Download Number Lines

Multi-Part Lesson
12-1
Rational Numbers
PART
A
B
C
Number Lines
Main Idea
Model rational
numbers.
BEACH Marcus and Silvio are at the beach. Marcus builds a sandhill
0.6 meter high. Silvio digs a ditch in the sand 0.8 meter deep.
NGSSS
MA.7.A.5.1 Express
rational numbers as
terminating or repeating
decimals.
0.6 m
0.8 m
glencoe.com
Just as you can graph integers on a number line, you can graph
positive and negative fractions and decimals. Recall that positive
numbers are to the right of zero on the number line and negative
numbers are to the left of zero.
Graph points on the number line to represent the hill and
the ditch.
Draw a number line from -1 to 1, with increments
of 0.2.
-1.0 -0.8 -0.6 -0.4 -0.2
0
0.2 0.4 0.6 0.8 1.0
The hill is above sea level. Its height is greater than
zero on the number line. So, draw a dot at 0.6 to
represent the hill.
-1.0 -0.8 -0.6 -0.4 -0.2
0
0.2 0.4 0.6 0.8 1.0
The ditch is below sea level. Its depth is less than zero
on the number line. So, draw a dot at -0.8 to
represent the ditch.
-1.0 -0.8 -0.6 -0.4 -0.2
0
0.2 0.4 0.6 0.8 1.0
the Results
1. Suppose Marcus built a hill 0.3 meter high. Would you graph the
number to the left or right of zero? Explain.
2. Choose a decimal amount less than zero. Would it be graphed to the
right or left of Silvio’s ditch? Explain.
3.
Compare and contrast graphing positive and negative
decimals on a number line.
You can also use models to graph rational numbers.
_3
Graph - on a number line.
4
3
Model -_
using fraction tiles. Draw a number
1
4
4
line from -1 to 0. Place the fraction tiles
above the number line starting at zero.
1
4
0
1
4
3
1
2
the number line with -_
, -_
, and -_
.
4
1
4
-1
Each fraction tile represents one fourth. Label
4
1
4
4
1
4
1
4
-1
-3
-2
-1
0
-1
-3
-2
-1
0
3
Remove the fraction tiles. Draw a dot at -_
.
4
1
4
4
4
4
4
4
4
and Apply
Graph each number on a number line. Use models if necessary.
4
4. -_
1
5. -_
5
6. -0.1
4
3
10. -_
8
9. 8.75
2
8. _
7. -4.5
7
12. _
11. -5.75
10
3
13. -2.4
the Results
1
1
14. REASONING Jaclyn thinks that -_
is greater than _
because it is farther
2
4
from zero on the number line. Is her thinking correct? Explain.
15.
Explain how you can use the number line to identify
3
3
and _
. Then identify two fractions that are greater
fractions between -_
4
4
3
3
and less than _
.
than -_
4
4
16. MAKE A CONJECTURE Write a rule that you can use to compare positive
and negative values without a number line.