How do you apply the Guesstimate technique to estimate complex quantities in math?

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Have you ever wondered how to estimate the number of piano tuners in Chicago, the weight of the Eiffel Tower, or the length of the Great Wall of China? These are examples of complex quantities that are difficult to measure directly, but can be approximated using a problem-solving strategy called the Guesstimate technique. In this article, you will learn what the Guesstimate technique is, why it is useful, and how to apply it to any math problem that involves estimation.

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1 What is the Guesstimate technique?

The Guesstimate technique is a method of breaking down a complex quantity into simpler and more manageable components, and then using assumptions, logic, and common sense to estimate each component. The final estimate is obtained by combining the estimates of the components using appropriate operations, such as multiplication, division, addition, or subtraction. The Guesstimate technique is also known as the Fermi problem, after the physicist Enrico Fermi, who was famous for his ability to make quick and accurate estimates of various phenomena.

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Gwen Nicodemus

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It's summertime and hot. The backyard swimming poo is empty. You're limited on how much water you can use and pay the bill. You can afford 900 gallons. Can you fill it? The pool is shaped like two circles stuck together. The first circle has an eyeballed diameter of about 6 ft and is 3 ft deep. The second pool is about 10 ft wide and is 8 ft deep. The volume of a circle is pi * radius * radius * height. Let's use 3 for pi. The first circle's volume = 3 * 3 * 3 * 3 = 81 ft^3. The second circle has a volume of 3 * 5 * 5 * 8 = 600 ft^3. 600 + 81 = 681. 1 ft^3 is about 7.5 gallons, so 680 * 7.5 = 5100 gallons. Guesstimation: Order of magnitude is the name of the game, and 5100 (order 4) is > 900 (order 3) and you shall bake this summer.

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2 Why is the Guesstimate technique useful?

The Guesstimate technique is useful for several reasons. First, it helps you develop your critical thinking and analytical skills, as you have to identify the relevant factors, make reasonable assumptions, and justify your choices. Second, it enhances your creativity and flexibility, as you have to find ways to estimate quantities that may not have readily available data or formulas. Third, it improves your numerical literacy and confidence, as you have to work with different units, orders of magnitude, and ranges of uncertainty.

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Gwen Nicodemus

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Guesstimation is useful when you don't need a precise answer. You get ballpark answers. For instance, a vet bill of $300 is pretty normal. A vet bill of $3000 is a bit shocking. To calculate the number of gallons in a pool, you need to know a few things. ? How to divide the pool into various shapes ? The formula for the area for each shape ? A guess on how deep each of the shapes are ? How many gallons are in a single cubed unit (gallons per ft^3, liters per meter^3, ...) For this example, you need to know your grammar school geometry, how long a foot (or meter, or yard) is, and the conversion rate from units ^ 2 to liters or gallons. Yeah for Google and the conversion calculators.

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3 How to apply the Guesstimate technique?

To apply the Guesstimate technique, you need to follow four steps: define the problem, decompose the problem, estimate the components, and combine the estimates. Let's look at each step in more detail.

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4 Define the problem

The first step is to define the problem clearly and precisely. What is the quantity that you want to estimate? What are the units of measurement? What are the boundaries or constraints of the problem? For example, if you want to estimate the number of piano tuners in Chicago, you need to specify what counts as a piano tuner, what area of Chicago you are considering, and what time frame you are interested in.

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5 Decompose the problem

The second step is to decompose the problem into smaller and simpler components. How can you split the quantity into factors that are easier to estimate? What are the relationships between the factors? For example, if you want to estimate the number of piano tuners in Chicago, you can decompose the problem into two factors: the number of pianos in Chicago, and the number of pianos that each tuner can service in a year.

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6 Estimate the components

The third step is to estimate each component using assumptions, logic, and common sense. How can you find or infer the values of the factors? What sources of information can you use? What level of accuracy do you need? For example, if you want to estimate the number of pianos in Chicago, you can use the population of Chicago, the percentage of households that own a piano, and the average number of pianos per household. If you want to estimate the number of pianos that each tuner can service in a year, you can use the average frequency of tuning, the average time of tuning, and the average working hours of a tuner.

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7 Combine the estimates

The fourth and final step is to combine the estimates of the components using appropriate operations, such as multiplication, division, addition, or subtraction. How can you calculate the final estimate from the estimates of the factors? What are the units of the final estimate? How can you express the range and uncertainty of the final estimate? For example, if you want to estimate the number of piano tuners in Chicago, you can multiply the number of pianos in Chicago by the inverse of the number of pianos that each tuner can service in a year. You can also give a lower and upper bound for your estimate, based on the possible variations of the factors.

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How do you apply the Guesstimate technique to estimate complex quantities in math?

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1 What is the Guesstimate technique?

2 Why is the Guesstimate technique useful?

3 How to apply the Guesstimate technique?

4 Define the problem

5 Decompose the problem

6 Estimate the components

7 Combine the estimates

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