Download Understanding Addition of Integers

Understanding Addition of
Integers
•
a. For each example above, what is the distance between 2 and the sum?
•
b. Does the sum lie to the right or left of 2 on a horizontal number line? Vertical
number line?
•
c. Given the expression 54 + 81, can you determine, without finding the sum, the
distance between 54 and the sum? Why?
•
d. Is the sum to the right or left of 54 on the horizontal number line? On a vertical
number line?
•
Given the expression 14 + (−3), can you determine, without finding the sum, the
distance between 14 and the sum? Why?
•
f. Is the sum to the right or left of 14 on the number line? On a vertical number
line?
Using Integer Chips
• Remember that every positive and negative
combine to make zero
• 3+6
• 7 + -4
• 5 + -9
• -2 + -4
Did you notice anything about the sign
of the sum?
• Can you create a rule for:
– Adding numbers with the same sign
– Adding numbers with different signs
Same Sign Sum
• RULE: Add integers with the same sign by
adding the absolute values and using the
common sign
Different Signs Difference
• RULE: Add integers with opposite signs by
subtracting the absolute values and using the
sign of the integer with the greater absolute
value.
Thinking about the problem:
Which addend has the greatest absolute value (length of the arrow)? What direction does
this arrow point?
What is the length of this arrow?
What is the final sign? What is the direction of the resulting arrow?
Closure
• What role does the |−16| = 16 play in
modeling the expression 2 + (−16)?
• Why do we keep the sign of the integer with
the larger absolute value when adding
numbers with different signs?
1)
a. Write an
equation for the
diagram to the
right.
b. Find the sum.
c. What integers
do the arrows
represent?
2) How do the models for
these two addition
problems differ on a
number line? How are
they the same?