LOUDOUN COUNTY PUBLIC SCHOOLS · 2016-11-27 · F. Bike Weights and Jump Heights: In BMX dirt-bike...

MATH CURRICULUM GUIDE

ALGEBRA I

LOUDOUN COUNTY PUBLIC SCHOOLS

LEESBURG, VIRGINIA

EDGAR B. HATRICK, ED.D. NED D. WATERHOUSESUPERINTENDENT OF SCHOOLS DEPUTY SUPERINTENDENT

SHARON D. ACKERMAN PETER R. HUGHESASST. SUPERINTENDENT DIRECTOR CURRICULUM AND INSTRUCTION CURRICULUM AND INSTRUCTION

CHERYL A. WIMERINSTRUCTIONAL SUPERVISOR – MATH

OCTOBER 2002

Mathematics Internet Safety Procedures

1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information.

2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites.

3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages.

4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.

ALGEBRA I CURRICULUM GUIDE 2002-2003

Page 1 of 30

A.1 The student will solve multi-step linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable and apply these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions.

OBJECTIVE: The student will be able to solve multi-step linear equations and inequalities in one variable.

SCOPE & SEQUENCE:

a. Solve multi-step linear equations by using: commutative properties associative properties distributive property order of operations addition and multiplication properties of equality closure property identity and inverse properties reflexive, symmetric and transitive properties of equality substitution property of equality.

b. Solve multi-step linear inequalities justify solution steps using properties of real numbers and order

c. Solve literal equations (formulas) and implicit equations for specified variable.

d. Apply to practical problems; e.g., Solve V = r 2 h 3

e. Confirm solutions on the graphing calculator

In an implicit equation, graph each side of the equation separately but on the same set ofaxes and find the coordinates of the point of intersection.

In an explicit equation, graph the equation and find the x-intercept.

f. Graph solution to a linear inequality in the coordinate plane Graph manually and confirm with technology

COMMENTS/NOTES:

1. Solution sets should include positive and negative values as well as basic fractions anddecimals

2. Include fractional and decimal coefficients in equations and inequalities3. Students should be assessed on showing procedure; i.e., steps in solution, in addition to

correct answer


Page 2 of 30

A.1 continued

SAMPLE RESOURCES:

Mathematics SOL Curriculum Frameworkhttp://www.pen.k12.va.us/VDOE/Instruction/Math/math_framework.html

SOL Test Blueprints

SOL Test Released Items

Virginia Algebra Resource Center

http://curry.edschool.virginia.edu/k12/algebra

NASA http://spacelink.nasa.gov/.index.html

The Math Forum http://forum.swarthmore.edu

4teachers http://www.4teachers.org

Appalachia Educational Laboratory (AEL)

http://www.ael.org/pnp/index.htm

Eisenhower National Clearinghouse

http://www.enc.org/

Algebra Instructional Modules: Solvingequations in One Variable p.1

SAMPLE ASSESSMENTS:

1. Graph linear equations.

A. Solve: -3 (x+2) = 4x -13

B. Solve and graph: -6x – 16 30

C. Solve for L: P = 2L + 2W

D. Express in symbols: Five more than twice a number is 9

E. The length of a rectangular garden is 3 more than twice its width. The perimeter is 42.

Find the dimension of the garden.

F. Three of Mary’s test scores are 82, 83 and 87. What score must she receive on the fourth

test to have an average of at least 85 for all the tests?


Page 3 of 30

A.2 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables. Students will choose an appropriate computational technique, such as mental mathematics, calculator, or paper and pencil.

OBJECTIVE: The student will be able to translate and evaluate verbal and algebraic expression.

SCOPE & SEQUENCE:

a. Translate verbal statements into mathematical ones stress relationship terminology; e.g., less than, at least, more than, is less than,

difference, sum, product, quotient, at most

b. Use algebraic expressions to describe mathematical relationships

c. Evaluate algebraic expressions for a given replacement set using order of operations. emphasize order of operation using manual computation

SAMPLE RESOURCES:


SOL Test Blueprints










http://www.enc.org/

SAMPLE ASSESSMENTS:

A. Evaluate: 3y + 2 (x - 4y) + 3 for x = 2 and y = 32


Page 4 of 30

A.3 The student will justify steps used in simplifying expressions and solving equations and inequalities. Justifications will include the use of concrete objects; pictorial representations; and the properties of real numbers, equality, and inequality.

OBJECTIVE: The student will be able to justify steps in simplifying expressions and solving equations and inequalities.

SCOPE & SEQUENCE:

a. Use the properties listed to justify steps in solving multi-step equations. commutative properties associative properties distributive property order of operations addition and multiplication properties of equality closure property identify and inverse properties reflexive, symmetric and transitive properties of equality substitution property of equality.

b. Justify steps in solving linear inequalities using properties of real numbers and order.c. Create and interpret pictorial and concrete representations and justifications for solving

equations.

SAMPLE RESOURCES: Mathematics SOL Curriculum Framework

http://www.pen.k12.va.us/VDOE/Instruction/Math/math_framework.html

SOL Test Blueprints









SAMPLE ASSESSMENTS:

A. Identify the property of the real numbers illustrated in the example. 6 (a+7) = 6 a + 6 7

B. Solve and justify each step. 3 (x + 4) = -2(3x - 5)

C. Show the physical setup and pictorial representation of: 4x + 5 = 2x + 13


Page 5 of 30

A.4 The student will use matrices to organize and manipulate data, including matrix addition, subtraction, and scalar multiplication. Data will arise from business, industrial, and consumer situations.

OBJECTIVE: The student will be able to use matrices.

SCOPE & SEQUENCE:

a. Define a matrix: include dimensions (rows, columns), element, location

b. Add and subtract matricesc. Multiply a matrix by a scalar factord. Use matrices to organize and interpret data arising from applications in business, industry

and consumerism.e. Represent a system of linear equations as a matrix.f. Require students to perform all operations manually prior to confirmation using the

calculator.g. Include fractions and decimals as the scalar multiplier and elements.

SAMPLE RESOURCES:

Algebra Instructional Modules:

- Linear REAL Problems p. 24

- Matrices p.72

- Matrices and the Square Patio p.75







http://www.enc.org/

SAMPLE ASSESSMENTS:

A. Find the resulting matrix:21

213394035.02

B. Table A represents a store’s current inventory. Table B represents a new shipment. Use matrices to find how many gray pleated pants does Ralph’s Men’s store have in stock

after the shipment?

A. Blue Gray Brown Khaki B. Blue Gray Brown Khaki

Plain 28 32 10 37 Plain 10 5 20 25 Pleated 25 20 8 4 Pleated 14 15 15 30 Cuffed 10 7 5 1 Cuffed 0 5 0 5


Page 6 of 30

Weight(pounds)

Height(inches)

19.0 10.3519.5 10.3020.0 10.2520.5 10.2021.0 10.1022.0 9.8522.5 9.8023.0 9.7923.5 9.7024.0 9.60

A.5 The student will create and use tabular, symbolic, graphical, verbal, and physicalrepresentations to analyze a given set of data for the existence of a pattern, determine the domain and range of relations, and identify the relations that are functions.

OBJECTIVE: The student will be able to create and interpret multiple representations of data.

SCOPE & SEQUENCE:

a. Recognize a pattern in a data set: represent the pattern symbolically (algebraically) represent pattern graphically develop the laws of exponents using pattern recognition reinforce special number sets; e.g., perfect squares, cubic numbers, using patterns use Alge-Blocks and Algebra Tiles as pictorial representations of polynomials

– combine like terms– add, subtract and multiply– factor

b. Determine the domain and range of relationsc. Define relations and functionsd. Differentiate between relations and function

SAMPLE RESOURCES: Algeblocks Algebra Tiles

SAMPLE ASSESSMENTS:

A. Draw the graph and find the domain for the set of ordered pairs:{(0,2) (1,2) (2,4) (3,6)}

B. Find the range for the set of ordered pairs:{(0,1) (1,2) (2,4) (3,6)}

C. Is this relation a function?{(0,2) (1,2) (2,4) (3,6)}

D. Apply the vertical line test to determine if the graph is afunction.

E. Graph the set of ordered pairs and determine if the relation is afunction:

{ (1,2), (2,4), (3,6), (4,8), (5,10) }

F. Bike Weights and Jump Heights: In BMX dirt-bike racing,jumping or “getting air” depends on many factors: the rider’sskill, the angle of the jump, and the weight of the bike. Here aredata about the maximum height for various bike weights. Plot(weight, height).1. If the data are linear, draw a trend or best-fit line.2. Is there positive, negative, or no association between bike


Page 7 of 30

weigh and jump height? Explain your answer.3. As the weight increases, the height ___________________?4. Find the slope or rate of change. What does this mean in words?5. Predict the maximum height for a bike that weighs 21.5 pound if all other factors are

held constant?


Page 8 of 30

A.6 The student will select, justify, and apply an appropriate technique to graph linear functions and linear inequalities in two variables. Techniques will include slope-intercept, x- and y-intercepts, graphing by transformation, and the use of the graphing calculator.

OBJECTIVE: The student will be able to graph linear functions and inequalities in two variables.

SCOPE & SEQUENCE:

a. Given the equation of a line, graph: using transformations using the slope and y-intercept using the x-intercept and y-intercept

b. Solve for the dependent variable in a function to graph manually using slope-intercept andcalculator methods

c. Using the line y = x as a reference, generalize the effect of changes in the equation on thegraph of the line. Use the graphing calculator to facilitate development of this concept. emphasize changes in slope and y-intercept on the graph include positive and negative values

d. Characterize the changes in the graph of the line as translations, reflections and dilationse. Graph an inequality in two variables.

emphasize significance of dashed versus solid line on graph as well as shading confirm solution using ordered pair not on the line use (0,0) when appropriate.

SAMPLE RESOURCES:


SOL Test Blueprints










http://www.enc.org/

SAMPLE ASSESSMENTS:

1. Graph a line given the point and the slope2. Solve and graph linear inequalities3. Graph horizontal and vertical lines by recognizing their equations. A. Graph –2x - y = 1 using each of the following methods:

slope interceptx & y interceptsand T-table

B. Solve and graph y 3x + 5


Page 9 of 30

A.7 The student will determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined. The graphing calculator will be used to investigate the effect of changes in the slope on the graph of the line.

OBJECTIVE: The student will be able to determine and interpret the slope of a line.

SCOPE & SEQUENCE:

a. Describe slope as a constant rate of change: use real life examples; e.g., miles per gallon, wages per hour

b. Recognize and describe a line with a slope that is positive, negative or zero. horizontal line has a slope of zero

c. Recognize and describe a line with a slope that is undefined. stress the term “undefined.” Do not use “no slope.” emphasize that a vertical line has an undefined slope

d. Calculate the slope of a line given: the coordinates of two points on the line the equation of the line the graph of the line

e. Use the graphing calculator to facilitate development of this concept.

COMMENTS/NOTES:

1. Have students memorize the slope formula.

SAMPLE ASSESSMENTS:

1. Recognize the relationship between slopes of parallel and perpendicular lines

A. Find the slope given the linear equation y - 2x = 4

B. Find the slope of the line in the graph.

C. Find the slope of the line through the points (2, 4)

and (3, 1)

D. Using the graphing calculator, graph: 3x + 2y = 10 5x + y = 3 6x + y = 10 What do you notice about these lines – similarities, differences?

E. Graph: -3x + 2y = 10-5x + y = 3-6x + y = 10

What can you conclude about the slope of a line and the direction of the line?


Page 10 of 30

A.8 The student will write an equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

OBJECTIVE: The student will be able to write a linear equation.

