Building on "How to Read a Ruler" and "Perfect Paper Cube"- another instructable designed to help you practice laying out projects and also introduce a few more sheet metal working processes.  If you haven't done the Perfect Paper cube yet, you may want to start there as this instructable builds on what was learned there.  Check them out here:

Perfect Paper Cube: https://www.instructables.com/id/Perfect-Paper-Cube-Laying-out-a-project-using-pa/

Also watch for the Perfect Paper Pyramid 2, coming soon.  It will demonstrate another way to make the same pyramid using different techniques.

Content Learning Objective:

By building a Perfect Paper Pyramid, students will continue to practice and develop their ability to read a ruler and demonstrate accuracy.  Additional sheet metal procedures will also be introduced. These skills will later be demonstrated again as students make projects out of sheet metal.

Please note that even though I do this activity with 7th and 8th graders, this instructable is hard for that age group to follow without guidance.

## Step 1: Gather Supplies

This is a pretty simple project.

Supplies:

8.5x11 sheet of paper
Glue or tape (glue is stronger, tape is easier to work with)
Pencil
Eraser
Ruler
Scissors

A desk or other hard work surface generally comes in pretty handy too...

## Step 2: A Little Groundwork- Review From Perfect Paper Cube

We are practicing PARALLEL LINE DEVELOPMENT, and to do this we need to know two different kinds of lines.  These are Parallel Lines and Perpendicular Lines.

Parallel Line:  Two lines on a plane that never meet. They are always the same distance apart.

Perpendicular Line: Lines that are at right angles (90°) to each other.

So before we begin drawing, we need to establish a few basic rules.  There are two main rules to keep you paper cube perfect.  They are:

Rule #1:  MARK TWO ARROWS AND SCRATCH A LINE. (Pictures 1-4)

Say it with me now, "MARK TWO ARROWS AND SCRATCH A LINE".  One more time, "MARK TWO ARROWS AND SCRATCH A LINE".  Can you tell its important?  So what does it mean!?  It means, whenever we mark a line that we want parallel to another surface, we must measure up from the first line a certain distance in TWO DIFFERENT LOCATIONS.  Mark both of them with an ARROW pointing to the correct measurement.  The arrow is made by placing the point of your pencil on the mark, pulling it out at an angle in one direction, then repeating but pulling the pencil out at an angle in the other direction.  You are left with a small "V" pointing at the measurement.  When we have two "arrows" or "V's", simply line your ruler up with the POINTS of the two arrows and "scratch" a line with your pencil.  We call it "scratching" a line, because when working with metal we use a Scratch Awl, which literally scratches a line in the metal.  One more time just to make sure, "MARK TWO ARROWS AND SCRATCH A LINE".

Rule #2:  MEASURE TWICE, CUT ONCE! (Picture 5)

Lets get this one pounded in to our brain also, so say it along with me:  "MEASURE TWICE, CUT ONCE!"  One more time for good measure, "MEASURE TWICE, CUT ONCE!"  This one really needs hammered in there, so find a piece of paper, and write it down just for good measure.  What does this one mean?  It means, after we have measured, marked out our arrows, and scratched the line, we need to go back AND MEASURE IT AGAIN to make sure its right!  Its easier to measure twice than cut twice.  Don't ask me how I know...

## Step 3: Basic Geometry- the Base

Now that we have a couple of basic rules, lets talk geometry.  This pyramid has a square base, meaning it will have 4 triangular sides.  This step will describe how to lay out the square base.

First Line

We are going to start with a line that is parallel to the edge of our paper.  Near one end of the paper measure from the edge of the long side up 3 inches, and mark an arrow as shown in Picture 1.  It really doesn't matter where you are to the left or right, just as long as you measure UP 3 inches.  Move to the other end of the paper, mark another arrow up from the bottom edge 3 inches.  Now line your ruler up with the points of the arrows, and scratch your line as shown in Picture 2.  It is usefully to make the line longer than needed, so just go all the way across the paper.

Now that the line is drawn, lets use our second rule and measure TWICE!  Check your line near each end and just make sure it is actually 3 inches from the bottom edge of the paper as shown in Picture 3.

Second Line

Repeat!  We are going to do the same thing, but instead of going from the edge of the paper, our next line will be 2 inches above our first line as shown in Picture 4.  You could also measure 5 inches from the other edge of the paper and get the same result.  Make sure you MARK TWO ARROWS AND SCRATCH A LINE and then MEASURE TWICE!  Make this line long also.  You can see this line at the top of Picture 4.

Perpendicular Lines

Now we start with the perpendicular lines.  From the side of the paper on the bottom line, measure over at least 3" and mark an arrow. Repeat for the top line.  Turn your ruler 90 degrees and scratch a line through your arrows as shown in Picture 5.  Remember to MEASURE TWICE and check your work!  From this line, measure over 2" and repeat the last set of directions, marking another line as shown in Picture 6.  You now should have a 2" square!

## Step 4: Basic Geometry- Triangular Sides

Moving on to the sides.  Each side of our base will have a triangle attached to it.  Each triangle will have a base of 2" (that's the edge on the square) and will be 3" tall.

To make the triangles 3 inches tall, we need to find a point 3 inches above the edge of our base.  The easiest way to do this is to center the point and measure up all at the same time.

Start by picking a side of the square.  It doesn't matter which, we are going to do the same thing to all 4 sides.  Each side is 2" long, so measure over 1" and mark the center of the line.  Repeat for the opposite side of the square, and then draw a line through the marks as shown in Picture 1.  Make it long!

Pick one side again.  On the line you just made measure up 3 inches from the edge of the square and make a mark as shown in Picture 2.  Using your ruler, make a line from this point to each corner of the square as shown in Pictures 3 and 4.  Viola!  One down, 3 to go.  Repeat for each side of the square.  Your drawing should now look like Picture 5!

## Step 5: Strengthining and Joining- Hems and Tabs Part 1

We need to be able to join all of the sides together. Each triangle needs to be joined to the triangle next to it, but its really hard to glue edges together.  We need to make a TAB.  What is a Tab?

Tab:  A small flap of material on something used to hold things in place.

We need one tab for each corner that needs to be joined.  That means there will be 4 tabs, one for each corner where the triangles are joined. They will be 2 inches long, 1/2 inch wide, and need to have tapered corners (a trapezoid).

Pick a side of one of the triangles.  Make a parallel line 1/2 inch away from the side by measuring up 1/2 inch in two different locations, marking arrows, and scratching a line as shown in Picture 1. Using your ruler, line up the marks with the line you just drew with the corner of the square as shown in Picture 2.  Mark the line as shown in Picture 3. Measure over from this line 2 inches along the edge of the triangle and the edge of the hem and mark another line as shown in Picture 4.  Now you have the basic shape of the Tab, but we still need to trim the corners!  Along the outside line of the tab, measure in 1/2 inch from each end and mark a line from the bottom corner of the tab to the mark as shown in Picture 5.  Clean up the extra lines as shown in Picture 6.

Repeat for the remaining three sides, and you're done with the tabs!  See Picture 7 for the completed version.

## Step 6: Strengthining and Joining- Hems and Tabs Part 2

Now we're going to introduce a new element when working with sheet metal.  This piece is called a Hem.  What is a Hem?

Hem - the edge of a piece of material (cloth, paper, metal, etc) that has been turned under to add strength and hide rough edges.

With paper, it doesn't do a whole lot to strengthen anything, but remember- we're practicing for metal!  Hem's hide the sharp edge of sheet metal and also make the thin metal much stronger.

With this particular layout, we need 4 hems.  The hems are much like the tabs, just skinnier and longer.  We will put one on each triangular side, opposite from the tab. Pick a side, again it doesn't matter which because we will be doing this to all 4.

We are going to make another parallel line along the side of the triangle, but this one is only 1/4 of an inch wide.  Measure out 1/4 inch and mark two arrows, then scratch your line as shown in Pictures 1 and 2.  At the tip of the triangle, make a perpendicular line like we did with the tabs, as shown in Picture 3.  Repeat at the bottom edge of the triangle.  Mark the 45 degree angles by measuring in from the edges 1/4 of an inch on the outside line as shown in Picture 4.  Clean up the angles and extra lines as shown in Picture 5

Repeat for the rest of the sides and your done laying out the pyramid!  See Picture 6.

## Step 7: Cut and Fold!

This step is pretty simple.  Cut it out!  See Picture 1.

Crease the paper on all of the lines- between each square and each tab.  Take your time though- all the work we spent getting our lines laid out straight will be pointless if the folds don't follow the lines!  Fold it and run your thumbnail along the fold to make a sharp edge, then unfold the paper.  See Pictures 2, 3, and 4.

With all the lines creased, it should come together pretty quickly!  Test it out before gluing, make sure all the corners line up.

## Step 8: Finish It Up! Glue and Measure

Start with the hems.  They are folded back over on themselves and glued directly to the triangle they are attached to as shown in Picture 1. Carefully apply a little glue to each hem and then stick the hem down tightly.  I recommend only putting glue on one hem at a time as shown in Picture 1, otherwise you are going to have a big glue mess everywhere.  Repeat for the other three hems.

Tabs-  each one is glued to the triangle next to it as shown in Picture 2.  Again, I recommend only putting glue on one hem at a time to avoid the mess.  Work your way around until everything is glued!  The last tab or two may be tricky but take your time and you can get it to stick.

Checking your Pyramid-  You can tell if you did a good job a few different ways.

Measuring:  Check the base to make sure that it is 2 inches across in both directions at multiple locations.  You can also measure diagonally- the measurement should be the same both ways if you measure diagonally.

Triangle tips-  The triangles should come together at the points perfectly.  If one is a little shorter than the rest it's easy to tell.  Also look at all the triangles from the side- its pretty easy to tell if any of them are "leaning" to the left or right.

Continuing on!  Now that you can make the pyramid, try out some of my other instructables and watch for a few more to come!
I love the alliterative title.