Lesson 1-1: Factors and Multiples

Factor: a number that be evenly divide into another number without a remainder.

Ex: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 .

One easy way to find factors is to find the factor pairs that can be multiplied to equal the number

Ex: Factor Pairs of 24 are 1,24 2, 12, 3,8 4, 6

Greatest common Factor (GCF): is the largest number that is a whole number factor of two or more numbers

To find the GCF

1. List the factors or factor pairs of each number

2. Find the common factors (numbers that are factors of both)

3. Your GCF is the largest of these common factors.

Multiple: a number that you get when you multiply a number by a whole number.

Ex: Multiplies of 6 are 6 (6x1), 12(6x2), 18(6x3), 24(6x4), 30(6x5), etc .

One easy way to find multiples of a number is to skip counting by the first number.

Least Common Multiple (LCM): is the smallest number that is a common multiple of two or more numbers.

To find the LCM

1. List the multiples of each number

2. Find the smallest number that is common (same) to all lists

Lesson 1-2: Ratios

Ratio: A comparison of two numbers by division. We most often express a ratio as a fraction but there are 3 different ways to write each ratio. Ratios should always be written in simplified form.

* It is important to write a ratio in the way you are asked to compare the items.

Ex: If I have 2 tennis balls and 5 soccer balls, there are many ways to express this comparison of tennis balls to soccer balls as a ratio. You can express a relationship between or

Fraction notation: or Word notation: 2 to 5 or 2 to 7 Odds notation: 2: 5 or 2:7

This means for every 2 tennis balls there are 5 soccer balls or there are 2 tennis balls out of 7 total balls.

To simplify a ratio:

1. Find a common factor of the numerator and the denominator (the GCF is best)

2. Divide the numerator and the denominator by the common factor.

3. Repeat steps 1 & 2 until there is no common factor other than 1.

This ratio expresses a relationship

Lesson 1-3: Rates

Rates: A ratio comparing two quantities with different units. We most often express a rate as a fraction with words but there are 3 different ways to write each rate. Rates should always be written in simplified form or as a unit rate.

Units: words that describe the number

Ex: 60 miles- 60 is the quantity (number) but miles is the unit.

* It is important to write a rate in the way you are asked to compare the items.

Ex: If I drove 60 miles in 24 minutes

or (simplified form)

Unit Rate: A rate with a denominator of 1 unit. We most often express a unit rate as a fraction with words and the denominator must be only 1 unit.

Unit Price or Unit cost: A rate with the cost as the numerator and a denominator of 1 unit.

To Find Unit Rate or Unit Price:

1. Set up your rate as a fraction with words

2. Divide both the numerator and the denominator by the denominator so the denominator will now equal 1..

Lesson 1-4: Ratio Tables

Ratio Tables:A table with units and numbers.

Each row contains a unit and numbers that go along with that unit.

Each column contains a pair of numbers that when scaled up (multiplied to make numbers bigger) orscaled down (divided to make numbers smaller) is equal to every other column.

Sometimes you need to scale down before scaling up so the numbers are more compatible.

Lesson 1-5: Graphing Ratio Tables

Coordinate Plane: is formed when two perpendicular number lines intersect at their zero points.

Origin: The intersection of the two zero points (0,0).

X-axis: The horizontal number line (left to right).

Y-axis: The vertical number line (up and down).

Ordered Pair: A pair of numbers used to give directions to a specific point on the coordinate plane such as (2, 3). These are always in the order of (x-coordinate, y-coordinate).

X-coordinate: The first number in an ordered pair. This numbers tells you how many units to move right (positive numbers) or left (negative numbers).

Y-coordinate: The second number in an ordered pair. This numbers tells you how many units to move up (positive numbers) ordown (negative numbers).

To graph an Ordered Pair

1. Start at the origin (0, 0)

2. Move left or right along the x-axis until you find the x-coordinate.

3. From that point move up or down along the vertical line you are on until you find the y-coodinate.

4. Put a dot on the intersection of the x and y coordinates.

To describe the pattern in the graph:

The pattern in the graph can always be described using this format

As the (fill this in with the label of the x-axis) increases by 1, the (fill this in with the label of the y-axis) (choose increases or decreases)by (fill this in with how much the graph is changing by)

As the number of CD’s increases by 1, the cost in dollars increasesby $3.

Lesson 1-6: Equivalent Rates

Determine if the pair of ratios or rates is equivalent. Explain why or why not.

Method #1 (Using Unit Rates)

1. Set up the first comparison as a rate then find its unit rate.

2. Set up the second comparison as a rate then find its unit rate.

3. Ask yourself if they are equivalent?

4. Explain why or why not?

Method #2 (Check to see if they are equivalent fractions)

1. Set up the first comparison as a rate.

2. Set up the second comparison as a rate.

3. Ask yourself if the numerator or denominator of one rate can be scaled (multiplied or divided) to get the corresponding (matching) value in the other rate?

4. If yes, when you do the same thing to the other part of the rate, does that corresponding part equal what it should?

5. Explain why or why not?

Method #3 (Scale each rate to simplest form)

1. Set up the first comparison as a rate and simplify it.

2. Set up the second comparison as a rate and simplify it.

3. Ask yourself if the simplest forms of each rate are equivalent?

4. Explain why or why not?

Page 1 of 9Glencoe Grade 6Chapter 1