STUDY GUIDE FOR INVESTIGATIONS 1 AND 2
INVESTIGATION 1
Number Systems Goal: to identify numbers as members of various sets.
 Counting Numbers 1, 2, 3, …
 Whole Numbers 0, 1, 2, …
 Integers – positive and negative whole numbers
 Rational Numbers – positive and negative numbers that can be represented by a
ratio of integers; Integers plus fractions and terminating or repeating decimals
Problem 1.1 Goal: to explore the use of and notation for positive and negative
numbers.
 Represent situations as integers:
o a loss of 5 yards is -5
o a withdrawal of $25 is -25
o an increase in temperature of 15° is +15
Problem 1.2 Goal: to be able to locate integers on a number line and to use that
knowledge to compare and order positive and negative numbers.
 As you go up the number line numbers increase in value (are greater)
 As you go down the number line numbers decrease in value (are less)
 Opposites are the same distance from zero in opposite directions on the number
line
Problem 1.3 Goal: to explore and understand addition and subtraction of integers by
using a number line and to represent that understanding in a number sentence.
 Start + Change = End
 The Change tells Distance (number) and Direction (sign)
 5 + -12 as represented on a number line: Start at +5, go down the number line 12
places, end at -7. In a number sentence: 5 + -12 = -7
Problem 1.4 Goal: to understand addition and subtraction of integers through the
use of a chipboard model.
 Red chips represent negative numbers
 Black chips represent positive numbers
 One red chip and one black chip = 0 and are called a Zero Pair
 Any number of zero pairs may be added to the chip board without changing the
value of the board.
 -5 - +3 as represented on the chipboard: start with 5Red chips. Since you need to
take 3Black chips away and you do not have any black chips, put three zero pairs
on the chipboard. You now have 8Red and 3Black chips. The value of the
chipboard is still -5. Take the 3Black chips away and you are left with 8Red
chips. In a number sentence: -5 - +3 = -8
INVESTIGATION 2
Problem 2.1 Goal: to develop algorithms for adding integers.
 When adding two numbers with the same sign, ignore the sign and add the
absolute values of the numbers, and keep the same sign.
o +4 + +17 = +21
o -4 + -17 = -21

When adding two numbers with different signs, subtract the absolute values of the
numbers, and then take the sign of the number that has the greater absolute value
(is further from zero).
o +4 + -17 = -13
o -4 + +17 = 13
Problem 2.2 Goal: to develop algorithms for subtracting integers.
 When subtracting two integers with the same signs or different signs, add the
opposite: change subtraction to addition, change the sign of the second number
(subtrahend), and then follow the rules for addition.
o -5 – 2 = -5 + -2 = -7
o +8 - +12 = +8 + -12 = -4
o 2 - - 5 = 2 + +5 = +7
o -8 - -12 = -8 + +12 = +4