# 6.3 - Understand Integers

6.3  The student will

a)  identify and represent integers;

b)  compare and order integers; and

c)  identify and describe absolute value of integers.

### BIG IDEAS

• I can determine yard line after each play of a football game, calculate amount of force required to stop a drag racer, figure golf score in relation to par, and track my finances over time.
• I will understand the role of negative values in practical situations.

• I can determine yard line after each play of a football game, calculate amount of force required to stop a drag racer, figure golf score in relation to par, and track my finances over time.
• I will understand numbers and their opposites are equal distance from zero on a number line and the role of negative values in practical situations.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - 6.3 Understanding

• The set of integers includes the set of whole numbers and their opposites {…-2, -1, 0, 1, 2, …}. Zero has no opposite and is an integer that is neither positive nor negative.
• Integers are used in practical situations, such as temperature (above/below zero), deposits/withdrawals in a checking account, golf (above/below par), time lines, football yardage, positive and negative electrical charges, and altitude (above/below sea level).
• Integers should be explored by modeling on a number line and using manipulatives, such as two-color counters, drawings, or algebra tiles.
• The opposite of a positive number is negative and the opposite of a negative number is positive.
• Positive integers are greater than zero.
• Negative integers are less than zero.
• A negative integer is always less than a positive integer.
• When comparing two negative integers, the negative integer that is closer to zero is greater.
• An integer and its opposite are the same distance from zero on a number line.
• Example: the opposite of 3 is −3 and the opposite of −10 is 10.
• On a conventional number line, a smaller number is always located to the left of a larger number (e.g.,–7 lies to the left of –3, thus –7 < –3; 5 lies to the left of 8 thus 5 is less than 8)
• The absolute value of a number is the distance of a number from zero on the number line regardless of direction. Absolute value is represented using the symbol (e.g.,  and).
• The absolute value of zero is zero.

### ESSENTIALS

• What role do negative integers play in practical situations?
Some examples of the use of negative integers are found in temperature (below 0), finance (owing money), below sea level. There are many other examples.
• How does the absolute value of an integer compare to the absolute value of its opposite?
They are the same because an integer and its opposite are the same distance from zero on a number line.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• 6.3a2  Identify an integer represented by a point on a number line.
• 6.3a1  Model integers, including models derived from practical situations.
• 6.3b1  Compare and order integers using a number line.
• 6.3b2  Compare integers, using mathematical symbols (<,≤,>,≥,=).
• 6.3c1  Identify and describe the absolute value of an integer.

### KEY VOCABULARY

integer, absolute value, positive integers, negative integers, whole numbers, number line, set, opposite

Updated: Aug 23, 2019