Transcript Math 6A

Portable
Assisted
Study
Sequence
Portable Assisted Study Sequence
a semi-independent-study
high school learning program
…PASS a good solution …?
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Standards-based
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Learner-centered
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Assisted course work
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Portable instruction packets
…PASS a good solution …?
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Builds student confidence
and motivation
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Addresses different learning
styles
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Minimal computer or Internet
access requirements
PASS Courses
Currently Available
 Language Arts
 Social Studies
 Mathematics
 Science
 Electives
CD includes…
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Algebra I (English and Spanish versions)
Algebra II
Geometry
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Algebra and Geometry Tutor Guide (Eng. and Sp.)
Personal Finance (English and Spanish)
Math 8
Integrated Math Concepts
Math On the Move (English and Spanish)
Economics
http://migrant.net/pass/
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Available downloads:
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Scope and sequence for every PASS course
Student/Mentor course evaluation forms
Style and usage guide
Student of the year nomination form
What’s New…
Math 8B
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Angles and Polygons
Coordinate Geometry, Circles, Graph
Theory
Transformational Geometry
Measurement
Logic
What’s New…
Geometry/Algebra Tutor Guide
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Glossary of Terms
Axioms
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Postulates
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Geometric axioms
Propositions
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Things that are accepted without proof
Theorems and ideas that are proven true
Hands on Activities
Avoiding “math anxiety”
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Axiom 11: If the first of three quantities is
greater than the second and the
second is greater than the third, then
the first is greater than the third.
If the first of three quantities is greater than the second
and the second is greater than the third, then the first is
greater than the third.
Consider three people…
If the first of three quantities is greater than the second
and the second is greater than the third, then the first is
greater than the third.
And we only know that,
Jim is taller than Marta, and Marta is taller than Steve.
If the first of three quantities is greater than the second
and the second is greater than the third, then the first is
greater than the third.
Without taking another measurement, we know
Jim is taller than Steve.
Math 8 B
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Angles and Polygons
Coordinate Geometry, Circles, and Graph
Theory
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Transformational Geometry
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Measurement
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Logic
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!
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Color for the first
time in PASS
history
Copier friendly
Need for Math On the Move
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Preserving meaning
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A different type of student
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Working away from “drill and kill”
Students come from different educational
backgrounds
Additional resources help students succeed in
a traditional GED course.
Readability
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Simplified language and sentences, without
“dumbing down” content
Math is meant to be
understood, not
memorized.
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Each concept is explained in depth
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Colorful visuals
Hands on activities
Each lesson has a story and a
“teacher voice”
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More in-depth than traditional textbooks
Develops problem solving skills
Math On the Move Organization
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Learning math is like climbing a tree.
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24 Lessons
Start with review of basic arithmetic concepts.
Gradually increase level of difficulty.
Concepts build on one another
 Accessing prior knowledge gained in previous
lessons
 “Think Back” and “Fact” Boxes
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Main concepts covered
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Basic Arithmetic
Rational Numbers
Algebra
Proportions
Geometry
Statistics
Math On the Move Organization
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Basic Arithmetic
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Whole Number Operations (Lesson 1)
Integer Operations (Lesson 2 and 3)
Factors and Multiples (Lesson 4)
Operations with Integers (L2)
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Rachel is leaving the Alaskan
Mountain range. She feels that the
temperature has risen 15 degrees
from what it was the day before,
-43. What is the new temperature?
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We must first understand the
problem. It says that the
temperature is rising 15 from -43.
Therefore, we must find
-43 + 15
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This problem has negative integers in
it, so:
Step 1: Ignore the signs.
- 43 + 15
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Step 2: 43 is bigger than 15.
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Step 3: Because 43 is the larger
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Step 4: We notice the signs of the
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number, we will use the sign in front
of the 43 (the “-” sign) in our answer.
two numbers are different, so we will
find the difference by subtracting the
numbers.
43 – 15 = 28
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Step 5: Now we will return to Step 3
and remember we must put a minus
sign “-” in front of the 28
-28
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So the temperature was -28 degrees
that day.
Try it!
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Find the sum or the difference.
1 – 3 = -2
-12 – 13 = -25
-8 + 3 = -5
- 47 + 100 = 53
30 – 22 = 8
Rational Numbers
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Definition of a fraction and equivalent
fractions (Lesson 5)
Operations with fractions (Lesson 6)
Mixed numbers (Lesson 7)
Decimals (Lessons 8 and 9)
Percentages (Lesson 10)
Real life applications (Lesson 6)
= 14/24
= 7/12
= 8/55
= 2/24
= 1/12
Algebra
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Variables and Substitution (Lesson 11)
Simplifying Algebraic Expressions (Lesson 12)
Converting Verbal expressions to Algebraic
expressions (Lesson 13)
Converting Measurements (Lesson 14)
Gaining a Better Understanding
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Classic Algebra Problem (From Lesson 11)
Solve for x.
3+x = 5
The classic explanation:
3+x=5
(Rewrite)
-3
-3
(Subtract 3)
x=2
(Answer)
Why not use a visual analogy
Solve for x.
3+x = 5
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Imagine this equation as some objects on
a balanced scale.
3+x
=
5
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In order to solve this, we need to get the
fancy stone (the x) by itself on the scale,
and still have the scales balance.
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That’s easy, let’s just take the three round
stones off the left pan.
x
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=
2
The scales aren’t balanced now! Since we took
three round stones from the left, we probably
should have taken three stones from the right as
well.
By removing three stones from the right pan, we
see the scale has become balanced.
Try It!
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1)
2)
3)
4)
5)
Solve for each variable
y+5 = 3
4 + a = 19
f + 20 = 57
17 = k + 4
-3 = c + 19
y = -2
a = 15
f = 37
k = 13
c = -22
Proportional Thinking
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Rates and Ratios (Lesson 15)
Proportions (Lesson 16)
Connections
Geometry
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Basic Definitions (Lesson 17)
Quadrilaterals (Lesson 18)
Properties of Triangles (Lesson 19)
Area, Perimeter, and Similarity with
Triangles
(Lesson 20)
Circles (Lesson 21)
3-Dimensional Solids (Lesson 22)
Coordinate Geometry (Lesson 23)
Example Activity (Lesson 18)
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Take a 8½” x 11” rectangular sheet of construction paper and find it’s
area.
Draw a line from the bottom right corner of that paper to anywhere
along the top.
Using scissors cut along that line and separate the two pieces.
Now take the triangular piece and bring it to the other side to make a
parallelogram as shown.
Without taking measurements, what is the area of the parallelogram.
8½
8½ x 11 = 93½
93½
11
Geometric Figures
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Generalize
h
A = bh
= ½bh
b
A labor of love…
The goal for this course has been to write
comprehensive, engaging lessons that are
conducive to a semi-independent learning
environment. Lessons are written with a story
line throughout, and narrated as if a teacher is
talking to his or her students. We find this helps
connect abstract topics with concrete models,
while avoiding the onset of “math anxiety”.
Math On the Move (MOM) is designed to assist
out-of-school youth in obtaining the basic
mathematical skills needed to function in a more
advanced GED Program.