Jumping Circles (Organizing Data and making Conjectures)
In this fun activity, students will work in pairs to observe the mathematics behind 3Doodled circle jumps, develop their own questions, organize their data, and extrapolate conjectures based on data. This engaging hands-on activity is designed to enrich mathematical reasoning, i.e., problem solving, reasoning and proof.
Knowledge
Students have- background and understanding of prime numbers, factors, rules of divisibility, graphing lines and angles.
- had time to practice with the 3Doodler.
Objectives
Students will- design and 3Doodle a series of polygons inside circles.
- analyze the relationship between the amount of dots on a circle, the size of the jump and the resulting shape.
- recognize how key concepts in math are utilized to complete this activity, e.g., prime numbers, factors, rules of divisibility, graphing lines and angles.
- design their own mathematical questions based on observations.
- organize their data.
- analyze data and make a conjecture about the relationship between the amount of dots on a circle, the size of the jump and the resulting shape.
Materials Needed
Students will need- 3Doodler (1 per pair)
- pencils (3 per pair)
- ruler (2 per pair)
- graph paper (1 per pair)
- (1 per pair)
Lesson Plan
State the goal: Students will work in pairs to connect dots on the Jumping Circles sheet to produce different types of polygons.
Project your computer or tablet screen on the board for students to view the Jumping Circles sheet (see Resources).
Begin with the 16-dot circle. Select a number, e.g., 15. This number will determine how far to move around the circle with each jump. Beginning on "0" connect the dots in straight lines with a pencil, jumping 15 dots each time until you end up back on "0."
Ask students to consider what would happen if we varied the number of dots that placed around the circle.
Pass out Jumping Circles sheet. As students work, guide to assist and assess.
Call students back as whole group: Model how to use the 3Doodler to trace over lines. Use 2-3 different color plastic sticks to enhance the aesthetic look of your art. After hardening, peel and mount on contrasting color paper. It should appear like string art.
Ask students how each of the following math concepts were involved in this activity: Geometry, angles, lines, patterns, symmetry, skip counting, multiples, prime numbers, factoring, rules of divisibility. Instruct students to design their own mathematical questions about this activity regarding the relationship between the shapes, the number of dots around the circle and the jump size. Students will organize their data in an output table with a rule in order to answer their own questions. Meet as a whole group to share their results. Students share their circles on Twitter #3DoodlerEDU
Review student’s work and participation in discussions to determine their level of understanding.
Students can create their own circles with a different number of dots and determine the size of the jump. Compare the outcome to the results in their output table. Do they follow the rule?
Reason abstractly and quantitatively.
Students will reason based on observation and data collected.
Model with mathematics.
Students will create mathematical models using the Jumping Circles sheet.
Look for and make use of structures and patterns.
Students will make conjectures about mathematical relationships based on patterns.
Engineering Design Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.
Students will create a series of jumping circles based on a set of criteria.
Engineering Design Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.
Students will make observations about mathematical relationships based on solutions to multiple Jumping Circles.
Decompose (break down) a larger problem into smaller sub-problems with teacher guidance or independently.
Students will break down the larger problem of analyzing and deciphering the relationship between the number of dots in a circle, the size of the jump and the resulting shapes, by designing a series of Jumping Circles.
Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.
Students will use the 3Doodler to visually demonstrate the the relationship between the number of dots in a circle, the size of the jump and the resulting shapes.
Exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.
Students will demonstrate willingness and competency within an open-ended task with more than one possible outcome.
Create original works or responsibly repurpose or remix digital resources into new creations.
Students will use a 3Doodler to design a series of Jumping Circles.
Use collaborative technologies to work with others, including peers, experts or community members, to examine issues and problems from multiple viewpoints.
Students will use a 3Doodler with a partner to complete a series of Jumping Circles.
