Time Required: One 45-minute session
Skill Level: Beginner
Recommended Grades: 3rd to 5th

This activity blends math and art. Students will work in small groups to practice working with multiples of 2 and 5. Students will organize multiples in a table and use them to create a design based on a repeated set of instructions: UP, RIGHT, DOWN, LEFT. The resulting design will engage your students while affording them practice in either skip counting or multiples, depending on the grade curriculum.

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

Lesson Plan


Step 1

Whole Group: Project your tablet or computer screen on the board for students to view the Charting Multiples Worksheet.

Step 2

Review either skip counting or finding multiples of 2. The results will be the same. Chart the numbers on the board in a table with two rows as recorded below in step 3.

Step 3

The first few digits in this sequence will be recorded in the same way in both the top and bottom rows.

Step 4

Chart the next few numbers in the sequence, which are double digits. Instruct students to add double digits, with the sum of the two digits inserted into the bottom row of the table.

Step 5

Share the goal: Students will create a design on graph paper using the numbers in the second row. The student will take the numbers recorded in each section of the second row sequentially, and each number will be used to figure out how many graph paper squares should be covered in a given line segment.

Step 6

Model how to chart the lines on the graph paper following the directions: up, right, down, left. Note that you are creating a series of spirals which will repeat until you connect back to the starting point.

Step 7

Begin the design as a whole group until students understand the process.

Step 8

Hand out the Charting Multiples Worksheets and pencils. Instruct students to fill in the table with multiples of 2. Check students' work before passing out graph paper to chart their designs.

Step 9

Circle to assist and assess.

Step 10

When students are done with their designs, call all of them together in a group to demonstrate how to use the 3Doodler to trace over lines (like a stencil) and then shade in selected areas in assorted colors. Pass out the 3Doodlers for your students to use. Feel free to show them these examples.

Wrap Up

Students share their DoodleMultiples. Their designs can be peeled off the paper and displayed like a mobile. Discuss students' observations. Other topics may include angles, symmetry, parallel and perpendicular lines, and patterns. Ask students to identify where the digit sums repeat in their tables. Please share your students' Doodles on Twitter. @3Doodler #3DoodlerEDU


The teacher will assess students’ work based on their final products.

Possible Extensions

Using the Charting Multiples Worksheet, students will predict the number of columns needed to record the multiples of 5, from start to end point. Students will graph and doodle the multiples of 5. Explore Scratch Spirolateral Generator.


The following images in the links below were created online using digital graph paper. Students may use graph paper or this online graphing tool.

Multiples of 2 Example

Multiples of 5 Example

This Spiralaterals information link may be a beneficial reference as well.


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

  • design - to prepare the preliminary sketch or the plans (for a work to be executed), especially to plan the form and structure of an object, building, bridge, etc...

  • drawing - the art or technique of representing an object or outlining a figure, plan, or sketch by means of lines.

  • following directions - acting in accordance with guidance or instruction in a given task or a series of tasks.

  • graph - a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

  • line - an infinite extent which is one-dimensional and straight.

  • line segment - a finite section of line with two end-points.

  • multiple - the product of a quantity by an integer.

  • multiplication - a mathematical operation that at its simplest is an abbreviated process of adding an integer to zero a specified number of times and that is extended to other numbers in accordance with laws that are valid for integers.

  • parallel lines - two lines which are always the same distance apart.

  • pattern - an artistic, musical, literary, or mechanical design or form.

  • perpendicular lines - two lines which intersect at a right angle.

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

  • skip counting - counting forwards or backwards by a number other than 1.

  • symmetry - the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts.

Educational Standards

Common Core

Generate and analyze patterns.

In This Lesson

Students will generate and analyze patterns formulated by multiples of 2 and 5.

Common Core

Gain familiarity with factors and multiples.

In This Lesson

Students will generate and analyze patterns formulated by multiples of 2 and 5.

CS Teachers

Decompose (break down) a larger problem into smaller sub-problems with teacher guidance or independently.

In This Lesson

Students will break down the process of designing a repeating spiral using their understanding of multiples of 2 and 5.


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 the 3Doodler to create designs formulated by multiples of 2 and 5.


Create original works or responsibly repurpose or remix digital resources into new creations.

In This Lesson

Students will use a 3Doodler to create a mathematical repeating spiral design based on multiples of 2 and 5.


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 seek feedback from a partner during the math and design processes of this project.

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