Introductory Integer Worksheet

 

There is an elephant named Eli who lives in the jungle and is always hungry.  Eli's favorite food is peanuts.  He likes peanuts so much that he always carries a little bag with him so that he can collect peanuts wherever he goes.

 

One day, while walking through the jungle, Eli spots a strange peanut bush that he has never seen before.  Eli gathers four of these strange peanuts and he puts them in his bag which already has six regular peanuts in it.  What Eli does not know is that the peanuts from this strange bush are magic.  Whenever a magic peanut comes in contact with a regular peanut both peanuts suddenly disappear.

                                                                                       

 

Eli's bag containing 6 regular peanuts     …with 6 regular and 4 magic peanuts

 

When Eli returns home, he is hungry from walking through the jungle all day.  He decides to eat some peanuts.  He opens his bag and is surprised because there are just two regular peanuts in the bag.  The rest have disappeared.

                                    

 

The story continues using other combinations of numbers and with episodes that demonstrate the properties of negative numbers.

 

Use this concept to complete these number sentences.  Sketch a picture for each.

 

1.                                2.                                3.                    

 

 

 

 

 

 

4.                                5.                                 6.        

 

 

 

 

 

7.                                 8.        

 

 

 

The Eli story (greatly loved by CSMP students) is a special case of the signed model.  In this type of model, positive and negative numbers are represented by two different things, maybe black chips for negatives and white chips for positives.  The number zero can be represented many ways as shown below. 

 

Let  = black chip and  = white chip.

6 + -6 = 0

3 + -3 = 0

-5 + 5 = 0

  0

 

1.         Sketch two more names for zero using this model.

 

 

 

 

 

 

Other numbers can be named in several ways by adding zero.

      3

       8

      -4

                                                          

To subtract 5 - 2, start with 5           and "take - away" 2 leaving 3.

 

To subtract  -6 - (-2), start with         and "take - away" -2 leaving -4.

 

2.         To subtract 5 - 8, start with 5 positives.   What could be done to get 8 positives to

take away?  Perhaps add zero in the form of 3 + -3.  If 8 positives are taken away, what is left?

 

 

Construct appropriate models for the following problems.

 

3.     4 - 6              4.     2 - 6                5.     -3 - 5             6.     5 - (-2)                 7.     -3 - (-4)