Lesson Plans SET B for Grades 9-10-PDF Lesson 10 Level 9-10 set B 3D Geometry. Genius Hour Class

PDF Lesson 10 Level 9-10 set B 3D Geometry. Genius Hour Class

Pdf Summary

The document is a series of math problems from the Math Kangaroo competition for levels 9-10, focusing on 3D geometry. It includes specific problem examples and solutions, along with general problem-solving strategies.<br /><br />**Example Problems and Solutions:**<br /><br />1. **Clock Hands Speed**: It asks how many times faster the minute hand of a clock moves than the hour hand. The answer is that the minute hand moves 12 times faster.<br /><br />2. **Bee on a Ball**: Involves a bee traveling on a ball's surface divided by circles. To return to its starting point, the bee must travel along a minimum of six quarter-circles.<br /><br />3. **Edges of a Solid**: A solid formed by removing the corners of a cube results in a structure with 36 edges.<br /><br />4. **Cube and Hemispheres**: For a cube with hemispherical recesses on its faces, the diameter of each recess is determined to be a specific measure based on the cube's size.<br /><br />5. **Pyramid of Spheres**: Discusses the reduction of an 8-pyramid to a 5-pyramid by removing outer spheres.<br /><br />6. **Painted Cube Faces**: Describes a painted cube broken into small cubes and asks how many had exactly one face painted.<br /><br />7. **Magic Octahedron**: A problem with assigning numbers to make the sum around vertices equal, leading to the result that values B and D equal six.<br /><br />8. **Unpainted Cubes**: This problem concerns a large cube made of smaller cubes, where some faces are painted. The solution finds how many faces were painted based on unpainted smaller cubes.<br /><br />**Strategies and Concepts**:<br /><br />The document also offers problem-solving tips: <br />- Draw figures to visualize scenarios.<br />- Use algebra and logic to solve problems.<br />- Represent 3D objects in 2D for better understanding.<br />  <br />Moreover, it introduces basic concepts of 3D geometry and spatial reasoning, offering a framework for analyzing geometric problems in-depth.

Keywords

Math Kangaroo

3D geometry

problem-solving

clock hands speed

bee on a ball

cube edges

pyramid of spheres

painted cube

magic octahedron

spatial reasoning