Multiplying Decimals

Contributed by Sarah Scott

MASSACHUSETTS

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Today, we're multiplying decimals to calculate production quantities, analyze historical baseball statistics, and explore everyday life in Boston during the 1950s, 60s, and 70s.

Read the Story

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Please read A Sweet Story.

Boston in 1932

Photo Credit: Boston Public Library

Baseball: Boston Red Sox in 1912

Photo Credit: Library of Congress

Teacher Note: Setting the Stage for Mathematics

• Relate to Math Objectives: Explain how the lesson will involve using mathematics to explore both the production of Sweetheart candies and historical baseball statistics. Emphasize the real-world application of multiplying decimals in these contexts.
• Engaging with Prior Knowledge: Encourage students to share what they know about Valentine's Day, candy production, and any familiarity with baseball, especially regarding the Red Sox.

Sweetheart Candy Calculations

Ingredient Calculations

Common Ingredients:

• 1,200 pounds of sugar
• 800 pounds of corn syrup
• 100 pounds of gelatin
• 10 pounds of food coloring

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Production Rate: The factory produces candies at a rate of 500 pounds per hour and operates 10 hours a day.

Cost Calculation

Sugar: $0.15/pound

Corn Syrup: $0.20/pound

Gelatin: $0.50/pound

Food Coloring: $2.00/pound

Cost Considerations

Is there anything else we need to account for in the production of this candy?

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TEACHER NOTES

Differentiation: Offer a simplified version of the task with fewer ingredients for students who need it, and an advanced version that includes additional cost factors like labor and utilities.

Teaching Approach

• Guided Inquiry: Begin with questions to stimulate thinking about the various aspects of candy production.
• Collaborative Problem-Solving: Have students work in groups to calculate total production weights and costs, fostering teamwork and practical application of decimal multiplication.
• Real-World Connection: Discuss how understanding these costs is crucial in a real business setting and how accountants play a key role in managing them.

One Thing to Consider:

Encourage students to realize the complexity of product manufacturing and the importance of considering all aspects of production, not just the direct materials. This will help them understand the broader picture of business operations and the real-world applications of their mathematical calculations.

This activity not only involves practical applications of decimal multiplication but also introduces students to basic concepts in accounting and business operations, making the learning experience both educational and relevant.

Boston Red Sox Statistical Analysis

Baseball Terms

Batting Average: dividing a player's hits by his total at-bats for a number between zero

Home Runs: The batter is able to circle all of the bases

RBIs: A run scored as the result from a hit

Stolen Bases: Baserunner advances to the next base while the pitcher is throwing to home plate

Quick Compare: Batting Averages

0.406, 0.356, 0.343, 0.328, 0.317

0.326

0.29

TED WILLIAMS

CARL YASTRZEMSKI

CARLTON FISK

Quick Compare: Batting Averages

During Ted Williams’s career, MLB batting averages were 0.28, 0.275, 0.27, 0.265, and 0.26.

During Carl Yastrzemski’s career, the MLB batting average was 0.255.

General MLB averages for other players:

• batting average was 0.275
• home run average was 25
• stolen bases were 15

Teacher Notes

TEACHER NOTES

Differentiation: Provide a basic analysis task for beginners and an advanced task that involves more detailed statistical comparisons for advanced students.

Teaching Approach

• Encourage Independent Analysis: Let students independently analyze the data and draw conclusions.
• Facilitate Group Discussions: Use group discussions to compare findings and explore different viewpoints.
• Connect to Historical Context: Link the activity to the historical context of the team and the era, making the mathematical analysis more engaging and relevant.

One thing to consider:

Prompt students to think about how statistics tell only part of the story in sports and history. Encourage them to consider other qualitative factors that can influence a team's success or failure.

Catering a Boston Seafood

Party in the 1960s

Planning a Seafood Party: Menu and Pricing

Seafood Platter: Choose one option per person

• Lobster and shrimp: $9.25
• Shrimp and scallops: $6.75
• Lobster, shrimp, and scallops: $12.50

Clam Chowder: $3.75 per person

Vegetables: Choose one option per person

• Grilled vegetables: $4.25
• Steamed broccoli: $3.50

Boston Cream Pie: $2.50 per person

Drinks: Choose one option per person

• Iced tea: $1.50
• Lemonade: $1.50

Planning a Seafood Party: Calculation

• Calculate costs for parties of 15, 29, 73, and 149.

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• Multiply the cost per person of chosen items by the number of guests for each party size.

TEACHER NOTES

Teaching Approach

• Choice and Strategy: Students exercise choice in menu selection and employ different multiplication strategies.
• Collaborative Discussions: Encourage group discussions about strategies and historical pricing.
• Real-World Connection: Connect the task to real-life budgeting and event planning, with a historical context.

One Thing to Consider:

Use this activity to highlight the relevance of mathematics in understanding economic contexts. Discuss how pricing and wages reflect the economic conditions of a time period, encouraging students to think critically about historical and current economic scenarios.

Think About It

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What were the problem-solving strategies and the results you obtained in each activity?

Think About It

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How could the candy’s messages help Valentine’s Day be more inclusive of all loving relationships?

If the Spangler company asked you to come up with new sayings for the conversation hearts, what would you choose?