Download TN Lesson: Ordering and Comparing Integers

Grade 6
TN Lesson:
Ordering and Comparing
Integers
Use with MiC unit Models You Can Count On
after page 60
TN Standard: MA.6.SPI 0606.3.1
Represent on a number line the solution of a linear inequality.
CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd
5/14/09
10:27 AM
Page 43
Focus On: Ordering and Comparing Integers
Inequality Symbols
Just as the equals sign (=) shows that two numbers have the same value, the following symbols
show when two numbers have different values:
<
stands for “is less than”
>
stands for “is greater than”
≤
stands for “is less than or equal to”
≥
stands for “is greater than or equal to”
You can use these symbols to order and compare integers.
Use < or > to compare –5 and 3.
–5 is negative and 3 is positive, so –5 is less than 3.
–5 < 3
Use < or > to order and compare –2, –9, and –6.
All three numbers are negative, so the numbers with
the smaller absolute value are the greater numbers.
–2 > –6 > –9
Showing Inequality on a Number Line
A number line can show inequalities. A shaded dot and all of the points where the number line is
thicker stand for possible values of x. An empty dot shows a number that is not a possible value.
Use a number line to show all the values for x when
x ≤ –2.
Find the given number on the number line. Draw a
shaded dot for ≤ or ≥. Thicken the line to the left of
the number for ≤. Thicken the line to the right of
the number for ≥.
–8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9
Use a number line to show all the values for x when
x > –5.
Find the given number on the number line. Draw an
empty dot for < or >. Thicken the line to the left of
the number for <. Thicken the line to the right of the
number for >.
–8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9
Inequality Expressions
Just like an equals sign can be used to write a number sentence or an expression, so can the
inequality symbols.
Use =, <, >, ≤, or ≥ to compare –2 and 3 - 6.
Find the value of the difference.
3 - 6 = –3
Compare this value with the given value.
–2 is greater than –3
Write a number sentence with the correct
inequality sign.
–2 > 3 - 6
© Encyclopædia Britannica, Inc.
Use =, <, >, ≤, or ≥ to complete the number sentence
x + 6 –1. The sentence is true when x = –8.
Substitute the value of x and find the value of the sum.
x + 6 = –8 + 6 = –2
Compare this value with the given value.
–2 is less than –1
Write a number sentence with an inequality sign.
x + 6 < –1
Integers
1
CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd
5/14/09
10:27 AM
Page 44
Ordering and Comparing Integers
Math Content
Students will order and compare positive and negative numbers using inequality symbols and
statements.
1. Compare each pair of numbers by filling
in the box with < or >.
4. Which number line shows all the values
that are less than or equal to –1?
5
2
A.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
b. –6
1
B.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
c. –14
–2
C.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
0
–8
D.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
a.
d.
2. Shade each number line to show the
possible values of x.
a. x < –4
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
b. x ≤ 0
5. Which number line shows all the possible
values for x > 3?
A.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
B.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
C.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
D.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
c. x > –7
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
d. x ≥ –6
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
3. Which number is not a possible value of
y when y ≤ 2?
6. Draw number lines to show the possible
values of x.
a. x < 0
A. 0
B. 1
C. 2
b. x ≤ 6
D. 3
2 TN Lesson
© Encyclopædia Britannica, Inc.
CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd
5/14/09
10:27 AM
Page 45
Ordering and Comparing Integers
7. Complete each number sentence by filling in each box with <, =, or >. Then
write the inequality using words.
a. 2 - 4
9. Use < or > to order and compare each
set of numbers.
a. –8, –1, –5
0
b. 0, 2, –2
b. 8 + (–9)
c. 4 - 12
–1
10. Catherine has a budget of $12 to buy a
gift for her little sister. She would like to
buy a picture book that costs $11. The
price of the book plus tax (T) must be
less than or equal to her budget in order
for her to afford it. Write an expression
using an inequality symbol to represent
this situation.
–1 - 8
8. a. Use =, <, >, ≤, or ≥ to complete the
number sentence below, when x = –3.
x+5
–4
b. Write the number sentence using
words.
© Encyclopædia Britannica, Inc.
11. Pedro currently has 65 points in math.
He needs a score of at least 70 points to
pass. How many points (P) will allow
him to pass math? Write an inequality
that represents this situation.
Integers
3
CPW_G7_978-1-60835-059-9_2010_INT.qxd:CPW_G7_978-1-60835-059-9_2010_INT.qxd
5/14/09
10:27 AM
Page 44
Ordering and Comparing Integers Answer Key
1a.
1b.
1c.
1d.
2a.
>
<
<
>
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
2b.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
2c.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
2d.
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
3. D
4. A
5. D
6a. –8 –7 –6 –5 –4 –3 –2 –1
6b.
0 1 2 3 4 5 6 7 8
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
7a. <; Two minus four is less than zero.
7b. =; Eight plus negative nine is equal to
negative one.
7c. >; Four minus twelve is greater than
negative one minus eight.
8a. x + 5 > – 4
8b. –3 plus five is greater than negative four.
9a. –1 > –5 > –8 or –8 < –5 < –1
9b. 2 > 0 > –2 or –2 < 0 < 2
10. $11 + T ≤ $12 or $12 ≥ $11 + T
11. 65 + P ≥ 70 or 70 ≤ 65 + P
4 TN Lesson
© Encyclopædia Britannica, Inc.