Learn on PengiIllustrative Mathematics, Grade 5Chapter 3: Multiplying and Dividing Fractions

Lesson 6: My Own Flag (Optional)

In this optional Grade 5 lesson from Illustrative Mathematics Chapter 3, students apply multiplication of fractions to a real-world design challenge by creating their own flag and calculating the area of fabric needed for each section. Students first explore principles of flag design from the North American Vexillological Association, then use those principles to design an original flag while solving fraction multiplication problems involving area. The lesson directly addresses standard 5.NF.B.6, connecting multiplying fractions to a meaningful, hands-on context.

Section 1

Principles of Good Flag Design

Property

Good flag design, or vexillology, follows five basic principles:

Keep It Simple: The flag should be so simple a child can draw it from memory.
Use Meaningful Symbolism: The flag's images, colors, and quadrants should relate to what it symbolizes.
Use 2-3 Basic Colors: Limit the number of colors to a few that contrast well.
No Lettering or Seals: Never use writing or an organization's seal.
Be Distinctive or Be Related: Avoid duplicating other flags, but use similarities to show connections.

Examples

Section 2

Designing Flags with Fractions

Property

To design a flag, you can divide a unit rectangle into different colored sections. The area of each rectangular section is found by multiplying its fractional length and width. The sum of the areas of all the colored sections must equal 1, representing the whole flag.

Examples

A flag is designed with a red section that is $\frac{1}{2}$ of the length and $\frac{2}{3}$ of the width. The area of the red section is $\frac{1}{2} \times \frac{2}{3} = \frac{2}{6}$ or $\frac{1}{3}$ of the flag.
To make a flag that is $\frac{1}{4}$ green, you could design a green rectangle with dimensions $\frac{1}{2}$ by $\frac{1}{2}$ . The area would be $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ .
A flag has a blue section covering $\frac{3}{5}$ of its width and $\frac{1}{4}$ of its length, and a yellow section covering the remaining $\frac{2}{5}$ of the width and the full $\frac{1}{4}$ of the length. The blue area is $\frac{3}{5} \times \frac{1}{4} = \frac{3}{20}$ . The yellow area is $\frac{2}{5} \times \frac{1}{4} = \frac{2}{20}$ .

Explanation

This skill applies fraction multiplication to a creative design project. By treating a flag as a unit area, you can plan the size of different colored rectangular sections. You calculate the area of each section by multiplying its fractional side lengths. This allows you to precisely control how much of the flag is dedicated to each color, ensuring your design matches your vision.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Principles of Good Flag Design

Property

Good flag design, or vexillology, follows five basic principles:

Keep It Simple: The flag should be so simple a child can draw it from memory.
Use Meaningful Symbolism: The flag's images, colors, and quadrants should relate to what it symbolizes.
Use 2-3 Basic Colors: Limit the number of colors to a few that contrast well.
No Lettering or Seals: Never use writing or an organization's seal.
Be Distinctive or Be Related: Avoid duplicating other flags, but use similarities to show connections.

Examples

Section 2

Designing Flags with Fractions

Property

Examples

A flag is designed with a red section that is $\frac{1}{2}$ of the length and $\frac{2}{3}$ of the width. The area of the red section is $\frac{1}{2} \times \frac{2}{3} = \frac{2}{6}$ or $\frac{1}{3}$ of the flag.
To make a flag that is $\frac{1}{4}$ green, you could design a green rectangle with dimensions $\frac{1}{2}$ by $\frac{1}{2}$ . The area would be $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ .
A flag has a blue section covering $\frac{3}{5}$ of its width and $\frac{1}{4}$ of its length, and a yellow section covering the remaining $\frac{2}{5}$ of the width and the full $\frac{1}{4}$ of the length. The blue area is $\frac{3}{5} \times \frac{1}{4} = \frac{3}{20}$ . The yellow area is $\frac{2}{5} \times \frac{1}{4} = \frac{2}{20}$ .

Explanation

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Principles of Good Flag Design

Property

Good flag design, or vexillology, follows five basic principles:

Keep It Simple: The flag should be so simple a child can draw it from memory.
Use Meaningful Symbolism: The flag's images, colors, and quadrants should relate to what it symbolizes.
Use 2-3 Basic Colors: Limit the number of colors to a few that contrast well.
No Lettering or Seals: Never use writing or an organization's seal.
Be Distinctive or Be Related: Avoid duplicating other flags, but use similarities to show connections.

Examples

Section 2

Designing Flags with Fractions

Property

Examples

A flag is designed with a red section that is $\frac{1}{2}$ of the length and $\frac{2}{3}$ of the width. The area of the red section is $\frac{1}{2} \times \frac{2}{3} = \frac{2}{6}$ or $\frac{1}{3}$ of the flag.
To make a flag that is $\frac{1}{4}$ green, you could design a green rectangle with dimensions $\frac{1}{2}$ by $\frac{1}{2}$ . The area would be $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ .
A flag has a blue section covering $\frac{3}{5}$ of its width and $\frac{1}{4}$ of its length, and a yellow section covering the remaining $\frac{2}{5}$ of the width and the full $\frac{1}{4}$ of the length. The blue area is $\frac{3}{5} \times \frac{1}{4} = \frac{3}{20}$ . The yellow area is $\frac{2}{5} \times \frac{1}{4} = \frac{2}{20}$ .