3-5, 6-8, 9-12
20 minutes
Arithmetic Design & Technology Engineering General
1.3 Knowledge Constructor– Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.
1.5 Computational Thinker– Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
NGSS Science & Engineering Practices
Using mathematics and computational thinking
Constructing explanations (for science) and designing solutions (for engineering)
Reflection Active listening
The spiral drawing set is more than just a fun art tool – it can be used to demonstrate and create mathematical patterns. Use this spiral drawing set to teach curves, radius, least common multiple (LCM), and radial symmetry in math, biology, and art! In this activity, students will make spiral drawings, recognize patterns, and find reflections and symmetry.
Theme
Thematic Questions
Standards:
1.3 Knowledge Constructor– Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.
1.5 Computational Thinker– Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
NGSS Science & Engineering Practices
Using mathematics and computational thinking
Constructing explanations (for science) and designing solutions (for engineering)
Get Ready:
Read through the activity details to review the steps for completing the activity.
Gather all of the materials needed to print the designs.
The table below has the number of teeth and holes in each wheel and ring. Use the table to mark the pieces with their corresponding letter so that students can find and use the disc and wheels quickly during the activities.
To familiarize yourself with the math behind the spirograph, watch Spirograph Math, a video by University or Missouri mathematics professor Carol DeFreese.
Production Time:
Assemble
Section 1 – Plan:
Section 2 - Customize and Create:
Have students form small groups of 2-3 students each.
Pass out sets, paper, and colored pens or markers, and the handouts to each group. Encourage students to take turns creating a drawing. They can use any combination of discs, colored pens, and pen holes to create their initial drawings.
Give the students time to explore different-sized wheels and discs and the pattern each makes. If using the Reference Guide handout as an exploration activity, have students count the teeth of each wheel and disc and record it on the reference chart.
Ask: “What do you notice when you change one of the variables?” and “How does the drawing change?” Give students time to think and time to share their ideas with others.
Introduce these math terms:
Have students work in groups to create one of each type of pattern. Have them label their drawings with the type of pattern and the wheel or disc they used to create it.
Once each group has created their patterns, ask: “What do you notice?” and “What do you wonder?” Record student answers on the whiteboard or a sheet of poster paper.
Have students count the petals of one of their patterns and record it under the drawing.
Ask students to use a ruler to draw a line in a contrasting color pen bisecting the pattern between two petals.
Ask: “What do you notice?” Students should recognize a line drawn anywhere through the drawing creates a reflection and because the line can bisect in multiple directions this is an example of radial symmetry.
Ask students to create three more drawings using only one disc (A-C) for their fixed disc and three different rotating discs (A-D). Have students line up the marked tooth on the fixed disc to the left of the marked tooth on the rotating disc. Tell students to move the disc slowly around the fixed disc and count revolutions each time the marked teeth pass each other. Have them record the variables of their drawings in a table like the example below. Their fixed disc should remain the same for each drawing.
Ask students to share their table with others. Ask: “What do you notice?” Students should recognize that the number of petals will also be the same when using the same fixed disc.
Now ask students to create three more drawings, this time only using one disc (B-D) for their rotating disc and three different fixed discs (A-D). Have students record the variables of their drawings in a table like the example below. Their rotating disc should remain the same each time.
Give students time to share their table with others. Ask: “What do you notice?” Students should recognize that the number of revolutions will be the same when the rotating disc also stays the same.
Ask students to look back at all the data they collected on their tables and the observations they made. Give students time to share an interesting piece of their learning from the activity.
Reflection Questions:
Help students consider...
Pro Tips:
Reimagine: