Edited by Jessica Argese and
Lauren Mazzotta
This is a magical tool that you can use to help guide Radius
throughout his journey. You may print out this copy or use your
own personal medallion! This story will teach you its special
purpose. Have fun and march onward!!!
Do you know what Radius’
name means?
A radius is a line segment that joins the
center of a circle with any point on its
circumference.
Lets look at the picture below!
More than anything, Radius wanted to be a knight. Every day, he practiced riding, sword
fighting, and archery. His teacher was brave, old Sir D’Grees. One day, Radius’ parents, Sir
Cumference and Lady Di of Ameter, came to watch his lessons. “Show us what you have
learned,” they said.
Sir Cumference’s name represents the
mathematical term “circumference.”
Do you know the definition of this
term?
A circumference is the measurement
around the perimeter of a circle.
Lady Di of Ameter’s name
represents the mathematical term
“diameter.” Do you know the
definition of this term?
A diameter is the distance across a
circle through its center point.
Angles are formed by two rays that share a
common endpoint.
Ray
Ray
In the riding ring, Radius mounted his horse and Sir D’Grees gave
directions. “Knightly right angle – trot!” shouted Sir D’Grees.
Radius rode his horse at a trot to the center of the ring and
made an exact right angle turn. It formed a perfect corner.
90°
A right angle equals 90° and
is formed by two radii of a
circle. The special box
symbol is used to label right
angles!
“Now, double the right angle to make a straight angle!” called out Sir D’Grees. Radius rode at a
full gallop straight across the ring. He came to an abrupt stop right in front of his parents.
“Wonderful!” they exclaimed. At supper, Sir D’Grees said, “Radius is ready to go on a quest.” “He
is not old enough,” said Sir Cumference looking worried.
What would be the
number value of
this straight angle?
90 °
90 °
180°
90° + 90° = 180°, so two 90°
angles make one 180° angle!
“I am ready, Father,” he said. “Please let me go.” Sir Cumference slowly
looked at each of them. Finally he smiled and nodded.
“Hurrah!” shouted Radius, “But how shall I find someone in need of help?” “Our neighbor, King
Lell, has disappeared,” Sir D’grees answered. “I will search until I find him!” promised Radius.
Do you know what this
special family medallion
is called?
It is called a protractor!
“Remember your knightly right angle, Radius,” counseled Sir D’Grees. “It will serve you well.” Sir Cumference and Lady Di
gave Radius an old family heirloom –a medallion in the shape of a perfect circle.
A protractor is a device used to measure angles from 0 degrees to 180
degrees. The symbol for degrees is a small raised circle (˚).
Click here for a fun
Protractor Song
There are two sets of numbers on a protractor so you can measure an angle from either side.
In order to choose the correct side, look at the angle that you want to measure.
- If it is an obtuse angle (greater than 90˚ and less than 180˚), use the scale that contains
numbers greater than 90˚. If it is an acute angle (less than 90˚), use the scale that contains
numbers less than 90˚.
When measuring, place the protractor on the angle so that the center point is directly on top of
the vertex of the angle and so that one side of the angle lines up with the zero line. Follow the
scale, starting at the zero, and read where the other side of the angle intersects with the
protractor. This will give you the angle’s measurement.
This angle is 60˚ because
it intersects with the
protractor at the 60
mark!
Vertex of
an angle
Zero line
Before we continue, let’s review the different types of angles!
Match each term to its correct definition!
Acute
An angle that is equal to 90 degrees
Obtuse
An angle that is equal to 180 degrees
Right
An angle that is more than 90 degrees
but less than 180 degrees
Straight
An angles that is less than 90 degrees
What types of angles
do you spot on the
rooftops?
These angles
are less than
90˚so they are
acute angles!!
What types of angles are
at the corners of the
squares?
These squares are
made up of right
angles!
Let’s review: How
many degrees is a
right angle?
Right angles
are 90˚!
