In this Grade 5 lesson from Illustrative Mathematics Chapter 6, students solve multi-step problems by converting between metric length units — centimeters, meters, and kilometers — using multiplication and division by powers of 10. Students work with decimal measurements and practice all four operations, choosing whether to convert to a smaller or larger unit to simplify their calculations. The lesson builds on students' understanding of place value and decimal arithmetic developed earlier in the unit.
Section 1
Relating Metric Units to Place Value
The relationship between larger and smaller metric units is analogous to the relationship between place value units.
The prefix 'kilo-' means 1,000 times the base unit, just as a 'thousand' is 1,000 times a 'one'.
Section 2
Metric System of Measurement
In the metric system, units are related by powers of 10.
The root words of their names reflect this relation.
The basic unit for measuring length is a meter.
One kilometer is 1,000 meters; the prefix kilo means thousand. One centimeter is of a meter.
To multiply by 10, 100, or 1,000, we move the decimal to the right one, two, or three places, respectively.
To multiply by 0.1, 0.01, or 0.001, we move the decimal to the left one, two, or three places, respectively.
Length
1 kilometer (km) = 1,000 meters (m)
1 meter (m) = 100 centimeters (cm)
1 meter (m) = 1,000 millimeters (mm)
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Section 1
Relating Metric Units to Place Value
The relationship between larger and smaller metric units is analogous to the relationship between place value units.
The prefix 'kilo-' means 1,000 times the base unit, just as a 'thousand' is 1,000 times a 'one'.
Section 2
Metric System of Measurement
In the metric system, units are related by powers of 10.
The root words of their names reflect this relation.
The basic unit for measuring length is a meter.
One kilometer is 1,000 meters; the prefix kilo means thousand. One centimeter is of a meter.
To multiply by 10, 100, or 1,000, we move the decimal to the right one, two, or three places, respectively.
To multiply by 0.1, 0.01, or 0.001, we move the decimal to the left one, two, or three places, respectively.
Length
1 kilometer (km) = 1,000 meters (m)
1 meter (m) = 100 centimeters (cm)
1 meter (m) = 1,000 millimeters (mm)
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter