Welcome to this week's critical math. The problems below are great to try out with your student to see how their critical thinking and number sense is developing. Answers along with solutions are provided just below each question, so try not to let them see that ahead of answering. The problem's are loosely separated by schooling level, but feel free to try out more than one with you child!
Lower Elementary:
Question: Each soccer team has the following players: 1 goalie, 4 defenders, 4 midfielders, and 2 forwards. How many players are on 5 soccer teams?
Answer: 55 players
Solution: Instead of adding each position individually, we can find the number of players on each team first. There are 1 + 4 + 4 + 2 = 11 players on each soccer team. So, on 5 teams, there are 11 × 5 = 55 players!
Upper Elementary:
Question: Jayce and Arianna are practicing their golf swings. They bring 32 golf balls to the course. Jayce hits all 32 first, then retrieves all but one. Then it’s Arianna’s turn to hit all the remaining golf balls and retrieve them, but she also loses one. If this pattern continues, who will take the 12th turn, and how many golf balls will he or she hit? Find a way to solve the problem without counting each turn.
Solution: Jayce has the odd numbered turns and Arianna has the even numbered turns. Since 12 is an even number, Arianna must have the 12th turn. By the 12th turn, only 11 (not 12) golf balls have gotten lost because the balls get lost at the end of the turn. So, Arianna hits 32 – 11 = 21 golf balls.
Answer: Arianna hits 21 golf balls.
Middle School:
Question: Chad and Michael play on the same baseball team. Last year, they both had a batting average of .240. Michael’s batting average increased by the same amount that Chad’s batting average decreased. If Michael has a batting average of .270 this season, then what fractional part of Michael’s new batting average is Chad’s new batting average?
Solution: Since Michael’s average goes up by .030, Chad’s must go down by .030 to .210. Next, we can find out what fractional part Chad’s batting average is of Michael’s by dividing .210 by .270. First, we multiply both numbers by 100 to get 21/27, then we can reduce the fraction to 7/9.
Answer: 7/9
Algebra and Up:
Question: Magenta and Tavia are both running toward a soccer ball. Magenta is 28 meters away and Tavia is 33 meters away. If Magenta can run 2.5 meters per second and Tavia can run 2.75 meters per second, then how much sooner does the player who reaches the ball first get there?
Solution: If Magenta runs 2.5 meters per second, then it takes her 28 meters ÷ 2.5 = 11.2 seconds to reach the ball. Tavia reaches the ball in 33 ÷ 2.75 = 12 seconds. This means that Magenta got there 12 – 11.2 = 0.8 seconds before Tavia.
Answer: Magenta reaches the ball 0.8 seconds before Tavia.
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