DoodleMultiples
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.
Knowledge
Students have
covered skip counting by 2's and 5's.
covered multiples of 2 and 5.
has practiced using the 3Doodler.
covered skip counting by 2's and 5's.
covered multiples of 2 and 5.
has practiced using the 3Doodler.
Objectives
Students will
use a 3Doodler and graph paper to create a mathematical design based on multiples of 2 and 5.
recognize multiples of 2 and 5.
correctly follow directions for graphing lines, i.e., up, right, down, left.
add double digits to plot lines on graph paper.
use a 3Doodler and graph paper to create a mathematical design based on multiples of 2 and 5.
recognize multiples of 2 and 5.
correctly follow directions for graphing lines, i.e., up, right, down, left.
add double digits to plot lines on graph paper.
Materials
Students will need
3Doodler (1 per pair)
graph paper (1 per pair)
pencil (2 per pair)
marker (1 per pair)
3Doodler (1 per pair)
graph paper (1 per pair)
pencil (2 per pair)
marker (1 per pair)
Lesson Plan
Instructions
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.
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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.
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Whole Group: Project your tablet or computer screen on the board for students to view the Charting Multiples Worksheet.
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.
The first few digits in this sequence will be recorded in the same way in both the top and bottom rows.
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.
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.
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.
Begin the design as a whole group until students understand the process.
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.
Circle to assist and assess.
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
Assessment
Possible Extensions
Resources
The following images in the links below were created online using digital graph paper. Students may use graph paper or this online graphing tool.
This Spiralaterals information link may be a beneficial reference as well.
Vocabulary
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
Generate and analyze patterns.
Students will generate and analyze patterns formulated by multiples of 2 and 5.
Gain familiarity with factors and multiples.
Students will generate and analyze patterns formulated by multiples of 2 and 5.
Decompose (break down) a larger problem into smaller sub-problems with teacher guidance or independently.
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.
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.
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.
Students will seek feedback from a partner during the math and design processes of this project.
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