# g7s1 integers

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```					     Grade 7                             Unit 2              Math. Dept
2007-2008
Worksheet No (1)        Positive & Negative Numbers     1st Semester

Positive & Negative Numbers

Objectives:                                               # of blocks:
By the end of lesson Student should be able to:           Date:
-    Represent integers on number line
-    Use positive and negative integers to represent
word description

Sea Level                                  0

Positive integer numbers +1, +2, +3, . . .
Negative integer numbers -1, -2, -3, . . .

FACTS:
  Zero is not positive or negative integers
  Zero less than any positive integer
  Zero more than any negative integer
(1)
Grade 7                               Unit 2            Math. Dept
2007-2008
Worksheet No (2)       Positive & Negative Numbers      1st Semester

Line number

Opposite:

Complete the following table

Integer                Opposite
-
18                   18
45
16
-
30
 Mark the following sets of integers on the number line
1)
-
5, 3, +1, -6

2)
-         +
1,           5, -4, 2, -2

(2)
Grade 7                           Unit 2             Math. Dept
2007-2008
Worksheet No (3)    Positive & Negative Numbers      1st Semester

Fill in the missing terms on the following number line:
a)

b)

Write the following numbers
 Positive six           :   .....................

 Negative ten           :   .....................

 Positive one hundred :     .....................

 Negative thirty four   :   .....................

Activity:
Write as positive or negative numbers to explain the following
situations.

 The temperature of Doha is 38 ْC
 A company had a lose of 3 million QR
 An airplane is 20,000 m above sea level
 A submarine is 250 m below sea level
 The temperature in a freezer is 18 ْC below 0
(3)
Grade 7                                  Unit 2               Math. Dept
2007-2008
Worksheet No (4)              Positive & Negative Numbers     1st Semester

ْC
Comparing & Ordering Integers (positive, negative)

Objectives:                                                     # of blocks:
By the end of lesson Student should be able to:                 Date:
- Compare integers and arrange them in order

Fill in the space with ( <،> ):
+             +
0          +
71                          2            4

-                                       -            -
1              0                        4            71

-               -                                    -
75              14                  32               35
 Arrange the following integers in ascending order:

1) -4 , 5 , -3 , 0,-12 ,1

2) -5 , 19 , 0 , -6 , -3

 Arrange the following integers in descending order:

-
1)       1, 0 , 71 , -23 , 25

(4)
Grade 7                            Unit 2             Math. Dept
2007-2008
Worksheet No (5)        Positive & Negative Numbers   1st Semester

2) 24 , -1 , 0 , -23 , 56
 Write all integers enclosed by every two numbers
-
3, 2
-
9, -2
-
3,0
5,6

Facts:

Zero is less than any positive integers

Zero is more than any negative integers

(5)
Grade 7                          Unit 2            Math. Dept
2007-2008
Worksheet No (6)   Positive & Negative Numbers     1st Semester

Objectives:                                             # of blocks:
By the end of lesson Student should be able to:         Date:
- Use the number line to add integers

0

 Evaluate by using number line

+
3 + +2=

+
5 + +1=

-
4 + -3=

-
1 + +7=

(6)
Grade 7                       Unit 2             Math. Dept
2007-2008
Worksheet No (7)   Positive & Negative Numbers   1st Semester

6 + -4=
+

(7)
Grade 7                               Unit 2                   Math. Dept
2007-2008
Worksheet No (8)           Positive & Negative Numbers         1st Semester

Evaluate:
+
2 + -1 =                                   0 + -24 =
6 + -6 =                               -
17 + -14 =
-                                          -
24 + 18 =                                  29 + -4       =
-                                          -
26 + 14 =                                  23 + 23       =

Write suitable number in the space

7 +         ……. = 7                                  …… + -12 = 0
……. + -2 =-2                                     -
17 + …….            = -17
+
10 + ……. = 4                                     ……. + -4                = 2
-
8 + …….          =2                              ……. + 20                = -2

Evaluate the following expressions if A=-2 , B=5, C=-4
 -11 + B =

 A + -15 =

 A+B+C=

(8)
Grade 7                           Unit 2                    Math. Dept
2007-2008
Worksheet No (9)     Positive & Negative Numbers            1st Semester

Subtracting positive & negative integers

Objectives:                                                      # of blocks:
By the end of lesson Student should be able to:                  Date:
-    Subtract integers

Rule:
For every two integers A,B
A – B = A + -B
 Evaluate:
8 - 2 =                                       2 - -4 =
3 - -5 =
3 - 7 =
-
7 - 3 =
15 - 21 =                                -
7 - -3 =
-
2 - 0 =                                      5 -5 =
6 - -6 =
0 - 8 =
-
7 -- 7 =

 Evaluate:
(14 – 95) + 2 =
-
2 – (18 – 10) =
(73 – 100) +25 =
(65 – 25) – 13 =
( 3 – 27 ) – -24 =

(9)
Grade 7                          Unit 2              Math. Dept
2007-2008
Worksheet No (10)     Positive & Negative Numbers    1st Semester

Applications:
1) A diver is at 35m below sea level. If he ascends 12m and then,
he dives down again another 20m, what is his distance from sea
level?

