30 Problem Bank
Problem 6
Harriet is part of a group of five children who share four pies. Jeff is part of a group of seven children who share four pies. Jean is part of a group of seven children who share six pies.
- Who gets more pie, Harriet or Jeff? Justify your answer!
- Who gets more pie, Jeff or Jean? Justify your answer!
- Who gets more pie, Harriet or Jean? Justify your answer!
Problem 7
Yesterday was Zoe’s birthday, and she had a big rectangular cake. Today, of the cake is left. The leftover cake is shown here.
Draw a picture of the original (whole) cake and explain your work.
Problem 8
Use benchmarks and intuitive methods to arrange the fractions below in ascending order. Explain how you decided. (The point of this problem is to think more and compute less!):
Problem 9
Which of these fractions has the larger value? Justify your choice.
Problem 10
Solve each division problem. Look for a shortcut, and explain your work.
Problem 11
Yoko says
because she cancels the sixes:
But note:
So is Yoko right? Does her cancelation rule always work? If it does not always work, can you find any other example where it works? Can you find every example where it works?
Problem 12
Jimmy says that a fraction does not change in value if you add the same amount to the numerator and the denominator. Is he right? If you were Jimmy’s teacher, how would you respond?
Problem 13
- Shelly says that if then . Is Shelly’s claim always true, sometimes true, or never true? If you were Shelly’s teacher, what would you say to her?
- Rob says that if then . Is Rob’s claim always true, sometimes true, or never true? If you were Rob’s teacher, what would you say to him?
Problem 14
Jill, her brother, and another partner own a pizza restaurant. If Jill owns of the restaurant and her brother owns of the restaurant, what fraction does the third partner own?
Problem 15
John spent a quarter of his life as a boy growing up, one-sixth of his life in college, and one-half of his life as a teacher. He spent his last six years in retirement. How old was he when he died?
Problem 16
Nana was planning to make a red, white, and blue quilt. One-third was to be red and two-fifths was to be white. If the area of the quilt was to be 30 square feet, how many square feet would be blue?[1]
Problem 17
Rafael ate one-fourth of a pizza and Rocco ate one-third of it. What fraction of the pizza did they eat?
Problem 18
Problem 18 (Tangrams). Tangrams[2] are a seven-piece puzzle, and the seven pieces can be assembled into a big square.
- If the large square shown above is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers.
- The tangram puzzle contains a small square. If the small square (the single tangram piece) is one whole, assign a fraction value to each of the seven tangram pieces. Justify your answers.
- The tangram set contains two large triangles. If a large triangle (the single tangram piece) is one whole, assign a fraction value to each of the seven