Chapter 1: Number Sense Section 2: Rational Numbers
Topics in Algebra 1 © 2001 Texas Instruments Teacher Notes 1-18
Number Sense: Rational Numbers Teacher Notes
Objectives
•
To review the definition of rational numbers as ratios and as terminating and repeating
decimals.
•
To review ordering and the reciprocal property of rational numbers.
•
To review operations with rational numbers.
Math Highlights
Students review rational numbers. This includes rational numbers as ratios, terminating
decimals, repeating decimals, and integers, as well as operations with fractions. In the
Observations
, students are reminded of the connection between fractions, decimals, and
percents.
Common Student Errors
•
Students might confuse the algorithms for addition, subtraction, multiplication, and division
of fractions.
•
Students may have trouble identifying whether a fraction is positive or negative. For
example:
M
1
M
3
=
1
3
or
1
M
3
=
M
1
3
=
M
1
3
•
Students may have problems because they use short cuts to change the decimal
representation of a number to a percent representation. Using short cuts does not provide an
understanding of why the representations are equal. Students should understand that the
quantity stays the same. Using the multiplicative identity, 1=100/100, is the key to the change
in the representation. For example, students change .1875 to a percent. A shift of the decimal
point gives the correct answer, but without any connection to the math they know. However,
multiplying by 1 in the form 100/100 gives the same result and makes the connection to the
math as well.
.1875
Q
100
100
=
18.75
100
= 18.75%
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