Lesson Plans SET A for Grades 9-10-Lesson 3 Level 9-10 Algebra ProblemSolving Homework

Lesson 3 Level 9-10 Algebra ProblemSolving Homework

Pdf Summary

The document presents a set of algebra-based problem-solving exercises tailored for Math Kangaroo class students specifically at levels 9-10. Here’s a concise summary of the problems and their solutions:<br /><br />1. **Travel Time Adjustment**: Tom planned to reach his destination by 5 p.m. but took a 30-minute break halfway. The need to increase his speed by 20% in the second half to compensate for the break, but ending up going 20% slower due to traffic, he arrived at 6:15 p.m. The goal was to determine his starting time, which is found to be 11 a.m.<br /><br />2. **Pebble Collection**: Four friends gathered pebbles in specific ratios: Anna to Bella (1:3), Bella to Cindy (4:5), and Cindy to Denise (2:1). The total number of pebbles collected was 154. The problem requires finding the number of pebbles Cindy collected, totaling 60 pebbles.<br /><br />3. **Boat Current Rate**: The man rode 20 miles downstream at 6 miles/hour. Returning at the same speed would take 2.5 hours longer. The problem asks for the stream's current rate, calculated as 2 miles/hour.<br /><br />4. **Clock Hands Alignment**: At exactly 12 o'clock, one must determine the next time the hour and minute hands are aligned in a straight line. The solution finds this alignment at 12 hours and \(32 \frac{8}{11}\) minutes.<br /><br />5. **Cell Number Doubling**: On a 3x3 grid initially filled with the number 1, a random 2x2 sub square is selected per step, and its numbers doubled. After several steps, the central cell becomes 512. The task involves finding the number A, located at a specific grid position, resulting in A being 32.<br /><br />These solutions highlight key algebraic and logical skills, including ratios, speed-time-distance calculations, and sequence growth within a grid.

Keywords

algebra

problem-solving

Math Kangaroo

travel time

pebble collection

boat current rate

clock hands alignment

cell number doubling

ratios

speed-time-distance