Introduction: Perfect Paper Cube: Laying Out a Project Using Parallel Line Development
Ever had an idea that sounded great in your mind? It can be easy to hash out some rough concept sketches, but when it comes time to get the ruler and pencil out, things get a bit more tough. If we know how to use a ruler to develop parallel lines, it can become a lot simpler and with some practice, you can be very accurate with nothing more than your ruler and pencil!
This activity is something I do with a 7th and 8th grade Metals class, and is geared to students in that age group. Many of the "Rules" I make them follow will help anyone to be more proficient with their projects. So what are we going to do?
Content Learning Objective:
By building a Perfect Paper Cube, students will practice and develop their ability to read a ruler and demonstrate accuracy. These skills will later be demonstrated again as students make projects out of sheet metal.
Update! A video I made showing the cube.
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. If you have a hard time reading a ruler, you may want to check out my instructable on "Drawing the Inch" first here: https://www.instructables.com/id/How-to-Read-a-Ruler-and-other-simple-tricks/
If you enjoyed this instructable you can continue on with the Perfect Paper Pyramid here: https://www.instructables.com/id/Perfect-Paper-Pyramid-More-practice-with-project-/
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...
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 Ground Work.
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.
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!
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...
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.
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!
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 Sides
Now that we have a couple of basic rules, lets talk geometry. A Cube is made up of 6 squares: 4 sides, one top, and one bottom. To make this a little more understandable as we go, I'm going to call the Sides S1, S2, S3, and S4. The top and bottom will be T5 and B6. This step will describe how to lay out the 4 sides.
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 (please note, several of these pictures are re-used from the explanations in the last step). 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 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 5.
Perpendicular Lines
Now we start with the perpendicular lines. From the side of the paper on the bottom line, measure over 2" and mark an arrow as shown in Picture 5. Repeat for the top line. Turn your ruler 90 degrees and scratch a line through your arrows as shown in Picture 6. You now have a 2 inch square! Remember to MEASURE TWICE and check your work as shown in Picture 7. If it doesn't line up, erase it and try again.
There are 4 sides. So far we have only drawn one of them. We are going to "cheat" and do the next 3 sides in one quick step. Lay your ruler back on the bottom line and line up zero at the side of the paper. You should already have a line at 2 inches, so mark an arrow at 4, 6, and 8 inches as shown in Picture 8. Move to the top line and repeat! Turn your ruler 90 degrees, line it up with the arrows, and draw 3 more lines. Make them a little long as shown in Picture 9. Now we have 4 sides!
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 (please note, several of these pictures are re-used from the explanations in the last step). 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 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 5.
Perpendicular Lines
Now we start with the perpendicular lines. From the side of the paper on the bottom line, measure over 2" and mark an arrow as shown in Picture 5. Repeat for the top line. Turn your ruler 90 degrees and scratch a line through your arrows as shown in Picture 6. You now have a 2 inch square! Remember to MEASURE TWICE and check your work as shown in Picture 7. If it doesn't line up, erase it and try again.
There are 4 sides. So far we have only drawn one of them. We are going to "cheat" and do the next 3 sides in one quick step. Lay your ruler back on the bottom line and line up zero at the side of the paper. You should already have a line at 2 inches, so mark an arrow at 4, 6, and 8 inches as shown in Picture 8. Move to the top line and repeat! Turn your ruler 90 degrees, line it up with the arrows, and draw 3 more lines. Make them a little long as shown in Picture 9. Now we have 4 sides!
Step 4: Basic Geometry- Top and Bottom
We're starting to catch on! We are going to add two more squares- one for the top and one for the bottom. It really doesn't matter WHERE they attach, as long as one is on the top side and one is on the bottom. It is easier to lay out if they are both attached to the same side. On my cube, I attached them to Side 3.
We are just going to continue with the theme- Measure 2 inches, mark two arrows, and scratch a line. This time, however, we are going to measure up from the top line and down from the bottom line. We can cheat and do them both at the same time! See Picture1 for more details.
All of the sides, top, and bottom are now marked out! To make this a little easier, I've labeled them in Picture 2.
We are just going to continue with the theme- Measure 2 inches, mark two arrows, and scratch a line. This time, however, we are going to measure up from the top line and down from the bottom line. We can cheat and do them both at the same time! See Picture1 for more details.
All of the sides, top, and bottom are now marked out! To make this a little easier, I've labeled them in Picture 2.
Step 5: Joining the Sides- Making Tabs.
This is the part that can get a little tricky. To make it a little easier to understand, take a look at my pretty crappy sketch in Picture 1. You can see the sides, top, and bottom labeled. The problem now is how to join any corner that isn't just folded. For example, Side 1is going to get folded around and attached to Side 4. Its really hard to glue edges together, so 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 3 tabs for the top (not 4, because the top is already attached to one side), 3 tabs for the bottom, and one tab for Side 1 to Side 4.
The tabs will be the length of the side of each box, which is 2 inches. They will only be 1/2 inch wide, and need to have tapered corners (a trapezoid).
Lets start with the tab on the end of Side 4. Mark a parallel line 1/2 inch away from the end of the last square as shown in Pictures 2 and 3. Remember to MARK TWO ARROWS and MEASURE TWICE! The angle on the edges is 45 degrees. This is very easy to do- a 45 degree triangle has two sides that are the same length. We know the tab is 1/2 inch thick, so we measure down 1/2 an inch and mark an arrow. Just one this time, see Picture 4! Line up the arrow with the corner of the square and draw a line as shown in Picture 5. Repeat for the other side- see Picture 6. Picture 7 shows the completed tab!
Now we need 6 more tabs- 3 on the open sides of the top, and 3 on the bottom. Start by marking an arrow 1/2 an inch out on one side of the top, then move to the bottom and mark another arrow. Draw a line to make two tabs as shown in Picture 8. Repeat for the other side Repeat for the other sides of the top and bottom, then add another tab on the top of the top, and the bottom of the bottom. Clear as mud!? See Picture 9 for a clearer explanation. You should now have a rectangle on each open side of the Top and Bottom.
Last thing to do on this step! Put the angles on each tab like we did with the first one. We have another little cheat here to speed things up though. Pick a corner, mark your first arrow 1/2 an inch in like we did last time. See Picture 10. Line up your ruler, same as before, and draw a line from the arrow to the corner of the square, but this time continue the line through the next tab as shown in Picture 11. Two birds with one stone! One arrow to mark two tabs. Repeat for the other side of the tab. The bottom of the tabs on the sides has to be done the old fashion way- Measure up 1/2 an inch, mark an arrow, scratch a line. All done! See what it should look like in Picture 12. Repeat for the Bottom square.
See Picture 13 for the completed drawing!
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 3 tabs for the top (not 4, because the top is already attached to one side), 3 tabs for the bottom, and one tab for Side 1 to Side 4.
The tabs will be the length of the side of each box, which is 2 inches. They will only be 1/2 inch wide, and need to have tapered corners (a trapezoid).
Lets start with the tab on the end of Side 4. Mark a parallel line 1/2 inch away from the end of the last square as shown in Pictures 2 and 3. Remember to MARK TWO ARROWS and MEASURE TWICE! The angle on the edges is 45 degrees. This is very easy to do- a 45 degree triangle has two sides that are the same length. We know the tab is 1/2 inch thick, so we measure down 1/2 an inch and mark an arrow. Just one this time, see Picture 4! Line up the arrow with the corner of the square and draw a line as shown in Picture 5. Repeat for the other side- see Picture 6. Picture 7 shows the completed tab!
Now we need 6 more tabs- 3 on the open sides of the top, and 3 on the bottom. Start by marking an arrow 1/2 an inch out on one side of the top, then move to the bottom and mark another arrow. Draw a line to make two tabs as shown in Picture 8. Repeat for the other side Repeat for the other sides of the top and bottom, then add another tab on the top of the top, and the bottom of the bottom. Clear as mud!? See Picture 9 for a clearer explanation. You should now have a rectangle on each open side of the Top and Bottom.
Last thing to do on this step! Put the angles on each tab like we did with the first one. We have another little cheat here to speed things up though. Pick a corner, mark your first arrow 1/2 an inch in like we did last time. See Picture 10. Line up your ruler, same as before, and draw a line from the arrow to the corner of the square, but this time continue the line through the next tab as shown in Picture 11. Two birds with one stone! One arrow to mark two tabs. Repeat for the other side of the tab. The bottom of the tabs on the sides has to be done the old fashion way- Measure up 1/2 an inch, mark an arrow, scratch a line. All done! See what it should look like in Picture 12. Repeat for the Bottom square.
See Picture 13 for the completed drawing!
Step 6: 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 Picture 2.
With all the lines creased, it should come together pretty quickly! Test it out before gluing, make sure all the corners line up.
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 Picture 2.
With all the lines creased, it should come together pretty quickly! Test it out before gluing, make sure all the corners line up.
Step 7: Finish It Up! Glue and Measure
Carefully apply a little glue to each tab and then stick the tab to the correct side. I recommend only putting glue on one tab at a time as shown in Picture 1, otherwise you are going to have a big glue mess everywhere. 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 cube- You can tell if you did a good job a few different ways.
Measuring: Check each side 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.
Corners- The three sides that come together at each corner should line up perfectly. If you have one side that doesn't quite meet the other two, you are a little off.
Tabs- with a 45 degree angle cut on the ends of the tabs, they should come together perfectly as shown in Picture 3.
Continuing on! Now that you can make the cube, try out my instructable on Pyramids and watch for a few more to come!
Pyramid instructable: https://www.instructables.com/id/Perfect-Paper-Pyramid-More-practice-with-project-/
Checking your cube- You can tell if you did a good job a few different ways.
Measuring: Check each side 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.
Corners- The three sides that come together at each corner should line up perfectly. If you have one side that doesn't quite meet the other two, you are a little off.
Tabs- with a 45 degree angle cut on the ends of the tabs, they should come together perfectly as shown in Picture 3.
Continuing on! Now that you can make the cube, try out my instructable on Pyramids and watch for a few more to come!
Pyramid instructable: https://www.instructables.com/id/Perfect-Paper-Pyramid-More-practice-with-project-/