• Home
  • About Me
  • Privacy Policy
  • Nav Social Menu

    • Facebook
    • Instagram
    • Pinterest
    • Twitter
    • YouTube

My World Their Way

Screen free Activities & Ideas for Families | Hands on Learning Activities for kids

  • My World Their Way
  • At Home Learning
    • Math
    • Literacy
    • Science
    • STEM
  • Kids Activities
    • Art and Craft
    • Games
  • Books
    • Books for Kids
  • Parenting
  • PRINTABLES
    • Coloring Pages

How to make a Protractor with Paper

Did you know that you can make your own protractor at home by folding a square piece of paper. We know that a square piece of paper has four 90° angles and by folding it in various ways we can divide the 90° angle into equally smaller angles. To begin with, you can bisect a right angle to form a 45° angle by folding the paper diagonally. But how do you find a 30 degree angle without a protractor or a 60° , 120°, 75°, and so on ? Let’s try to work that out.

What can You use if YOU don’t have a protractor

paper protractor material
  • A square piece of paper
  • a Protractor for testing the paper protractor ( Optional )
  • a pen

How do you find an angle without a protractor

Take a square piece of paper and fold it in half and then unfold it.

fold the paper in half

Pick up the upper left corner ( with an angle of 90° ) and fold so that the corner point touches the mid line you created in step 1, and move it such that the creased line passes through the top right corner of the square. This fold will create a 30-60-90 triangle.

make the 30-60-90 triangle

Now fold the bottom left corner so that the fold being made lines up with the edge of the already folded over 30-60-90 triangle. It will create the second 30-60-90 triangle. Tuck it under the bigger 30-60-90 triangle you created in step 2.

Second set of 30-60-90 triangle

Tuck it under the bigger 30-60-90 triangle you created in step 2 and mark the angles.

Fold the two triangles - paper protractor

Fold the paper so that the remaining unfolded top right corner is bisected in such a way that the bottom right corner meets the edge of the 30-60-90 triangle you formed in step 2.

third and final fold for paper protractor

You protractor is ready and you can now find and mark all the angles on it.

Paper protractor

Open the paper and you can see that one edge of the paper has been divided into three equal angles of 60° each.

The 120 degree angle - paper protractor

MATHEMATICAL PROOF

So what’s going on? How can you prove that the right angle triangle formed in step1 and step 2 are 30-60-90 triangle ?

Let’s assume the length of the square side is 2a. The line A’B aligns with the side AB of the square when the fold is made, so it is also 2a.

Explaining and proving paper protractor

In the right angled triangle A’EB, length of side BE is ‘a’ and the hypotenuse is ‘2a’. therefore it is a special right angle triangle. Hence, the angle EA’B is 30° and the other angle EBA’ in the triangle must be 60°.

Explaining and proving paper protractor

Now, in the quadrilateral AE’A’B, we already know that some of the angles are 90° and 60° . Angles E’AB = 90°, angle E’A’B = 90° and angle ABA’ = 60°. Since the angle sum of a quadrilateral is 360° and the fold line BE’ is a line of symmetry, the missing two angles ( angle AE’B and angle E’A’B ) must each be 60°.

That’s how we can prove that the triangle created in the first fold is a 30-60-90 triangle.

RELATED POST : How to prove that the sum of all angles of a triangle is 180 degrees

The mathematical magic of demonstrating geometry principles and constructing geometric figures using paper-folding doesn’t end here. There are many books written on it.

( Disclosure : Some of the links below are affiliate link, meaning, at no additional cost to you, I will earn a commission if you click through and make a purchase )

Buy on Amazon

I hope your kids will enjoying understanding how to make a protractor using paper and learn the basic concepts of geometry just by folding a piece of paper.

Tweet
Share
Share
Pin56
56 Shares
«
»

Math 8

Subscribe

Reader Interactions

Comments

  1. Kelsi H says

    August 6, 2020 at 9:04 am

    Amazing!! Definitely pinning this for when my kids are a bit older (or for myself 😂), but many of my friends with school-age kids will love this!

    Reply
  2. Audrey says

    August 6, 2020 at 9:41 am

    This is really cool!!! Thanks for sharing this DIY protractor.

    Reply
  3. Bennett Flaherty says

    August 6, 2020 at 10:50 am

    This is so cool and resourceful! My kiddo will love this as he gets older, and might actually enjoy geometry 😉

    Reply
  4. Lynn says

    August 6, 2020 at 4:14 pm

    I could have used this in college! Perfect tip when my kids are older!

    Reply
  5. TheHappyMommie says

    August 7, 2020 at 12:05 am

    Wow, this is so creative and useful, saving it for my kids 😊

    Reply
  6. Alyssa says

    August 7, 2020 at 5:00 am

    Wow, what a great idea! This is helpful for students since they can learn how to be resourceful and create their own protractor. Thanks for the guide!

    Reply
  7. Sankhamala says

    August 7, 2020 at 11:00 pm

    Great idea ! I have shown it to my son and he is inspired to prepare one.

    Reply
  8. Celina says

    August 10, 2020 at 5:55 pm

    Such a simple but genius idea! thanks for sharing!

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Primary Sidebar

  • Facebook
  • Instagram
  • Pinterest
  • Twitter
  • YouTube

Get connected

Subscribe to our newsletter to get updates on all our latest product releases, sales, and some free goodies!

Hooked On Phonics

Search all of my posts

Categories

Our Privacy Policy

  • Cart
  • Checkout
  • FREE PRINTABLES
  • My account
  • Shop
  • Privacy Policy

Amazon Affiliate Disclosure

I am a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.

Footer

About the Designer

Follow on Instagram

As a math lover, all I see is a #fibonacci pattern As a math lover, all I see is a #fibonacci pattern in the spirals of Romanesco Broccoli. Math is everywhere around us. Love the variety of vegetables and fruits offered at #saratogafarmersmarket
🔸 WHY DOES A BALLOON AMPLIFY SOUND 🔸 When y 🔸 WHY DOES A BALLOON AMPLIFY SOUND 🔸

When you think of speakers, loud sounds are typically the first thing that comes to mind. Speakers have amplifiers built in to make sounds louder. But did you know that a balloon may also be used as an amplifier to boost the volume?

Find out how in this science experiment for kids! 

https://myworldtheirway.com/2022/01/balloon-amplifier/

#scienceexperimentsforkids #kidsactivities
🧩 NEW YEAR MATH PUZZLES 🧩 Put your math ski 🧩 NEW YEAR MATH PUZZLES 🧩

Put your math skills to the test with some fun new year’s activities. We've got puzzles and exercises to get you in the spirit for celebrating the holidays and kicking off the new year right by exercising your brain.

https://myworldtheirway.com/2022/01/new-year-2022-math-puzzles/

#newyear #puzzles #kidsactivities
🔸 LOGIC PUZZLE - FORK IN THE ROAD 🔸 A logic 🔸 LOGIC PUZZLE - FORK IN THE ROAD 🔸

A logician went on vacation to an island. There were two different tribes that lived on the island. One tribe always told the truth and one tribe always lied. When he reaches to a fork in the road, he must ask a local person which way to go to reach the village. The logician has no way of knowing if the person is telling the truth or lying. He pause for a bit, then asks only one question. He knows which path to take based on the response.

What question does he ask?

Let us know your answer in the comments or find out the answer here 

https://myworldtheirway.com/2021/12/fork-in-the-road-logic-puzzle/

  #puzzle #logicalpuzzle #kidsactivities
🧩 Rebus Puzzle 🧩 If you like riddles or lo 🧩 Rebus Puzzle 🧩 

If you like riddles or logic problems, then you’ll love these fun picture puzzles and their creative answers ! 

Grab the free printable on the blog www.Myworldtheirway.com

#puzzle #rebus #kidsactivities
🎄 Christmas Words Rebus Puzzle 🎄 This holi 🎄 Christmas Words Rebus Puzzle 🎄 

This holiday season I gave my kids these rebus puzzles to solve and they had so much fun 
while it gave me some time to finish up the task on hand.. grab the printable on the blog.

#puzzle #rebus #christmas
Wishing all my readers a very Merry Christmas ! # Wishing all my readers a very Merry Christmas !  #christmas #xmas
Do you need some STEM scavenger hunt ideas ? Then Do you need some STEM scavenger hunt ideas ? Then create a scavenger hunt to get your kids interested in learning more about the how things work in this hands on learning approach. #stem #scavengerhunt #kidsactivities
A day spent outdoor is the perfect day to unwind a A day spent outdoor is the perfect day to unwind and enjoy nature. Scavenger hunts themed around Nature are a fun ways for kids to learn about the world around them. They can go on a nature scavenger hunts in their own backyards or go on adventure quest to a park nearby,  so it’s never too early  or too late to start exploring. Grab the FREE printable on the blog . Link in bio #scavengerhunt #outdooractivities #kidsactivities
Follow on Instagram

Subscribe for Updates

Copyright © 2022 · Darling Theme on Genesis Framework · WordPress · Log in