{everything here in a Google Doc : https://docs.google.com/document/d/102GJToD7jxomUFt5cC0YCigcrVP4HvovjypZ75z5v1k/edit?usp=sharing }

SCIENCE :

Snowflakes are ice crystals. About 200 crystals per flake. Snowflakes are translucent, and the reflected light comes back to us and they seem white. They require low temperatures and moisture to form. The shape evolves as it falls, dependent on the temperature and humidity. It is said that each snowflake is unique, even two that fall next to each other because of the slight variation in temperature/humidity. 70% of the United States see them. It might be a good discussion to have on whether all 50 states can get snow...and students need to give their rationale. I keep seeing that ⅔ of the world's population has never experienced snow - but I cannot find any verification. I often wonder about the song “White Christmas” and how many people for which it has no meaning.

Flat icon has some nice examples that you could share to get ideas flowing https://www.flaticon.com/packs/snowflakes (could also be used later on for laser cutting, though I really want students to make/cut their own).

LEARNING IDEAS :

The learning is in the discussions.

Being a water crystal, snowflakes have 6-fold symmetry. Obviously you could have discussions about symmetry. You could have discussions about the chemistry of water freezing (elements, formula, reason for shape, expansion vs contraction). A six sided shape is a hexagon, so you can talk about interior and exterior angles and greek prefixes. I am sure there have been some historical impacts of snow...closing of mountain passes, warfare, Blizzard of 1978 (NE Ohio). A good librarian could help you find books where snow is a central theme or background for a story. Of course, there have been a few movies. Frozen comes quickly to mind for kids. But don’t forget Ground Hog Day. Imagine how much you can get to know about your students while talking about movies and exploring 6-fold symmetry. The learning is in the discussions, no matter what topic and what you are making.

MAKING :

Let us get to making snowflakes. I will start with low complexity and work up. At its core, it is about creating 6-fold symmetry. So any way that you can do that is great. With blocks, on paper, on the computer, with a laser cutter, with a 3D printer, maybe a Cricut/Cameo craft cutter. Whatever you have is what you will use.

People have even created Star Wars snowflakes (http://www.anthonyherreradesigns.com/starwarssnowflakes ) so it can be personal and fun.

It doesn’t have to be ONLY geometric shapes.

TACTILE :

Templates :

You could give them some templates of basic geometric shapes to cut out and some glue sticks to create snowflakes. Here are two :

Though I really think it is always best that students create their own shapes.

Maybe they should create cardboard templates to be able to reproduce their shapes on paper.

Protractor/compass/ruler?

What would you/they use to create shapes to print?

Google Slides :

Geogebra :

Make some polygons, regular or otherwise. Even circles,

You can hide the points & labels by right clicking on a point, choosing “Settings” , then unchecking “Show Label”. You could also uncheck “Show Object” . IMPORTANT NOTE --- once you uncheck “Show Object” you can no longer change the size of a regular polygon...there is no more point to adjust. But you can change a polygon, because the sides are not fixed.

They might need some help with the 6 fold symmetry, so make sure they have a regular hexagon as the center or some lines to guide them. Though I think they should make their own guides. Protractor, compass, ruler...how DO you construct a regular hexagon???

VIRTUAL :

First, if you just want to play with 6 fold symmetry, go to https://www.mathsisfun.com/geometry/symmetry-artist.html and remember to choose “6”. Now doodle.

Math Manipulative :

There are probably many virtual math manipulative/pattern block websites. They might not have “export image” options, so you might need to screenshot. Here is one https://www.coolmath4kids.com/manipulatives/pattern-blocks

Paper Cutting 1 :

This is one where students do some virtual cutting to get a snowflake that can be downloaded as a png. https://dangries.com/rectangleworld/PaperSnowflake/

I clicked, moved the cursor, clicked again, moved, clicked...to draw a closed polygon on the right, selected “make snowflake” and got the image on the left. You can adjust points and click “make snowflake” to update the image. If you click “add” you can add another polygon, but that finalizes the previous one. Their “save image” didn’t work for me, so I screenshot it. Now the question is “how do you print out something that is white??? Without using up lots of ink to print a colored background??

I don’t know …. Yet. (I know that some vector design software can “trace” images, but not everyone has those)

Paper Cutting 2

Geogebra :

Geogebra https://www.geogebra.org/geometry .

We can create any shape, then rotate it about a center point by 60 degrees, then rotate that rotation by 60, then that one by 60…

HINT… if you “un-show” the original points BEFORE you rotate...all the children don’t have points.

Non-Regular polygons can still be adjusted by dragging their sides, but Regular polygons cannot, because their sides are fixed.

