Preparing for Algebra: By Building the Concepts, Preliminary Edition, 1/e
Martha Haehl, Maple Woods Community College
Published November, 1997 by Prentice Hall Engineering/Science/Mathematics
Copyright 1998, 430 pp.
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Prealgebra (Basic Math with very Early Algebra)-Mathematics
This text provides material for an instructor who wants to integrate
the topics of arithmetic and algebra. It introduces topics with discovery,
hands-on exercises that allow students to put their learning into
action. Estimation skills and number sense are emphasized as students
collect and analyze data that allow them to write reports. The text
has a balanced approach; skills are taught with concepts, while technology
is integrated with paper and pencil processes. Many of the applications
involve real data, requiring students to interpret information given
to them in written, chart or graph form.
Basic topics are introduced with cooperative student discovery
The use of manipulatives help students see the relevance
- These discovery exercises provide activities and applications
that allow the student see the concepts they are learning in action.
- Coins and bills are used to introduce place value and
increase understanding of arithmetic processes of whole and decimal
- Students learn to work with slopes by first measuring
physical objects. These objects provide a basis for understanding
the concept behind graphing. Rather than learning to graph first,
and then working on applicaiton problems, students begin
with the application and then learn to graph by drawing a diagram
of a ramp.
Emphasis on estimation skills, number sense and Reasonableness
- To study fractions as well as linear units, students
make a ruler from a non-standard unit. They then put squares together
to discover the area and perimeter formulas while learning about square
versus linear units. These rectangles and squares are used as a means
to introduce factoring. In a geometric context, they are also introduced
to the concept of a variable.
Applications use real data in applications that involve
multiple tasks projects in which students collect and analyze data.
- Students learn to estimate and to use a calculator as
they practice the skills in the text.
- Students are taught and encouraged to use visual techniques
for estimation and rounding-off in arithmetic problems.
Quantitative literacy is emphasized.
- Students get a better understanding of how math is used
outside of the classroom.
Students learn to use scientific calculators effectively.
- Students see how math is relevant to the understanding
of current issues.
- Students are asked to interpret quantitative information
from articles about current issues.
- Students interpret current data given in charts and graphs.
1. Arithmetic of Whole and Decimal Numbers, the Money Model.
2. Signed Numbers Bean Arithmetic, Checkbook Arithmetic, and the Number Line.
3. Linear and Square Units, Factors, Geometry.
5. Ratios, Proportions, Unit Conversions and Rates.
7. Statistical Information, Pie and Bar Charts, and Other Graphical Data.
8. Floor Plans and Other Summary Exercises.
Appendix I. Names of the Numbers.
Appendix II. Math Facts--Addition and Times Tables.
Appendix III. String Operations--the Calculator and Fractions.