1. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
Problem Set Lesson 5 Answers
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2. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
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3. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
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4. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
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5. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
MODULE 3 Raonal Numbers
Topic A: Understanding Posive and Negave
Lesson 6: Raonal Numbers on the Number Line
Student Outcomes
§
Students use number lines that extend in both direcons and use 0 and 1 to locate integers and raonal numbers on the number line.
Students know that the sign of a nonzero raonal number is posive or negave, depending on whether the number is greater than zero
(posive) or less than zero (negave), and use an appropriate scale when graphing raonal numbers on the number line.
§
Students know that the opposites of raonal numbers are similar to the opposites of integers. Students know that two raonal numbers
have opposite signs if they are on different sides of zero, and that they have the same sign if they are on the same side of zero on the number
line.
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6. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
What is a rational number?
A rational number is a number that can be
written as a fraction. (The denominator cannot
be zero.)
Integers, Whole Numbers, Some Decimals
Decimals are rational when:
~it terminates (ends)
~it repeats with a pattern
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7. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
So what about a number like Pi?
Pi does not terminate and
it never repeats or
develops a pattern.
What do we call it?
Irrational
number and
are written
with a symbol
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8. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
Classwork Opening Exercises
1. Write the decimal equivalent
2.
Write the fracon equivalent of each decimal.
a.
a.
0.42
b.
b.
3.75
c.
c.
36.90
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9. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
Example 1: Graphing Raonal Numbers
Locate and graph the number and its opposite on a number line.
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10. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
Exercise 1:
Use what you know about the points, and its opposite, to graph both points on the number line below. The
fracon, , is located between which two consecuve integers? Explain your reasoning.
0
On the number line, each segment will have an equal length of . In the fracon ,
the numerator is and the denominator is . The fracon is located
between and .
Explanaon:
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11. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
Example 2: Raonal Numbers and the Real World
The water level of a lake rose 1.25 feet aer it rained. Answer the quesons below using the
diagram below.
a.
Write a raonal number to represent the situaon.
b.
What two integers is 1.25 between on a number line?
c.
Write the length of each segment on the number line as a decimal and a fracon.
d.
What will be the water level aer it rained? Graph the point on the number line.
e. Aer two weeks of rain, the water level of the lake is the opposite of the water level before
it rained. What will be the new water level? Graph the point on the number line. Explain how
you got your answer.
f. State a raonal number that is not an integer whose value is less than 1.25, and describe its
locaon between two consecuve integers on the number line.
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12. Module 3 Lesson 6 Rational Numbers on the Number LIne.notebook
January 31, 2014
Closing
Please take out your exit ticket for Lesson 6, close your
binder, and complete the exit ticket. This will be collected.
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