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Adding and Subtracting Integers Using Manipulatives
Name _____________________________
Adding and Subtracting Positive and Negative Numbers using
Manipulatives
When you are adding and subtracting positive and negative numbers using manipulatives, you can
use any similar objects of two different colors. One color will represent positive numbers and the
other color will represent negative numbers.
We will use counter chips. The red side will represent positive numbers and the yellow side will
represent negative numbers.
When you are solving a problem, you lay out the chips that are represented in the problem.
For example, in the following problem, lay out 3 red chips and 7 yellow chips.
-3 + 7
Next, you match up each negative chip with a positive chip. The chips that are left are your answer!
You will always be left with either positive chips or negative chips.
Practice adding positive and negative numbers
Show each of these operations with the chips, and fill in the answers.
+
2 + +3 = _______
─
+
2 + +1= _______
3 + ─1= _______
─
2 + ─3 = _______
+
1 + +3 = _______
+
+
5 + ─1 = _______
4 + +3 = _______
─
3 + ─3 = _______
2 + ─2 = _______
+
4 + ─3 = _______
2 + ─1= _______
+
2 + ─4 = _______
4 + +3 = _______
+2
3 + ─5 = _______
─
+
2 + +4 = _______
+ 3 = _______
1 + +4 = _______
+4
+ 6 = _______
Adding and Subtracting Integers Using Manipulatives
1. Look at the problems you just completed and write the rule for adding two
positive numbers without using the counters. What operation did you do, and
what is the sign of the answer?
______________________________________________________
______________________________________________________
2. Look at the problems you just completed and write the rule for adding two
negative numbers without using the counters. What operation do you do, and
what is the sign of the answer?
______________________________________________________
______________________________________________________
3. Look at the problems you just completed and write the rule for adding a
positive and a negative number without using the counters. What operation
do you do, and what is the sign of the answer?
______________________________________________________
______________________________________________________
4. When you add positive and negative numbers, does it matter what order the
numbers are in?
______________________________________________________
Adding and Subtracting Integers Using Manipulatives
Subtracting positive and negative numbers
Show each of these operations with the counters, and fill in the answers. Before
you start any question, make sure that you have several positive and negative
counters on your workspace, and that their total value is 0. Notice that some of the
questions ask you to add, and some ask you to subtract.
+
3  +2 = _______
+
3 + ─2 = _______
+
2  ─1= _______
+
2 + +1 = _______
3  +3 = _______
─
3  ─1= _______
─
2  ─2 = _______
─
4  ─3 = _______
+
5  ─1= _______
─
5  +2 = _______
─
+
4  ─3 = _______
+
4 + +3 = _______
+
4  ─4 = _______
+
4 + +4 = _______
─
─
─
+
─
─
3 + ─3 = _______
3 + +1= _______
2 + +2 = _______
4 + +3 = _______
5 + +1= _______
5 + ─2 = _______
1. What do you notice about the two answers in each row?
__________________________________________________
2. Are the questions the same in each row? ____________________
3. In each row, what is the difference between the first question and the second
question? ________________________________________
______________________________________________________
Hint:
Is the first number the same or different? ____________
Is the operation sign the same or different? ___________
Is the second number the same or different? __________
4. Write the rule for subtracting positive and negative numbers:
________________________________________________________________
________________________________________________________________