SCOPE & SEQUENCE:

a. Write the equation of a line given: the coordinates of two points on the line.– when given two points, use the slope formula to find the slope and then use the point-

slope formula to write the equation. the slope and the y-intercept of the line one point on a vertical line– emphasize x = a form

one point on a horizontal line– emphasize y = b form

the graph of the line.

b. Use the following linear equation forms: Slope intercept: y = mx + b Point-slope: y – y1 = m (x - x1) Standard: Ax + By = C ( A, B & C are integers. A & B not both = 0 )

SAMPLE RESOURCES:

Algebra Instructional Modules:– Investigating Transformations p.5– Math the Equation, Graph and Table p. 16– Equation of a line from a Graph p.21

COMMENTS/NOTES:

1. Have students memorize all linear equation forms above.

SAMPLE ASSESSMENTS:

1. Write the equation of a line parallel or perpendicular to a given line and passing through aspecific point.

2. Write linear equations in both standard and slope intercept form.A. Find the equation of the line through the point (5, 2) and (6, 4)B. Find the equation of the line with a slope of –5 and passing through the point (0, 7).C. Write the equation of a line parallel to 2x + 3y = 7 and write the equation of a line perpendicular to 2x + 3y = 7


Page 11 of 30

A.9 The student will solve systems of two linear equations in two variables both algebraically and graphically and apply these techniques to solve practical problems.Graphing calculators will be used both as a primary tool for solution and to confirm an algebraic solution.

OBJECTIVE: The student will be able to solve systems of two linear equations in two variables.

SCOPE & SEQUENCE:

a. Solve using graphical techniques: graph the equations on the same set of axes and find the coordinates of the point of

intersection. determine if a system of linear equations has one solution, no solution or infinitely many

solutions interpret the number of solutions to a system of equations in terms of the graph of the

system and the geometry of the lines

b. Solve using algebraic techniques: substitution linear combinations, also termed “elimination” -using addition/subtraction and multiplication where appropriate

determine if a system of linear equations has one solution, no solution or infinitely manysolutions.

find the ordered pair that satisfies both equations simultaneously and solves thesystem.

-check the solution set in both equations.

c. Interpret the solution to a system of equations that describes a practical situation in terms ofthe practical situation. decide if the solution to a system of equations is reasonable.

SAMPLE RESOURCES:


SOL Test Blueprints










http://www.enc.org/


Page 12 of 30

A.9 continued

SAMPLE ASSESSMENTS:

1. Systems must include one, no or many solutions (T, F)2. Solve systems of two linear equations with rational co-efficients using graphing, elimination and

substitutionA. Solve 2x + 2y = 4

5x – 3y = 10

B. Solve y = 3x + 42x - y = 24

C. Write a system to solve:

If two adults and three children’s tickets cost $17.00 and tickets for three adults andone child cost $15.00, then what is the cost of an adult ticket?


Page 13 of 30

A.10 The student will apply the laws of exponents to perform operations on expressions with integral exponents, using scientific notation when appropriate.

OBJECTIVE: The student will be able to apply the laws of exponents.

SCOPE & SEQUENCE:

a. Develop the laws of exponents using: graphing calculator pattern recognition manipulatives

b. Include integer exponents; i.e., positive, negative and zero.c. Use scientific notation as an application

express very large number and very small numbers using scientific notations add, subtract, multiply and divide numbers written in scientific notation.

SAMPLE RESOURCES:


SOL Test Blueprints


Virginia Algebra Resource Center http://curry.edschool.virginia.edu/k12/algebra

SAMPLE ASSESSMENTS:

A. Simplify: (2x2) (3x3)

B. Simplify: 843

325

zyxzyx

C. Simplify: (32

x5)2

D. Express in scientific notation 316.51

E. Simplify: (3x 5) (2x 2)

F. Simplify: 3x 5 + 2x 2


Page 14 of 30

A.11 The student will add, subtract, and multiply polynomials and divide polynomials with monomial divisors, using concrete objects, pictorial and area representations, and algebraic manipulations.

