Suppose you have a poster that is 12 inches by 15 inches and a lot of 3 inch by 5 inch index cards (“3-by-5 cards” for short).
(a)
What is the area of your poster in 3-by-5 cards? How do you know? Be sure to draw a picture. Write down your answer, including the units, and be ready to explain this to the class.
(b)
Is there another way that you could have done part (a)? If yes, explain your second method. Write down your answer, including the units, and be ready to explain this to the class. If no, explain why not.
Suppose you have a lot of 1 inch by 1 inch squares also known as “square inches”. What is the area of your poster in square inches? How do you know your answer is correct? If you used a formula, why does it work? If you did not use a formula, explain your method.
Now suppose you have a lot of 1 foot by 1 foot squares, also known as “square feet”.
(a)
Draw a picture of one square foot.
(b)
What is the area of your poster in square feet? How do you know your answer is correct? If you used a formula, why does it work? If you did not use a formula, explain your method using a picture and Math 1125 reasoning about the meaning of multiplication. (If you did not use this book when you took Math 1125 - see Chapter 4.1 in our current text.)

If you used multiplication to solve the previous problems, you might have noticed a pattern that has something to do with the familiar “ formula you learned in school. If you didn’t use multiplication in the previous problems, look again with this idea in mind!
(a)
Explain how the “” method is related to the other methods we have been using to measure area. Be as specific as you can!
(b)
Using your ruler, try out the “” method on the purple rectangle shown below. What is the area of that rectangle? How do you know? What are the units? Where are the units? How is this related to our problem with the poster?
(c)
How did measurement of two LENGTHS generate an answer in an area unit?
2025-09-14 02:53:08