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:

  1. When a split occurs – the smaller number is on the left.
  2. 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)
  3. Prime numbers are dark.
  4. Numbers that have been previously encountered higher up the tree are dark.
  5. 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!

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

MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

 
MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.

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

Please use MathPickle in your classrooms. If you have improvements to make, please contact us. We'll give you credit 😉

Gordon Hamilton

(MMath, PhD)

 

Lora Saarnio

(CEO)