Zero Model, Negative & Positive Numbers

3D model description

This zero model is intended for young children to make sense of mathematical ideas involving negative numbers. The essential idea is that every number has an additive inverse so that (+A) + (-A) =0. For example, (+1) + (-1) = 0 and (+5) + (-5) = 0. This big idea, together with the connections between addition and subtraction, can be used to explain why 0 – (-1)= +1, and eventually why (-1)(-1) = +1. It is really a fun perspective and has healthy implications for higher mathematics. And, yes, subtraction can be interpreted as “take away.” Thus, 0 – (-1) means taking (-1) from 0. Well, 0 is “(+1)+(-1)”, thus, the result is (+1).

There are two types of 3D models here. One allows the assertion of small magnets (5mm diameter x 1mm) into the small box on each side (at about 80% completion when printing). The magnets will then be fully sealed inside. The other model has the two pieces connected in a wedge structure. Be very careful when using small magnets with children.

3D printing settings

Printer Brand:

FlashForge

Printer:

Finder

Rafts:

No

Supports:

No

Resolution:

0.1mm to 0.2mm

Infill:

5% - 25%

Notes:
If you want to insert some small magnets into the little boxes, please pause the printer and do so at 80% to 90% time or before the top of the box closes.

Overview and Background
Negative numbers are inevitable in elementary mathematics and can be very meaningful and mind opening if taught in appropriate ways. Rules like "negative and negative makes positive" do not work and are misleading!

The essential idea is that every number has an additive inverse so that (+A) + (-A) =0. For example, (+1) + (-1) = 0 and (+5) + (-5) = 0. This big idea, together with the connections between addition and subtraction, can be used to explain why 0 – (-1)= +1, and eventually why (-1)(-1) = +1. It is really a fun perspective and has healthy implications for higher mathematics. And, yes, subtraction can be interpreted as “take away.” Thus, 0 – (-1) means taking (-1) from 0. Well, 0 is “(+1)+(-1)”, thus, the result is (+1).

Lesson Plan and Activity
Have children discuss their current knowledge of negative numbers in life and share what they do know to figure out operations such as "1 - (-3)". Then, use models to reconstruct their knowledge and allow them to grow ....

Duration of Lesson
45min to 90min, depending on grade levels.

• 3D model format: STL

Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU