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Mini-Lecture 1.2
Symbols and Sets of Numbers
Learning Objectives:
1. Use a number line to order numbers.
2. Translate sentences into mathematical statements.
3. Identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and
real numbers.
4. Find the absolute value of a real number.
Examples:
1. Insert <, >, or = in the space between the paired numbers to make each statement true.
a)
2 ____ 8
b) 41 ____ 14
c) 2.12 ____ -2.12
d)
3
9
____
7
21
h)
6 11

7 14
Determine whether each statement is true or false.
e) 15 < 20
f) 3.002 > 3.202
g)
14 7

18 9
2. Translate each sentence into a mathematical statement.
a) Negative eleven is less than
or equal to negative four.
b) Fourteen is greater than one
3. Tell which set or sets each number belongs to: natural numbers, whole numbers, integers,
rational numbers, irrational numbers, and real numbers.
a)
5
b) -3
c)
8
3
c)

d)
5
d)
0.03
e) 0
4. Find each absolute value.
a) 6.2
b)
14
2
9
e)
0
Teaching Notes:




Some students need to be reminded to read the expression and inequality symbols from left to
right.
Some students are not familiar with < or > and need to be told to point the symbol at the smaller
value.
Many students need to see value plotted on a number line to visually understand less than or
greater than.
Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning.
Answers: 1a) <; 1b) >; 1c) >; 1d) =; 1e) false; 1f) false; 1g) false; 1h) false; 2a) -11 < -4; 2b) 14 > 1;
3a) N, W, ., Rat., Real; 3b) I, Rat., Real; 3c) Rat., Real; 3d) Irr., Real; 3e) W, I, Real; 4a) 6.2; 4b) 14;
4c) 2/9; 4d) 0.03; 4e) 0
M-2