## Coins Division

Join a pirate crew on their search for adventure!

In this activity, students are tasked with equally sharing a hoard of pirate treasure. Pirates join and leave the crew, and the number of coins to share changes.

This provides students with an intuitive and meaningful context to explore important aspects of division.
There are three variants:

## Learning objectives

Perform partitive division in a realistic and relatable context - dividing a set into subsets equally and observing the size of the share.
Understand the different roles played by the dividend, divisor, and quotient when modelling a sharing problem.

## Aligns with Matific’s principles

As with all of Matific’s activities, we designed this division episode to:

• Develop true conceptual understanding of division, focusing students on the fundamentals
• Bring the subject to life in a meaningful context
• Encourage critical thinking as students solve problems
• Build intrinsic engagement with the subject matter - making division itself the fun part!

## I want to know more!

Mathematical background

Division is the most conceptually difficult operation of the “big four,” and naturally arises in the context of sharing.

This episode helps students master partitive division, where the size of the original whole is known, the number of subgroups is known, but the size of the subgroups is not known. In other words, “How many does each person receive?”. This contrasts with quotative division, where the sizes of the original whole and the subgroups are known, but the number of subgroups is not, answering the question: “How many people can receive a given share?”

Matific helps educators highlight the distinction between these division modes, which is often lost on both students and educators because they both reduce to the same arithmetic operation. However, it is critically important for young learners to experience both models of division in a hands-on context to ensure the right foundations are laid for future development. Learning that X ÷ A = ? and X ÷ ? = A both have the same solution aids in connecting division to multiplication for even deeper conceptual understanding.

In this episode, Matific highlights sharing by giving one piece of gold per pirate until the gold is gone. This approach offers a clear and natural presentation of the subject matter and provides fertile ground upon which to develop an abstract understanding of division.

## Highlights

In this exciting adventure story, the number of pirates and total number of coins change, helping students develop number sense. Students discover that more pirates mean fewer coins per pirate in a share; more coins equals a larger share.

Students are first invited to draw the connection between what they are doing and the formal, abstract language of equations.

The final question builds upon the UI and patterns already established in the episode to expose students to an “unknown dividend” problem.

Matific keeps the interactions smooth and clean. Students have great fun sharing one coin with each pirate in a single click while also reinforcing concepts.

As always, the episode is designed for maximum engagement and enjoyment. Curiosity and interest grow each time students play the episode when they meet more pirates and learn more details about them!

In the episode, students enjoy sailing around the world! From snow-covered islands, across the open sea, through the tropics, and across a sun-scorched desert, students are never bored.
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