E Mathematics Operations & Applications: C. Geometry: Activity: Circuit Board Geometry

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Chloe Randall
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1 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 Mathematics Operations & Applicataions: C. Geometry 1

2 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 Mathematics Operations & Applicataions: C. Geometry 2

3 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 1.) Schematic blueprints of the correct layout of the shapes/snaps to complete the circuit must be created for each team. E Mathematics Operations & Applicataions: C. Geometry

4 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. Hexagon A polygon having six sides and six angles. 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. Parallel Lines Lines in the same plane which do not intersect. Parallelogram A quadrilateral whose opposite sides are parallel. Pentagon A polygon having five sides and five angles. Perpendicular Lines Two lines in the same plane that intersect at right angles. Polygon A simple, closed plane figure having line segments as sides. Quadrant One section of a coordinate plane formed by the intersection of the x- and y-axes. 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. Vertical A line that is perpendicular to a horizontal base line. X-axis The horizontal axis of a graph or coordinate plane. Y-axis The vertical axis of a graph or coordinate plane. E Mathematics Operations & Applicataions: C. Geometry 4

5 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 II I -X III IV +X -Y E Mathematics Operations & Applicataions: C. Geometry 5

6 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. 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. 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.. 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 Mathematics Operations & Applicataions: C. Geometry 6

7 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, (,-7) Team B, Hit!, etc.. 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 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 Mathematics Operations & Applicataions: C. Geometry 7

8 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 0 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 Mathematics Operations & Applicataions: C. Geometry 8

9 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.. Which point is closer to the origin: (1, -) or (2, -)? 4. If you plot the ordered pair (, -2), how would you get to (6, -4)? E Mathematics Operations & Applicataions: C. Geometry 9

10 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. Which point is closer to the origin: (1, -) or (2, -)? Answer: (1,-) Synthesis 4. If you plot the ordered pair (, -2), how would you get to (6, -4)? Answer: They would go right steps and down 2 steps. E Mathematics Operations & Applicataions: C. Geometry 10

11 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 Harcourt, Inc.: Orlando. E Mathematics Operations & Applicataions: C. Geometry 11

12 V B1-1 A -2 B - C -4 D -5 E -6 F -7 G S1 OFF ON 4 _ 4 L

13 V B1-1 A -2 B - C -4 D -5 E -6 F -7 G S1 OFF ON 4 _ 4 L

14 Y-axis X-axis

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16 0 Horizontal number line +Y 0 -X X Vertical number line -Y X and Y axes +Y II 4 2 I -X X III IV -Y Four quadrants of a coordinate plane

Describe Plane Shapes

Lesson 12.1 Describe Plane Shapes You can use math words to describe plane shapes. point an exact position or location line endpoints line segment ray a straight path that goes in two directions without