M3: Sections 1.5 to 1.8 NotesPage 1 of 16

Academic

Pre-Algebra

Sections 1.5 to 1.8 Notes

Variables, Expressions, & Integers

Name______Pd___

Sections 1.5-1.6 VocabularyWords

Mean, Median, Mode, and Range Notes:

  • Mean
  • Median
  • Mode
  • Range

Section 1.5 Notes:

  • Additive inverse
  • Whole numbers

Sections 1.7-1.8 Vocabulary Words

Section 1.8 Notes:

  • Origin
  • Scatter plot
  • Quadrant
  • Coordinate plane
  • Ordered pair
  • X-coordinate
  • Y-coordinate
  • X-axis
  • Y-axis

Mean, Median, Mode, and Range

Learning Goal: We will find the mean, median, mode, and range of a set of data.

Mean – the sum of the data values divided by the number of data values

Median – the middle value when the values are written in numerical order

Mode – the data value that occurs most often (may have no mode or more than one)

Range – the difference of the greatest data value and the least data value

Practice:

Section 1.5: Adding Integers

Learning Goal: We will add positive and negative integers.

USING A NUMBER LINE:

Example 1: Adding Integers Using a Number Line

ON YOUR OWN:

ADDING INTEGERS:

  1. Same Signs
  1. Different Signs
  1. Opposites

Additive Inverse Property:

Additive Inverse –

Example 2: Adding Two Integers

Example 3: Adding More Than Two Integers

Find the sum

ON YOUR OWN:

Example 4: Evaluating Variable Expressions

ON YOUR OWN:

Section 1.6: Subtracting Integers

Learning Goal: We will subtract positive and negative integers.

Relating Subtraction to Addition:

Example 1: Subtracting Integers

a. / b. / c.

ON YOUR OWN:

Example 2: Evaluating Variable Expressions

ON YOUR OWN:

Finding Change Using Subtraction

**You can use subtraction to find the change of a variable quantity.

***Subtract the ______of the quantity from the

______.

Example 3: Evaluating Change

Eruptions have caused the volcano to grow. In 1962, the summit elevation of Kick-‘em-Jenny was -235 meters. In 2002, the summit elevation was -182 meters. By how many meters did the elevation of the volcano change?

ON YOUR OWN:

Section 1.7: Multiplying Integers and Dividing

Learning Goal: We will multiply and divide integers.

Multiplying Two Integers:

  1. Product of Same Signs
  1. Product of Different Signs
  1. Product of An Integer and Zero

Example 1: Multiplying Integers

a. / b. / c.

ON YOUR OWN:

Find the product.

Example 2: Multiplying Integers

Dividing Integers

  1. Quotient of Same Signs
  1. Quotient of Different Signs
  1. Quotient of An Integer and Zero

Example 3: Dividing Integers

a. / b. / c.

ON YOUR OWN:

Find the quotient.

Example 4: Finding a Mean

Section 1.8: The Coordinate Plane

Learning Goal: We identify and plot points in a coordinate plane.

Vocabulary:

Coordinate plane – a system formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis

Ordered pair – a pair of numbers (x, y) that can be used to represent a point in a coordinate plane. The first number is the x-coordinate, and the second number is the y-coordinate.

Quadrant – one of four regions that a coordinate plane is divided into by the x-axis and y-axis.

Origin – the point (0, 0) where the x-axis intersects the y-axis

x-axis – the horizontal number line in a coordinate plane

y-axis – the vertical number line in a coordinate plane

Example 1: Naming Points in a Coordinate Plane

ON YOUR OWN:

Give the coordinates o the point.

  1. C
/
  1. D
/
  1. E

Example 2: Plotting Points in a Coordinate Plane

ON YOUR OWN:

  • scatter plot - a graph in a coordinateplane that displays paired data. Each data pair is plotted as a point.

Example 3: Making a Scatter Plot