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Proportional Relationships
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 What PROPORTIONAL relationships are.
 How to identify proportional relationships in data tables, equations AND graphs.
 That this knowledge can help us bake, play sports, and even learn about animals.

Discussion Questions

Before VideoHow is the following sequence of numbers related? 3, 6, 9, 12, 15ANSWER

Add 3 each time to find the next number. Or multiply 3 by 1, 2, 3, 4, 5 to get the sequence.

Add 3 each time to find the next number. Or multiply 3 by 1, 2, 3, 4, 5 and then add 1 to each answer to get the sequence.

The table has two columns, one representing the number of muffins and one representing teaspoons of sugar. For one muffin, I need 5 teaspoons of sugar, for 2 muffins I need 2 × 5 = 10 teaspoons, for 3 muffins I need 3 × 5 = 15 teaspoons. I can keep going, but usually I only need about five pairs of values to observe a relation.

I can plug in a value for x to find the corresponding value of y. I can try this with a few values, usually starting with 1, until I have enough data to make observations.

I can use a coordinate plane, which is a graph that uses two variables to describe the location of a point. The vertical line represents yvalues and the horizontal line represents xvalues.


After VideoEach person gets 3 scoops of ice cream. Is the relationship between the number of people and the number of scoops proportional?ANSWER

It is proportional. 1 person means 3 scoops, 2 people means 6 scoops, 3 people means 9 scoops. I always multiply the number of people by 3 to get the number of scoops.

No, it is nonproportional. Some of the number pairs are related by multiplying by 3, but some of them are related by multiplying by 2.

The constant of proportionality is 3.5. I can always find the constant of proportionality by dividing the second number in a pair by the first number. For each pair, multiply the first number by 3.5 to get the second number.

No. All proportional relationships are represented by equations that relate variables only through multiplication and are in the form y=kx, where k is any number. Since 1 is added in this equation, it is not proportional.

Yes, if I connect the points and extend a line through them, the line goes through the origin.



Vocabulary

Proportional relationship
DEFINE
When two variables are always related in the same way through multiplication.

Constant of proportionality
DEFINE
The number that you always multiply by to define a proportional relationship.

Nonproportional relationship
DEFINE
When variables are not always related in the same way.

Equations
DEFINE
Two expressions that have the same value and are separated by an equal sign.

Coordinate Plane
DEFINE
A graph that uses two variables to describe the location of a point.

Xaxis
DEFINE
The horizontal line on a graph.

Yaxis
DEFINE
The vertical line on a graph.

