Hot and Cold Cubes Positive and Negative Counters

thingiverse

Human beings find learning addition and subtraction of positive and negative numbers a daunting challenge for many pupils. Conventionally, students illustrate concepts using a number line and arrows showing magnitude and direction, but this depiction has its limitations. A different strategy is to demonstrate with positive and negative counters. One effective introduction to this method is by reading the engaging story "Chef's Cubes" available at Interactive Mathematics (http://mathimp.org/), which ties traditional counters to temperature-control cubes for a magical soup. I have witnessed tremendous success in using this hook activity but lacked hands-on manipulatives for students - they had to rely on drawing + or - signs on their paper. This model addresses that deficiency and allows them to grasp the story's relevance by modeling addition and subtraction of positive and negative numbers with hot and cold cubes. Project: Mastering Hot and Cold Cubes Objectives: Pupils are expected to create their own hot and cold cubes for use as manipulatives in modeling addition and subtraction of integers. This concept can be further developed to model multiplication and division of positive and negative numbers. Audience: Mathematics students in grade 6 and 7. Preparation: Students should already have a solid grasp of basic operations with positive integers. Steps: Start by reading the Chef's Cubes story available online at (link provided) Then, have them print their own cubes to use – if this is part of an interdisciplinary learning experience or Maker/STEM class, let them design and print custom versions of the cubes Once they possess a set of cubes, guide them in understanding operations with positive and negative integers. Show them what adding hot and cold cubes means - for instance: 1 + (-1) = 0. This concept is fundamental for modeling using cubes Move on to having students incorporate zero-pairs into their demonstrations For example: 5 - 8 = -3. They start by possessing five hot cubes, then since we are removing a larger number than we started with, we need three zero pairs. Documentation and lesson plans for positive and negative counters can be found in separate sources. Results: By using the tangible hot and cold cubes, students reveal an increased understanding and connection to concepts of addition and subtraction of positive and negative integers.