E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Science as Inquiry: As a result of activities in grades 5-8, all students should develop
• Understanding about scientific inquiry.
• Abilities necessary to do scientific inquiry: identify questions, design an investigation, collect and interpret
data, use evidence, think critically, analyze and predict, communicate, and use mathematics.
Source: National Science Education Standards
NCTM Expectations:
•Specify locations and describe spatial
relationships using coordinate geometry
and other representational systems.
•Apply transformations and use symmetry
to analyze mathematical situations.
•Use visualization, spatial reasoning, and
geometric modeling to solve problems.
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 1
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Science Process Skills:
• Following Directions
• Communicating
Objective:
The learner will recognize geometric properties and
relationships and apply them to other disciplines and to
problems that arise in the classroom or in everyday life.
Math Process Skills:
•
•
•
•
•
•
Observing
Comparing
Sorting
Classifying
Matching
Problem Solving
Time: 45 Minutes
Materials:
•
Tri-fold display board cut in half to use as
visual dividers between teams (1 per team)
•
Examples of number lines and four quadrants of a coordinate plane for projection
(see Resources)
•
Printed and laminated grids of right, lower
quadrant of coordinate grid (2 per team)
•
Laminated battleship shapes (5 per team)
•
Grease pencil or some type of washable
marker (1 per team)
•
RadioShack Electronics 202 Snap-Kit
(1-2 per team)
•
The Engineering Team receives 2 blueprints: one of the preassembled circuit
board without geometric shapes and the
other of the preassembled circuit board
with geometric shapes
•
The STARBASE Crew receives the RadioShack Circuit Board and the 7 geometric shapes
•
Circuit Board Geometry Mission projected
on screen
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 2
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Instructor Preparation :
Circuit Board Geometry Activity
This activity is designed for the students to works in teams or
crews. Each team is made up of four students. Two of the students act as the Engineering Team and the other two are the
STARBASE Crew stationed at the Pentagon.
Place a set (seven pieces) of geometric shapes into plastic bags –
one for each team.
Boards must be preassembled to create a broken circuit route
which is completed by correctly placing the metal snaps mounted on the back of pre-fabricated geometric shapes. (See diagram
on page 13.) Schematic blueprints of the correct layout of the
shapes/snaps to complete the circuit must be created for each
team.
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 3
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Instructor Background Information:
Key Vocabulary
Adjacent—Close to or
nearby.
Angle—A figure formed by
two rays having a common
endpoint (vertex).
Axis—A number line which
may be vertical or horizontal.
Base—A side of a geometric figure.
Coordinate—An ordered
pair of numbers which give
the location of a point on a
plane.
Coordinate Plane—A grid
on a plane with two perpendicular and intersecting
lines of axes.
Edge—A line segment
formed by the intersection
of two faces of a geometric
space figure.
Ellipse—A curved line
forming a closed loop,
where the sum of the
distances from two points
(foci) to every point on the
line is constant.
Face—A plane region
serving as a side of a space
figure.
Geometry—The study of
space and figures in space.
Grid—A set of horizontal
and vertical lines spaced
uiniformly.
Polygon—A simple, closed
plane figure having line
segments as sides.
Hexagon—A polygon having six sides and six angles.
Quadrant—One section of
a coordinate plane formed
by the intersection of the xand y-axes.
Horizontal—A line that
runs parallel to a base.
Octagon—A polygon having eight sides and eight
angles.
Ordered Pair—Also called
coordinate. A pair of numbers used to locate a point
on a grid. The first number
tells the left-right position
(x-axis) and the second
number tells the up-down
position (y-axis).
Origin—The point where
the two axes of a coordinate
plane intersect.
Rhombus—An equilateral
parallelogram.
Square—A parallelogram
with four equal sides and
four right angles.
Triangle—Plane figure
bounded by three sides and
having three angles.
Trapezoid—A quadrilateral
having only two sides that
are parallel.
Vertex—The point where
the two sides meet.
Parallel Lines—Lines in the
same plane which do not
intersect.
Vertical—A line that is perpendicular to a horizontal
base line.
Parallelogram—A quadrilateral whose opposite sides
are parallel.
X-axis—The horizontal axis
of a graph or coordinate
plane.
Pentagon—A polygon
having five sides and five
angles.
Y-axis—The vertical axis of
a graph or coordinate plane.
Perpendicular Lines—Two
lines in the same plane that
intersect at right angles.
