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64 Mathematics

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568
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Mathematics Section Opener

Start-Up Activity

Share with students the etymology of the word mathematics:

  • Plural of mathematic (obsolete Middle English)

  • From mathematique (Old French)

  • From ars mathematica—"the art of mathematics" (Latin)

  • From mathēmatikē—"the craft of mathematics" (Greek)

  • From manthanein—"learning" (Greek)

So, mathematics is both the craft and art of learning. Students will probably recognize the "craft" part from the Greek root (mathema)tekhnē, which is the origin of our word technology. Math certainly has a ready connection to technology and science. However, students might be surprised by the "art" part.

Point out that painting is a science that requires the right mixtures of pigments and other compounds, applied to a canvas properly stretched over a geometric surface. Point out that the grand staff in music is basically a graph plotting pitch on the y axis and time on the x axis. Sculpture is mathematical. So is theater. Math isn't just numbers and functions. It's a way of learning, and it is part of everything humans do.

Think About It

“Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers.”

—Shakuntala Devi

TEKS Covered in This Chapter

TEKS Covered in This Chapter

Page 569 from Write Ahead

Multiplication/Division, Decimals, and Roman Numerals

Show your students the three charts on this page. They help with multiplying numbers 1 through 10, converting fractions to decimals, and converting Roman numerals to Arabic ones.

As to fractions and decimals, point out that these two systems of notation relate to the problem of converting American units to metric. Most US units are fractions. We have a gallon, a half gallon, a quarter gallon (a quart), an eighth gallon (a pint), and a sixteenth gallon (a half-pint). This fraction approach is based on progressively dividing what you have by two.

However, the metric system is about measuring in increments of 10. It really is about multiplying. You can easily multiply a centimeter into a decimeter into a meter into a kilometer. But if you divide a kilometer by two, what do you get? If you divide a half a kilometer by two, what then? The metric system gets messy with halves, fourths, eighths, or sixteenths, just as the US system gets messy when multiplying.

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Page 570 from Write Ahead

Math Terms

Use this page and the one that follows as an illustrated glossary of some of the most important math terms. Though these definitions are specific to math, help students see the broader applications. For example, addition just means gathering more stuff. The word and is the linguistic equivalent of the plus sign. And area describes not just a Euclidean plane but also a back yard and the surface of a desk. Students can find averages everywhere—but does the average student best reflect what is happening currently in education? Average may be what most people are, but it is rarely what most people aspire to be.

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Page 571 from Write Ahead

Math Terms (Cont.)

Have students bookmark these pages as a quick reference for mathematical terms. Also, try to connect these terms to life in general, as described on the previous page.

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Page 572 from Write Ahead

Math Terms (Cont.)

This page provides excellent connections to everyday life. The first entry, geometry, means "measuring the earth." The shapes in geometry are shapes we find in nature and human construction. The second word, horizontal, of course comes from the horizon of our world. We have a sense of horizontal and vertical because of gravity. Also, the terms intersection, length, line, lowest common denominator, mean, median, and multiple all have many real-world applications.

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Page 573 from Write Ahead

Math Terms (Cont.)

This page also has many terms with real-world applications: parallel, percent, perimeter, perpendicular, point, radius, and ratio. Help students understand that mathematics is another language for understanding reality—a language central to science, medicine, politics, engineering, trade, architecture, music, art, and pretty much every human endeavor.

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Page 574 from Write Ahead

Math Terms (Cont.)

Have students read through the terms and definitions on this page. Then challenge them to find real world examples of as many terms as they can. (For example, rectangles and right angles abound, though students will have to be a bit more creative to find examples of rounding.)

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