OBJECTIVE: The student will be able to perform operations on polynomials and identify and use terminology associated with polynomials.

SCOPE & SEQUENCE:

a. Identify the base, exponent and coefficient of a monomial.b. Recognize polynomials and classify them according to the number of terms they have or

the degree of the polynomial. emphasize terminology– number of terms: monomial, binomial, trinomial, polynomial– degree of term; e.g., x2y is degree of 3– degree of polynomial; e.g., 5x – 3x2 + 7 is degree of 2– order: descending, ascending by specified variable– constant: degree of zero; e.g., 3 = 3xo

– lead coefficient: coefficient of highest degree term

c. Perform operations on polynomials add, subtract and multiply polynomials of multiple terms

– emphasize binomial square pattern divide polynomials using monomial and binomial divisors simplify expressions involving polynomials. use algebra manipulatives to develop strategies for adding, subtracting, multiplying and

dividing polynomials.

COMMENTS/NOTES:

1. Polynomials must have terms of whole number degrees, not negative or fractionalexponents.

SAMPLE RESOURCES:




Appalachia Educational Laboratory (AEL) http://www.ael.org/pnp/index.htm

Eisenhower National Clearinghouse http://www.enc.org/

Algebra Instructional Modules: Factoring p. 46


Page 15 of 30

A.11 continued

SAMPLE ASSESSMENTS:

1. Simplify polynomial and rational expressions

A. Add: (3x2 + 2x + 5) + (7x2 - x - 4)

B. Subtract: (5x3 + 2x - 3) – (x3 - 4x2 - x - 1)

C. Multiply: 3x2y (2x + 5y)

D. Multiply: (2x + 7) (x - 4)

E. Multiply: (3x + 1)2

F. Divide:xy

xyxyx2

624 23

G. 32

xx

+ 158

52 xxx

H. x

x3

3 - 12

62 xxx

I. 32

52

34

bayx

53

73

126

yxba

J. (2x – 3y) (2x + 3y)


Page 16 of 30

A.12 The student will factor completely first- and second-degree binomials and trinomials in one or two variables. The graphing calculator will be used as a tool for factoring and for confirming algebraic factorizations.

OBJECTIVE: The student will be able to factor polynomials.

SCOPE & SEQUENCE:

a. First, Identify GCF (greatest common factor) for a given polynomial relate to the distributive property

b. Identify patterns difference of two squares: a2 – b2

perfect square trinomial: a2 + 2ab + b2, a2 – 2ab + b2

factoring by grouping:ax + ay – bx – by = a (x + y) – b (x + y) = (a – b) (x + y)

SAMPLE RESOURCES:






Algebra Instructional Modules: Factoring p. 46

SAMPLE ASSESSMENTS:

A. Factor completely: 9x4y + 6x2y2

B. Factor completely: 4x2 - 9

C. Factor completely: 2x2 + 17x + 30

D. Factor completely: 3x4 – 243 and use your graphing calculator to confirm results.

E. Factor by grouping: 8m2n – 5m – 24mm + 15


Page 17 of 30

A.13 The student will express the square root of a whole number in simplest radical form and approximate square roots to the nearest tenth.

OBJECTIVE: The student will be able to evaluate square roots.

SCOPE & SEQUENCE:

a. Memorize perfect squares through 202

b. Estimate the square root of a number to the nearest tenthc. Use a calculator to find decimal approximations of radical expressionsd. Use correct radical terminology.

radical symbol, radicand, index, principal square root3 64 =4 64 – radicand

3 – index 4 – root

e. Write the square root of a whole number in simplest radical form. apply properties of radicals

ab = a b a b + c b = (a + c) b

ba =

ba

rationalize the denominator

ba

bb

= bab

COMMENTS/NOTES:

1. Constant radicand 25 = 5 5 -- principal square root, constant radical yields a positive root only

2. Squared variable as radicand: x2 = 25

2x = 25

x = 5

x = + 5


Page 18 of 30

A.13 continued

SAMPLE RESOURCES:


SOL Test Blueprints


Virginia Algebra Resource Center http://curry.edschool.virginia.edu/k12/algebra






SAMPLE ASSESSMENTS:

A. Name the number systems that area subset of the real numbers and explain characteristics

that make them different.

B. Explain what steps are needed to simplify radical expressions.

C. Describe the process used to solve radical equations.

D. State the Pythagorean Theorem and write an application problem which uses it. Exchange

your problem with a partner and solve. Compare results when completed.

E. Simplify: 81

F. Simplify:94

G. Estimate 40 to the nearest tenth

H. Find 40 in simplified radical form

I. Simplify:23

J. Simplify:23

5

K. Simplify:yx

185

L. Simplify: 962 xx

M. Simplify: 72 + 402 + 32


Page 19 of 30

A.13 continued

N. Simplify: 7 +37

O. Simplify: 72 48

P. Simplify: 2 ( 18 + 4 3 )

Q. Simplify: ( 4 + 5 )2

R. Solve: 4 x + 17 = 10

S. Solve: x + 1 = 5

T. Solve: x4 - 3 = 6 – x

U. Solve: The person on third base fields the ball directly on the third base line

20 ft. beyond third base. How far must she throw the ball to reach

first base?


Page 20 of 30

A.14 The student will solve quadratic equations in one variable both algebraically and graphically. Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.

OBJECTIVE: The student will be able to solve quadratic equations.

SCOPE & SEQUENCE:

a. Solve quadratic equation algebraically factoring, using zero product property quadratic formula– Identify number and type of solutions using the discriminant

b. Relate the algebraic and graphical solutions emphasize equivalent terminology; i.e., zeros, roots, solution, x-intercepts given x-intercepts, write the equation in factored form confirm algebraic solutions with the graphing calculator

COMMENTS/NOTES:

1. See A.LC.3 for completing the square method2. Have students memorize the quadratic formula

solve quadratic equations graphically by using the graphing calculator and finding the x-intercepts of the graph.

SAMPLE RESOURCES:


– Investigating Transformations p. 5

– Match the Equation, Graph and Table p. 16

– Equation of a Line from a Graph p. 21

– Linear REAL Problems p.24

– Patterns p. 54

– Square Patio Patterns p. 56

– Line of Best Fit p. 79

– Inverse Variations p. 62

– Domain and Range p. 60

SAMPLE ASSESSMENTS:

A. Solve by factoring x2 + 2x – 8 = 0

B. Solve by taking the square root of both sides x2 – 5 = 0

C. Solve using the graphing calculator x2 – x – 12 = 0


Page 21 of 30

A.15 The student will, given a rule, find the values of a function for elements in its domain and locate the zeros of the function both algebraically and with a graphing calculator. The value of f(x) will be related to the ordinate on the graph.

OBJECTIVE: The student will be able to analyze functions.

SCOPE & SEQUENCE:

a. Identify domain and range for a linear relation when given: set of ordered pairs table of values mapping graph

b. Distinguish between a relation and function justify this classification using- set of ordered pairs- table of value- mapping- graph

c. For values of x in the domain of a function, find the associated values of f(x) in the range ofthe function.

d. Determine the domain and range of quadratic relations.

e. Use proper function notation; e.g., s(t) = 16t2 – 40t + 10; s(10) – use termsindependent/dependent variable, abscissa/ordinate, input/output

f. Recognize the value of f(x) as the ordinate on the graph

SAMPLE RESOURCES:


–Solving Quadratics Graphically p.38

–Domain and Range p. 60

SAMPLE ASSESSMENTS:

A. Given: f(x) = 7x + 3, find: f(-2)

B. Given; f(x) = x2 – x – 12, find: f(x)

C. Given: f(x) = x2 + 5x + 7, find: f(-3)


Page 22 of 30

A.16 The student will, given a set of data points, write an equation for a line of best fit and use the equation to make predictions.

