Packing Parcels

thingiverse

Packing Parcels: A Math Puzzle Inspired by Everyday Life Mathematics can be a thrilling adventure, especially when it's applied to our daily routines. Packing parcels is one of those everyday tasks that requires mathematical thinking. We all try to fit things neatly into boxes or trunks, but have you ever stopped to think about the math behind it? Project Overview Packing Parcels is an engaging math puzzle designed for students aged 14 and above. The goal is to pack nine parcels (green boxes) into a larger box (red box) within 20 minutes. This project aims to help students develop their spatial thinking, problem-solving skills, and mathematical understanding. How I Designed This To create this puzzle, I used OpenSCAD to design the three-dimensional components: 1. Box 1: A cube with dimensions 20x20x20 mm. 2. Box 2: A larger cube with dimensions 40x40x20 mm. 3. Box 3: The main box with dimensions 66x66x66 mm and a smaller inner box. 4. Stick: A long, thin piece used to remove misplaced parcels. Project Objectives By the end of this project, students will understand: * Geometry: shapes, sizes, and relationships * Volume: calculating the volume of objects * Area: determining the surface area of objects * How geometry, volume, and area are interconnected in solving puzzles Activity The teacher presents a math challenge to the class: "Packing Parcels" Challenge You have 20 minutes to pack all nine parcels into the larger box. Use the stick to remove any misplaced pieces. Math Behind the Puzzle Solving this puzzle involves geometry, volume, and area calculations. The different shapes used in the puzzle require unique mathematical properties for determining their volumes or areas. Why it's Challenging? The puzzle requires students to think creatively about packing objects of varying sizes into a smaller space. The math involved is not trivial, as students need to calculate the volume of each box and ensure that the total volume of the parcels does not exceed the capacity of the larger box. Physics and Chemistry Connection Atoms and molecules are packed together to form solids, liquids, and gases. Particles in a solid are usually more tightly packed than those in a liquid or gas. This concept is relevant when packing objects into a smaller space, as students need to consider the packing efficiency of different shapes. Solution for the Puzzle A future project will showcase the solution using augmented reality technology with Aurasma. Students can download the trigger image and use it to view the solution. Preparation * Print the puzzle components * Have phones or tablets with the Aurasma app installed * Provide students with 20-25 minutes to solve the puzzle References The math involved in this puzzle is relatively simple, so no references are provided at this time. Rubric & Assessment Most students will be able to solve the puzzle within the given time frame. For a more challenging experience, consider designing pieces that reach the volume of 27 box1s (smaller boxes), allowing students to create their own puzzles and challenges. Handouts & Assets You can download the trigger.png image to view the solution using Aurasma.