2021年大联盟(Math League)国际夏季五年级数学挑战活动一

2021 美国"大联盟"(Math League)国际夏季数学挑战活动2021 Math League International Summer Challenge Grade 5, Individual Questions & Solutions Question 1: Sarah is using popsicle sticks to build some grids for her city planning project. She needs 4 popsicle sticks to make a 1 by 1 grid, and 12 sticks to make a 2 by 2 grid as shown below. How many sticks does she need to make a 10 by 20 grid? Answer: 430 Solution: Analyze the 2 by 2 grid. To create it Sarah used 3 rows of 2 sticks each and 3 columns of 2 sticks each. Similar to it, there would be 11 rows and there should be 20 sticks in each row. So, there are 20 × 11 = 220 sticks (placed horizontally). There would also be 21 columns and there should be 10 sticks in each. Therefore, there are 21 × 10 = 210 sticks placed vertically. Total = 220 + 210 = 430 popsicle sticks Question 2: The sides of the large rectangle are 20 m and 16 m, figure below, not drawn to scale. All six shaded rectangles are identical. What is the total area of all the shaded regions, in square meters? ( 11 ) 学科网（北京）股份有限公司 Answer: 192 Solution: Find the dimension of the small rectangle. The length: 16 ÷ 2 = 8 m. The width: 20 – 8 – 8 = 4 m. The total area of all the shaded regions: 6 × (8 × 4) = 192 m2. Question 3: If two sides of a square field were increased by five feet, as seen in the diagram below, not drawn to scale, the area of the field would increase by 245 square feet. Find the area of the original square. Answer: 484 Solution: The area of the shaded square is 5 × 5 = 25, figure below. The area of each of the two “new” rectangles is (245 – 25) ÷ 2 = 110. Thus the length of the “new” rectangle, or the side length of the original square, is 110 ÷ 5 = 22. So the area of the original square is 22 × 22 = 484. Question 4: During practice, Dana’s six arrows land on the target shown. Each arrow is inside one of the regions of the target. Which of the following total scores is possible: 44, 31, 26, 16? (If an arrow lands inside the smallest circle in the cent