Kevin Delahoy
dela6225@fredonia.edu
Talena Baideme
baid7981@fredonia.edu
Introduction to Coordinate Geometry
Introduction:
Before students learn the slope of a line, teachers introduce coordinate geometry by
making shapes and working with transformations. With this lesson we will introduce some
fun games and pictures for the use of coordinate geometry, along with games to practice
transformations.
NYS MST Standards:
• 5. G.12 Identify and plot points in the first quadrant
• 6. G.10 Identify and plot points in all four quadrants
• 8. G.7 Describe and identify transformations in the plane, using proper
function notation (rotations, reflections, translations, and dilations)
• 8. G.8 Draw the image of a figure under rotations of 90 and 180 degrees
• 8. G.9 Draw the image of a figure under a reflection over a given line
• 8. G.10 Draw the image of a figure under a translation
• 8. G.11 Draw the image of a figure under a dilation
• 8. G.12 Identify the properties preserved and not preserved under a reflection,
rotation, translation, and dilation
Instructional Objectives:
Objectives for these lessons include:
• Introduce coordinate geometry through the interactive lessons of “Looking at the
Stars” and “Navigation Investigation.”
• Increase understanding and proficiency of the coordinate plane transformations
through the “Build a Block” game.
• Build creative thought and intriguing discussions
Itinerary/ Protocol:
The different activities are a fun reinforcement of a lesson on coordinate geometry.
The “Looking at the Stars” worksheet should take students ten to fifteen minutes to
complete as an exercise individually. This would mainly be used in a fifth or sixth grade
setting.
Navigation Investigation is an interactive activity to help students practice
coordinate geometry without having to sit and plot a list of points. It can be done in pairs;
Navigation Investigation is best for fifth and sixth grade setting.
The Build a Block game is made for seventh and eight grade students. This game can
be used in a small group setting or as an individual contest to practice coordinate plane
transformations. Most puzzles should not take students more then ten minutes to complete,
depending on the difficulty level. This can be used as a review session for students.
Looking At the Stars
Michael got a new telescope for Christmas. He loves to go out at night and look at the stars.
Michael wondered if he was looking at the same stars each time. Michael decided that he
would put the center of his telescope on the North Star. Then he would make a grid with
the North Star as the origin. From here, Mike decided to write in his journal the location of
the stars that he thought were interesting by telling how many times he turns his dial up,
down, left or right of the North Star.
Activity for Fifth Grade: First Quadrant points only
On the first night Mike saw stars at:
(8,4), (2,16), (2,20), (3,23), (4,25), (5,26), (7,27), (13,27), (15,26), (16,25), (17,23), (18,20),
(18,16), (12,4)
On the second night:
(9,13), (8,13), (6,14), (4,17), (4,19), (6,19), (8,17), (9,14)
On the third night:
(11,13), (12,13), (14,14), (16,17), (16,19), (14,19), (12,17), (11,14)
On the fourth night:
(9,9), (9,10), (8,10)
On the fifth night:
(11,9), (11,10), (12,10)
On the sixth night:
(8,7), (10,7), (12,7)
Mike decided to make constellations
out of each of his nights discoveries.
What did Mike see in the sky?
This Activity is for Sixth Grade or Higher: Coordinates in all four quadrants
On the first night Mike saw stars at:
(-2,-9), (-8,3), (-8,7), (-7,10), (-6,12), (-5,13), (-3,14), (3,14), (5,13), (6,12), (7,10), (8,7), (8,3),
(2,-9)
On the second night:
(1,0), (1,1), (2,4), (4,6), (6,6), (6,4), (4,1), (2,0)
On the third night:
(-6,6), (-6,4), (-4,1), (-2,0), (-1,0), (-1,1), (-2,4), (-4,6)
On the fourth night:
(1,-3), (2,-3), (1,-4)
On the fifth night:
(-2,-3), (-1,-4), (-1,-3)
On the sixth night:
(-2,-9), (0,-9), (2,-9)
Mike decided to make
constellations out of
each of his nights
discoveries. What did
Mike see in the sky?
Navigation Investigation
In the graph below there are hidden points! Use the answers to the following equations to
find out how many points there are in each quadrant.
1) 6(2) – 5 = ______ Number of points in Quadrant 1
2) -12 + 4(3) = ______ Number of points in Quadrant 2
3) 10(3) – 24 = ______ Number of points in Quadrant 3
4) -2(3) +10 = ______ Number of points in Quadrant 4
Once you know how many points are in each quadrant, you will choose a specific to ask the
teacher. The teacher will state if the coordinate was a hit or miss.
Make an “x” on points that are MISSES.
Mark a dot on the points that are HITS.
All points are in a pattern as follows:
One set of 2 points in a row/column.
Two sets of 3 points in a row/column.
One set of 4 points in a row/column.
One set of 5 points in a row/column.
*REMEMBER* Sets of points CAN cross the x- or y-axis!*
Can you find all the hidden points?
Build a Block
Materials Needed: Build-a-Block worksheet, copy of rules, cut out shapes,
paper, and pencil
Introduction: This exercise was developed to have students work as a group
and to help them understand and gain proficiency with the four
transformations: rotation, reflection, size dilation, and translation.
In this exercise we will use R( Po int, Degree) to describe rotations around a fixed
point,
M
( x − axis )
to describe a reflection over the x-axis, or
M
( y − axis )
to
describe reflection over the y-axis, or M ( Origin) to describe reflection over
the origin,
dilation.
T
( X ,Y )
to describe translations, and
S
( Po int, ScaleRatio )
to describe size
Rules:
Transformations must be clearly described as stated below:
1. You must describe reflections over the x axis, y axis, or the origin.
2. You must describe rotation around a fixed point on the object and the
degree of rotations.
3. For this game rotations are always in counter clockwise direction.
4. You must describe Dilations using a point on the figure and scale ratio.
5. You must describe translations as x and y scalars.
This is an example of dilation
larger or smaller using Point D
Rotation of 180 degrees
around Point B
Reflection
over y-axis
Translation by 8 in the x
and -12 in the Y
Reflection
over x-axis
Reflection over
the origin
Answer Key to One: There are
several different answers to these
questions but these are the most
efficient found so far.
1. L-Shaped:
T
R
then
( B ,180 )
( 4 , −6 )
2. Square:
T
(12 , −8 )
3. T-Shaped:
( y − axis )
4.
( origin )
5.
M
U-Shaped: M
Z-Shaped: S
T
1
(G ,, )
2
then
( 5 , −18 )
Answer Key to Two:
1. Quadrilateral KLMN:
then
T
( A,180 )
then
T
3. Triangle DEF:
T
( y − axis )
( 4 , −4 )
2. Triangle ABC:
R
M
S
3
(C , )
1
then
( 6 , −10 )
R
( F , 90 )
then
( −1, −25 )
4. Quadrilateral GHIJ:
M
( origin)
For other Fun Activities checkout: Transformation Golf at
http://www.mathsonline.co.uk/freesite_tour/gamesroom/transform/golftra
ns.html
Build – A- Block Answer Sheet
Translations: Rotation: Reflection: Size Dilation: Step 1
Step 2
Step 3
Step 4