Andre is building a tower out of different foam blocks. These blocks come in three different thicknesses: \(\frac{1}{2}\) foot, \(\frac{1}{4}\) foot, and \(\frac{1}{8}\) foot. 

Andre stacks two \(\frac{1}{2}\)-foot blocks, two \(\frac{1}{4}\)-foot blocks, and two \(\frac{1}{8}\)-foot blocks to create a tower. What is the height of the tower in feet? Explain or show how you know.

Find the value of each of the following sums. Show your reasoning. Use number lines if you find them helpful.

1. \(\frac{1}{10} + \frac{3}{100}\)

   

2. \(\frac{24}{100} + \frac{4}{10}\)

   

3. \(\frac{7}{10} + \frac{13}{100}\)

   

Is the value of each expression greater than, less than, or equal to 1? Explain how you know.

1. \(\frac{3}{10} + \frac{7}{100}\)
2. \(\frac{13}{10} + \frac{7}{100}\)
3. \(\frac{30}{100} + \frac{7}{10}\)

A chocolate cake recipe calls for 2 cups of flour. You gather your measuring cups and notice you have the following sizes: \(\frac{1}{2}\) cup, \(\frac{1}{3}\) cup, \(\frac{1}{4}\) cup, and \(\frac{1}{6}\) cup.

1. What are the different ways you could use all 4 measuring cups to measure 2 cups of flour?

2. What are other ways you could use just some of the 4 measuring cups to measure exactly 2 cups of flour?

A dime is worth \(\frac{1}{10}\) of a dollar and a penny is worth \(\frac{1}{100}\) of a dollar.

1. What are different combinations of dimes and pennies that represent \(\frac{89}{100}\) of a dollar? Use equations to show your reasoning.
2. A nickel is worth \(\frac{5}{100}\) of a dollar. What are some different combinations of dimes, nickels, and pennies that represent \(\frac{89}{100}\) of a dollar? Use equations to show your reasoning.