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 4
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Coordinate Geometry
Coordinate graphing is a visual method of showing relationships between numbers. Coordinate graphs are one way to
represent the relationship between the x- and y-values of a
function table and to illustrate linear geometric relationships.
On a coordinate graph, numbers are plotted on a grid created
with intersecting perpendicular lines (the x- and y-axes), which
are labeled with positive and negative integers like a number
line. The point at which the lines intersect is the “origin” with the
value of (0,0).
Points on the grid are related to the number of steps to the left
or right along the horizontal x-axis, and up or down along the
vertical y-axis from the point of origin. The points are represented by an ordered pair of numbers — the first number in the pair
gives the horizontal distance, and the second number gives the
vertical distance.
The x- and y-axes of a coordinate plane divide the plane into
four quadrants. See illustration below.
+Y
4
II
3
I
2
1
-X
-4 -3 -2 -1
-1
III
-2
-3
1
2
3
4
+X
IV
-4
-Y
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 5
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Lesson
Coordinate Geometry
1. Introduce students to the concept of coordinate geometry
by reviewing what they already know about number lines.
Project a sample horizontal number line with the “0” in the
center, and select a student to fill in the appropriate positive
integers to complete one half of the number line.
Ask: What numbers belong on left half of the number line?
(Negative integers that correspond to the positive integers.)
Allow another volunteer to complete the number line using
negative integers.
2. Demonstrate that a number line can also be vertical by
projecting a sample number line oriented vertically. Repeat
the procedure of completing both the positive and negative
integers on the number line. Strategic Questions:
After #5
What is the y-value of all of
the points on the x-axis? (0)
What is the x-value of all of
the points on the y-axis? (0)
Note:
You may point out the use of
ordered pairs is also used in
navigation to indicate latitude and longitude. However,
cardinal and intermediate directional labels (N,S,E,W) are
used to indicate the quadrant
in relation to the Equator
(x-axis) and Prime Meridian
(y-axis) , rather than positive
or negative integers.
3. Project an example of the two perpendicular number lines
intersecting at the “0” mark. Explain that these two intersecting number lines can be used to express number relationships and have many mathematical applications. The two
number lines have formed two axes, called the x-axis (horizontal) and the y-axis (vertical).
4. Project the two axes onto gridlines to demonstrate the four
quadrants. Explain to the students the four sections created
by the intersection are four quadrants of a “coordinate plane”.
The intersection of the two axes is called the “origin” and is
designated by the ordered pair (0,0). Locations in each quadrant relate to the numbers on the number line. Each step on
the number line is designated by a number on the number
scale. The numbers to the right and above the origin are
positive, and the numbers to the left and below the origin are
negative.
5. Allow volunteers to locate several example coordinates or
ordered pairs on the projected coordinate grid. E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 6
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Practice Activity:
1. Project the example of the right, lower quadrant that will be
used in this activity. (See resources.) Explain to the students
that this represents the right, lower quadrant of a coordinate
grid, and has the points 0 through 10 along the x-axis and 0
through -7 along the y-axis.
2. Ask students if they recall the popular board game Battleship. Relate the coordinate grid to the grid used in the board
game. Pass out two printed grids and one set of battleship
shapes to each team of two students. Each group of four
students also receives a divider board. Explain that each team
will place the “battleships” on one of their grids in locations of
their choice. The other grid is used for marking their “hits” and
“misses” when trying to locate the other team’s ships. Each
team will attempt to locate the positions of the ships using
ordered pairs, without either team being able to see what the
other team is doing.
Note:
You may need to model for
the students how to make
guesses using ordered pairs.
For example: Team A, “(3,-7)”
Team B, “Hit!”, etc.
3. Using the steps of the traditional “Battleship” game, have students complete a quick game to practice relating the ordered
pairs to coordinating points on the grid. (If unfamiliar with
the game, go to http://www.gameideasforkids.com/battleship.htm for printable game and instructions.)
4
Check for Understanding:
While students are completing their practice game
of Battleship, circulate and monitor to assure their
understanding of the use of ordered pairs. Clarify
and re-teach as needed.
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 7
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Circuit Board Geometry Activity:
Mission
While preparing to demonstrate a newly engineered circuit
board used on the DoD Satellite Station, the STARBASE
Crew accidentally knocked it off the table and onto the
floor. All of the geometric pieces that make up the connections on the board have fallen off and have to be reassembled correctly in order for the circuit board to work
properly. The crew doesn’t know how to reassemble it, and
the presentation is in less than 30 minutes!
