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# ZingPath: Proportions and Measurement

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## Proportions and Measurement

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### Lesson Focus

#### Conversion of Area Measures

Math Foundations

You will determine the different sections of lands that have the same area by making necessary metric conversions.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Make reasonable estimates of a given area of land.
• Make simple metric conversions involving area measures.

### Everything You'll Have Covered

In order for students to be successful with this Activity Object, they will need to know the various terms for the metric measures as well as the process for converting one metric unit to another metric unit. It is strongly suggested that students explore this Activity Object after they have learned how to convert metric units of area.

The Metric System uses a base-ten system. By multiplying or dividing by 10, you can convert any metric unit to another metric unit.

The metric system was devised in France in the 18th century. The goal was to replace the inconsistent collection of units being used with a system based on one standard.

The standard for length was created by dividing the quarter of the Earth diameter by ten millions. The resulting length was named meter. The definition of meter changed several times since to make it more precise. The latest and the most precise definition of meter is "the distance light travels in a vacuum in 1/299,792,458 second". The standards for other measurements in metric system were set in a similar way.

The metric system, or International System of Units (SI), is based on seven base units. The quantities are: length (meter), mass (kilogram), time (second), electric current (ampere), thermodynamic temperature (Kelvin), amount of substance (mole), and luminous intensity (candela).

To convert from a larger to smaller metric unit you always multiply. To convert from a smaller to larger unit you always divide.

The Latin prefixes used in the metric system literally mean the number they represent. For example, 1 kilogram = 1,000 grams. A kilo is 1,000 of something just like a dozen is 12 of something. Meter, liter, or gram can be used interchangeably.  In this Activity Object, we will focus on area measurement units such as meters or square centimeters.

The square meter is the basic unit of area of the metric system.

Area is length by length, so the area of a square that is 1 meter on each side is 1 square meter, which is written m2 (square meters). A square meter is about half the area of a doorway.

Example: How big is this rectangle?

1 km2 = 1,000,000 m2

1 hm2 = 10,000 m2

1 dam2 = 100 m2

100 dm2 = 1 m2

10,000 cm2 = 1 m2

1,000,000 mm2 = 1 m2

Ares and hectares are used to measure large areas of land.

Are is a metric unit of area measure equal to 100 square meters.

In other words, a piece of land measuring

10 m × 10 m = 100 m2 = 1 are

A hectare is a metric unit of area equal to 100 ares or 10,000 square meters.

In other words, a piece of land measuring

100 m × 100 m = 10,000 m2 = 1 hectare

In this Activity Object, students will use the various forms of meters as well as ares and hectares to measure areas of land. Ares and hectares are not commonly known units of measure. Be sure to introduce these terms and provide some point of reference for the size of each unit to the class before exploring the Activity Object. (See Engaging the Learners for an activity introducing ares and hectares.

Consider the following conversions when working with square meters, ares, and hectares:

1 km2 = 1,000,000 m2

1 ha = 10,000 m2

1 are = 100 m2

100 dm2 = 1 m2

10,000 cm2 = 1 m2

1,000,000 mm2 = 1 m2

### Tutorial Details

 Approximate Time 15 Minutes Pre-requisite Concepts Students should be familiar with metric volume measures, unit conversions in metric area measures, and operations on decimals. Course Math Foundations Type of Tutorial Skills Application Key Vocabulary area, measurement, plot