Summary of Value Equivalence: buying and selling

INTRODUCTION

The Relevance of the Theme

In the world of exchanges and purchases, playing at selling and buying is more than fun, it's a training for life! Mathematics is in stores, markets, amusement parks, and even in the allowance. Understanding about value equivalence is like having a superpower to not get lost in the midst of prices and change, and, who knows, even help adults with their purchases!

Contextualization

Value equivalence is a treasure on the mathematics map that appears in our 3rd-year adventure! It is a relative of additions and subtractions, but with a special touch of 'reality'. Imagine that in the sea of numbers, values have their own islands, and we can navigate between them with the compass of buying and selling. Here, each product has its label, each payment has its value, and each change has its mystery. This adventure is an important part of the curriculum because it helps to understand not only the numbers but also how they dance to the rhythm of everyday life.

THEORETICAL DEVELOPMENT

Components

• Product Value: Everything we can buy has a price, a label that says how much it costs. It's like a numeric name for toys and treats.
• Money: Coins and bills are the superheroes we use to pay. Knowing them well is being a friend of accounts because each one has its strength: R$1, R$2, R$5, and so on.
• Change: It's what we receive back when we give more money than the product's value. It seems like a gift, but it's just mathematics: subtraction in action!

Key Terms

• Buying: Giving money to take something home. It's the moment when we choose something we like and use money to make it ours.
• Selling: Receiving money for something we have. It's like being the captain of a store, saying 'Goodbye!' to a product and 'Hello!' to the little money.
• Equivalence: Means that one thing has the same value as another. Like saying that a $3 ice cream is equivalent to three $1 coins.

Examples and Cases

• Buying a pencil: If a pencil costs $2 and we pay with a $5 bill, we need to know how much change we will receive. We observe that $5 - $2 = $3 in change.
• Selling stickers: Imagine you have stickers worth $1 each. If someone gives you $5 for five stickers, you don't need to give change, as the amount paid is equivalent to the value of the stickers.
• Equivalence in toys: Two toys cost $10 each. If we exchange a $20 bill for them, we are making an equivalence of values. There is no leftover or missing: it's a perfect exchange!

Remember that each step is like a puzzle: we fit pieces of values, change, and prices together to form a complete picture of buying and selling.

DETAILED SUMMARY

Key Points

• Knowing Money: Coins and bills have different values. Being able to identify them helps when paying and receiving change.
• Calculating Change: When the payment is higher than the product's value, we must calculate the change. Subtracting the price from the amount given is the key.
• Practice of Equivalence: Understanding that exchanging a higher-value note for products or coins of equivalent value does not generate change.
• Performing Purchases and Sales: The practice of buying and selling helps to solidify the process of calculating and understanding values and change.
• Importance of Cents: Sometimes, values involve cents, and it is important to know how to add and subtract with them as well.

Conclusions

• The mathematics of buying and selling is applied in everyday life, improving our understanding of the value of money.
• Knowing how to calculate change develops subtraction skills and prepares for real situations of value exchange.
• Understanding and practicing value equivalence increases confidence in using money and financial transactions.

Exercises

1. Purchase with Change Calculation: You buy a game that costs $12 with a $20 bill. How much change should you receive?
2. Sale without Change: You sell four stickers for $2 each. Your friend pays you with two $5 bills. Does he need change? Why?
3. Value Equivalence: You have a $10 bill and want to buy two snacks for $5 each. If you pay with the $10 bill, will you receive change? Explain.

Remember that each purchase and sale is a small mathematical adventure. The more you practice, the more skilled you become in this art of numbers and values!