“His castle lies beyond the Mountains of Obtuse,” said the villager, pointing to the east. “ But take heed!
There are tales of strange creatures and dangerous labyrinths.” “Farewell, and thank you” said Radius. He
rode through the Mountains of Obtuse. Finally, Radius came upon a walled castle surrounded by a watery
moat. He rode cautiously onto the drawbridge. It creaked and groaned with every step.
As he neared the middle, the draw bridge began to crumble. Quickly Radius urged his horse across. Just as
they reached the other side, the old drawbridge collapsed into the water with a tremendous splash. “That
was close!” Radius exclaimed. He rode through the high gates of the castle.
In the courtyard, Radius
saw a parchment hanging
on a door. He read the
faded writing. Warning,
stranger, friend, or foe,
Dangers wait as forth you
go. You must make a
Knightly Right, Finding new
Big, Straight, and Slight.
Find the Right to reach the
kind, Or you will feel the
dragon’s sting!
The Brothers Zig and Zag
What is this angle called?
How many degrees is this
angle?
It is called a straight
angle and it is equal to
180˚.
Clutching his medallion, he rode through the doorway into a circular chamber. In the middle of the stone floor, Radius
could see a carved circle with a line across its center. All around him, arches led to different rooms. “Which way should I
go?” He read from the parchment, “You must make a Knightly Right.” Just then, something flapped out of the shadows and
bumped his arm. “Oof!” grunted Radius as his medallion went flying.
90˚
0˚
“What is big?” he wondered. As Radius looked around for a way out, he saw several hallways. Each had a circle carved in
front of it. “If I hold the medallion over a circle, then the number measures the angle to the hallway,” he said. As Radius
measured the angle of the two hallways, he found only one that was bigger than a right angle.
Measure the angles of both hallways using your
protractor. What hallway should Radius go down?
We need to find the one that has the “bigger” angle!
Determine the
measurement of
the angle to
Hallway 2.
_______
Determine the
measurement of
the angle to
Hallway 1.
_______
= 55˚
Answer: Hallway 2
= 120˚
Radius entered that hallway, but it ended at a curving stairway. The stairway down was narrow and steep. The stairs came
to an end at the fiery pit. Two bridges spanned the inferno. They both started from the same spot, but they crossed the
fire pit at different angles.
Let’s apply our knowledge of angles to the world around us! Which of these objects also
contains a “straight angle”? The gas gage or the bird’s beak?
Answer: The bottom of the
gas gage is an 180˚ angle!
A straight angle equals 180˚.
“After ‘Big,’ the parchment reads ‘Straight,” Radius remembered. “That’s 180 on my medallion.
You can’t get an angle straighter than that!” He took a deep breath and ran across the bridge
that went straight over the roaring fire. On the other side, Radius heaved a sigh of relief. He
opened a heavy door and entered a dark tunnel. The door clanged shut behind him.
Raspy snuffling came from deep within the darkness. Four glowing eyes appeared and began moving
slowly toward him. Clutching his medallion, Radius hurtled down the tunnel.
What hallway should Radius go down?
We need the smallest angle!
The smallest angle is 40˚.
The tunnel ended. Other tunnels shot off at different angles. In front of each was a carved circle glowing
with its own light. “The parchment says a ‘Slight’ angle,” Radius mumbled, “like the rooftops in that cute
little village I passed through. A cute little angle is what I need, something less than 90 on the medallion.”
The smallest angle measured 40, so he turned there.
What are the values of these angles?
85˚
93˚
90˚
Can you see how Radius might have thought that
these angles were all 90˚ at a quick glance?!
89˚
Radius was
caught inside a
dark cloud.
Coughing and
sputtering, he felt
his way along to
the remaining
corridor. “I hope
this is the one,”
he whispered.
THUMP -THUMP THUMP.
Something was
lurching toward
him. Suddenly,
Radius ran into a
wall of stone. He
was trapped! The
thumping grew
louder. Whatever
it was, it was big
and it was right
behind him!
