Discovering Fractions

BANGLADESH

Contributed by Sarah Scott

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• Today, we're applying multiplication of fractions and mixed numbers using area models.

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• We will be able to relate mathematical concepts to real-world contexts, including the ship breaking industry and cricket.

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• We will reflect on ethical issues related to labor practices.

The Global Math Story

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Please read Cemetery for Ships.

Shipbreaking in Chittagong

Shipbreaking #30 used with permission from Edward Burtynsky

Shipbreaking in Chittagong

Shipbreaking #11 used with permission from Edward Burtynsky

Shipbreaking in Chittagong

Shipbreaking #23 used with permission from Edward Burtynsky

What is cricket?

BANGLADESH

Cricket and baseball share some similarities, such as their bat-and-ball structures. In both sports, players hit a pitched ball and run to score. However, the specifics of gameplay, equipment, field layout, and rules differ significantly.

Cricket

Scenario: Shipbreaking and Area

In Chittagong, Bangladesh, shipbreaking is a major industry. Old ships are dismantled to recycle steel and other materials. Imagine the vast area covered by these ships as they're broken down. This scenario will help us explore the multiplication of mixed numbers through area models.

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Shipbreaking #49 used with permission from Edward Burtynsky

A ship’s captain’s quarters measures 7 1/2 meters by 6 meters. Use an area model to calculate the area of this section. What is the area (size of the room) being dismantled?

Photo Credit: Ian Abbott

The engine room is 8 2/5 meters by 9 3/4 meters. Calculate the area of this section using an area model. What is the area (size of the room) being dismantled?

If a shipbreaking yard plans to dismantle a ship into 15 pieces of equal area, and one piece has been measured to be 12 1/2 feet by 10 2/3 feet, what is the total area that will be recycled from these pieces? Use area models to solve.

Suppose the shipbreaking yard separates steel into pieces that are all 3 1/4 feet by 2 2/5 feet. How many of these pieces can be created from a section that is 65 feet by 48 feet? Use area models to explore the concept of dividing large areas into smaller sections through multiplication.

Note for the Teacher on Scenario 1

While solving these problems, ask students to think about the real-world situation in Bangladesh. They might wonder what it's like to live in Chittagong and how mathematics is applicable in everyday jobs, such as ship breaking. This context brings the problems alive for them, connecting classroom mathematics to real-world applications and challenges.

Scenario: Cricket Scoring

Cricket is a popular sport in Bangladesh played between two teams of eleven players each. The batting team attempts to score runs while the other fields, and then they switch. Runs can be scored in several ways:

• one run — hitting the ball and running to the opposite end of the pitch
• “boundaries”
• four runs — hitting the ball to the boundary with it landing on the ground first (called a “four”)
• six runs — hitting the ball to the boundary without it touching the ground (called a “six”)

In a match, a team scored a total of 260 runs, 3/4 of which were scored through boundaries. Calculate the total number of runs scored through boundaries.

In cricket, an “over” is six legal deliveries bowled from one end of a pitch to the player batting at the other end. A team needs to score 120 runs to win in the last 20 overs. If they manage to score at a rate of 1 1/5 runs per ball, will they achieve their target before 20 overs? How many overs will they take to reach the target?

Two players scored a total of 160 runs between them. Player A scored 2 1/3 times as many runs as Player B. Calculate the individual scores of Player A and Player B.

In a tournament, a team played five matches and scored the following fractions of a thousand runs in each match: 1/2, 2/5, 3/4, 1/3, and 1/5. Calculate the total runs scored by the team in the tournament.

A player scores 1/6 of their runs in the first five overs and the rest through boundaries in the remaining overs. If they scored 72 runs in total, how many runs did they score in the first five overs and through boundaries?

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Note for the Teacher on Scenario 2

While solving these problems, reflect on the strategy and precision required in cricket, both on the field and in scoring. Think about how fractions and multiplication are not just numbers on paper but represent real outcomes in the fast-paced world of sports.