Note:
Explain to the students that
an electrical circuit has to
be closed (no gaps) in order
for electricity to flow. If they
correctly place their geometric
shapes, the metal snaps will
complete the circuit, and the
bulb will light.
The light switch on the circuit
board should be moved to the
“on” position before starting
the activity. This can be done
prior to passing out the circuit
boards or by asking the Engineering Team to provide this
instruction to the STARBASE
Crew..
The STARBASE crew has contacted the engineering team at
the manufacturer’s location. Since this is the team of engineers that originally designed the circuit board, they have
the blueprint and know exactly how the shapes must fit on
the circuit board to work properly.
It is up to the engineering team to read the blueprint and
communicate to the STARBASE crew the coordinates of
the geometric shapes on the circuit board. The STARBASE
crew cannot see the blueprint. They have to follow verbal
directions and be careful to do exactly what the engineering team tells them to do so that their circuit board will be
operational in time for their demonstration.
9. Review geometric shapes and the other vocabulary associated with the shapes.
10. Choose one team of two students to represent the STARBASE
Crew and the other team of two students to represent the
Engineering Team. Pass out the dividers to each team. Give
the preassembled circuit board and the geometric shapes to
the STARBASE crew and the blueprints of the circuit board to
the Engineering team.
11. The Engineering Team reads the blueprints and directs the
STARBASE Crew where to place the geometric shapes using
the correct coordinates. Students should also use the correct
names for the shapes.
When the light bulb goes on, the team is successful!
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 8
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Suggested Final Assessment Questions
1. In a coordinate grid, the intersection of the x-axis and y-axis
forms how many quadrants?
2. Explain how an ordered pair is used to plot a location on a
coordinate grid.
3. Which point is closer to the origin: (1, -3) or (2, -3)?
4. If you plot the ordered pair (3, -2), how would you get to (6, -4)? E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 9
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Suggested Final Assessment Questions
Comprehension
1. In a coordinate grid, the intersection of the x-axis and y-axis
forms how many quadrants?
Answer: 4
Application
2. Explain how an ordered pair is used to plot a location on a
coordinate grid.
Answer: The first number tells you how many steps to the left
or right of the origin along the x-axis, and the second number
tells you how many steps up or down of the origin along the
y-axis.
Knowledge
Synthesis
3. Which point is closer to the origin: (1, -3) or (2, -3)?
Answer: (1,-3)
4. If you plot the ordered pair (3, -2), how would you get to (6, -4)? Answer: They would go right 3 steps and down 2 steps.
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 10
E 3.1.1.5. Mathematics Operations & Applications: C. Geometry:
Activity: Circuit Board Geometry
Resources
Examples of number lines and axes for projection
Grid of circuit board
Blueprints of circuit board
Laminated images for Battleship game
Sources:
Harcourt Math: Louisiana Edition. 2005. Harcourt, Inc.: Orlando.
http://www.eduplace.com/math/mathsteps/4/c/index.html
http://www.gameideasforkids.com/battleship.htm
E 3.1.1.5 Mathematics Operations & Applicataions: C. Geometry 11
-7
G
F
-6
E
-5
D
-4
3
3
3
7
4
4
6
5
3
6
OFF
C
-3
-2
B
2
7
8
9
+
B1
_
3V
-1
A
1
L2
S1
ON
4
5
10
-7
G
-6
F
-5
E
-4
D
3
3
3
7
4
4
6
5
3
6
OFF
-3
C
-2
B
2
7
8
9
+
B1
_
3V
-1
A
1
L2
S1
ON
4
5
10
Y-axis
-7
-6
-5
-4
-3
-2
-1
X-axis
Cruiser
Cruiser
Amphibious
Amphibious
Destroyer
Destroyer
Special Ops Craft
Special Ops Craft
Aircraft Carrier
Aircraft Carrier
Cruiser
Cruiser
Amphibious
Amphibious
Destroyer
Destroyer
Special Ops Craft
Special Ops Craft
Aircraft Carrier
Aircraft Carrier
0
Horizontal number line
0
+Y
4
3
2
1
-X
-4 -3 -2 -1
-1
1
2
3
4
Vertical number line
+X
-2
-3
-4
-Y
X and Y axes
+Y
4
II
3
I
2
1
-X
-4 -3 -2 -1
-1
III
-2
-3
1
2
3
4
IV
-4
-Y
Four quadrants of a coordinate plane
+X