Primitive Lightning (composite divisors)

Show your class a lightning strike with the number 88. This is how it looks. Pause for two minutes. Let them try to figure out some of the rules governing its construction. You can think too.

What observations do you make?

Here is a possible list:

When a split occurs – the smaller number is on the left.
When two numbers split from one above it they are equi-spaced from it. Example – when 32 splits – it does so into 27 (32-5) and 37 (32+5)
Prime numbers are dark.
Numbers that have been previously encountered higher up the tree are dark.
Dark numbers are a dead end.

The proper divisors of a number are critical to how a number splits…

It is the number of proper factors that determines how far left and right the next split happens. Example: 77 has the proper factors 1,7, and 11 so it splits 77-3 and 77+3. Students should start exploring the world of primitive lightning. What is the longest bolt of lightning. I’ve found this one under a hundred:

75 – 70 – 63 – 58 – 55 – 52 – 57 – 60 – 49 – 51 – 48 – 39 – 42 – 35 – 32 – 27 – 24…

(see diagram)

What is the longest lightning strike under 20?

What do you think happens to these lightning strikes if the top number is large?

Do they always get longer?

Are they sometimes infinitely long? If so – what is the first number that generates an infinite lightning strike? I don’t know.

Primitive Lightning

(MathPickle, 2017)

This is a great way to get your students practice with the scientific method within the strict definitions of a mathematical mini universe. The key discovery that students must make is that the lightning is branching off with some very precise rules. Your class must figure out these rules. As they do it they will gain factoring practice.

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. Try pairing up elementary students and getting older students to work in threes.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Use the right tools!

Students should use the right tools: 0-99 wall charts, graph paper, mathigon.org. etc.

MP6 Be precise!

Students learn to communicate using precise terminology. Students should not only use the precise terms of others but invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist! 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?

(http://www.corestandards.org/Math/Practice/)

Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go here.