Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 5 Algebra

Problem
Hint
1) Gemma is 12 years old. Gemma is five years older than Rebecca, and Jared is three times as old as Rebecca. How much older than Gemma is Jared? 1. If Gemma is 12 and is 5 years older than Rebecca, then Rebecca is ____ years old.
2. If Jared is 3 times as old as Rebecca, then he is ____.
3. Subtract Gemma's age from Jared's = _____.
2) Carson collects pennies, nickels, and dimes in a jar. He pulls out a handful of coins at random and counts them. If Carson pulls out 38 coins totaling $1.14 and he only has 1 nickel, how many of the coins are pennies? 1. Subtract the 5 cents from $1.14 = $______.
2. This is the sum of the pennies and dimes and now there are ____ coins left.
3. This is now a guess-and-check problem. Use this table: (make sure the number of pennies and dimes adds to ____ coins)
Guess ## dimes# penniesTotal $
12017$2.17
    
    
    
    
    
3) Reese is braiding several lengths of colored string together with a repeating pattern of green, blue, green, red, and purple. What will the color of the 47th braid be? 1. There are ___ colors in the repeating pattern.
2. Divide 47 by this and the remainder is _____.
3. This is the number of the 47th color in the pattern = _____.

Problem
Hint
4) A farm keeps chickens (with 2 legs) and pigs (with 4 legs) in a pen. There are a total of 55 chickens and pigs in the pen. There are a total of 178 legs amongst them all. How many pigs are in the pen? Wow! Another guess-and-check problem! Use this table: (make sure the number of heads adds to 55)
Guess
#
#
Chickens
# PigsTotal
heads
Total
feet
1302555160
     
     
     
     
     
5) How many times must you fold a piece of paper in half to create more than 500 layers? 1. Each fold doubles the previous # of layers, so complete this sequence until you get to a number higher than 500:
    Folds:   1   2   3   ...
    Layers: 2   4   8 ...
# Folds = _____