# Doodle-the-Dots (Multiplication Patterns)

In this activity, students will work independently to practice multiplication by connecting-the-dots with a 3Doodler. Students will predict which numbers will result in the same shapes. Students will combine shapes to create an artistic display of their multiplication facts.

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### Knowledge

had practice with multiplication facts for multiples of 2 through 9.

had experience using 3Doodler to create stencils and weld.

### Objectives

fluently multiply within 100.

recognize patterns.

predict patterns.

identify numbers whose multiples produce that same shape.

### Materials

3Doodler (1 per pair)

pencils (3-4 per pair)

pens (3-4 per pair)

white copy paper (1 per pair)

paper plate (1 per per pair)

Doodle-the-Dots sheet

### Lesson Plan

#### Instructions

Project your tablet or computer screen on the board and display the Doodle-the-Dots sheet for students to view.

Model how to Doodle-the-Dots for circle C.

*This is like a connect-the-dots.

Have students identify multiples of 3 beginning with "0."

*0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

Record the multiples of 3 on the board and underline each digit in the one's place for 2-digit numbers. For each 2-digit number, look only at the one's digit:

Beginning at the "0," in pencil, draw a line to the point that has that digit.

(Draw lines from 0 to 3, 3 to 6, 6 to 9, 9 to 2, 2 to 5, 5 to 8, 8 to 1, 1 to 4, 4 to 7, and 7 back to 0.).

Note that we begin and end the circle shape back at "0." .

Trace over the shape with your 3Doodler.

Ask students to identify the shape that was created with multiples of 3.

*A star.

Record its number of sides and vertices on the Doodle-the-Dots sheet.

Ask students to identify the multiples of 4 for circle D, beginning with 0.

*0, 4, 8, 12, 16, 20. Stop at 20.

Model how to connect the dots in the circle beginning with 0 and then moving to 4, 8, 12, 16 and ending at 20.

Ask students to identify the shape, numbers of sides and vertices. Record them on the Doodle-the-Dots sheet.

Ask students to predict if any other numbers will result in the same shape as the ones we created with multiples of 3 and 4.

Divide students into pairs. Hand out Doodle-the-Dots sheet. Circle to assist and assess.

#### Wrap Up

#### Assessment

#### Possible Extensions

Have students work backwards identifying the factors of a multiple, e.g., 20. Have students connect the factors in order from smallest to largest beginning with "0" and compare to their original Doodle-the-Dots.

Have students doodle-the-dots by skip counting by n on unnumbered circles.

Practice addition and subtraction facts by skip counting by n - 1 dots or n + 2 dots, etc.

#### Resources

Tips and Tricks for 3Doodler: As you connect the dots, work slowly to allow a steady stream that does not break as you move from dot to dot. Press down firmly on a dot to allow the plastic to adhere

before lifting up to connect the next dot.

Doodle-the-Dots Observations

1 and 9 result in the same polygon: a 10-sided decagon.

2 and 8 result in the same polygon: a 5-sided pentagon.

3 and 7 result in the same polygon with 10 vertices, skip counting by 3s.

4 and 6 result in the same polygon: a pentagram/star with 5 vertices, skip counting by 2s.

5 results in a 'degenerate' polygon, as the connectors are always 0 and 5.

10 results in a 'degenerate' polygon, as the connectors are always 0.

#### Vocabulary

**degenerate**- lacking some property, order, or distinctness of structure previously or usually present.**polygon**- a plane figure with at least three straight sides and angles, and typically five or more.

#### Educational Standards

Fluently multiply and divide within 100

Students will Doodle the Dots to practice multiplication facts for multiples of 3 through 9.

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even,

Students will identify patterns in multiples, e.g., even numbers, odd numbers, etc.

Define a simple design problem that can be solved through the development of an object, tool, process, or system and includes several criteria for success and constraints on materials, time, or cost.

Students will work with a partner to 3Doodle a concrete reminder of the multiplication facts for multiples of 1-10.

Plan and create a design document to illustrate thoughts, ideas, and stories in a sequential (step-by-step) manner (e.g., story map, storyboard, sequential graphic organizer).

Students will sketch their connectors first in a sequential manner before using the 3Doodler to connect the dots.

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

Students will break down the process of multiplication by creating a visual display of multiples in a circular pattern.

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 a multiplication circle for multiples of 1-10.

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

Students will create multiple circles with a 3Doodler.

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 their partner as they create their doodle-the-dots circles.