Lesson Plans SET B for Grades 7-8-Lesson 8 Level 7-8 3D Geometry and Spatial Reasoning-HW

Lesson 8 Level 7-8 3D Geometry and Spatial Reasoning-HW

Pdf Summary

The document contains a set of five geometry and spatial reasoning problems from a Level 7-8 Math Kangaroo class, focusing on 3D Geometry and Spatial Reasoning. Here's a summary of the problems and their solutions:<br /><br />1. **Cube Painting**: A large cube made up of 1x1x1 small cubes is painted, and the task is to find how many small cubes have less than two sides painted. The solution to this problem concludes that 432 such cubes exist.<br /><br />2. **Mechanical Kangaroo's Path**: A mechanical kangaroo walks on a grid, starting at square C3 and follows movement rules including avoiding shaded squares and unable to leave the grid. Once the kangaroo cannot move forward, it turns left. The problem asks where the kangaroo will stop and the solution states "It will never stop," suggesting continual movement or a repeating cycle.<br /><br />3. **Rolling Cube**: A cube rolls across a plane touching specific positions in sequence. The question is to identify which face is equivalent to the starting face after the cube finishes rolling to position 7. The provided answer is face "7."<br /><br />4. **Rope Folding**: A rope undergoes a series of folds and is then cut, resulting in different strand lengths. The problem is to determine if the original length is certain to be less than 100 m. The answer states "No," indicating possibilities of 48m, 64m, 80m, or an indeterminable length, showing the lack of certainty based on given strand lengths.<br /><br />5. **Popsicle Licking**: Peter licks a rectangular prism-shaped popsicle reducing its size by half in 3.5 minutes. The question asked for the time it would take for him to finish if this rate continues. The solution suggests an additional 30 seconds for the popsicle to be completely gone.<br /><br />These are high-level geometry problems requiring spatial reasoning and calculation skills for effective problem-solving.

Keywords

3D Geometry

Spatial Reasoning

Cube Painting

Mechanical Kangaroo

Rolling Cube

Rope Folding

Popsicle Licking

Math Kangaroo

Level 7-8

Problem Solving