2) The temperature in the afternoon is 8 ْC. At night, the
temperature is -3 ْC. What is the difference in temperature?

3) Look at the 3 by 3 table. Fill in the missing numbers so that
each row adds up to 3                             -
2
each column adds up to 3                           3       1
each diagonal adds up to 3                         2                  4

(10)
Grade 7                                Unit 2                        Math. Dept
2007-2008
Worksheet No (11)           Positive & Negative Numbers              1st Semester

Multiplying integers
Objectives:                                                            # of blocks:
By the end of lesson Student should be able to:                        Date:
-    Multiply integers

 Rule:
* The product of two positive or two negative integers is a positive
integer.
Positive x Positive = Positive                3 x 4 = 12

Negative x Negative = Positive                (-3) x (-5) = 15

* The product of positive and negative integer is a negative integer.
Negative x Positive = Negative                (-3) x 2 = -6

Positive x Negative = Negative                3 x (-2) = -6

 Estate the sign of the following:
5  8              (   )                    92  -3        (         )

-
32  4         (   )                    -
2  -66    (         )

-
9  -23        (   )                    -
6  82     (         )

(11)
Grade 7                            Unit 2                    Math. Dept
2007-2008
Worksheet No (12)       Positive & Negative Numbers          1st Semester

 Evaluate:
2  5 =. . .                                 -
2  -3 =. . .
3  7 =. . .                                 -
4  -3 =. . .
9  6 =. . .                                 -
6  -7 =. . .

 Evaluate:
-
7  4 =. . .                             -
7  -3 =. . .
-
3  5 =. . .                             -
10  -3 =. . .
-
8  -6 =. . .                            5  -7 =. . .

 Evaluate:
4  -7 = -7  4 = . . .                2  -5 = -5  2 =. . .
-
6  7 = 7  -6 = . . .             4  -3 = -3  4 =. . .

In general:
A  B =..........= .....              , A,B are integers

 Complete the following:

4  0 = 0  4 = 0                            0  -5 = . . . 0 =. . .
-
6  0 = 0  ... =...                     12  0 = . . .  12 =. . .

In general:

(12)
Grade 7                            Unit 2              Math. Dept
2007-2008
Worksheet No (13)    Positive & Negative Numbers       1st Semester

A  0 =..... A = .....           , A is an integer
 Complete the following:

4  1 = 1  4 = 4                         1  -5 = . . .  1 = . . .
-
6  1 = 1  ... =...                  12  1 = . . .  12 = . . .

In general:
A  1 =..... A = .....           , A is an integer

  If A=3 , B= -2 , C= -4 then evaluate the following:
C  5 =

 -2  B =

 3A =

 -4C + 2 =

 3C – 2B + 5A =

(2A)+(CB)=

Evaluate:
77  -4 =. . .                   -
72  3 =. . .

-
3  -1 =. . .             20  -4 =. . .
-
1  -1 =. . .             -
73  -2 =. . .

(13)
Grade 7                                       Unit 2          Math. Dept
2007-2008
Worksheet No (14)               Positive & Negative Numbers   1st Semester

Evaluate:
-
2(54)=..........

-
3  ( 3 + 7 ) =. . . . . . . . . .

(-4  5 ) + ( -2  10 ) =. . . . . . . . . .

-
6 + (-3  7) – 5 =. . . . . . . . . .

Write the suitable number in the space
-
7  …… =-21

……  5 =20

-
8  …… =24

……  -3 = 0

………… =25

-
5  …… =-35

(14)
Grade 7                                   Unit 2                      Math. Dept
2007-2008
Worksheet No (15)            Positive & Negative Numbers              1st Semester

Dividing integers

Objectives:                                                          # of blocks:
By the end of lesson Student should be able to:                      Date:
-    Divide integers

 Rule:
* The quotient of two positive integers or two negative integers is a
positive integer.
Positive ÷ Positive = Positive             18 ÷ 3 = 6

Negative ÷ Negative = Positive             (-18) ÷ (-3) = 6

* The quotient of a positive integer and a negative integer is a
negative integer.
Negative ÷ Positive = Negative             (-18) ÷ 3 = -6

Positive ÷ Negative = Negative             18 ÷ (-3) = -6

 Estate the sign of the following:
8      2     (      )                         92  -2        (                  )
-
32  4        (      )                         -
12  -3    (                  )
-
9  -3        (      )                         -
72  8     (                  )

(15)
Grade 7                        Unit 2                      Math. Dept
2007-2008
Worksheet No (16)   Positive & Negative Numbers            1st Semester

 Evaluate:

24  6 =                                      -
48  8 =
13  -3 =
-                                             -
18  2 =
28  -7 =
-
128  -4 =

 Evaluate:

50  -6 =
-                                             -
48  6 =
24  -3 =
-                                             -
18  3 =
28  -4 =
-
120  -4 =

 Complete the following:

0  4 = 0                              0  -3 = . . .
0  -5 = . . .                         0  A = . . ., A is an integer

 Write the suitable number in the space
-
28  …… =-4                                 ……  -3 = 0
……  -5 =6                            49…… = -7
-
24  …… =3                            -
45  …… =-9

(16)
Grade 7                            Unit 2                  Math. Dept
2007-2008
Worksheet No (17)       Positive & Negative Numbers        1st Semester

 Evaluate:

6(4 2) =                                  18 ( -24 2 ) = . . .