What are these “cute
little angles” called?
Acute angles!!
Radius turned around and stood with his back to the wall. His arm bumped into…a latch…a
handle…he pushed with all his strength, and a door swung open.
Can you recall what type of
mathematical tool Radius’
medallion is? What is it called?
A protractor!
Why is a protractor useful?
Protractors help people measure
angles from 0˚ to 180˚ in
degrees. Protractors can also be
used to construct angles.
A whimpering came from behind the door. King Lell opened it wider. Radius jumped back. “Dragons!” he gulped.
“They are my loyal pets,” explained the king. He scratched their heads. “The poor beasts and I were trapped in
the maze by my evil cousins Zig and Zag but we are free now.” He continued, “Young squire, anyone brave enough
and smart enough to figure out that maze deserves his knighthood!”
What are the names of the
highlighted angles?
Obtuse
There are more examples of
these angles that can be found
on this page, can you find
them?
Acute
Straight angle
Right
When King Lell whistled and called out, “Pair of Lells!”, the two dragons stretched
across the moat, side by side. They became a living drawbridge for the guests to cross.
Did you know that there are other types of angles
called supplementary and complementary angles?
What are their definitions?
Supplementary angles are two
angles that add up to 180˚. Just
think… “s” for supplementary
stands for “s” in straight angle.
Therefore, supplementary angles
always add up to 180˚.
Complementary angles are two
angles that add up to 90˚. Just
think… “c” for complementary
stands for “c” in corner. Right angles
are at the corners of squares!
Therefore, complementary angles
always add up to 90˚.
With Radius’s medallion, they easily found their way back through the maze. To celebrate King
Lell’s freedom, invitations were sent to all the neighboring knights and ladies. Sir Cumference,
Lady Di of Ameter, and even old Sir D’Grees came. Radius and King Lell went to the moat to
greet each group of guests.
Radius explained his success: “I discovered the secret of the medallion! The numbers divide a circle into 360 parts. I can
use those parts to measure any angle. I call the parts of a circle degrees in honor of my teacher, Sir D’Grees.”
Complementary Angles
65˚
100˚
80˚
Supplementary Angles
25˚
Calculate the missing value of this
supplementary angle (in degrees).
Write your answer on the pink box
below.
Calculate the missing value of this
complementary angle (in degrees).
Write your answer on the green box
below.
Answer: 150˚
Answer: 30˚
King Lell told Radius to kneel. “For your bravery and intelligence, I knight you Sir Radius!” the king
proclaimed. “From this day forth, let this Kingdom be called Angleland. Banners will fly on every castle
tower! They shall show knightly right angles of 90 degrees, small acute angles, large obtuse angles, and
straight angles of 180 degrees. Rise now, great knight of Angleland!” The crowd cheered, and Radius rose
to greet them.
Angleland was the only kingdom to have a castle with a living drawbridge. The cry “Pair of Lells!” brought the two
dragons over the moat. They became so famous that today parallel means any straight lines side by side, the same
distance apart, like the Lell Dragons. Angleland is still there on very old maps, but today we call it England.
Use your protractor to create your own supplementary
angle on the line provided below! Write each angle’s
value in degrees.
These Lell dragons create
parallel lines. Parallel
lines never intersect and
go on forever.
Some possible answers
include but are not
limited to:
 40 ˚ and 120 ˚
 110 ˚ and 70 ˚
 145 ˚ and 35 ˚
What is a radius?
A radius is a line segment that joins the center of a circle with any
point on its circumference.
What is the circumference of a circle?
A circumference is the
measurement around the
perimeter of a circle.
What is the diameter of a circle?
A diameter is the distance
across a circle through its
center point
Match the types of angles in Column A to the correct image in Column B
Column A
Right Angle
Acute Angles
Obtuse Angles
Straight Angle
Column B
Column A
Complementary Angle
Supplementary Angle
Parallel Lines
Column B
The End
Radius wants to thank you for
helping him on his mathematical
journey!