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Use the numbers and units from the list to find as many equivalent measurements as you can. For example, you might write “30 minutes is hour.”
You can use the numbers and units more than once.
1
12
0.4
8
50
40
100
30
0.3
24
6
2
centimeter (cm)
meter (m)
kilometer (km)
inch (in)
foot (ft)
yard (yd)
Your teacher will give you some cards with a scale on each card.
Take turns with your partner to sort the cards into sets of equivalent scales. Each set should have at least two cards.
For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
Trade places with another group and check each other’s work. If you disagree about how the scales should be sorted, work to reach an agreement.
Pause here so your teacher can review your work.
Next, record one of the sets with three equivalent scales and explain why they are equivalent.
As of 2016, Tunisia holds the world record for the largest version of a national flag. It was almost as long as four soccer fields. The flag has a circle in the center, a crescent moon inside the circle, and a star inside the crescent moon.
| flag length | flag height | height of crescent moon |
|
|---|---|---|---|
| actual | 396 m | 99 m | |
| at 1 to 2,000 scale | 13.2 cm |
Complete each scale with the value that makes it equivalent to the scale of 1 to 2,000. Explain or show your reasoning.
Your teacher will give you a floor plan of a recreation center.
Sometimes scales come with units, and sometimes they don’t. For example, a map of Nebraska may have a scale of 1 mm to 1 km. This means that each millimeter of distance on the map represents 1 kilometer of distance in Nebraska. Notice that there are 1,000 millimeters in 1 meter and 1,000 meters in 1 kilometer. This means there are or 1,000,000 millimeters in 1 kilometer. So, the same scale without units is 1 to 1,000,000, which means that each unit of distance on the map represents 1,000,000 units of distance in Nebraska. This is true for any choice of unit to express the scale of this map.
Sometimes when a scale comes with units, it is useful to rewrite it without units. For example, let's say we have a different map of Rhode Island, and we want to use the two maps to compare the size of Nebraska and Rhode Island. It is important to know if the maps are at the same scale. The scale of the map of Rhode Island is 1 inch to 10 miles. There are 5,280 feet in 1 mile, and 12 inches in 1 foot, so there are 63,360 inches in 1 mile (because ). Therefore, there are 633,600 inches in 10 miles. The scale of the map of Rhode Island without units is 1 to 633,600. The two maps are not at the same scale, so we should not use these maps to compare the size of Nebraska to the size of Rhode Island.
Here is some information about equal lengths that you may find useful.
Customary Units
1 foot (ft) = 12 inches (in)
1 yard (yd) = 36 inches
1 yard = 3 feet
1 mile = 5,280 feet
Metric Units
1 centimeter (cm) = 10 millimeters (mm)
1 meter (m) = 1,000 millimeters (mm)
1 meter = 100 centimeters
1 kilometer (km) = 1,000 meters
Equal Lengths in Different Systems
1 inch = 2.54 centimeters
1 foot 0.30 meter
1 mile 1.61 kilometers
1 centimeter 0.39 inch
1 meter 39.37 inches
1 kilometer 0.62 mile