Initiating the Excursion
To introduce this excursion, distribute two coffee stirs and one twisty tie to each student. Demonstrate how to attach the stirs together with the twisty ties to create a moveable angle manipulative. Students should use these twist ties to produce angles and measures of 45 and 90degrees. This will help them understand the relationship of the angle to the shape of the triangle.
My Triangles Activity Sheet
Distribute a copy of the My Triangles Activity Sheet to students and ask them to draw the different types of angles they created using the manipulative.
Once the angles have been illustrated on the activity sheet, discuss the properties of the different triangles, and ask students to share their triangles with the class.
Developing the Excursion
Place students into teams of two and distribute a Make My Path Activity Sheet to each group.
If this is the first time your students have used the Hiding Ladybug Applet, you should provide a brief overview of the four directional buttons used to navigate the ladybug at the interactive applet. It is important for students to understand how clicking each of the buttons affects the direction of the ladybug. Remember to include movements for left, right, forward and backward. (See directional figures below). Students should also review strategies that can be used to help the ladybug turn corners.
move backward
 move forward
 45 degree  90 degree

After students understand how to manipulate the directional buttons, they should visit the Hiding Ladybug Applet.
Hiding Ladybug Applet
Working together, partners share the responsibilities of "Mouse Driver" and "Reader/Recorder." The "Reader/Recorder" will read the directions from the activity sheet and record observations while guiding the activity. The "Mouse Driver" controls the action of the mouse and movement on the computer screen. Partners should switch roles until all have moved the ladybug.
Demonstrate that two "small turns" (45degrees) are required to equal a "big turn". Ask students to predict how many cornerturns are required to equal a "big turn" (90degrees).
Students should experiment with specific strategies to plan the route for the ladybug to reach the leaf, based on an understanding of the 45 and 90degree options that are available on the applet. As the students are developing solutions for the ladybug to hide under the leaf, the following guided questions will encourage reflection.
Closing
Now that the students have experimented with the ladybug applet, distribute the Make My Path Activity Sheet to each member of the class. The mission is to help the ladybug navigate a path to the leaf using a different route from the one they created on the applet. Ask students to compare their first route with the second describing the similarities and differences with particular emphasis on the 45 or 90degree angles.
For example you could have students consider questions similar to the Questions for Students.
Extension
An extension to this activity would be for one student to create a ladybug path and then orally describe it to a partner. The partner would then try to duplicate the path, and record his efforts on paper.
Learning Objectives
Students will:
 Use 45 and 90degree angles to create triangles
 Develop an understanding of the relationship between angles and the shape of a triangle
 Name, describe and use orientation, direction and measurement concepts in planning paths
NCTM Standards and Expectations
 Recognize, name, build, draw, compare, and sort two and threedimensional shapes.
 Describe, name, and interpret relative positions in space and apply ideas about relative position.
Common Core State Standards – Mathematics
Kindergarten, Geometry
 CCSS.Math.Content.K.G.B.5
Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
Grade 1, Geometry
 CCSS.Math.Content.1.G.A.1
Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size) ; build and draw shapes to possess defining attributes.
Grade 2, Geometry
 CCSS.Math.Content.2.G.A.1
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Grade 6, The Number System
 CCSS.Math.Content.6.NS.C.8
Solve realworld and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Grade 7, Geometry
 CCSS.Math.Content.7.G.A.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Common Core State Standards – Practice
 CCSS.Math.Practice.MP4
Model with mathematics.