Overview
QUESTION 1
When changing a mixed number to an improper fraction, many students say, "multiply the denominator of the fraction to the whole number and then add the numerator." This algorithm is certainly correct, but why does it work?
Change 2 3/5 to 13/5 explaining why the two amounts are equal. Do not use the algorithm above. Give the conceptual model.
QUESTION 2
Find the sum and difference for the following pair of mixed numbers keeping your numbers as mixed numbers. Show all of your thought processes.
QUESTION 3
Use the properties of fraction addition to calculate the following sum mentally. What properties would you use? Show your process.
QUESTION 4
Show your work for the following word problem:
Rafael ate 1/4 of a pizza and Rocco ate 1/3 of it. What fraction of the pizza did they eat? How much was left?
QUESTION 5
Show your work for the following word problem:
Greg plants two-thirds of his garden in potatoes and one eighth in carrots. What fraction of the garden remains for his other crops?
QUESTION 6
The Egyptians were said to use only unitary fractions (a fraction with a numerator of 1), with the exception of 2/3. It is know that every unitary fraction can be expressed as the sum of two unitary fractions. If the fraction 1/3 is the sum of 
where a < b, that are the values of a and b?