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User Manual
2014-2015 Guide for Teachers
1
What is SAILS
“Seamless Alignment and Integrated Learning Support: A High School/
Community College Collaboration”
SAILS Background
Movie 1.1 Intro to SAILS
SAILS (Seamless Alignment and Integrated
money while accelerating their path to
Learning Support) introduces the college
graduation.
developmental math curriculum in the high
school senior year. By embedding the Tennessee Board of Regents (TBR) Learning Support Math program in the
high school Bridge Math course, students
can get a head start on their college career. Students who successfully complete the program are ready to take a
college math course, saving them time and
Students who take the ACT their junior
year and score less than a 19 in Math are
required to take the Bridge Math course
their senior year. In SAILS, these students
can complete the college Learning Support Math program, preparing them for
a college-level math course, which will
give them a jump-start on their college career.
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Overview
Advantages to Students
Trying Something New
In a SAILS classroom, students who have
Students who have struggled in the struggled in math can become successful.
traditional lecture format of the high school
The program blends online instruction with
math class will enjoy SAILS, which individual assistance to give students the
introduces blended learning, a help they need. Students in SAILS save
combination of online instruction and both time and money, gaining up to three
individual assistance. By trying a new semesters and saving $1,500 in college approach, students who have struggled in
tuition. Students completing the program
math can now succeed.
in the fall are eligible to take a college-level
math class in spring and may qualify for
Dual Enrollment Grant funds.
Impact
Goal: Graduation
SAILS has already been piloted at four
community colleges with fifteen of their Studies have shown that giving students a
local high schools and involving over 500
head start in college increases both students. Based on these results, we enrollment and graduation rates. Currently,
expect approximately 90 percent of the dual enrollment programs are available for
students to save at least one semester in
the best students to start their college college, 60 percent to have two semesters,
career early, but SAILS expands these and 25 percent to save three semesters.
opportunities to all students.
The students who save two semesters
The Time is Right
have completed the program and are ready
for college math, while students saving
three semesters have finished a Several initiatives in Tennessee have the
college-level math course as well. If spread
goal of increasing college graduation rates,
throughout Tennessee, SAILS could including the College Complete Act and
positively impact over 40,000 students
the Tennessee Diploma Project. By having
each year!
TBR community colleges partner with their
local high schools, SAILS can help Tennessee achieve its educational goals.
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High Schools
As a high school who offers the bridge
math class to seniors, you can participate
in the SAILS program by partnering with
the Tennessee community college in your
area. By blending the bridge math standards and the college Learning Support Math competencies, public
school systems can now help prepare seniors for college-level math. You will be
able to track students’ progress on a daily
basis and offer on-ground support through
your regular bridge math teacher who will facilitate the class. The high schools exercise complete control over the enrollment and daily operations of the
class while benefiting from the blended curriculum and support from your community college.
Parents and Students
If you are a rising senior who is not yet
teacher/facilitator, a coordinator, and the
community college faculty and administration. This program is totally free
and will save you time and money in your
college studies. You may also elect to take
ready for college-level math (scored <19
an actual college-level math class in the
on ACT math subtest), you now have a
spring semester after completing your
great opportunity to eliminate the need for
Learning Support Math in the fall.
remedial math when you go to college! The
SAILS model will allow you to master the
Each student who completes the SAILS
math competencies needed to be Learning Support program will receive a
successful in college math while at the
certificate This certificate is your ticket to
same time earning your high school bridge
college-level math when you enroll in a
math credit required for graduation. You’ll
TBR college or university!
be working in a computer lab in your high
school with the support of your HS
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Community Colleges
The Tennessee community colleges are the backbone of the SAILS initiative. Each
community college will support the high schools in its service region with the implementation of the program. SAILS’ most critical element is the college-high
school partnership…this synergy is where SAILS will get its ‘wind.’ The student support network includes both the college and high school faculty members who will
be working together to ensure student progress, learning, and success, as well as
the coordinator who provides technical, content, and logistical support to both the
college and the HS team members. Teamwork is the foundation of SAILS, and by having professionals from the community colleges and the high schools work together, the project will benefit thousands of students in Tennessee.
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2
The SAILS Model
“Seamless Alignment and Integrated Learning Support: A High School/
Community College Collaboration”
SAILS Model
Community College
High School
Field Coordinator
Teacher/Facilitator
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The SAILS Model
Classroom
*At least 50% of class time must be in computer lab.
*Students work on course software and receive individual assistance from HS
teachers.
*Students complete Learning Support
Math competencies as part of their HS
Ways to Fail
*Students NOT On Task
*Teachers NOT Engaged
*Negative Attitude
*NOT giving students information *Lack of Teamwork
Bridge Math course.
What Does it Look Like
*Student work is banked at local *Instruction on daily topics community college, saving them tuition
*Lab practice (homework)
and giving them a head start in college.
*Quizzes online
*Tests online
Teamwork
Helpful Hints
*High school teachers work with SAILS
Field Coordinators to ensure proper and
*Set Weekly Benchmarks
successful implementation and minimize
*Weekly updates to school grade book
road bumps.
*Student Tracking Log
*Encourage student collaboration in lab
Keys to Success
*NO Calculator usage on Unit 1
(if applicable)
*Students On Task
*Only ONE attempt at a Pre-Test
*Provide Individualized Assistance *Positive Attitude
*Selling SAILS
*Teamwork
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My Labs Plus
“Seamless Alignment and Integrated Learning Support: A High School/
Community College Collaboration”
MyLabsPlus
http://sailstn.mylabsplus.com
Logging In
Use Google Chrome! When logging in, make sure your username is correct, caps lock is
not on, keep trying, and if it doesn’t work on 1 computer try on another. Don’t take your
students’ word for it that they can’t log in- try with them and make sure their username
and password is correct (last name student ID- password is name of the college usually)
Student Example: Username-Smith12345 Password-Chattstate
*Field Coordinators must give the spreadsheet of usernames and passwords to the teachers
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MyLabsPlus
Assignment Manager
*Use Assignment Manager to change password and number of attempts
*MAKE THE PASSWORD DIFFICULT!
*DO NOT change the pre-requisites or the name of a test
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MyLabsPlus
Gradebook
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MyLabsPlus
Gradebook
*Students won’t appear in the gradebook until they have logged in and made progress
*If you have more than 1 section, students must log into every section (Roane and Northeast)
*Check your enrollment number in the grade book- It must match the following items:
!
!
*Teacher Roster
!
!
*Admin Tools
!
!
*State Report
!
!Click here to view all
gradebooks
Click here for more
gradebook tools
Quick and easy way to
check for progress
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MyLabsPlus
More Gradebook Tools
Where College ID Numbers are housed
Grant student access to
test if student requires additional time
Refer to Page 21
Change from points to percentage
and current to cumulative average
Quick and easy way to
view by class, homework,
quizzes or tests.
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MyLabsPlus
*Look at each students’ profile and check for daily progress
Watch for Dates and
View By Student
Make sure percentage
Times of tests-Must be
is passing
during school hours
Teachers can click review
to view any test or assignment
*UNBLOCK popups
FC or teacher can change
student score WITH FC approval
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MyLabsPlus
Grade book Helpful Hints
*Check grade books AT LEAST once a week and before every school visit
*Do not let your students skip around
*Check with your community college for expected passing scores for homework, quizzes,
and tests
*Passing a test is what banks competencies
* Students should be making daily progress
* Schools with slow progress must be visited frequently
* If you see a STAR* next to a grade this indicates a changed grade-Teachers should notify
Field Coordinators prior to changing and to gain approval
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MyLabsPlus
Instructor Resources
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Instructor Resources
Academic Integrity
The importance of protecting our academic integrity is paramount. You are an advocate and
representative for your community college in this regard whether you like it or not. We
stress that teachers should pick up the keyboard to type in the password, but some teachers get lazy and think there’s another way, but there is not. We actually have teachers
who are no longer working with their school because they violated our academic integrity
by giving students the password. WE WILL FIND OUT IF THIS HAPPENS, and this is a
strike one of two kind of deal.