Circles cannot be changed because they are based on two points (a radius)

So do you want to be able to adjust the sizes and orientations or not...

Tinkercad :

Speaking of Tinkercad (https://www.tinkercad.com/dashboard ), we can make snowflakes in tinkercad. There are lots of shapes to choose from.

It might be a good idea to set a hexagon in the center to help with the symmetry.

Or at least a center point.

Make sure your shapes overlap each other.

You can easily rotate objects by 60 degrees (and 120, 180, 240, 300)

Explore beyond the “Basic Shapes”.

They even have "Making at home" items.

Once you get the shape to the proper 60 orientation, you could even rotate it just a bit more....and do the same to all of its sextuplets (eg, 7, 67, 127, 187, 247, 307)

Snowflake Generator :

Here is a snowflake generator https://www.misha.studio/snowflaker/

Though it is not so much students creating as picking by adjusting “strokeWidth” and “subBranches” and “Regenerate”

This exports as an svg, which “should” be good for laser, 3D printing, Cricut/Cameo. But the svg did not work in Tinkercad, nor Lightburn. I did not play with it for too long. Maybe you can make it work.

I had better luck with the “Trace Image” tool of Lightburn using a screenshot… it quickly gave me a good image to laser cut.

CODING :

A good practice for coding...

start small

save that program

make a copy and work with the copy to add other elements

Tinkercad Codeblocks :

Click on Codeblocks, then “Create new Codeblock”

See all the shapes we can play with. And they all have adjustments that we can make to them.

Choose an object and click the “play button”

Fiddle with the adjustments and click “play” again to make them happen

Yes.

Just remember, we want one to rotate 60, one to rotate 120, one to rotate 180…

We need to make our angle a variable (something that changes) in order to do that.

Grab the “Create Variable” block from "Math" and rename it a meaningful name (like "angle" or "degree" or...)

Two more things to do and we are done.

First, replace the 60 in “rotate” to “angle” (your variable)

There should be a round ended block under "Data"

Drag and drop it onto the 60.

Next, we need to change that variable “angle” by 60.

So, find the “Change item block, drag it into the bottom of the Repeat loop and change “item” to “angle” and change 0 to 60.

Now, you need to play with it.

Pick some shapes.

Create a new “Repeat” loop for each new shape you want to add to your snowflake.

Obviously you can print this out on paper...somehow.

But you can also 3D print or laser cut or vinyl cut.

I was worried because in codeblocks, the workplane cuts the shape in half vertically...ie. it is half below the plane and half above it. That wouldn’t work for printing, half below the print bed. If you are 3D printing, be sure to check that all shapes get on the workplane/print bed. If it needs fixed, I imagine the solution is to move each shape half of its size in the z direction inside the repeat loop.

Turtle Art blocks :

Turtle Art Blocks (browser based)

https://www.playfulinvention.com/webturtleart/

WARNING there is no way to save your code… you will need to screenshot your code. You can download the picture of the snowflake you make as a png or even export an svg.

You could email the original creators and ask for a copy to download https://turtleart.org/programming/index.html

Now draw.

Put in some combinations of forward, right, left, back.

Even try the arc.

Right & Left are just turning in place NOT actually going to the right or left.

They are degrees, so 90 gets you AIMED to the right

{this program starts with 0 degrees/initial heading being up/North}

Press play to have it go from the beginning (or click on the blocks)

Watch the turtle.

Tinker. Fiddle, Play.

Can you put in negative numbers?

Run it.

OOPS....

That doesn't look like 6-fold symmetry

2 problems

a) we want to start at (0,0) for every branch

b) what direction are we pointing, aka "heading", at the end of our motion???

so we are adding 60 to what???

These are things we need to make sure happen correctly

Problem a) is easy to fix…. Put a “setxy (0,0) at the bottom of the loop

But first get rid of that "set heading=heading + 60", then put the "setxy" in its place

Now run this.

(good practice is to change one thing at a time, get that to work correctly. Then change next thing)

Much better. Everything is starting at the origin...but it is not 6-fold.

Again, the problem is relying on a "heading" that we don't know what it is. We know it is the direction the turtle is pointing, we just don’t know the number.

We need to create a "variable" (a thing that can change value) and set the heading to it AND we control the variable.

Find the “store in box 1” (that is their idea of variable, a box that can hold a number) and set it equal to “0” and place that before the “Repeat”. This is so we start at 0 degrees.

They have a help document at https://www.playfulinvention.com/webturtleart/webhelp/reference.html

You can do more actions to the same drawing

We can copy the Repeat block and replace the movements

Copying a set of blocks is done by holding down shift, left clicking the top block and dragging it away.

