School Administrative District #4
Unity of purpose
CORE CURRICULUM: SCOPE AND SEQUENCE
Department: Mathematics
CONTENT STANDARD: ALGEBRA CONCEPTS
Students will understand and apply algebraic concepts. Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.
Performance Indicators: The learner will·
|
Kindergarten |
1. Review and extend prior learning
2. Use language to express numerical relationships
3. Solve one-step linear word problems by
á Listening to a situation, determining the appropriate operation (addition or subtraction), and solving for an unknown, using manipulatives
|
Grade 1 |
1. Review and extend prior learning
2. Use symbols to express numerical relationships
3. Model and solve algebraic equations, using manipulatives
4. Recognize and use algebraic properties
á Zero property/identity property
á Addition
á Subtraction
5. Solve one-step linear word problems by
á Listening to a situation, determining the appropriate operation (addition or subtraction), and solving for an unknown, using an equation
|
Grade 2 |
1. Review and extend prior learning
2. Solve problems by completing a numerical sequence involving basic addition and subtraction facts (e.g., 3 + __ = 7 or 7 - __ = 3)
3. Recognize and use algebraic properties
á Commutative property for
á Addition
4. Solve one-step linear word problems by
á Reading about a situation, determining the appropriate operation (addition or subtraction), and solving for an unknown, using an equation
|
Grade 3 |
1. Review and extend prior learning
2. Demonstrate an initial understanding of a variable by
á Describing the concept of a variable
á Using a variable to represent a given verbal quantitative expression, involving one operation
á Writing an expression, using a variable to represent a given mathematical relationship
3. Recognize and use algebraic properties
á Identity property
á Multiplication
á Division
á Zero property
á Multiplication
á Division
á Commutative property for
á Multiplication
4. Solve one-step linear word problems by
á Reading about a situation, determining the appropriate operation (addition, subtraction, multiplication or division), and solving for an unknown, using manipulatives
|
Grade 4 |
1. Review and extend prior learning
2. Identify and locate missing whole numbers on a given number line
3. Identify and graph ordered pairs in Quadrant I of a coordinate plane
4. Solve one-step linear word problems by
á Reading about a situation, determining the appropriate operation (addition, subtraction, multiplication or division), and solving for an unknown, using an equation
|
Grade 5 |
1. Review and extend prior learning
2. Create and solve a problem situation based upon a given expression, using a single variable
3. Recognize and use algebraic properties
á Distributive property
|
Grade 6 |
1. Review and extend prior learning
2. Recognize and use algebraic properties
á Associative property for
á Addition
á Multiplication
3. Solve two-step linear word problems by
á Reading about a situation, determining the appropriate operations (addition, subtraction, multiplication or division), and solving for an unknown, using an equation
|
Grade 7 |
1. Review and extend prior learning
2. Investigate and describe concepts of exponents, perfect squares, and square roots
3. Write verbal expressions/sentences as algebraic expressions/equations
4. Recognize and use algebraic properties
á Multiplicative inverse property
á Inverse property of addition
5. Use algebraic terms appropriately
á Equation
á Inequality
á Variable
á Expression
á Domain
á Range
6. Create and translate a pattern into a two-step linear equation that can be verified
7. Compute with integers, using
á Number line
á Additive inverse
8. Identify and graph ordered pairs in the four quadrants of a coordinate plane
|
Grade 8 |
1. Review and extend prior learning
2. Use algebraic terms appropriately
á Term
á Coefficient
á Non-linear equation
3. Manipulate algebraic expressions by
á Adding
á Subtracting
á Multiplying
á Dividing
4. Recognize and use algebraic properties
á Addition property of equality
á Multiplication property of equality
5. Demonstrate an initial understanding of how to distinguish and compute between the various sets of complex numbers, including
á Real numbers
á Rational numbers
á Whole numbers
á Integers
á Fractions and decimals
6. Solve two-step linear equations and inequalities in one variable, using strategies involving inverse operations and integers
7. Solve real-life problems requiring the solution of a two-step linear equation
8. Graph a linear equation in two variables on the coordinate plane, using a table of ordered pairs
9. Describe and represent relations using tables, graphs, and rules
10. Create and solve problems using proportions, formulas, and functions
11. Demonstrate an initial understanding of the laws of exponents
12. Collect and analyze data to make predictions, write equations, and solve real-life problems
|
Grade 9 |
NOTE: The following performance indicators also apply to those students taking eighth-grade Algebra I.
1. Review and extend prior learning
2. Distinguish and compute between the various sets of complex numbers, including
á Real numbers
á Rational numbers
á Whole numbers
á Integers
á Fractions and decimals
á Irrational numbers
3. Apply scientific notation to algebraic situations
4. Compute with integers, using
á Absolute value
á Exponents
5. Solve and graph exponential situations, involving
á Growth
á Decay
á Simple interest
á Compound interest
6. Understand and apply the laws of exponents
7. Understand and manipulate polynomials
á Determine degree of polynomials
á Classify polynomials
á Simplify polynomials
á Add, subtract, and multiply polynomials
8. Factor polynomials by
á Finding the greatest common factor
á Grouping
á Using the Difference of Two Squares Theorem
á Trinomial factoring
á Using the Factor Theorem
á Using the Quadratic Formula to find roots
9. Solve quadratic equations by
á Factoring
á Using the Quadratic Formula
á Finding the nature of roots using the discriminant
á Graphing (e.g., calculator, computer, graph paper)
á Using the Difference of Two Squares Theorem
10. Manipulate rational expressions by
á Simplifying by adding, subtracting, multiplying, and dividing rational expressions
á Simplifying complex rational expressions
11. Solve multi-step linear equations involving
á One variable
á Multi-variables
á Proportions
á Absolute value
á Rational expressions
á Radical expressions
12. Solve linear systems of equations and inequalities by
á Graphing
á Substitution
13. Find the distance between two points on a coordinate plane, using the
á Pythagorean Theorem
á Distance Formula
14. Write and graph linear equations by
á Finding slope and intercepts
á Recognizing the slope-intercept form
á Recognizing point-slope form
á Recognizing general form
á Recognizing standard form
á Finding the equations of horizontal and vertical lines
15. Solve word problems, involving
á Distance
á Cost
á Motion
á Consecutive integers
á Even
á Odd
á Age
á Percent
16. Justify steps used in simplifying expressions and solving equations and inequalities
|
Grade 10 |
1. Review and extend prior learning
|
Grade 11 |
1. Review and extend prior learning
2. Distinguish and compute between the various sets of complex numbers, including
á Imaginary numbers
3. Expand binomials, using the Binomial Theorem
4. Understand and manipulate polynomials
á Divide polynomials with monomial and binomial divisors
á Expand polynomials by using the Binomial Theorem
5. Understand and apply the Remainder Theorem
á Synthetic division
á Rational Root Theorem
á Factor Theorem
6. Manipulate radicals by
á Translating to fractional exponential form
á Simplifying by adding, subtracting, multiplying, and dividing radicals
á Converting radicals to decimals
7. Solve word problems, involving
á Work
á Coin
á Mixture
á Abstract rate problems
á Ideal Gas Law
á Direct, inverse, and linear variation
á Joint and combined variation
8. Solve linear and non-linear systems of equations and inequalities by using
á Multiplication/addition method, i.e., elimination method
á Cramer's Rule
á Matrices/determinants
9. Solve and graph inequalities
á Compound inequalities
á Absolute value
á Non-linear inequalities
á Linear programming
10. Complete the square in order to
á Solve quadratic equations
á Develop the Quadratic Formula
á Write the standard form of conic sections
11. Write and graph linear equations by
á Using parallel and perpendicular lines
á Finding the equation of a perpendicular to a line
12. Solve second-, third-, and fourth-degree equations, using
á Factor Theorem
á Rational Root Theorem
á Graphs
á Quadratic Formula
13. Demonstrate an initial understanding of how to manipulate matrices by
á Adding
á Subtracting
á Multiplying
á Finding the inverse
á Finding the determinant
14. Demonstrate an initial understanding of the kinds of conic sections
á Circle
á Parabola
á Hyperbola
á Ellipse
15. Manipulate conic sections by
á Graphing the conics
á Writing equations of conics
á Finding the asymptotes of hyperbolas
á Finding the foci of an ellipse
á Translating the axis
16. Use vectors
17. Use an x-y coordinate plane to
á Convert rectangular coordinates to polar coordinates and vice versa
18. Use conjunctions and disjunctions
19. Demonstrate an initial understanding of exponential equations in order to
á Graph exponential equations
á Solve exponential equations
á Translate to log form
á Solve problems involving exponentials
20. Demonstrate an initial understanding of the laws of logarithms in order to
á Graph the log of a function
á Solve log equations
á Convert to and from different bases
á Solve anti-logs
á Translate to exponential form
á Solve problems involving logarithms
21. Demonstrate an initial understanding of the kinds of progressions
á Arithmetic
á Explicit
á Recursive
á Geometric
á Explicit
á Recursive
22. Demonstrate an initial understanding of how to manipulate progressions by
á Finding the arithmetic and geometric means
á Finding the nth term of arithmetic and geometric progressions
23. Demonstrate an initial understanding of the kinds of series
á Arithmetic
á Geometric
24. Demonstrate an initial understanding of how to manipulate series by
á Finding the nth term of arithmetic and geometric series
á Finding the sum of arithmetic and geometric series
á Finding the sum of infinite geometric series
á Solving problems involving series
|
Grade 12 |
NOTE: The following performance indicators apply to only those students taking Functions, Statistics, and Trigonometry (FST).
1. Review and extend prior learning
2. Recognize the kinds of series
á Infinite
á Convergent
3. Understand and manipulate polynomials
á Divide polynomials with trinomial divisors
4. Manipulate matrices by
á Adding
á Subtracting
á Multiplying
á Finding the inverse
á Finding the determinant
5. Recognize kinds of conic sections
á Circle
á Parabola
á Hyperbola
á Ellipse
6. Understand exponential equations in order to
á Graph exponential equations
á Solve exponential equations
á Translate to log form
á Solve problems involving exponentials
7. Understand and apply the laws of logarithms in order to
á Graph the log of a function
á Solve log equations
á Convert to and from different bases
á Solve anti-logs
á Translate to exponential form
á Solve problems involving logarithms
8. Recognize the kinds of progressions
á Arithmetic
á Explicit
á Recursive
á Geometric
á Explicit
á Recursive
9. Manipulate progressions by
á Finding the arithmetic and geometric means
á Finding the nth term of arithmetic and geometric progressions
10. Recognize the kinds of series
á Arithmetic
á Geometric
11. Manipulate series by
á Finding the nth term of arithmetic and geometric series
á Finding the sum of arithmetic and geometric series
á Finding the sum of infinite geometric series
á Solving problems involving series