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Scenario: Cricket Match

In this activity, we explore cricket match statistics to engage with multiplying fractions and mixed numbers. The aim is to collaboratively build understanding through the investigation of real-world scenarios found in cricket.

Investigate how many legal deliveries a bowler makes if 5/6 of his deliveries per over are legal and he bowls 4 1/2 overs. Use objects, drawings, or numbers to represent your thinking.

A batsman scores 2/3 of his total runs through boundaries. If he scores 72 runs in a match, determine the runs scored through boundaries. Represent your solution using different methods.

If a fielder stops 7/8 of the balls that come his way, preventing runs, and he faces 24 balls, explore how many balls he successfully stops. Try to model your solution in various ways.

In a 50-over match, a team scores 1 1/4 times as many runs in the second half of the innings as in the first half. With 160 runs scored in the first half, delve into calculating the total runs in the second half using different representations.

Note for the Teacher on Scenario 3

Encourage students to use multiple representations (such as diagrams, physical models, and equations) to understand and solve problems. This approach not only deepens mathematical comprehension but also caters to diverse learning styles, making abstract concepts more accessible.

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Scenario: Estimating Steel in a Ship’s Hull

Imagine you are part of a shipbreaking crew in Chittagong, tasked with dismantling the main body (the “hull”) of a massive ship. The hull includes the bottom, sides, and deck. Consider how large these ships can be, often stretching longer than a football field and towering many meters into the air.

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Shipbreaking #49 used with permission from Edward Burtynsky

Task Details

In groups, decide on the dimensions of the ship you'll be working with—how long, wide, and tall you imagine it to be. Use fractions to make your estimates more precise. For example, you might say the ship is 2 1/2 football fields long, 1/3 of a football field wide, and 1 1/4 stories tall.

Based on your dimensions, discuss and determine how much steel you think could be extracted from the hull of your ship. Consider the area of the ship's hull and how the thickness of the steel might impact your estimate of the total steel content.

If time and resources permit, create a model of the ship's hull using paper to help visualize and refine your estimates. Remember, the focus here is on your thought process, how you justify your estimates, and how you apply understanding of area and volume with fractions.

Note for the Teacher on Scenario 4

Reflect on the importance of estimation and justification in mathematics. How does explaining your reasoning help deepen your understanding and communication of mathematical concepts? Consider how using fractions in your estimates enhances precision and clarity in your mathematical thinking.

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Think About It

Many shipbreaking workers, including boys as young as 13, do their jobs in dangerous conditions without safety equipment and sometimes live within the yards themselves. Given that for some, this work is their only means of earning money for food and shelter, how do we reconcile the need for economic survival with the right to safety and childhood? What are your thoughts on what could be done to improve these conditions?

Note for the Teacher

• Background Context: Provide a brief overview of the ship-breaking industry, emphasizing its economic importance in countries like Bangladesh and the harsh labor conditions often encountered. Highlight that while this work provides essential income for many families, it comes with significant risks, especially for young workers.
• Discussion Guidance: Encourage students to think critically about the balance between economic necessity and human rights. Urge them to consider multiple perspectives, including the workers' immediate needs for survival and the broader implications of child labor on education, health, and future opportunities.
• Ethical Considerations: Guide students to explore ethical questions surrounding responsibility. Discuss the roles of various stakeholders, including local and international businesses, governments, and NGOs, in addressing these issues.
• Real-World Connections: Connect the discussion to broader themes of global inequality, the importance of education, and potential solutions to reduce reliance on hazardous labor for survival. This might include social safety nets, education programs, or international labor standards.
• Sensitivity and Respect: Remind students to approach the discussion with empathy and respect for the individuals involved. Emphasize the importance of understanding complex situations without resorting to simple judgments.
• Encouraging Action: Inspire students to think about how they can contribute to positive change, whether through advocacy, informed consumer choices, or support for organizations working to improve labor conditions globally.

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