |
Standard Reference
AI.3.3.1, AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve inequalities with one variable in computational
or word problems. |
Ch. 10-2, 10-3, 10-5, 10-6 |
TMA, EOC |
|
Instructional Objective
0813.35 Solve problems that involve varying
quantities with variables, expressions, equations,
inequalities, and absolute values. |
Standard Reference
AI.1.3.1, AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve problems that involve varying quantities
variables, expressions, equations, inequalities,
and absolute values. |
Ch. 10-2, 10-3, 10-5, 10-6 |
TMA, EOC |
|
Instructional Objective
0813.36 Understand and use appropriate procedures
to solve simple linear systems of equations
and inequalities such as
x + y = 7
2x + 3y = 21
or
x + y < 7
2x + 3y > 21 |
Standard Reference
AI.3.1.1, AI.3.2.1, AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Evaluate an inequality in two variables. |
Ch. 10-7, 10-8 |
TMA, EOC |
|
02 |
Write an inequality to represent a problem situation
or write a possible situation that an inequality
could represent. |
Ch. 10-3 |
TMA, EOC |
|
03 |
Find the solutions set for an inequality. |
Ch. 10 |
TMA, EOC |
|
Back to Top |
|
Unit
11 |
Rational and Irrational
Numbers |
2 weeks |
|
Instructional Objective
0813.37 Understand properties of roots, exponents,
and logarithms. |
Standard Reference
AI.1.1.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Perform operations on numerical expressions
containing roots and integral exponents. |
Ch. 11-3, 11-4, 11-5, 11-7, 11-8 |
TMA, EOC |
|
02 |
Perform basic operations to simplify radical
expressions containing variables. |
Ch. 11-5, 11-6, 11-10 |
TMA, EOC |
|
Instructional Objective
0813.38 Understand properties of the real
number system. |
Standard Reference
AI.1.1.2, AI.1.3.1, AI.3.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Solve radical equations. |
Ch. 11-10 |
TMA, EOC |
|
Instructional Objective
0813.39 Know and apply the Pythagorean Theorem
to solve real world problems. |
Standard Reference
AI.1.3.1, AI.1.3.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Find the lengths of the sides or a right triangle
using the Pythagorean Theorem, and use the distance
formula to find the distance between any two
points in a Cartesian plane. |
Ch. 11.6 |
TMA, EOC |
|
Instructional Objective
0813.40 Understand and use procedures for
operating on algebraic expressions. |
Standard Reference
AI.1.2.1, AI.1.1.2, AI.1.3.3 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Evaluate an algebraic expression using rational
numbers. |
Ch. 12-1 |
TMA, EOC |
|
02 |
Evaluate an expression using exponents. |
Ch. 12-1 |
TMA, EOC |
|
Instructional Objective
0813.41 Use appropriate procedures to simplify
and solve polynomial equations and inequalities
such as
x2 + 3x = 7
or
x2 + 3x < 7 |
Standard Reference
AI.1.3.3, AI.3.2.2, AI.5.2.2 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
State and apply the quadratic formula to simple
quadratic equations. |
Ch. 12-3 |
TMA, EOC |
|
Instructional Objective
0813.45 Understand the nature and use of mathematical
models. |
Standard Reference
AI.2.1.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Understand the nature and use of mathematical
models. |
Throughout Text |
TMA, EOC |
|
Instructional Objective
0813.46 Determine length, area, capacity,
weight, time, and temperature with appropriate
units. |
Standard Reference
AI.2.1.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Use US customary and metric units of measurement
to calculate perimeter, area, surface area, and
volume. |
Throughout Text |
TMA, EOC |
|
Instructional Objective
0813.47 Understand equivalent units, comparable
units, and conversions |
Standard Reference
AI.2.1.1, AI.2.2.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Understand equivalent units, comparable units,
and conversions. |
Throughout Text |
TMA, EOC |
|
Instructional Objective
0813.48 Understand units and their relationship
to one another and to real world applications. |
Standard Reference
AI.2.1.1, AI.2.2.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Use measurement in word problems (e.g., rate,
work, distance, power, percent mixture) |
Throughout Text and specifically Ch. 8.5, 10.7-10.8 |
TMA, EOC |
|
Instructional Objective
0813.49 Understand that error accumulates
in a computation when there is rounding at
intermediate steps. |
Standard Reference
AI.2.1.1 |
|
No.
|
Performance Objective |
Resource Reference |
Assessment Correlation |
|
01 |
Determine the reasonableness to computation
and word problems, choosing an appropriate method
(e.g., using estimation, evaluating according
to context). |
Throughout Text |
TMA, EOC |
Back to Top
|
|
|
|
|
Mathematics curriculum contact:
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