Or you can just create another “Repeat” loop.

Remember what has to go at the top & bottom : (set heading = box1 ; get it back to (0,0) and change box 1 by 60)Yeah, I added a "set color"

It does not matter which set of motion or repeat you put in the spacer blocks.

This site even have a “save as svg” for laser cutters/3D printers

I tried "outline" and "plain"

Again, you do not have to have the blocks attached to get all of your drawing pieces. To run blocks, simply click on each set. You have to be aware of your settings (box 1, pensive, pencolor…)

Also, wait for each block to finish.

It all works out nicely for us because of symmetry...starting at 0, turning 60 degrees 6 times gets us back to 0.

(Changing color isnt always a good thing)...

Turtle Art Python :

fyi some videos if you prefer

https://www.youtube.com/playlist?list=PLo6W7Aw8EPRDn0mS1HywhnHPtJPF3YKKY

If you want to do turtle art via text based coding, I suggest two waysIf you can download software, try https://www.python.org/downloads/ If you cannot, then go to https://repl.it/signup , sign up for an account (they have a free option). Now find “Python (with Turtle)” and work in your browser.

Text based coding is more difficult because you don’t have the commands sitting nicely in a sidebar. We have to find a resource with them.

Here is one https://docs.python.org/3/library/turtle.html

The first thing we have to do is bring in the turtle libraries and name your turtle. You don’t HAVE to name your turtle, you can just call it “turtle”. But all commands must start with its name.

The code :

import turtle #bring in some libraries

t=turtle.Turtle() #name your turtle, this one is named “t”

The # tells the program to ignore words after… it is called “commenting” , to tell people what you are having a line or command do

Basic commands :

forward(number)

backward(number)

right(degrees) #turning, not moving

left(degrees) #turning, not moving

Put a number in for “number” and “degrees”

So a command of

t.forward(20) #Tells my turtle , named t, to move forward 20 steps

Let us try a combination of moves, enter these and click “run”

(If are using the downloaded version of IDLE, you need to save it first. Then click “Run” , then click “Run Module”)

formatting issue:

1) commands all need to be on separate lines in python

2) no blank lines are "needed" but often used to make things look neat/separated

3) copy & paste from here will function, but there will be an "empty" line in between each

4) indenting means something (more later)

Our first code :

import turtle

t = turtle.Turtle()

t.forward(70)

t.right(30)

t.backward(50)

t.left(20)

t.forward(70)

Some good commands to use are :

t.goto(x,y)

Put in coordinates for “x” & “y”

And

t.home()

Home returns to the origin AND resets the heading to the original.

Adjust your code to have these in it :

Oh.

It seems like the pen is automatically and always down (always writing).

We are going to need to learn how to manipulate the pen.

t.penup()

t.pendown()

t.pensize(number)

t.pencolor(“color”)

I don’t know yet what numbers are allowed for size (I went up to 200 and still getting bigger), nor what colors are understood by name.

Let us try some things.

Lift the pen before moving (goto & home).

Put it down after moving (goto & home).

Add a pencolor --- the color name must be in quotes : “colorname”

And let us try pensize for the last bit.

Understand what each line is doing. See what each line is doing on the drawing.

I didn’t comment b/c i used commands that are words we all know.

Act like you are moving a toy car with it facing to the right to start off.

Now try this for color : t.pencolor("#66ffff")

(change the “orange” to “#66fff” )

This is what we mean by RGB hexcode …

https://www.rapidtables.com/web/color/RGB_Color.html

Now try this : t.pencolor(255,65,240)

So you have three ways to do color. I think the name one is very limited, while the other two give you almost 17 million colors (256 to the third power)

{NOTE : if you are using IDLE, mine didn’t like the (255,65,240) way, but it was okay with the other two.}

Whew. That is a bunch of info. We have just a little more to go.

Loops. (as in repeating something)

One way to do this is “for” statements :

for i in range (number) :

Yes you need the colon. And the number is how many times to repeat

Let us make a square.

Yes, the commands/statements “under” the “for” have to be indented.

That is how python knows what to repeat

What happens if you do not indent the t.right(90) ?

And yes, there is a colon at the end of the "for" line...that is something i seem to forget a bunch.

You only need one more piece of code.

In order to do 6-fold symmetry, we always want to return to the origin, then turn 60 degrees. We will have to use a variable for this, I will name it degree and we will set the heading to it towards the beginning of the loop and change it by 60 at the end of the loop. We have to do this because heading is always the current direction the cursor is pointing towards.

