PPortableortableAAssistedssistedSStudytudySSequenceequence

Portable Assisted Study Sequence

a semi-independent-study

high school learning program

……PASS a good solution PASS a good solution …?…?

* Standards-based Standards-based

* Learner-centeredLearner-centered

* AssistedAssisted course work course work

* Portable instruction packetsPortable instruction packets

……PASS a good solution PASS a good solution …?…?* Builds student confidence Builds student confidence and and

motivationmotivation

* Addresses different learning Addresses different learning stylesstyles

* Minimal computer or Internet Minimal computer or Internet access requirementsaccess requirements

PASS CoursesPASS CoursesCurrently AvailableCurrently Available

Language ArtsLanguage Arts Social StudiesSocial Studies MathematicsMathematics ScienceScience ElectivesElectives

CD includes…CD includes… Algebra I (English and Spanish versions)Algebra I (English and Spanish versions) Algebra IIAlgebra II GeometryGeometry

Algebra and Geometry Tutor Guide (Eng. and Algebra and Geometry Tutor Guide (Eng. and Sp.)Sp.)

Personal Finance (English and Spanish)Personal Finance (English and Spanish) Math 8Math 8 Integrated Math ConceptsIntegrated Math Concepts Math On the Move (English and Spanish)Math On the Move (English and Spanish) EconomicsEconomics

http://migrant.net/pass/http://migrant.net/pass/

Available downloads:Available downloads: Scope and sequence for every PASS Scope and sequence for every PASS

coursecourse Student/Mentor course evaluation formsStudent/Mentor course evaluation forms Style and usage guideStyle and usage guide Student of the year nomination formStudent of the year nomination form

Angles and PolygonsAngles and Polygons Coordinate Geometry, Circles, Graph Coordinate Geometry, Circles, Graph

TheoryTheory Transformational GeometryTransformational Geometry MeasurementMeasurement LogicLogic

Math 8BMath 8B

What’s New…What’s New…

Geometry/Algebra Tutor GuideGeometry/Algebra Tutor Guide Glossary of TermsGlossary of Terms AxiomsAxioms

Things that are accepted without proofThings that are accepted without proof PostulatesPostulates

Geometric axiomsGeometric axioms PropositionsPropositions

Theorems and ideas that are proven Theorems and ideas that are proven truetrue

Hands on ActivitiesHands on Activities

What’s New…What’s New…

Avoiding “math anxiety”Avoiding “math anxiety”

Axiom 11: If the first of three quantities Axiom 11: If the first of three quantities is is greater than the second and the greater than the second and the second is greater than the third, then second is greater than the third, then the first is greater than the third.the first is greater than the third.

If the first of three quantities is If the first of three quantities is greater than the greater than the second and the second is greater than the third, second and the second is greater than the third, then the first is greater than the third.then the first is greater than the third.

Consider three people…Consider three people…

If the first of three quantities is If the first of three quantities is greater than the greater than the second and the second is greater than the third, second and the second is greater than the third, then the first is greater than the third.then the first is greater than the third.

And we only know that,And we only know that,

Jim is taller than Marta,Jim is taller than Marta,and Marta is taller than and Marta is taller than Steve.Steve.

If the first of three quantities is If the first of three quantities is greater than the greater than the second and the second is greater than the third, second and the second is greater than the third, then the first is greater than the third.then the first is greater than the third.

Without taking another measurement, we Without taking another measurement, we knowknow

Jim is taller than Jim is taller than Steve.Steve.

Math 8 BMath 8 B Angles and PolygonsAngles and Polygons

Coordinate Geometry, Circles, and Coordinate Geometry, Circles, and Graph TheoryGraph Theory

Transformational GeometryTransformational Geometry

MeasurementMeasurement

LogicLogic

Developed by the National PASS Center under the leadership of the National PASS Coordinating Committee with funding from the Region 20 Education Service Center, San Antonio, Texas, as part of the Mathematics Achievement = Success (MAS) Migrant Education Program Consortium Incentive project. In addition, program support from the Opportunities for Success for Out-of-School Youth (OSY) Migrant Education Program Consortium Incentive project under the leadership of the Kansas Migrant Education Program.Copyright © 2009 by the National PASS Center. All rights reserved. No part of this book may be reproduced in any form without written permission from the National PASS Center.

Let there be light!Let there be light!

Color for the Color for the first time in first time in PASS historyPASS history

Copier friendlyCopier friendly

Need for Math On the MoveNeed for Math On the Move Preserving meaningPreserving meaning

Working away from “drill and kill”Working away from “drill and kill” A different type of studentA different type of student

Students come from different educational backgroundsStudents come from different educational backgrounds Additional resources help students succeed in a traditional GED Additional resources help students succeed in a traditional GED

course.course.

ReadabilityReadability Simplified language and sentences, without Simplified language and sentences, without

“dumbing down” content“dumbing down” content

Math is meant to be Math is meant to be understood, not understood, not

memorizedmemorized.. Each concept is explained in depthEach concept is explained in depth

Colorful visualsColorful visuals Hands on activitiesHands on activities

Each lesson has a story and a “teacher voice”Each lesson has a story and a “teacher voice” More in-depth than traditional textbooksMore in-depth than traditional textbooks Develops problem solving skillsDevelops problem solving skills

Math On the Move Math On the Move OrganizationOrganization

Learning math is like climbing a tree.Learning math is like climbing a tree. 24 Lessons24 Lessons Start with review of basic arithmetic Start with review of basic arithmetic

concepts.concepts. Gradually increase level of difficulty.Gradually increase level of difficulty.

Concepts build on one anotherConcepts build on one another Accessing prior knowledge gained in previous Accessing prior knowledge gained in previous

lessonslessons ““Think Back” and “Fact” BoxesThink Back” and “Fact” Boxes

Main concepts coveredMain concepts covered

Basic ArithmeticBasic Arithmetic Rational NumbersRational Numbers AlgebraAlgebra ProportionsProportions GeometryGeometry StatisticsStatistics

Math On the Move Math On the Move OrganizationOrganization

Basic ArithmeticBasic Arithmetic Whole Number Operations (Lesson 1)Whole Number Operations (Lesson 1) Integer Operations (Lesson 2 and 3)Integer Operations (Lesson 2 and 3) Factors and Multiples (Lesson 4)Factors and Multiples (Lesson 4)

Operations with Integers Operations with Integers (L2)(L2)

Rachel is leaving the Alaskan Rachel is leaving the Alaskan Mountain range. She feels that Mountain range. She feels that the temperature has risen 15 the temperature has risen 15 degrees from what it was the degrees from what it was the day before, -43. What is the day before, -43. What is the new temperature?new temperature?

We must first understand the We must first understand the problem. It says that the problem. It says that the temperature is temperature is risingrising 15 from - 15 from -43.43.

Therefore, we must findTherefore, we must find

-43 + 15-43 + 15

This problem has negative This problem has negative integers in it, so: integers in it, so:

Step 1: Step 1: Ignore the signs.Ignore the signs.

43 1543 15- +

Step 2: Step 2: 43 is bigger than 15.43 is bigger than 15.

Step 3:Step 3: Because 43 is the larger Because 43 is the larger number, we will use the sign in number, we will use the sign in front of the 43 (the “-” sign) in front of the 43 (the “-” sign) in our answer.our answer.

Step 4:Step 4: We notice the signs of We notice the signs of the two numbers are different, the two numbers are different, so we will find the difference by so we will find the difference by subtracting the numbers.subtracting the numbers.

43 – 15 = 2843 – 15 = 28

Step 5: Step 5: Now we will return to Now we will return to Step 3 and remember we must put Step 3 and remember we must put a minus sign “-” in front of the 28a minus sign “-” in front of the 28

-28-28

So the temperature was -28 So the temperature was -28 degrees that day.degrees that day.

Try it!Try it! Find the sum or the difference.Find the sum or the difference.

1)1) 1 – 31 – 3

2)2) -12 – 13-12 – 13

3)3) -8 + 3-8 + 3

4)4) - 47 + 100- 47 + 100

5)5) 30 – 2230 – 22

= -2

= -25

= -5= 53

= 8

Rational NumbersRational Numbers Definition of a fraction and equivalent Definition of a fraction and equivalent

fractions (Lesson 5)fractions (Lesson 5) Operations with fractions (Lesson 6)Operations with fractions (Lesson 6) Mixed numbers (Lesson 7)Mixed numbers (Lesson 7) Decimals (Lessons 8 and 9)Decimals (Lessons 8 and 9) Percentages (Lesson 10)Percentages (Lesson 10)

Real life applications Real life applications (Lesson 6)(Lesson 6)

= 14/24

= 7/12

= 8/55 = 2/24

= 1/12

AlgebraAlgebra

Variables and Substitution (Lesson 11)Variables and Substitution (Lesson 11) Simplifying Algebraic Expressions Simplifying Algebraic Expressions

(Lesson 12)(Lesson 12) Converting Verbal expressions to Converting Verbal expressions to

Algebraic expressions (Lesson 13)Algebraic expressions (Lesson 13) Converting Measurements (Lesson 14)Converting Measurements (Lesson 14)

Gaining a Better Gaining a Better UnderstandingUnderstanding

Classic Algebra Problem (From Lesson Classic Algebra Problem (From Lesson 11)11)

Solve for Solve for xx..

3+3+xx = 5 = 5

The classic explanation:The classic explanation:

3 + 3 + xx = 5 = 5 (Rewrite)(Rewrite)

-3-3 -3 -3 (Subtract 3)(Subtract 3)

x x = 2= 2 (Answer)(Answer)

Solve for Solve for xx..3+3+xx = 5 = 5

Imagine this equation as some Imagine this equation as some objects on a balanced scale.objects on a balanced scale.

Why not use a visual Why not use a visual analogyanalogy

3+3+xx = 5 = 5

In order to solve this, we need to get In order to solve this, we need to get the fancy stone (the the fancy stone (the xx) by itself on ) by itself on the scale, and still have the scales the scale, and still have the scales balance.balance. That’s easy, let’s just take the three That’s easy, let’s just take the three

round stones off the left pan. round stones off the left pan.

The scales aren’t balanced now! Since we The scales aren’t balanced now! Since we took three round stones from the left, we took three round stones from the left, we probably should have taken three stones probably should have taken three stones from the right as well. from the right as well.

By removing three stones from the right By removing three stones from the right pan, we see the scale has become pan, we see the scale has become balanced.balanced.

x x = 2= 2

Solve for each variableSolve for each variable

1)1) y + 5 = 3y + 5 = 3

2)2) 4 + a = 194 + a = 19

3)3) f + 20 = 57f + 20 = 57

4)4) 17 = k + 417 = k + 4

5)5) -3 = c + 19-3 = c + 19

Try It!Try It!

y = -2

a = 15f = 37

k = 13

c = -22

Proportional ThinkingProportional Thinking

Rates and Ratios (Lesson 15)Rates and Ratios (Lesson 15) Proportions (Lesson 16)Proportions (Lesson 16)

ConnectionsConnections

GeometryGeometry Basic Definitions (Lesson 17)Basic Definitions (Lesson 17) Quadrilaterals (Lesson 18)Quadrilaterals (Lesson 18) Properties of Triangles (Lesson 19)Properties of Triangles (Lesson 19) Area, Perimeter, and Similarity with Area, Perimeter, and Similarity with

TrianglesTriangles (Lesson 20)(Lesson 20) Circles (Lesson 21)Circles (Lesson 21) 3-Dimensional Solids (Lesson 22)3-Dimensional Solids (Lesson 22) Coordinate Geometry (Lesson 23)Coordinate Geometry (Lesson 23)

Example Activity (Lesson Example Activity (Lesson 18)18)

Take a 8½” x 11” rectangular sheet of construction paper and Take a 8½” x 11” rectangular sheet of construction paper and find it’s area.find it’s area.

Draw a line from the bottom right corner of that paper to Draw a line from the bottom right corner of that paper to anywhere along the top.anywhere along the top.

Using scissors cut along that line and separate the two pieces.Using scissors cut along that line and separate the two pieces. Now take the triangular piece and bring it to the other side to Now take the triangular piece and bring it to the other side to

make a parallelogram as shown.make a parallelogram as shown. Without taking measurements, what is the area of the Without taking measurements, what is the area of the

parallelogram.parallelogram.

8½

11

8½ x 11 = 93½

93½

Geometric FiguresGeometric Figures GeneralizeGeneralize

b

h A = bh

= ½bh

A labor of love…A labor of love…The goal for this course has been to write The goal for this course has been to write comprehensive, engaging lessons that are comprehensive, engaging lessons that are conducive to a semi-independent learning conducive to a semi-independent learning environment. Lessons are written with a environment. Lessons are written with a story line throughout, and narrated as if a story line throughout, and narrated as if a teacher is talking to his or her students. teacher is talking to his or her students. We find this helps connect abstract topics We find this helps connect abstract topics with concrete models, while avoiding the with concrete models, while avoiding the onset of “math anxiety”. Math On the onset of “math anxiety”. Math On the Move (MOM) is designed to assist out-of-Move (MOM) is designed to assist out-of-school youth in obtaining the basic school youth in obtaining the basic mathematical skills needed to function in a mathematical skills needed to function in a more advanced GED Program. more advanced GED Program.