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Proportional Relationships
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What you will learn from this videoWhat you will learn
- 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 Video
How is the following sequence of numbers related? 3, 6, 9, 12, 15ANSWERAdd 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 y-values and the horizontal line represents x-values.
After Video
Each person gets 3 scoops of ice cream. Is the relationship between the number of people and the number of scoops proportional?ANSWERIt 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 non-proportional. 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.
- Non-proportional 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.
- X-axis DEFINE
The horizontal line on a graph.
- Y-axis DEFINE
The vertical line on a graph.
- Proportional relationship DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide