9.18-Babylonian-style base 60 multiplication table for 45

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9.23-Thoughts on word problems

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I believe students often avoid word problems because they find concepts like taxes or interest intimidating, especially when decimals are involved. After learning more about the history of word problems, I’d like to incorporate both that history and students' everyday lives into my teaching. I’d start by discussing with students where they might already encounter math without realizing it. For example, I might ask if they’ve ever thought about how much a discounted item costs or how long it takes to travel a certain distance. These are practical problems they’ve likely faced but don’t necessarily associate with math. Together, we’d turn these situations into word problems, helping them see that math is already a part of their daily lives. For the more challenging topics, like calculating taxes or interest, I’d create scenarios that are relatable. Instead of giving a generic tax problem, I might ask them to imagine buying a new phone with an option to pay in installments. We’d ca...
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9.23-Response-Ancient Egyptian mathematics: Numeration

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Similarities: Both systems use symbols to represent numbers. The Babylonians used wedge-shaped marks, while the Egyptians used pictures, like lines and symbols, for different amounts. Both systems had separate symbols for larger numbers. There is no single numbers like 2,3,4… The Egyptians used one symbol for 10,100,1000,10000…while the Babylonians used their base-60 system to handle large numbers. Differences: The Babylonian system is a positional system, where the value of a symbol changes based on its place in the number, similar to our system today. The Egyptian system is an additive system, where you simply add the symbols together to get the number. Each symbol represents a fixed value (e.g., 1, 10, 100) regardless of where it appears.Base system: The Roman numeral system is similar to the Egyptian system because it's also additive. However, Roman numerals use some subtraction rules (e.g., IV for 4), which the Egyptian system does not. Advantages and Disadvantages: Egyptian ...
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9.11-Why base 60?

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  Speculative Phase: When I think about why the Babylonians might have chosen base 60, one of the first things that comes to mind is how divisible the number 60 is. It can be division by so many numbers—1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. This makes it really convenient for doing calculations, no matter odd numbers, even numbers, multiples of five. In comparison, base 10 is much simpler, but it only divides easily by 2, 5, and 10. Using 60 would have made dividing things like goods, land, or even time much easier and more precise. I also think about how we still use 60 in modern life. For example, we divide an hour into 60 minutes and a minute into 60 seconds. Maybe they noticed patterns in the movements of the stars or planets that led them to use 60. In some ways, it reminds me of how the Chinese zodiac is based on a 60-year cycle, and the traditional 60-year cycle , known as the Ganzhi or sexagenary cycle, is used to track years. This system combines 10 heavenly stems...
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