Click here for Academic Integrity Contract- Must be printed, filled out, and returned to Lead
Field Coordinator
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MyLabsPlus Contact Information
MyLabsPlus Client Services
*Rhea Jost
*[email protected]
Student Tech Support
*http://247.pearsoned.com
*Chat and email (24/7) ◦ 800-677-6337
*Monday – Friday 12:00 pm – 8:00pm EDT
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4
Beyond SAILS
“Seamless Alignment and Integrated Learning Support: A High School/
Community College Collaboration”
Early College Bridging the Gap
Advantages to Students
Students who complete SAILS in the fall semester are eligible to take an early college math class in the spring, and can receive the Dual Enrollment Grant to help with
their tuition.
Dual Enrollment
Dual Enrollment is the enrollment of a high school student in one or more specified college
courses for which the student will be awarded both high school and college credit. High
school students can take college courses at their high school (where available), on any
TBR campus, or online. Courses will not be expected to count toward the student’s high
school diploma unless the student has made prior arrangement with the high school, umbrella school and/or local board of education. The student is responsible for obtaining
verification of transfer credit to their chosen university.
To enroll in the Dual Enrollment program applicants must:
1.
Be a junior or senior in high school.
2.
Have a minimum sub-score of 19 on the ACT in math and reading and a sub-score of 18 on the English portion.
3.
Meet all prerequisites of the course or courses in which they wish to enroll.
4.
Have written permission from their high school principals and parents or guardians.
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Registering for College
Student College ID Numbers
Students registering for college must provide their student college ID number AND SAILS completion certificate upon registration and/or scheduling classes.
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5
Guidelines and
Standards
“Seamless Alignment and Integrated Learning Support: A High School/
Community College Collaboration”
Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
In alignment with the Developmental Studies Program for Mathematics (DSPM) outcomes, the curriculum standards have been organized into groups of mathematical skills. Certain mathematical skills are required in order to prepare a
DSPM student for college level mathematics courses. However, these particular
skills should be developed in an environment that promotes learning beyond skill
and drill techniques. These new skills should be introduced in conjunction with appropriate mathematical concepts and should be related to previous learning. Applications of these skills should play a principal role in the learning and assessment process. Technology should be used to strategically enhance the student’s understanding of core concepts via the use of multiple problem solving
strategies.
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Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
I. Ways of Looking: Revisiting Concepts
Students learn mathematics best by being introduced to concepts that they have previously studied in a new approach. The concepts in this section appear in a manner that emphasizes their basic definition. This presentation of each concept is based
upon the format that would be a “best practice” of introducing the particular concept.
3181.1.1 Diagrammatic Mathematics
*3181.1.1.1 Identify the graph of a linear inequality on the number line.
*3181.1.1.2 Create and use absolute value functions to model and solve *3181.1.1.3 Given an equation of a line, write an accurate definition of a line
by determining the unique characteristics that define it (i.e. slope and intercepts). *3181.1.1.4 Compute the perimeter of simple composite geometric figures with
*3181.1.1.5 Apply a variety of strategies to determine the circumference and *3181.1.1.6 Investigate the area of a sector and the arc length of a circle. problems in common settings. unknown side lengths. the area for circles. 26
Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
I. Ways of Looking: Revisiting Concepts
3181.1.2 Verbal Mathematics *3181.1.2.1 Understand that a line parallel to one side of a triangle divides the
*3181.1.2.2 Apply similar triangles to solve problems, such as finding heights
*3181.1.2.3 Use several angle properties to find an unknown angle measure (i.e. supplementary, complementary, vertical, angles along a transversal, and
sum of angles in a polygon). *3181.1.2.4 Describe, compare, and contrast plane and solid figures using their *3181.1.2.5 Multiply, divide and simplify radicals. *3181.1.2.6 Use mathematical grammar and appropriate mathematical symbols
other two proportionally, and conversely. and distances. attributes. to represent contextual situations.
