Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 5 Number Sense


Problem
Solution
1) Carla baked 36 cookies for the bake sale. She called Daniel and discovered that he baked 45. They decide to combine their cookies and put them into packages with an equal number of cookies in each package. If they put more than one cookie in each package, what is the smallest number of cookies per package that they can make that makes all the packages even and how many packages will they fill? 1. The total number of cookies = 81.
2. What are the factors of this number? 3,9,27
3. Find the smallest factor of this number = 3
  This is the number of cookies per package.
4. Divide the total number of cookies by this factor to get the number of packages = 27 of 3 cookies each.

2) Kelly and Kylie are swimming. Kelly is much faster than Kylie and swims 5 laps to every 2 laps Kylie makes. In the time Kelly swims 35 laps, how many laps does Kylie swim?		 1. What is the ratio of Kylie's laps to Kelly's laps? = 2/5
2. Multiply this ratio time Kelly's laps to get Kylie's laps =
    2/5 x 35 = 14 laps.

3) Sally is thinking of a three digit number and tells you this:
No digit is repeated.
greatest common factor of the three digits is 1.
The least common multiple of the three digits is 12. The number is also the area of a square with a whole number side length. What is her number?		 1. Since the LCM of her number is 12, all the digits must evenly divide into 12. The only digits that fit this requirement are 1,2,3,4 and 6. So the 3-digit number must consist of 3 of these numbers.
2. The number is a square, so list the 3-digit numbers that are the squares of a whole number that consist only of these digits:
    The only number that fits is 324 which is 182.

Problem
Solution
4) Eric dropped a ball from his deck. On the 1st bounce it bounced up one-half the distance of the drop and fell back to the ground. On the 2nd bounce it bounced one-third the distance of the 1st bounce and fell back to the ground. On the 3rd bounce it bounced one-fourth of the distance of the 2nd bounce and fell back to the ground. On the 4th bounce it bounced one-fifth of the distance of the 3rd bounce and fell one inch to the ground before rolling away. How high off the ground was the ball when Eric dropped it? Work this problem backwards:
1. Since the 4th bounce fell 1 inch to the ground,
    that was the height of the 4th bounce.
2. If the 4th bounce was 1/5 of the 3rd bounce,
    then the 3rd bounce was 5 inches high.
3. If the 3rd bounce was 1/4 of the 2nd bounce,
    then the 2nd bounce was 20 inches high.
4. If the 2nd bounce was 1/3 of the 1st bounce,
    then the 1st bounce was 60 inches high.
5. This 1st bounce was 1/2 of the deck height,
    so the height when Eric dropped the ball was 120 inches.

5) Susan set a whole pizza in a circular pan on the dinner table. Sam took one fourth of the pizza. Keenan took half of what was left. Miguel then cut one third of what remained. What portion of the pizza is left in the pan? Express your answer as a fraction in lowest terms (i.e. as a reduced fraction) .		 1. If Sam took 1/4 of the pizza, that left 3/4 of the pizza.
2. If Keenan took half of that, he left 3/8 of the pizza.
3. If Miguel then took 1/3 of that, then what was left was
    1/3 x 3/8 = 1/8 of the pizza, so what was left was 2/8.
4. Reduce: 1/4 of the pizza