Compare(how are they alike)

and Contrast (how are they

different)these situations.

There are fifteen candy bars in a basket to be shared by four people.

After a flood, an animal shelter had fifteen dogs that needed to be fostered. Four people volunteered to foster these dogs.

Journal Writing Warm UpBell Quiz 1-1

Reporting QuantitiesAccuracy and Limitations

Words to KnowAccuracy – Calculation – Estimation – Measurement - Power of ten – Precision – Rounding –

EstimatingThe late great physicist Enrico Fermi used to solve problems by making educated guesses or estimates.

Say you want to estimate the number of cans of soda drunk in San Francisco in one year. You’ll come pretty close if you guess that there are about 800,000 people in S.F. and that one person drinks on average about 100 cans per year. So, around 80,000,000 cans are consumed every year.

Sure, this answer is not exactly right, but it is likely not off by more than a factor of 10 (i.e., an “order of magnitude”). That is, even though we guessed, we’re going to be in the ballpark of the right answer. This is often the first step in working out a problem.

Estimating Vs. MeasuringSome situations only require or can only be predicted by using estimation, but in other situations it is necessary to actually measure. Just like shooting, the smaller the target the more you need to aim. When accuracy counts you must be more precise in your measurements.

Surveying or land surveying is the technique and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them.

Surveying has been an essential element in the development of the human environment since the beginning of recorded history (about 5,000 years ago). It is required in the planning and execution of nearly every form of construction. Its most familiar modern uses are in the fields of transport, building and construction, communications, mapping, and the definition of legal boundaries for land ownership.

How accurate do you think they could measure 5,000 years ago? What about 100 years ago?

What level of accuracy is possible today? Why? When is it important to use this level of

precision?

An all-female surveying crew in Idaho, 1918

Putting a limb in 4 different states? Well, maybe you thought you were ...

SALT LAKE CITY — Tourists who think they're putting a hand or foot in each of four U.S. states at the Four Corners area are apparently missing the mark — by about .25 miles. National Geodetic Survey officials say the Four Corners marker showing the intersection of Arizona, Colorado, New Mexico and Utah is about 2.5 miles (4 kilometers) west of where it should be, the Deseret News reported.The only place in the United States where four state boundaries come together was first surveyed by the government in 1868 during the initial survey of Colorado's southern boundary. The survey was inaccurate.Officials said Monday the accurate location lies to the east of U.S. 160 in Colorado and northeast of the San Juan River as it flows into New Mexico.

Associated PressApril 20, 2010

According to Dave Doyle of the National Geodetic Survey, the monument marking the intersection of Arizona, Colorado, New Mexico and Utah is actually only about 1,807 feet east of where it should have been placed in 1875. Doyle says the monument's location has been legally adopted by all the states as the official corner.

Rounding and calculations If we round our measurements, we are

limiting the accuracy of any calculations using those measures.

Consider the placement of the Four Corners Marker. How does this error in measurement affect calculating the area of the state of Utah?

What level of accuracy do you need?

A veterinarian gives tranquilizers based upon the weight of an animal. If an animal receives too much it will die.

What units would you use to weigh an elephant? Why? What units would work for a dog? Why? What about a hamster? Why?

Missile trajectory is based on the angle of elevation.

(Remember errors compound over distance.)

Shooting a basket in a practice game. Shooting a basket in a championship game. A missile being launched at a practice target 2 miles away. Launching a rocket to Mars.

Fractions vs. Decimals

A general rule is that if a problem is given in fractions, the answer should be in fractions. Same with decimals or radicals.

This is especially true when we look at repeating decimals. If we round a repeating decimal, it is not as accurate as the fraction equivalent.

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o.3

Irrational numbers can’t be written as a fraction. To maintain accuracy we often leave them in a symbolic or radical form.

Actual vs. Rounded

HomeworkMath 1

Reporting Quantities worksheet

Honors Math 1 Reporting

Quantities worksheet