Understanding Proportional Relationships

In this lesson, Mrs. Lopez teaches Grade 7 students about identifying proportional and non-proportional relationships in graphs. The lesson begins with an introduction to the concept, followed by an exercise involving candy bar sales to determine proportionality. Students then engage in an exploratory challenge to create tables showing proportional relationships. The lesson continues with graphing exercises to compare examples and concludes with a discussion on determining proportional relationships in graphs, emphasizing the importance of a straight line starting from the origin.

What is a key characteristic of a proportional relationship?

• It has a variable unit rate.

• It involves a constant unit rate.

• It involves division only.

• It only uses subtraction.

What is the first step in determining if a relationship is proportional using a table?

• Check if the unit rate is constant.

• Check if the values are increasing.

• Check if the values are equal.

• Check if the values are decreasing.

In the candy bar example, what indicates that the relationship is not proportional?

• The money received is always the same.

• The unit rate is constant.

• The number of candy bars is always the same.

• The unit rate varies.

In the candy bar example, what is the unit rate for the first data point?

• 0.5

• 3

• 2

• 1.5

How can you create a proportional relationship using a given ratio?

• By dividing both terms by different numbers.

• By multiplying both terms by the same number.

• By subtracting the same number from both terms.

• By adding the same number to both terms.

What is the significance of the point (0,0) in a proportional graph?

• It indicates the graph is non-proportional.

• It means the graph is a curve.

• It suggests the graph is incomplete.

• It shows the graph starts from the origin.

What happens to the graph if the relationship is not proportional?

• It forms a circle.

• It forms a straight line.

• It does not form a straight line.

• It starts from the origin.

What is the main difference between the graphs in example one and two?

• Example one is a line, example two is not.

• Example two is a line, example one is not.

• Both are lines.

• Neither are lines.

Which of the following is true about a graph that represents a proportional relationship?

• It does not start from the origin.

• It starts from the origin and is a straight line.

• It is a zigzag line.

• It is a curved line.

Which of the following is NOT a rule for a proportional relationship in a graph?

• The graph is a straight line.

• The graph starts from the origin.

• The graph is a curve.

• The graph has a constant slope.