Estimating and Measuring Mass (Grams and Kilograms) - Third Grade Mathematics
Mass is the scientific measurement of the amount of matter inside an object. While people often use the word "weight" in everyday conversation, in mathematics and science we measure mass using the metric system units of grams and kilograms. In this chapter, you will discover the difference between grams and kilograms, build real-life tactile benchmarks to estimate mass accurately, and solve addition, subtraction, multiplication, and division problems with mass.
Metric Units of Mass
The metric system measures mass using two primary units:
Unit Abbreviation Benchmark Object
Gram g A single standard metal paperclip
Kilogram kg A thick hardcover textbook or a dictionary
The fundamental relationship between grams and kilograms is: 1 Kilogram (kg) = 1,000 Grams (g)
[ @ ] <- 1 Gram (g): Extremely light!
Feels like a single paperclip or a dried raisin.
+----------+
| | <- 1 Kilogram (kg): Substantial and heavy!
| Math | Has the mass of 1,000 paperclips combined.
| Book | About the mass of a thick textbook.
+----------+
Everyday Benchmarks for Mass
To become an expert at estimating mass, memorize these practical benchmarks:
Objects Measured in Grams (g):
- A nickel coin: about 5 g
- A standard pencil: about 10 g
- A slice of sandwich bread: about 30 g
- A medium apple: about 150 g
- A baseball: about 145 g
Objects Measured in Kilograms (kg):
- A bag of flour or sugar: about 1 kg or 2 kg
- A pair of running shoes: about 1 kg
- A domestic house cat: about 4 to 5 kg
- A third-grade student: about 25 to 35 kg
- A bicycle: about 12 kg
Reading a Balance Scale
A balance scale compares the mass of two objects or measures the unknown mass of an object against known gram or kilogram weights.
[ Object ] [ 50g ] [ 20g ]
====================^====================
Balanced in perfect equilibrium!
When the scale beam is completely horizontal and level, the mass on the left equals the mass on the right! In the diagram above: Mass of the object = 50 g + 20 g = 70 grams.
Solving Word Problems Involving Mass
All four operations apply to mass problems. Make sure all quantities share the same unit before performing calculations.
Example 1: Total Mass (Multiplication)
A box contains 8 identical science textbooks. Each textbook has a mass of 2 kg. What is the total mass of the textbooks? 8 x 2 kg = 16 kilograms.
Example 2: Fair Share of Mass (Division)
A baker has 45 grams of cinnamon and divides it equally among 9 spice jars. How many grams of cinnamon go into each jar? 45 g ÷ 9 = 5 grams per jar.
Example 3: Comparison of Mass (Subtraction)
A backpack full of books has a mass of 9 kg. An empty backpack has a mass of 1 kg. What is the mass of the books alone? 9 kg - 1 kg = 8 kilograms.
Chapter Practice Exercises
- Which unit would you use to measure the mass of each object (write "grams" or "kilograms"): a. A feather b. A golden retriever dog c. A grape d. A school desk e. A cell phone
- Choose the best estimate for each item: a. An apple: 150 g or 150 kg? b. A full-grown horse: 500 g or 500 kg? c. A dime coin: 2 g or 2 kg? d. A bowling ball: 6 g or 6 kg?
- A bag of apples has a mass of 3 kg. A bag of potatoes has a mass of 5 kg. What is the total mass of both bags combined?
- A post office package has a mass of 720 grams. A smaller package has a mass of 350 grams. How many more grams does the heavier package weigh?
- A farmer packs berries into 6 small baskets. Each basket has a mass of 80 grams. What is the total mass of all 6 berry baskets?
Solutions and Step-by-Step Answers
- Grams vs. Kilograms: a. Feather -> Grams. b. Golden retriever dog -> Kilograms. c. Grape -> Grams. d. School desk -> Kilograms. e. Cell phone -> Grams.
- Best estimates: a. Apple -> 150 g. b. Horse -> 500 kg. c. Dime -> 2 g. d. Bowling ball -> 6 kg.
- Total mass: 3 kg + 5 kg = 8 kilograms.
- Difference in mass: 720 g - 350 g = 370 grams.
- 6 baskets with 80 g each: 6 x 80 g = 480 grams total.