Learn on PengiPengi Math (Grade 4)Chapter 9: Measurement, Data & Real-World Math

Lesson 2: The Metric System: Conversions & Operations

In this Grade 4 Pengi Math lesson, students explore the metric system by learning how units of length (km, m, cm), mass (kg, g), and capacity (L, mL) relate to the base-ten place value system. They practice converting mixed metric units to smaller units and back, then apply regrouping strategies to add and subtract mixed metric measurements. The lesson wraps up with real-world problems involving metric distances, liquid volumes, and masses from Chapter 9.

Section 1

Metric Units of Length

Property

Metric Units of Length:

1 centimeter=10 millimeters1 \text{ centimeter} = 10 \text{ millimeters}
1 meter=100 centimeters1 \text{ meter} = 100 \text{ centimeters}
1 kilometer=1000 meters1 \text{ kilometer} = 1000 \text{ meters}

The conversion factors in the metric system are all powers of 10.
This property makes the metric system easy to use, because we can convert between units simply by moving the decimal point.

Examples

  • A table is 2 meters long. To convert this to centimeters, multiply by 100:
2 m×100=200 cm2 \text{ m} \times 100 = 200 \text{ cm}
  • A small insect measures 60 millimeters long. To convert this to centimeters, divide by 10:
60÷10=6 cm60 \div 10 = 6 \text{ cm}

Section 2

Metric Units of Capacity and Mass

Property

The metric system measures capacity using liters (L) and milliliters (mL), and mass using kilograms (kg), grams (g) and milligrams(mg). The relationships are based on the number 1,000.

  • Capacity: 1 liter is 1,000 times larger than 1 milliliter.

Section 3

Solve Multi-Step Measurement Problems

Property

To solve a multi-step measurement word problem, identify the known and unknown quantities, then determine the sequence of addition and subtraction operations needed to find the solution. Finally, assess whether the answer is reasonable in the context of the problem.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Metric Units of Length

Property

Metric Units of Length:

1 centimeter=10 millimeters1 \text{ centimeter} = 10 \text{ millimeters}
1 meter=100 centimeters1 \text{ meter} = 100 \text{ centimeters}
1 kilometer=1000 meters1 \text{ kilometer} = 1000 \text{ meters}

The conversion factors in the metric system are all powers of 10.
This property makes the metric system easy to use, because we can convert between units simply by moving the decimal point.

Examples

  • A table is 2 meters long. To convert this to centimeters, multiply by 100:
2 m×100=200 cm2 \text{ m} \times 100 = 200 \text{ cm}
  • A small insect measures 60 millimeters long. To convert this to centimeters, divide by 10:
60÷10=6 cm60 \div 10 = 6 \text{ cm}

Section 2

Metric Units of Capacity and Mass

Property

The metric system measures capacity using liters (L) and milliliters (mL), and mass using kilograms (kg), grams (g) and milligrams(mg). The relationships are based on the number 1,000.

  • Capacity: 1 liter is 1,000 times larger than 1 milliliter.

Section 3

Solve Multi-Step Measurement Problems

Property

To solve a multi-step measurement word problem, identify the known and unknown quantities, then determine the sequence of addition and subtraction operations needed to find the solution. Finally, assess whether the answer is reasonable in the context of the problem.

Examples