MATH: Doodler Tree Anglers (Constructing and Testing Conditions for Triangles)

Time Required: One 45-minute session
Skill Level: Beginner
Recommended Grades: 6th to 8th

In this activity, students will work in pairs to doodle a forked tree limb, find the angles, determine the type of triangle created when a third side is added, and determine whether it is possible to draw more than one triangle with these given conditions.

Note: Any links outside of the3doodler.com are optional resources. We can’t ensure their upkeep or accuracy.

Knowledge

Students have
  • practiced identifying different types of triangles, e.g, attributes of equilateral, isosceles, scalene, right triangle, acute, and obtuse triangles.

  • practiced labeling angles as seen here.

  • practiced measuring angles with a protractor.

  • practiced identifying intersecting and congruent lines.

  • practiced with a 3Doodler using the wrapping technique to wrap the Eco-plastic around a pencil or another thin, elongated object, e.g., dowel, stick.

Objectives

Students will
  • recognize lines that meet and/or intersect.

  • recognize congruent lines.

  • doodle a third line to doodled angles in order to make triangles.

  • recognize what would make it possible to draw one or more than one triangle with these given conditions.

  • recognize conditions that would make it impossible to draw a triangle.

  • explain their reasoning about conditions that are possible or impossible.

Materials

Students will need
  • Doodler Angler Journal

  • 3Doodler (1 per pair)

  • forked tree branch (1 per pair)

  • protractor (1 per pair)

  • pencil (1 per student)

  • large sheet of bulletin board paper (1 per pair)

  • metric ruler (1 per pair)

Lesson Plan

Instructions

Step 1 - PREPARATION

Ask students to bring in 2-3 forked tree branches from home between 10-14 inches in length.
Project Geogebra on the board for students to view.

Step 2

Share the goal: Students will use a 3Doodler to wrap their branches in Eco-Plastic, using a winding motion around the branch to create different types angles as they go. Demonstrate how to do this with a branch and 3Doodler.

Step 3

Point out the angles that have been created. Note how some are obtuse, while others are acute. Some have longer sides. Others have shorter sides.

Step 4

Share the goal: Students will note the conditions, i.e., 3 angles or 3 sides, that make it possible or impossible to form a triangle.

Step 5

Use a protractor and metric ruler to measure 3 different sides and angles spread out on your branch and record their measurements (sides and angles) in the Doodler Angler Journal.

Step 6

Demonstrate how to doodle a third line to make a triangle out of each angle. Measure and record its length in the Doodler Angler Journall.

Step 7

Ask students, "True or False: All angles can form triangles."

Step 8

Allow students to test this statement using Geogebra as a whole group. Test out various angles and line lengths to check and verify.

Will the lines always meet? Or do some angles form congruent lines that never meet?

Step 9

In the Doodler Angler Journal, challenge students to record three conditions which make it

a) possible to doodle one unique triangle,

b) conditions which are possible to doodle more than one triangle, and

c) conditions in which it is impossible to doodle a triangle.

Step 10

Clean off the branches. Instruct students to demonstrate the three conditions using a 3Doodler and branch.

Step 11

Circle to assist and assess.

Wrap Up

Students will share their doodled branches and conditions with the class, as well as on Twitter. #3DoodlerEDU @3Doodler Students will explain the conditions and whether they made it possible or impossible to doodle more than one triangle.

Assessment

The teacher will assess students' work throughout the process, as well as by their final product and input during the discussion.

Possible Extensions

  • Have students swap sets of conditions and challenge other pairs to doodle them, determining whether they are possible (with a unique or more than one solution) or impossible.

Resources

Vocabulary

  • angles - the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

  • collaboration - to work jointly with others or together especially in an intellectual endeavor.

  • conditions - the state of something, especially with regard to its appearance, quality, or working order.

  • creative thinking - a way of looking at problems or situations from a fresh and imaginative perspective.

  • math - the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.

  • mathematics - the abstract science of number, quantity, and space. Mathematics may be studied in its own right ( pure mathematics ), or as it is applied to other disciplines such as physics and engineering ( applied mathematics ).

  • problem-solving - the process or act of finding a solution to a problem.

  • proofs - in mathematics, a proof is an inferential argument for a mathematical statement.

  • reasoning - the drawing of inferences or conclusions through the use of reason.

  • triangle - a polygon having three sides.

Educational Standards

Common Core
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.

In This Lesson

Students will attempt to draw triangles based on a given set of conditions involving angles and/or sides. Students will create their own set of conditions for possible or impossible triangles.

CS Teachers
MS-ETS1-1 Engineering Design:

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution.

In This Lesson

Students will attempt to draw triangles based on a given set of conditions involving angles and/or sides. Students will create their own set of conditions for possible or impossible triangles.

CS Teachers
MS-ETS1-2 Engineering Design

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

In This Lesson

Students will evaluate and consider the design solutions of other groups during a shared activity, presentation and discussion.

CS Teachers
MS-ETS1-1 Engineering Design

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution

In This Lesson

Students will attempt to draw triangles based on a given set of conditions involving angles and/or sides. Students will create their own set of conditions for possible or impossible triangles.

CS Teachers
MS-ETS1-2 Engineering Design

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

In This Lesson

Students will evaluate and consider the design solutions of other groups during a shared activity, presentation and discussion.

ISTE
1A

Articulate and set personal learning goals, develop strategies leveraging technology to achieve them and reflect on the learning process itself to improve learning outcomes.

In This Lesson

Students will attempt to draw triangles based on a given set of conditions involving angles and/or sides. Students will create their own set of conditions for possible or impossible triangles.

ISTE
1C

Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

In This Lesson

Students will use a 3Doodler to doodle various types of angles and triangles of varying lengths, thus testing and verifying the mathematical conditions.

ISTE
4D

Exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.

In This Lesson

Students will need to create their own possible or impossible conditions.

ISTE
6C

Communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.

In This Lesson

Students will use a doodled tree branch to demonstrate possible and impossible conditions.

ISTE
7A

Use collaborative technologies to work with others, including peers, experts or community members, to examine issues and problems from multiple viewpoints

In This Lesson

Students will share a doodled tree branch to demonstrate possible and impossible conditions.

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