(70  -5) + -6 = . . .                      (78 - -2)  -16 = .. .

      If A= -4 , B= -3 , C= 5 then evaluate the following:

70A
                       =
2C

-2C+1
                       =
3B

(17)
Grade 7                            Unit 2                Math. Dept
2007-2008
Worksheet No (18)      Positive & Negative Numbers       1st Semester

Order of Operations

Objectives:                                                 # of blocks:
By the end of lesson Student should be able to:             Date:
- Know the order of operations
- Insert brackets into expressions to get true statement

To help us remember the order of operations, we can use the mnemonic
PEMDAS, which stands for:
Please Excuse My Dear Aunt Sally

Parentheses, Exponents, Multiplication & Division, Addition & Subtraction
Note that although there are six words, they correspond to four rules.

(18)
Grade 7                                 Unit 2             Math. Dept
2007-2008
Worksheet No (19)          Positive & Negative Numbers     1st Semester

Example: Evaluate each expression using the rules for order of operations.

Solution:               Order of Operations
Expression Evaluation Operation
6+7x8         =6+7x8          Multiplication
= 62
16 ÷ 8 - 2 = 16 ÷ 8 - 2 Division
=2-2            Subtraction
=0
(25 - 11) x 3 = (25 - 11) x 3 Parentheses
= 14 x 3        Multiplication
= 42
Evaluate using the order of operations
a) 9 + 6 × 8

b) 32 ÷ 4 + 42

c) (14 - 5) ÷ (9 - 6)

d) 5 × 8 + 6 ÷ 6 - 12 × 2

(19)
Grade 7                        Unit 2             Math. Dept
2007-2008
Worksheet No (20)   Positive & Negative Numbers   1st Semester

90  30
e) 3  5

f)      (132  5 2 )

g) 150 ÷ [20 – (7-2)]

h) (5 + 4)2 × 4 ÷ 6

Insert brackets in these expressions to make them true:
a) 2 × 9 – 1 = 16

b) 5 + 3 × 2 = 16

c) 3 + 7 × 4 – 1 = 24

d) 2 + 3 × 1 + 4 = 25
(20)
Grade 7                                          Unit 2                 Math. Dept
2007-2008
Worksheet No (21)               Positive & Negative Numbers             1st Semester

Exponent and Square Root
Objectives:                                                                   # of blocks:
By the end of lesson Student should be able to:                               Date:
- Write expressions in Exponential form
- Find square roots for positive perfect integers

Exponent
Exercise1:
Complete the following.
a) 53=. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
b) 24=. 2×. . . . . . . . . . . . . . . . . . . . . . . . . . . .
c) (-3)5=. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
d)
Power                  Base               Exponent              Standard form
25
43
3                     2
5× 5× 5× 5

Exercise2:
Write in Exponential form.
8=                                                     27=

16=                                                    25=

9=                                                     125=

64=                                                    81=

(21)
Grade 7                                  Unit 2            Math. Dept
2007-2008
Worksheet No (22)            Positive & Negative Numbers   1st Semester

Exercise3:
Find the values without using a calculator.
103=

(-9)2=

23×32=

52+25=

Exercise4:
a) Find the values using a calculator.
92=                                 47=
73=                                           (-12)4=
34+52- (-2)2=
b) Complete
- If a=2, then a3= . . . . . . . . . . .

- If b=3, then b2=. . . . . . . . . ..

- If d=5, then d4=. . . . . . . . . . .

- If g3=27, then g= . . . . . . . . .

c) Look at the numbers below. Which is the largest? Which is equal

to 92?

16         25           34           43    52       61

(22)
Grade 7                                Unit 2               Math. Dept
2007-2008
Worksheet No (22)          Positive & Negative Numbers      1st Semester

Square Root

Exercise1:
Which of the following is perfect square (using factorizing ).
a) 32
b) 16
c) 25
d) 84
e)     900

Exercise2:
Evaluate

1)    81 =                       2)    121 =

3)        225                   4)      144

5)   0.04 =                     6)     1.96    =

7)   0.25 =                      8)     0.0009 =

Exercise3:
a) Explain why 8<         70   <9

b) If     81 <n< 144     then n could be which of the following numbers
9        11            12              13

(22)

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