OBJECTIVE: The student will be able to write and use an equation for a line of best fit.

SCOPE & SEQUENCE:

a. Given a set of data points in a table, on a graph, or from a practical problem, write the equationof a line of best fit.

use two data points to write the equation algebraically use the linear regression capabilities of the calculator to produce the line of best fit

b. Using the equation of the best fit line, make predictions about unknown outcomes given an independent variable value, predict the related dependent variable value

c. Given a scattterplot of the data points, determine the type of correlation; positive, negative,strong, weak or none.

SAMPLE RESOURCES:TBD

SAMPLE ASSESSMENTS:

A. Enter the following data into your graphing calculator, graph it and determine the best fitequations, interpolate to find x when y = 2. Extrapolate to find y when x = 10.

x y

-3

-2

-1

0

1

2

3

8

3

0

-1

0

3

8

y = _______

B. Find the median-median fit equation for the following set of data.

x -4 -3 -1 0 2 3 4 5 6y 5 3 0 2 8 6 10 12 11

C. Find the linear regression equation for the data in B.

Discuss the difference and which equation is a better fit.


Page 23 of 30

A.17 The student will compare and contrast multiple one-variable data sets, usingstatistical techniques that include measures of central tendency, range, and box-and-whisker graphs.

OBJECTIVE: The student will be able to analyze one-variable data set.

SCOPE & SEQUENCE:

a. Organize a set of datab. Calculate the mean, median, mode, range and upper and lower quartiles of a set of data.c. Use the calculated values for median, range and quartile to create box-and-whisker plotsd. Use terminology below:

measure of central tendency – mean, median, mode measures of variation – range, inter-quartile range

e. Compare and contrast multiple one-variable data sets using these statistical techniques.


SAMPLE ASSESSMENTS:

Use the following data to find the mean, median, mode and range. Make a box-and-whisker graph and make a stem and leaf plot.

Tio’s Grades: 83, 70, 92, 98, 97, 83, 88, 90

Chang’s Grades: 82, 90, 75, 65, 60, 100, 88, 99


Page 24 of 30

A.18 The student will analyze a relation to determine whether a direct variation exists andrepresent it algebraically and graphically, if possible.

OBJECTIVE: The student will be able to analyze a relation for direct variation.

SCOPE & SEQUENCE:

a. Recognize and describe direct variation from a graph or a table of values.b. Given a set of data, determine whether a direct relationship exists and write the equation for

the variation, if one exists.


SAMPLE ASSESSMENTS:

A. Does the equation y = 3x + 2 represent a direct variation? Why or why not? Is athunderstorm approaches, you see lightening as it occurs, but you hear the accompanyingsound of thunder a short time afterward. The distance y, in miles, that sound travels in tseconds is given by the equation: y = 5t

B. Estimate how long it will take you to hear the thunder from a storm that is 3 miles away.

t y

0

2


Page 25 of 30

*A.LC.1 The student will add, subtract, multiply and divide rational expressions. The student will solve proportions and simple rational equations.

OBJECTIVE: The student will be able to use rational expressions and equations.

SCOPE & SEQUENCE:

a. Solve proportions using cross multiplication (multiplying by least common denominator);

e.g.21x

= 35

; 21x

= 35

;

b. Apply operations to rational expressions multiply and divide add and subtract

c. Solve simple rational equations; e.g.

x1 +

32 =

25 ;

1057x

+23x

= 4

Check solution for extraneous solutions; note any domain restrictions (denominatorcannot = 0).


SAMPLE ASSESSMENTS:

A. Multiply:65107

2

2

xxxx

1529

2

2

xxx

B. Divide:652

2

2

xxxx ÷

12732

2

2

xxxx

C. Solve:21 +

x1 =

43 ; x 0

D. Solve:x3 -

x4 =

92 ; x 0

E. Solve:34 x =

2x

F. Solve:mm

12

+13

2mm = 1 ; m -1, 1


Page 26 of 30

*A.LC.2 The student will distinguish between rates and ratios; solve application problems involving percents, proportions, ratios and rates.

OBJECTIVE: The student will be able to applying ratios to problem solving.

SCOPE & SEQUENCE:

a. Distinguish between ratios and rates (ratio is dimensionless; rate requires units).b. Use percents to solve practical problemsc. Write and use proportions to solve practical problems


SAMPLE ASSESSMENTS:

A. Hecht’s having a Red Dot Sale with 50% off. If the original price of a jacket is $34.99, howmuch will it cost during the Red Dot Sale?

B. Is 10% off the sales price of 25% off, the same as 35% off the original price? Why or why not?

C. Write an example of a ratio. Write an example of a rate. Explain the difference between rateand ratio.

D. What is a proportion and how do you solve it?


Page 27 of 30

*A.LC.3 The student will solve basic quadratic equations by completing the square and applying the process to identify center and radius of a circle.

OBJECTIVE: The student will be able to solve a quadratic equation using complete-the-square.

SCOPE & SEQUENCE:

a. Solve quadratic equations by completing the square. ax2 + bx + c = 0, a = 1 & b is even integer

b. Use the circle formula as an application


SAMPLE ASSESSMENTS:

A. Solve by completing the square for: x2 + 6x + 4 = 0

B. Solve by completing the square for: x2 + 8x – 7 = 0

C. Solve by completing the square: x2 + 10 = -8xD. Solve by completing the square: x2 + 8x + 9 = 0

E. Complete the square for x and y to find the center and radius of a circle with equationx2 - 2x + y2 - 8y = 8


Page 28 of 30

*A.LC.4 The student will solve compound inequalities using appropriate terminology and symbols.

OBJECTIVE: The student will be able to solve compound inequalities.

SCOPE & SEQUENCE:

a. Use the following terminology and notation Conjunction , “and,” intersection, 3 x 7

Disjunction , V “or,” union, x < - 2 or x 3

b. Graph simple and compound equality statements on a number line (use open and closedcircles)

c. Solve compound inequalities algebraically

d. Emphasize solution sets as intervals; e.g., x > 7, o7


SAMPLE ASSESSMENTS:

A. Solve: 3x – 7 > 4 and 4x > -2

B. Solve: 3x – 7 > 4 or 4x > -2

C. Solve and graph the solution to 5x + 2< -8 and -6x + 4 > 1

D. Graph: x < -4 U x > 5

E. Graph: x > 2 x > -1

F. Graph: -4 < x < 7

G. Graph: x > -1 x < 4


Page 29 of 30

*A.LC.5 The student will solve basic absolute value inequalities and equations algebraically and graphically.

OBJECTIVE: The student will be able to solve absolute value inequalities and equations.

SCOPE & SEQUENCE:

a. Solve absolute value equations Emphasize there are, at most, two solutions; e.g., x – 4 = 3; x = 1 or x = 7 Graph solution set on number line

1 7

b. Solve absolute value inequalities emphasize that solution sets may be number intervals.

x - 4 > 3; x > 7 or x < 1 1 7

x - 4 < 3; 1 < x < 7 1 7

graph solution set on number line

COMMENTS/NOTES: d d

x – r = d |x1 r x2

d d

x – r > d |

x1 r x2

d d

x – r d |r

x


Page 30 of 30

A.LC.5 continued


SAMPLE ASSESSMENTS:

A. Solve: x – 2 > 4

B. Solve: x + 1 < 5

C. Solve and graph: x + 6 > 7

Solve and graph: x - 7 = 10

LOUDOUN COUNTY PUBLIC SCHOOLS · 2016-11-27 · F. Bike Weights and Jump Heights: In BMX dirt-bike...

Documents

Transcript of LOUDOUN COUNTY PUBLIC SCHOOLS · 2016-11-27 · F. Bike Weights and Jump Heights: In BMX dirt-bike...