Understanding Relationships Between Variables

Mrs. Lucky introduces lesson 16, focusing on related quantities and ratios. The lesson includes a warm-up exercise comparing honey jar prices using ratios. It explains dependent and independent variables, and how to use ratios to mix paint and create tables. The lesson concludes with creating equations and graphs from these tables.

What is the primary goal of using equations and graphs in this lesson?

• To solve complex algebraic equations

• To describe relationships with ratios

• To learn about historical mathematicians

• To memorize mathematical formulas

Which honey jar offers a better deal based on cost per pound?

• 1.5-pound jar for $2.90

• 1.5-pound jar for $3.90

• 5-pound jar for $20.00

• 5-pound jar for $15.35

In the boat example, what is the dependent variable?

• The boat's speed

• The time traveled

• The distance traveled

• The boat's fuel consumption

What is the ratio of red paint to yellow paint in the mixing table?

• 5 to 2

• 3 to 2

• 2 to 3

• 1 to 1

How do you calculate the total cups of paint in the mixing table?

• Subtract the cups of yellow paint from red paint

• Multiply the cups of red paint by 2

• Add the cups of red and yellow paint

• Divide the cups of yellow paint by 2

What equation represents the relationship between R and T?

• R = 3/5 * T

• R = 2/5 * T

• R = 5/2 * T

• R = T/2

Which variable is considered independent in the equation R = 2/5 * T?

• T

• R

• Both R and T

• Neither R nor T

How is the relationship between Y and R expressed when R is the independent variable?

• Y = 2/3 * R

• Y = R/2

• Y = 3/2 * R

• Y = R/3

What should you expect when plotting the points from the table on a graph?

• The points will form a circle

• The points will be scattered randomly

• The points will form a straight line

• The points will form a triangle

What is the purpose of creating graphs in this lesson?

• To visualize the relationship between variables

• To make the lesson more colorful

• To confuse the students

• To replace the need for equations