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Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
I. Ways of Looking: Revisiting Concepts
3181.1.3 Symbolic Mathematics *3181.1.3.1 Operations with numbers expressed in scientific notation. *3181.1.3.2 Develop a thorough understanding of both rational and irrational numbers: make both historical and concrete connections between irrational numbers and the real world. *3181.1.3.3 Use mathematical symbols and variables to express a relationship
*3181.1.3.4 Model a variety of problem situations with expressions. *3181.1.3.5 Skillfully manipulate formulas involving exponents. *3181.1.3.6 Understand how mathematical properties yield equivalent
equations and can be used in determining if two expressions are equivalent. *3181.1.3.7 Perform polynomial arithmetic, including addition, subtraction,
*3181.1.3.8 Demonstrate fluency with techniques needed to simplify radical expressions and calculate with them, including addition, subtraction, and
multiplication. *3181.1.3.9 Rationalize denominators in order to perform division with radicals.
between quantities. multiplying, dividing, factoring, and simplifying results. 28
Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
I. Ways of Looking: Revisiting Concepts
3181.1.4 Graphic Mathematics *3181.1.4.1 Understand that a linear function models a situation in which a quantity
*3181.1.4.2 Graph quadratic equations and identify key characteristics of the *3181.1.4.3 Find the solution of a quadratic equation and/or zeros of a quadratic *3181.1.4.4 Operate (add, subtract, multiply, and divide) with and evaluate rational *3181.1.4.5 Operate (add, subtract, multiply, divide, simplify, powers) with radicals
and radical expressions including radicands involving rational numbers
and algebraic expressions. *3181.1.4.6 Identify and calculate the measures of central tendency and spread in a
*3181.1.4.7 Understand the correlation coefficient and its role in measuring the *3181.1.4.8 Analyze data to make predictions based on an understanding of the data
set, for example, use a scatter-plot to determine if a linear relationship exists and describe the association between the variables.
*3181.1.4.9 Use algebra and geometry to solve problems involving midpoints and changes at a constant rate, m, relative to another. function. function. expressions. set of data. goodness of fit for a model for a data set.
distances (i.e. geometric figures).
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Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
I. Ways of Looking: Revisiting Concepts
3181.1.5 Numeric Mathematics
*3181.1.5.1 Understand that there are numbers that are not rational numbers, called
irrational numbers, e.g., π, e, and √2, which together with the rational numbers form the real number system that satisfies the laws of arithmetic.
*3181.1.5.2 Apply and use elementary number concepts and number properties to
*3181.1.5.3 Determine if a data set represents a line through numerically analyzing
*3181.1.5.4 Find the probability of simple events, disjoint events, compound events,
and independent events in a variety of settings using a variety of counting
techniques. *3181.1.5.5 Develop fluency with the basic operations of complex numbers.
model and solve non-routine problems that involve new ideas. slope calculations. If appropriate, interpret the slope in terms of a rate. 30
Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
II. Making Connections Making connections allows those concepts that need a more complex look to be studied through two different modalities. This allows connections to be made between the
concepts, and allows for a more in-depth understanding of the topics supporting the
foundation for problem solving application. In addition, building topics in this manner
helps students work problems of a higher depth of knowledge level. 3181.2.1 Symbolic & Diagrammatic Mathematics *3181.2.1.1 Use the laws of exponents to simplify and interpret expressions for exponential functions, recognizing positive rational exponents as indicating roots of the base and negative exponents as indicating the reciprocal of a power. *3181.2.1.2 Solve a linear inequality and provide an interpretation of the solution. *3181.2.1.3 Recognize special products and factors of polynomials to facilitate problem solving with polynomials; in particular, find the zeros of a quadratic polynomial. *3181.2.1.4 Investigate the properties of plane figures, developing precise mathematical descriptions of geometric shapes, both in the plane and in
space. *3181.2.1.5 Apply a variety of strategies using relationships between perimeter, area,
and volume to calculate desired measures in composite figures.
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Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
II. Making Connections
3181.2.2 Symbolic & Verbal Mathematics
*3181.2.2.1 Explain, solve, and/or draw conclusions for complex problems using *3181.2.2.2 Solve simple rational and radical equations in one variable, noting
*3181.2.2.3 Write ratios, proportions, and solve proportions in a contextual *3181.2.2.4 Solve literal equations for any variable; interpret the results based on
relationships and elementary number concepts.
and explaining extraneous solutions. setting for an unknown value. units.
3181.2.3 Symbolic & Numeric Mathematics *3181.2.3.1 In the context of exponential models, solve equations of the form a•bct = d where a, c, and d are specific numbers and the base b is
2, 10, or e. *3181.2.3.2 Use the rules of exponents to develop an understanding of the
*3181.2.3.3 Recognize functions as mappings of an independent variable into a
*3181.2.3.4 Evaluate polynomial and exponential functions that use function *3181.2.3.5 Recognize composite functions as an application of substitution
difference between the rational and real numbers. dependent variable. notation. and use this understanding to write expressions for and evaluate 32
Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
II. Making Connections
3181.2.4 Symbolic & Graphic Mathematics *3181.2.4.1 Graphically represent the solution to a linear equation and the solution to
*3181.2.4.2 Graphically represent the solution to a linear inequality and the solution to
*3181.2.4.3 Relate the basic definitions of the trigonometric ratios to the right triangle. *3181.2.4.4 Identify the graphs of basic trigonometric functions and shifts of those
*3181.2.4.5 Solve a simple system consisting of one linear equation and one quadratic equation in two variables; for example, find points of intersection between the line y = –3x and the circle x2 + y2 = 3. Illustrate
the solution graphically.
a system of linear equations in two variables. a system of linear inequalities in two variables. graphs. 33
Standards Alignment
Tennessee Math Standards
Approved July 30, 2010
Bridge Math Course # 3181
III. Applications: Ways of Looking at the World
3181.3.3 Applications with Functions
*3181.3.3.1 Solve problems involving applications of linear equations.
*3181.3.3.2 Solve problems involving direct and inverse variations, such as
*3181.3.3.3 Solve problems involving systems of equations such as mixture *3181.3.3.4 Solve problems involving quadratic equations such as area and
gravity; additionally examine the fact that quadratic functions have
maximum or minimum values and can be used to model problems
with optimum solutions. *3181.3.3.5 Solve problems involving radical equations, such as wind chill and
*3181.3.3.6 Solve problems involving rational equations such as work problems. *3181.3.3.7 Solve problems involving exponential applications such as half-life
frequency, interest, and pressure. problems. body mass index. and continuous interest.
3181.3.4 Applications with Data *3181.3.4.1 Solve problems involving constructing and interpreting pie charts. *3181.3.4.2 Solve problems that use the construction and interpretation of
Venn diagrams to analyze the attributes of a set of data, for example logic
and counting problems. *3181.3.4.3 Solve problems involving geometric probabilities.
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Standards Alignment
Bridge Standards Covered by
Mylabsplus Software
Unit 1
*Order of Operations and Whole Numbers
*Converting Decimals to Fractions *Problem Solving *Percent Notation *Simplifying Fractions – GCF and Factors *Percent and Decimal Conversions Method *Percent and Fraction Conversions *Multiplying Fractions *Percent Applications *Dividing Fractions *Finding Perimeter *Writing Fractions with an LCD *Finding Area *Adding and Subtracting Like Fractions *Finding Circumference *Adding and Subtracting Unlike Fractions
*Find Area of Circle *Changing a Mixed Number to an Improper
*U.S. Length Fraction *U.S. Weight and Capacity *Introduction to Real Numbers *Metric Length *Graphing Rational Numbers Using a *Metric Mass and Capacity Number Line *Converting between U.S. and Metric Units
*Finding the Absolute Value of a Real *Finding Volume
Number *Adding Real Numbers with the Same Sign Unit 3
*Adding Real Numbers with Different Signs
*Introduction to Expressions *Subtracting Real Numbers *Evaluating Algebraic Expressions *Multiplying Real Numbers *Simplifying Expressions *Dividing Real Numbers *Simplifying Expressions with *Exponents and the Order of Operations
Parentheses Unit 2
*Translating Words into Symbols *The Distributive Property *Comparing Decimals *Introduction to Polynomials *Rounding Decimals *Addition of Polynomials *Converting Fractions to Decimals
*Subtraction of Polynomials
35
Standards Alignment
Bridge Standards Covered by
Mylabsplus Software
Cont. Unit 3
*Product Rule for Exponents *Square Roots *The Quotient Rule *Supplemental Lesson – Simplifying *Integer Exponents Radicals *Scientific Notation *The Pythagorean Theorem
*Power Rule for Exponents *Multiplying by a Monomial Unit 5
*Multiplying Binomials *Relations and Functions *Multiplying Polynomials
*Function Notation Unit 4
*Linear Equations and Solutions *Using the Addition Property of Equality *Using the Multiplication Property of *Equality *Using the Addition and Multiplication *Properties Together *Solving Equations with Variables on Both Sides *Solving Equations with Parentheses *Solving a Variety of Equations *Solving Equations and Formulas for a Variable *Solving and Graphing Linear Inequalities
*Proportions *Evaluating Functions *The Rectangular Coordinate System
*Graphing Linear Equations by Plotting Points *Graphing Linear Equations Using Intercepts *Graphing Linear Equations of the Form
x=a, y=b, and y=mx *Graphing Lines Using the Slope and y-Intercept *Slope of a Line and y-Intercept *Slope-Intercept Form *Writing Equations of Lines Using a Point
and Slope *Graphing Linear Inequalities in Two Variables
*Direct Variation *Applications of Direct Variation
36
Standards Alignment
Bridge Standards Covered by
Mylabsplus Software
Unit 6
Revisiting Concepts
*Mean *Operations on Radical Expressions *Median *Rationalize Denominators *Mode *Operations with Radical Expresions *Introduction to Systems of Linear *Identify and Calculate the Measures of
Equations Central Tendency and Spread *Solving by the Graphing Method *Solve Problems Involving Midpoints and
*Solving by Substitution Distance *Supplemental Lesson – Solving by *Operations with Rational Expressions
Linear Combinations *Supplemental Lesson – Solving by Cramer’s Rule *Basic Probability and Statistics *Factoring Polynomials using the GCF *Factoring by Grouping *Factoring Trinomials of the Form x2 + bx + c *Supplemental Lesson – Factoring Trinomials of the Form ax2 + bx + c *Special Cases of Factoring Making Connections
*Use the laws of Exponents to Simplify and Interpret Exponential Functions *Recognize Special Products *Use relationships between Perimeter,
Area, and Volume to Calculate Measures of Composite Figures *Solve Simple Rational and Radical Equations
*Solving Quadratic Equations by Factoring *Solving Quadratic Equations using the
Quadratic Formula *Applications of Quadratic Formula
37
Standards Alignment
Bridge Standards Covered by
Mylabsplus Software
Applications
*Surface Area and Volume of 3
Subtracting, Multiplying, and Dividing dimensional figures Rational Expressions.
*Direct and Inverse Variation *Solve Problems involving Exponential *Operate (add, subtract, multiply, divide,
Applications such as Half-life and simplify, powers) with radicals and radical
Continuous Interest expressions including radicands involving
*Construct and Interpret Pie Charts
rational numbers and algebraic expressions. Adding, Subtracting, Extra Materials also covered in Bridge
Multiplying and Dividing Radical Standards and Mylabsplus Software
Expressions.
State Standard Covered in Mylabsplus
*Identify and calculate the measures of *Demonstrate fluency with techniques
central tendency and spread in a set of
needed to simplify radical expressions data. Mean and Median.
and calculate with them, including addition, subtraction, and multiplication.
Adding, Subtracting, Multiplying and Dividing Radical Expressions.
*Rationalize denominators in order to perform division with radicals. Rationalizing the denominator.
*Use algebra and geometry to solve problems involving midpoints and distances (i.e. geometric figures) The Distance Formula
*Use the laws of exponents to simplify and interpret expressions for exponential functions, recognizing positive rational *Operate (add, subtract, multiply, and exponents as indicating roots of the base
divide) with and evaluate rational and negative exponents as indicating the
expressions. Simplifying, Adding,
reciprocal of a power. Simplifying Radicals
and Rational Exponents
38
Standards Alignment
Bridge Standards Covered by
Mylabsplus Software
Extra Materials also covered in Bridge
Standards and Mylabsplus Software
State Standard Covered in Mylabsplus
Cont.
*Recognize special products and factors of
polynomials to facilitate problem solving
with polynomials; in particular, find the zeros of a quadratic polynomial. Finding
Intercepts of a Quadratic Equation.
*Apply a variety of strategies using relationships between perimeter, area, and
volume to calculate desired measures in
composite figures. Finding Perimeter, Finding Area, and Finding Volume
*Solve simple rational and radical equations in one variable, noting and explaining extraneous solutions. Solving
Rational Equations.
*Apply special right-triangle properties and
the Pythagorean Theorem to solve congruent, similar shape, and contextual
problems. Pythagorean Theorem
*Understand and use basic counting techniques in contextual settings.
*Solve problems involving evaluation of exponential functions, for example applications involving a quadratic equation. Solving Radical Equations and
Solve by Factoring
*Solve problems involving surface areas
and volumes of 3-dimensional figures, including maximization, scale, and increment problems. Finding Area, Finding
Volume
*Solve problems involving direct and inverse variations, such as frequency, interest, and pressure. Direct Variation, Indirect Variations, and Applications
*Solve problems involving exponential applications such as half-life and continuous interest. Solving Radical Equations
*Solve problems involving constructing
and interpreting pie charts. Circle Graphs.
39
Standards Alignment
· *Solve a simple system of one linear Bridge Standards NOT equation and one quadratic equation in
Addressed by Mylabsplus
two variables; for example, find points of
intersection between the line y = -3x and
Software
the circle x2+y2=3.
*Investigate the area of a sector and the
*Use appropriate technology to find the
arc length of a circle.
mathematical model for a set of non-linear
data.
*Understand that a line parallel to one side
of a triangle divides the other two *Use counting techniques to calculate
proportionally and conversely.
probabilities for conditional and independent events.
*Use several angle properties to find an unknown angle measure (supplementary,
*Compare a theoretical probability model complementary, vertical, angles along a
to an experimental probability model for
transversal, and sum of angles in a the same process.
polygon.
*Understand the correlation coefficient and
its role in measuring the goodness of fit
for a model for a set of data.
*Analyze data to make predictions based
on an understanding of the data set, for
example, use a scatter-plot to determine if *Solve problems involving angles of elevation and angles of declination.
*Solve problems involving radical equations, such as wind chill and body
mass index.
*Solve problems involving half-life.
a linear relationship exists and describe
*Solve problems that use the construction
the association between variables.
and interpretation of Venn diagrams to
*Relate the basic definitions of the trigonometric ratios to the right triangle.
*Identify graphs of basic trigonometric
functions and shifts of those graphs.
analyze the attributes of a set of data, for example logic and counting problems.
*Solve problems involving geometric probabilities.
40