Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 5 Number Sense
Problem
Solution
1) Michael and Terry are folding paper cranes. Terry is much faster and makes 7 cranes for every 4 that Michael makes. In the time Terry takes to make 42 cranes, how many does Michael make? 1. The fraction of Michael's rate to Terry's is 4/7.
2. Apply this fraction to Terry's cranes to get Michael's cranes =
    4/7 x 42 = 24 cranes.

2) A company makes two kinds of figurines. Each figurine weighs either 5 pounds or 9 pounds. They ship the figurines in boxes that can hold up to 91 pounds. How many of the 9-pound figurines can the company ship in a box if they want to load the box up to its maximum possible weight and they want to ship more of the 5-pound figurines?		 Solve this problem with guess-and-check. Here's the table:
(Remember, the number of 9-pound figurines must be less than the 5-pound ones.)
# 5 pound
figurines		# 9 pound
figurines		Total weight
11411x5 + 4x9 = 91

3) Anna has 10 more sheets of paper than Mary. Mary has 7 more sheets of paper than Caroline. They decide to split all of the paper between them equally. How many less sheets of paper would Anna have?		 1. Suppose that Caroline has 1 sheet. Then how many total sheets of paper are there? = 1 + 8 + 18 = 27 sheets.
2. Divide this by 3 = 9 sheets.
3. Anna has 18-9 = 9 less sheets.

Problem
Solution
4) Jeremy baked a cake. Sue cut the cake into equal-sized pieces and took one piece. Nathan took 1/5 of the remaining pieces. Finally, Jeremy took 1/3 of the remaining pieces. If 1/2 of the cake is still remaining, how many pieces did Sue cut the cake into? Work this problem backwards:
1. If Jeremy took 1/3 of the remaining pieces (X) and that left 1/2 of the cake, then the amount of the cake that was there before Jeremy was
    X - (1/3)X = 1/2.
    (2/3)X = 1/2
    X = 3/4 of the cake.
2. If Nathan took 1/5 of the remaining pieces (Y) and that left 3/4, then:
    Y - (1/5)Y = 3/4
    (4/5)Y = 3/4
    Y = 15/16 of the cake.
3. Then, what's left, (1 - 15/16) = 1/16th of the cake.
Sue cut the cake into 16 pieces.

5) Melissa is competing in a rowing race. She can row 4 miles in 30 minutes. How long would it take her to row the 30 miles in the race if she keeps the same pace? (Express your answer in hours and minutes)		 1. Compute Melissa's rate in miles/hour =
    4 miles x 60 min = 8 miles/hour.
      30 min     hour
2. Multiply this time the distance she has to row =
    30 miles at 8 miles/hour = 30/8 = 3 3/4 hours.
3. Convert this to hours and minutes =
    3 hours 45 minutes.