Calculating Area and Expansion

This video tutorial covers a seventh-grade lesson on mathematical area problems, focusing on a practical example involving Patty's garden. The lesson begins with calculating the area of Patty's current garden and explores how expanding the garden affects its area. The tutorial includes drawing diagrams to visualize the problem, exploring alternative methods for area calculation, and analyzing the impact of changing dimensions separately. It concludes with example problems and introduces variables and algebraic expressions to solve area problems.

What is the current area of Patty's garden?

• 12 square feet

• 15 square feet

• 10 square feet

• 9 square feet

How much does Patty plan to increase the length of her garden?

• 5 feet

• 4 feet

• 3 feet

• 2 feet

What is the new area of Patty's garden after expansion?

• 35 square feet

• 32 square feet

• 28 square feet

• 30 square feet

How can the area of the garden be calculated alternatively?

• By adding the smaller sections

• By multiplying the length and width

• By dividing the length by the width

• By subtracting the width from the length

If only the length is increased, how much does the area increase?

• 8 square feet

• 11 square feet

• 10 square feet

• 9 square feet

What is the increase in area if only the width is expanded?

• 10 square feet

• 7 square feet

• 8 square feet

• 9 square feet

What additional area is gained from the bonus section?

• 5 square feet

• 6 square feet

• 7 square feet

• 8 square feet

In the new example, what is the area of the original 3x3 square?

• 8 square feet

• 6 square feet

• 10 square feet

• 9 square feet

What is the area of the 2x2 section in the new example?

• 3 square feet

• 2 square feet

• 5 square feet

• 4 square feet

What is the expression for the area when using variables a and b?

• (a + b)^2

• a^2 - b^2

• a^2 + 2ab + b^2

• a^2 + b^2