Proportional relationship
DEFINE

Reading Material
Download as PDF Download PDF View as Separate PageWHAT ARE PROPORTIONAL RELATIONSHIPS?A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph.
To better understand proportional relationships…
WHAT ARE PROPORTIONAL RELATIONSHIPS?. A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph. To better understand proportional relationships…LET’S BREAK IT DOWN!
Make muffins using a proportional relationship.
To make 1 dozen muffins, you need 2 eggs. If you want to make 2 dozen muffins, you need 4 eggs. To make 3 dozen muffins, you need 6 eggs. 1 times 2 is 2, 2 times 2 is 4, 3 times 2 is 6. The number of eggs is always 2 times the number of batches of muffins. This is called a proportional relationship. Now you try: How can you tell if the following data represents a proportional relationship? 1:3, 2:6, 3:9, 4:12
Make muffins using a proportional relationship. To make 1 dozen muffins, you need 2 eggs. If you want to make 2 dozen muffins, you need 4 eggs. To make 3 dozen muffins, you need 6 eggs. 1 times 2 is 2, 2 times 2 is 4, 3 times 2 is 6. The number of eggs is always 2 times the number of batches of muffins. This is called a proportional relationship. Now you try: How can you tell if the following data represents a proportional relationship? 1:3, 2:6, 3:9, 4:12The constant of proportionality is the multiplication factor.
Adesina works different numbers of hours at a skating rink. The amount of money she makes for each number of hours she works is represented by this relationship: 1:$5, 2:$10, 3:$15, 4:$20, 5:$25. Is the relationship proportional? 1 times 5 is 5, 2 times 5 is 10, and so on. The number of dollars earned is always 5 times the number of hours worked. The relationship is proportional. The number that you always multiply by is called the constant of proportionality. The constant of proportionality of this relationship is 5. Now you try: What is the constant of proportionality for the following set of ratios? 2:14, 3:21, 4:28, 5:35
The constant of proportionality is the multiplication factor. Adesina works different numbers of hours at a skating rink. The amount of money she makes for each number of hours she works is represented by this relationship: 1:$5, 2:$10, 3:$15, 4:$20, 5:$25. Is the relationship proportional? 1 times 5 is 5, 2 times 5 is 10, and so on. The number of dollars earned is always 5 times the number of hours worked. The relationship is proportional. The number that you always multiply by is called the constant of proportionality. The constant of proportionality of this relationship is 5. Now you try: What is the constant of proportionality for the following set of ratios? 2:14, 3:21, 4:28, 5:35You can identify if a relationship is proportional.
The following data shows the number of soccer games you played related to the number of goals you scored: 2:8, 3:12, 4:20, 5:36, 6:50. 2 times 4 is 8, and 3 times 4 is 12. But 4 times 4 is 16, not 20. And 5 times 4 is 20, not 36. You can't always multiply the number of games played by the same number to get the number of goals scored. This is a nonproportional relationship. Now you try: Identify if the following data represents a proportional relationship: 3:9, 5:15, 6:24, 8:32
You can identify if a relationship is proportional. The following data shows the number of soccer games you played related to the number of goals you scored: 2:8, 3:12, 4:20, 5:36, 6:50. 2 times 4 is 8, and 3 times 4 is 12. But 4 times 4 is 16, not 20. And 5 times 4 is 20, not 36. You can't always multiply the number of games played by the same number to get the number of goals scored. This is a nonproportional relationship. Now you try: Identify if the following data represents a proportional relationship: 3:9, 5:15, 6:24, 8:32You can describe proportional relationships using equations.
Every kitten has 2 ears. You can write an equation to show how the number of kittens is related to the number of ears. Let x be the number of kittens and y be the number of ears. So, y=2x, since the number of ears is always twice the number of kittens. You can plug in any number of kittens for x to find the number of ears, y. For example, 5 kittens have y = 2 × 5 = 10 ears. Now you try: Write an equation to describe the relationship between the number of dogs and the number of legs in all.
You can describe proportional relationships using equations. Every kitten has 2 ears. You can write an equation to show how the number of kittens is related to the number of ears. Let x be the number of kittens and y be the number of ears. So, y=2x, since the number of ears is always twice the number of kittens. You can plug in any number of kittens for x to find the number of ears, y. For example, 5 kittens have y = 2 × 5 = 10 ears. Now you try: Write an equation to describe the relationship between the number of dogs and the number of legs in all.You can recognize proportional relationships in equations and graphs.
You can recognize proportional relationships in equations and graphs. Equations that represent proportional relationships are always in the form y=kx, where k is the constant of proportionality. That means that the relationship between x and y is always multiplicative, with nothing added or subtracted. Unlike y=2x, y=2x+4 and y=2x5 do not represent proportional relationships. 4 is added or 5 is subtracted from the product. The graph of a proportional relationship is always a straight line that passes through the origin, (0, 0). Now you try: Identify which equation(s) represent proportional relationships: a) y=7.7x b) y=3x+5 c) y=13x 
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Science & Math$_{/yr}

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Identify the constant of proportionality in the relationship: 2:8, 3:12, 5:20, 7:28.
Decide if the data represents a proportional relationship. Explain why or why not. 5:20, 8:32, 9:27, 11:33.
Write an equation to represent the proportional relationship between dining chairs and chair legs, assuming each chair has 4 legs.
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