Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 5 Algebra

Problem
1) Joe and Sue are planting trees in the park for Arbor Day. On the first day they planted 38 trees. Joe did not work the next day, but Sue planted the same number of trees that she had planted the first day. Together Sue and Joe planted 60 trees over the two days. What was the number of trees Joe planted?
2) One angle of a triangle has a measurement of 70 degrees. The ratio of the other two angles of the triangle is 5 : 6. What are the measurements of the other 2 angles?
3) Kara made this sequence of shapes with blocks:
If she continues this pattern, at what stage will she use 28 blocks in a shape?
4) A group of scientists is duplicating cells for a science experiment. They observe that during each 10-minute period, one-quarter of the cells present died and the rest of the cells all doubled. If there were 32 cells initially, how many cells were there after 40 minutes?
5) Nadia and I went to the aquarium. I liked the tank with only squid and octopus. Each squid had 10 tentacles and each octopus had 8 tentacles. It was really hard to count them all, but I saw 46 tentacles. If my count was correct, how many octopus and how many squid are in the tank?