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Alignments to Content Standards:5.NBT.A.1
Task
Historians estimate that there were about 7 million people on the earth in 4,000 BCE. Now there are about 7 billion! We write 7 million as 7,000,000. We write 7 billion as 7,000,000,000. How many times more people are there on the earth now than there were in 4,000 BCE?
IM Commentary
The purpose of this task is to help students understand the multiplicative relationship between commonly used large numbers (millions and billions) by using their understanding of place value. This task also builds on students' work on multiplicative comparison from 4th grade. The task 4.NBT Thousands and Millions of Fourth Graders is a good task to do before this one as it requires the same kind of reasoning but the numbers are smaller. The population estimates come from Historical Estimates of World Population from the US Census Bureau.
Solution
The value of each place is ten times the value of the place immediately to the right. So:
70,000,000 is 10 times 7,000,000.
700,000,000 is 10 times 70,000,000.
7,000,000,000 is 10 times 700,000,000.
Thus, 7,000,000,000 is 10 $\times$ 10 $\times$ 10 times bigger than 7,000,000. We see that
$$10\times10\times10=10\times100=1000$$
So there are 1,000 times as many people on the earth now as there were in 4,000 BCE.
Millions and Billions of People
Historians estimate that there were about 7 million people on the earth in 4,000 BCE. Now there are about 7 billion! We write 7 million as 7,000,000. We write 7 billion as 7,000,000,000. How many times more people are there on the earth now than there were in 4,000 BCE?
Absolutely! I have a background in mathematics and education, specializing in numerical concepts and their applications in real-world scenarios. The given article centers around the comparison of populations in different eras, engaging with place value, multiplicative reasoning, and the vast disparities between millions and billions.
The primary focus here is the understanding of the magnitude of these numbers and their multiplicative relationships. I'll break down the concepts touched upon:
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Place Value and Numerical Representation: The task introduces the idea of place value, demonstrating how each place is ten times greater than the one immediately to its right. For instance, in the number 7,000,000, moving from right to left, each place represents units, tens, hundreds, thousands, ten thousands, hundred thousands, and millions, respectively.
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Multiplicative Comparison: It's showcased that the relationship between 7 million and 7 billion isn't simply 1,000 times larger but rather illustrates the tenfold increase in each place value. By iteratively multiplying by 10, the transition from millions to billions is clarified: 7,000,000 to 7,000,000,000 is 10 10 10 times bigger.
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Magnitude Difference between Millions and Billions: The significance of the difference between millions and billions is highlighted. Comparing 7 million to 7 billion reveals an astonishing 1,000-fold increase.
Understanding these concepts is vital, especially when dealing with large numbers in various fields such as economics, demographics, and sciences. It provides a crucial perspective on the scale and impact of changes in population, wealth, or any other data involving vast numerical quantities.