Let us make a design with 6 fold symmetry

Remember :

Pick penup

Move to home

Put pen down

set heading

Walk through it with your toy car.

The first time in the loop, t.penup() and t.home() seem odd, because we are already there. But think of where you are at the end of the first time through. We need to get back home and pick the penup so we don’t draw while going there. Those commands are there for every time through after and don’t do anything to affect the first time.

You can have as many “for” loops as you want in your code, one right after the other if you want. It is like drawing the snowflake in layers.

You can have “for” loops inside of “for” loops. (called nesting)

It might be difficult to see both indents here, but the second “for” is actually indented to be inside the first one.

Time to combine a bunch of moves (forward, backward, right, left, ) to make a pattern, then repeat it 6 times. Remember about heading (and the variable degree) home, penup, pendown, pencolor, pensize and changing the variable by 60 each time through the loop.

An example, with two different “for” loops to make the flake in 2 layers, inner & outer. Wlak through it, line by line, with the toy car. (remember, anything after # is a comment, not a command)

import turtle

t = turtle.Turtle()

degree=0 #set variable to 0 to start

t.pensize(8)

for i in range (6) :

t.pencolor("purple")

t.penup()

t.home()

t.pendown()

t.setheading(degree) #set the heading to the variable

t.forward(50)#start with a line

t.right(30)#make a branch at 30 degrees

t.forward(25)#length 25

t.backward(25)#back to the line

t.left(60)#turn to the other side ;

#since our heading is 30 to the right, we need to turn 60 to be

#30 degrees to the left

t.forward(25)#length 25

degree=degree+60

#a new piece of the drawing

degree=0 #reset degree to zero just to be sure

for i in range (6) :

t.pencolor("teal")

t.penup()

t.home()#start back at (0,0)

t.setheading(degree)

t.forward(60) #get to the end of the first line

# i went more than 50 b/c the side branches have thickness

t.pendown()#now we can start drawing

t.forward(60)

t.right(30)#make a branch at 30 degrees

t.forward(45)#length 45

t.backward(45)#get back to the line

t.left(60)#branch on the left side

t.forward(45)#length 45

t.backward(45)#back to the line

t.right(30) #back to the original heading ; could I have used

# t.setheading(degree) ???

t.right(70)#a second branch on the right but at 70 degrees

t.forward(60)#length 60

t.backward(60)#get back to the line

t.left(140)#turn to be symmetrical on the left

t.forward(60)#branch length 60

degree=degree+60

https://repl.it/@PaulShircliff/snowflake6#main.py

ADVANCED ADVANCED ADVANCED ADVANCED

Say you want something to happen many times in your code, like draw a triangle. We don’t want to have to type those lines of code again and again.

So we create a “function” at the beginning of the program, then call it by name (one word) when we want it in the code :

def triangle() : #create a function called triangle to draw a triangle

for i in range (3) :

t.forward(10)

t.right(120)

“Def” is short for “define”

Yes, the commands under the function must be indented so python knows they are part of the function (you already know to indent the commands under “for”)

Then whenever we want to draw a triangle, we type :

triangle()

Example

import turtle

t = turtle.Turtle()

def triangle() : #create a function called triangle to draw triangle

for i in range (3) :

t.forward(10)

t.right(120)

degree=0

for i in range (6) :

t.penup()

t.home()

t.pendown()

t.setheading(degree)

t.forward(50)

triangle() #draw a triangle

t.right(30)

t.forward(25)

triangle() #draw a triangle

t.left(60)

triangle() #draw a triangle

degree=degree+60

There is one more layer of complexity…. I can make them different sizes every time I call it…by using an “x” (yes, the variable)

def triangle(x) : #create a function called triangle to draw a triangle of variable size

for i in range (3) :

t.forward(x) #move forward x steps, x comes when i call the function

t.right(120)

Then call it with different numbers in parenthesis

triangle(30)

triangle(40)

BTW, whether you go forward then turn, or turn then go forward, does make things look different. Order matters.

Who wants to make circles and arcs?

t.circle(50)

Makes a full circle radius 50, in a counterclockwise direction

t.circle(-50)

Make a full circle radius 50, in a clockwise direction

Yes, clockwise and counterclockwise are in different locations

t.circle(45,80)

Make a circle radius 45, counterclockwise, but only make 80 degrees of it.

Example :

I didnt even talk about using

Illustrator,

Inkscape,

CorelDraw,

Lightburn.

Which I am sure you could do. This would be a good project to explore the tools and features of those softwares if you have them.

WOODSHOP

Do you have a woodshop??

Do you want to talk about how to make lawn ornament snowflakes?

Contact me

Contact me :