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Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Number, Number Sense and Operations · Meaning of Operations (I) · Computation and Estimation (G) 4. Demonstrate fluency in computations using real numbers. 3. Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. (Gr. 8) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY / RESOURCES

ASSESSMENT

Algebra 1 Red book: PEMDAS

1st NINE WEEKS

Purple book: Positive / Negative numbers, Dividing a fraction, Number line

· Number and Number Systems (D) 2. Compare, order and determine equivalent forms for rational and irrational numbers. Venn diagram Reviewing Math (Red Book) Rational, Irrational, Real, Integers, Whole / Natural, Square Roots Cut and paste worksheet, Handwritten worksheets: Closure, Associative, Commutative, Identity, Inverse, Opposites, Property of Zero

(C)

1.

Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication.

Warren City Schools (WCS)

Department of Teaching & Learning

1

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Number, Number Sense and Operations · Meaning of Operations (F) 3. Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. * Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. (Gr. 8) Use order of operations, including use of parentheses, to simplify numerical expressions. (Gr. 5) Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. (Gr. 5) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY/ RESOURCES

ASSESSMENT

Powers, Exponents, Square roots Distributive Property, Exponents, Variables, Like terms, Coefficients, Monomials times polynomial MAX AXIS

1st NINE WEEKS

(I)

3.

9. 7.

Warren City Schools (WCS)

Department of Teaching & Learning

2

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Number, Number Sense and Operations · Number and Number Systems (I) 5. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100. (Gr. 6) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY / RESOURCES

ASSESSMENT

Dr. Pollack's activities: Solve equations using box and arrows (diagramming equations), relative of vs. off, absolute, percent

2nd NINE WEEKS

Patterns, Functions and Algebra · Use Patterns, Relations and Functions (C) 1. *Define function with ordered pairs in which each domain element is assigned exactly one range element. Red book & Purple book: Solve for one variable, linear only, function, properties of equality, domain / range, tables, solutions, no solutions, all solutions

(A)

2.

Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

(D)

3.

Warren City Schools (WCS)

Department of Teaching & Learning

3

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Patterns, Functions and Algebra · Use Patterns, Relations and Functions (D) 4. Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words. Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. Define function formally and with f(x) notation. (Gr. 10) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY

ASSESSMENT

(D)

5.

2nd NINE WEEKS

(D) · Use Algebraic Representations (D) (F) (F)

1.

8.

Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (Gr. 8) Solve linear equations and inequalities graphically, symbolically and using technology. (Gr. 8) Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.

9. 9.

Warren City Schools (WCS)

Department of Teaching & Learning

4

Grade: 9

2007 ­ 2008

BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Measurement · Measurement Units (A) · Use Measurement Techniques and Tools (A) (B) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY / RESOURCES

ASSESSMENT

1.

Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second.

Purple book: Rate/slope, Ratio Red book: Areas, Volumes

2. 3.

Use unit analysis to check computations involving measurement. Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively. Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. Solve problems involving unit conversion for situations involving distances, areas, volumes and rate within the same measurement system.

3rd NINE WEEKS

4. (D) 5. (D) Patterns, Functions and Algebra · Use Patterns, Relations and Functions (B) · Use Algebraic Representations (B)

3.

Identify functions as linear or nonlinear based on information given in a table, graph or equation. (Gr. 8)

Box arrow diagrams, Red book, Purple book: solving equations, linear, quadratic, dependent, independent, nonlinear, functions, inequalities

4.

Extend the uses of variables to include covariants where y depends on x. (Gr. 8)

Department of Teaching & Learning 5

Warren City Schools (WCS)

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Patterns, Functions and Algebra · Use Patterns, Relations and Functions (C) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY / RESOURCES

ASSESSMENT

1.

* Define function with ordered pairs in which each domain element is assigned exactly one range element.

Purple book: Slope, Direct, Linear Ch. 4 and 5 in Red book

·

3rd NINE WEEKS

Use Algebraic Representations (D)

6.

Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form. Use formulas to solve problems involving exponential growth and decay. Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.

Slope, Slope Intercept form, Point-slope form

(D) (D)

7. 8.

·

Analyze Change (E) (E)

13. Model and solve problems involving direct and inverse variation using proportional reasoning. 14. Describe the relationship between slope and the graph of a direct variation and inverse variation. 15. Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs.

Warren City Schools (WCS)

Department of Teaching & Learning

6

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Patterns, Functions and Algebra · Use Algebraic Representations (H) (H) (F) Geometry and Spatial Sense · Characteristics and Properties (I) INDICATORS

BOLD­EXPANSION FROM PREVIOUS YR.

VOCABULARY / RESOURCES

ASSESSMENT

10. Solve 2 by 2 systems of linear equations graphically and by simple substitution. (Gr. 8) 11. Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. (Gr. 8) 10. Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.

Red book, Purple book, Hand generated worksheets: Point Solution No solution Quadratics Roots

4th NINE WEEKS

1. 2.

Define basic trigonometric ratios in right triangles: sine, cosine and tangent. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures. Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram. Quadrilateral Parallelogram Types of Quad. Angles

·

Visualization and Geometric Models (E)

3.

Number, Number Sense and Operations · Computation and Estimation (G)

5.

Estimate the solutions for problem situations involving square and cube roots.

Square root, cube root Pythagorean Theorem Hypotenuse, legs

7

Warren City Schools (WCS)

Department of Teaching & Learning

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

BOLD­EXPANSION FROM PREVIOUS YR.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Patterns, Functions and Algebra · Use Algebraic Representations (D) INDICATORS

VOCABULARY/ RESOURCES

ASSESSMENT

11. Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). 12. Simplify rational expressions by eliminating common factors and applying properties of integer exponents.

4th NINE WEEKS (Possible if time permits)

(D) Data Analysis and Probability · Data Collection (A)

1.

Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data. Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.

(A)

2.

·

Statistical Methods (E) (G)

3. 4.

Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers. Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data.

Warren City Schools (WCS)

Department of Teaching & Learning

8

Grade 9

2007 ­ 2008 BASIC ALGEBRA CURRICULUM MAP Problem-Solving Activities & Calculator Usage should begin in September and be ongoing throughout the year.

BOLD­EXPANSION FROM PREVIOUS YR.

~ INDICATOR REPEATED FROM PREVIOUS YR. * INDICATOR REPEATED DURING SAME YEAR + PARTIAL INDICATOR

STANDARDS (Benchmarks) Data Analysis and Probability · Statistical Methods (B) 6. Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation. Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population. Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations. Describe, create and analyze a sample space and use it to calculate probability. Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events. INDICATORS

VOCABULARY / RESOURCES

ASSESSMENT

4th NINE WEEKS (Possible if time permits)

(B)

5.

·

Probability (H) 7.

(A) (D)

8. 9.

(E)

10. Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.

Warren City Schools (WCS)

Department of Teaching & Learning

9

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