Cow Pen Area and Modifications

This video tutorial covers the use of area models and algebra tiles to understand multiplying linear expressions and adding quadratic expressions. It begins with calculating the area of a duck pen, then extends to a cow pen by increasing dimensions. The tutorial demonstrates using algebra tiles and substitution to find areas, and explores adjusting pen sizes to understand changes in area calculations.

What is the main objective of this lesson?

• To explore the history of the North Carolina State Fair

• To learn about the history of algebra

• To develop and solidify understanding of area models and algebra tiles

• To memorize mathematical formulas

How do you calculate the area of the duck pen?

• Multiply the length by the width

• Add the length and width

• Subtract the width from the length

• Divide the length by the width

What changes are made to the duck pen to create the cow pen?

• Increase both sides by two feet

• Decrease both sides by one foot

• Keep the dimensions the same

• Increase one side by four feet and the other by three feet

What is the shape of the cow pen after the modifications?

• Triangle

• Rectangle

• Circle

• Square

How many spaces have an area of X in the cow pen model?

• 7

• 9

• 11

• 5

What is the expression for the area of the cow pen using the distributive property?

• X squared plus 5X plus 10

• X squared plus 7X plus 12

• X squared plus 6X plus 9

• X squared plus 8X plus 16

What is the result when substituting X with 5 in the area expression?

• 80 square feet

• 72 square feet

• 90 square feet

• 60 square feet

What modification is made to the cow pen in problem 6a?

• Reduce both sides by one foot

• Extend both sides by two feet

• Keep the dimensions the same

• Extend one side by five feet and reduce the other by three feet

What is the new area expression for the goat pen in problem 6c?

• X squared plus 6X minus 10

• X squared minus 6X plus 10

• X squared minus 8X plus 15

• X squared plus 8X minus 15