Solved Exercises on Measuring Mass in Grade 3

Master measuring mass: using balances, comparing masses, converting units, solving word problems, and understanding grams and kilograms through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Using a balance scale
Exercise 1
A balance scale shows that 3 identical apples balance with 450 grams of weights. What is the mass of one apple?
Definition:

Mass: How much matter is in an object. We measure mass in grams (g) and kilograms (kg). Balance scale: A tool that compares masses by balancing objects against known weights.

Balancing method:
  1. Identify what is on each side of the balance
  2. Set up an equation showing both sides are equal
  3. Solve for the unknown mass
  4. Divide the total mass by the number of objects if needed
3 apples
= 450 g
1 apple
= 450 ÷ 3
Result
= 150 g
Step 1: Understand the balance

The 3 apples on one side balance with 450 grams on the other side, so 3 apples = 450 grams

Step 2: Find the mass of one apple

To find the mass of 1 apple, divide the total mass by the number of apples: 450 ÷ 3

Step 3: Perform the division

450 ÷ 3 = 150

Step 4: State the answer

Each apple has a mass of 150 grams

One apple = 150 grams
Final answer:

Each apple has a mass of 150 grams

Applied rules:

• Balance principle: When a scale balances, both sides have equal mass

• Equal sharing: To find individual mass, divide total mass by number of items

• Units: Always include the unit of measurement (grams)

2 Comparing masses
Exercise 2
A bag of rice has a mass of 2.5 kilograms. A bag of sugar has a mass of 2300 grams. Which bag is heavier and by how much?
Definition:

Comparing masses: Finding out which object has more matter by converting to the same units and comparing the numbers.

Rice
2.5 kg
Sugar
2300 g
Difference
2500 - 2300 = 200 g
Step 1: Convert to the same units

Convert 2.5 kg to grams: 2.5 kg = 2.5 × 1000 = 2500 grams

Step 2: Compare the masses

Rice: 2500 g, Sugar: 2300 g. Since 2500 > 2300, rice is heavier

Step 3: Find the difference

Subtract the smaller mass from the larger: 2500 - 2300 = 200 grams

Step 4: State the answer

The rice is 200 grams heavier than the sugar

Rice is 200 grams heavier
Final answer:

The bag of rice is heavier by 200 grams

Applied rules:

• Unit conversion: Convert to the same unit before comparing

• Comparison: Use >, <, or = symbols to compare measurements

• Difference: Subtract to find how much more or less

3 Converting units
Exercise 3
Convert 4.7 kilograms to grams. How many grams are in 4.7 kilograms?
Definition:

Unit conversion: Changing a measurement from one unit to another using known relationships (1 kilogram = 1000 grams).

Starting unit
4.7 kg
Conversion factor
1 kg = 1000 g
Result
4.7 × 1000 = 4700 g
Step 1: Know the conversion relationship

Remember that 1 kilogram = 1000 grams

Step 2: Set up the conversion

4.7 kilograms = ? grams

Step 3: Multiply by the conversion factor

4.7 kg × 1000 g/kg = 4700 grams

Step 4: Check your work

Since 1 kg is 1000 g, 4.7 kg should be 4700 g (4.7 × 1000 = 4700)

4.7 kg = 4700 g
Final answer:

There are 4700 grams in 4.7 kilograms

Applied rules:

• Conversion factor: 1 kilogram = 1000 grams

• Multiplication: To convert from larger to smaller units, multiply

• Verification: Check that your answer makes sense

Rules and methods, laws,...
1 kg = 1000 g
Mass Conversion
Mass Units
1 kg = 1000 g
Kilograms to Grams
Half Kilogram
0.5 kg = 500 g
Half Kilogram to Grams
Quarter Kilogram
0.25 kg = 250 g
Quarter Kilogram to Grams
Key definitions:

Mass: The amount of matter in an object (measured in grams and kilograms)

Gram (g): A small unit of mass, used for lighter objects

Kilogram (kg): A larger unit of mass, used for heavier objects

Balance scale: A tool that compares masses by balancing objects against known weights

Weight: The force of gravity on an object (often used interchangeably with mass in elementary school)

Measuring methodology:
  1. Choose the right tool: Balance scales for comparing, digital scales for precise measurement
  2. Calibrate if necessary: Ensure the scale reads zero when empty
  3. Place object correctly: Put the object on the scale platform
  4. Read the measurement: Look at the displayed number
  5. Record the mass: Include the unit (g, kg)
Tip 1: Remember: 1 kilogram = 1000 grams. To convert kg to g, multiply by 1000.
Tip 2: Light objects are measured in grams, heavy objects in kilograms.
Tip 3: When comparing masses, always convert to the same unit first.
Tip 4: A paperclip weighs about 1 gram, and a textbook weighs about 1 kilogram.
Common errors: Mixing up units, not converting before comparing, forgetting to include units, misreading decimal points.
Real-world applications: Cooking, shopping, shipping, science experiments, weighing luggage.
Formulas to know by heart:

• 1 kilogram = 1000 grams

• To convert from kg to g: multiply by 1000

• To convert from g to kg: divide by 1000

• When comparing masses: convert to same units first

• Balance scales: both sides equal when balanced

Solution: Exercises 4 to 5
4 Shopping scenario
Exercise 4
At the grocery store, Maria buys 1.5 kg of bananas, 800 g of grapes, and 2.2 kg of apples. What is the total mass of her groceries in grams?
Definition:

Total mass: The combined mass of multiple objects, found by adding all individual masses together after converting to the same unit.

Bananas
1.5 kg = 1500 g
Grapes
800 g
Apples
2.2 kg = 2200 g
Total
1500 + 800 + 2200 = 4500 g
Step 1: List all items and their masses

Bananas: 1.5 kg, Grapes: 800 g, Apples: 2.2 kg

Step 2: Convert all to the same unit (grams)

1.5 kg = 1.5 × 1000 = 1500 g, 800 g stays 800 g, 2.2 kg = 2.2 × 1000 = 2200 g

Step 3: Add all masses together

1500 + 800 + 2200 = 4500 grams

Step 4: State the answer

The total mass of groceries is 4500 grams

Total = 4500 grams
Final answer:

The total mass of Maria's groceries is 4500 grams

Applied rules:

• Unit conversion: Convert all measurements to the same unit before adding

• Addition: Add all individual masses to find the total

• Organization: List items separately before combining

5 Word problem with division
Exercise 5
A teacher has a box of clay with a mass of 2.4 kilograms. She wants to divide it equally among 8 students. How many grams of clay will each student receive?
Definition:

Equal sharing: Dividing a total amount equally among a number of recipients to find how much each gets.

Total clay
2.4 kg = 2400 g
Number of students
8
Per student
2400 ÷ 8 = 300 g
Step 1: Identify the total mass and number of recipients

Total clay = 2.4 kg, Number of students = 8

Step 2: Convert to the desired unit

Convert kg to g: 2.4 kg = 2.4 × 1000 = 2400 g

Step 3: Divide the total by the number of recipients

2400 g ÷ 8 students = 300 g per student

Step 4: State the answer

Each student receives 300 grams of clay

Step 5: Verify the answer

Check: 8 × 300 g = 2400 g = 2.4 kg ✓

Each student gets 300 grams
Final answer:

Each student will receive 300 grams of clay

Applied rules:

• Unit conversion: Convert to the unit required in the answer

• Equal sharing: Divide the total by the number of recipients

• Verification: Multiply back to check your division

Complete Summary: Measuring Mass
1 kg = 1000 g
Mass Conversion
Key definitions:

Mass: The amount of matter in an object, measured in grams (g) and kilograms (kg). Mass does not change regardless of location.

Gram (g): A small unit of mass used for lightweight objects (e.g., a paperclip weighs about 1 gram).

Kilogram (kg): A larger unit of mass used for heavier objects (e.g., a textbook weighs about 1 kilogram).

Balance scale: A device that compares masses by balancing objects against known weights.

Conversion: Changing a measurement from one unit to another using mathematical relationships.

Comparison: Determining which object has more or less mass by examining their measurements.

Complete methodology:
  1. Identify the unit: Determine if the measurement is in grams or kilograms
  2. Select appropriate tool: Use balance scales for comparison, digital scales for precision
  3. Perform conversion if needed: Convert all measurements to the same unit before comparing or calculating
  4. Apply the operation: Add for totals, subtract for differences, divide for equal sharing
  5. Include units: Always record the unit of measurement in your answer
Tip 1: Remember: 1 kg = 1000 g. To convert kg to g, move the decimal point 3 places to the right.
Tip 2: When comparing masses, always convert to the same unit first.
Tip 3: Use benchmarks: paperclip ≈ 1 g, textbook ≈ 1 kg.
Tip 4: When dividing mass equally, divide the total mass by the number of parts.
Tip 5: Always verify your answer by performing the inverse operation.
Common errors: Mixing up grams and kilograms, forgetting to convert units before comparing, not including units in answers, misplacing decimal points during conversion.
Real-world applications: Grocery shopping (produce weights), cooking (ingredient amounts), shipping (package weights), science experiments, weighing pets or people.
Key formulas and conversions:

• 1 kilogram = 1000 grams

• To convert kg to g: multiply by 1000 (move decimal 3 places right)

• To convert g to kg: divide by 1000 (move decimal 3 places left)

• When adding/subtracting masses: use same units

• Equal sharing: divide total mass by number of recipients

• Balance scales: both sides equal when balanced

Visual Guide to Measuring Mass

⚖️
Unit Relationships

1 kilogram (kg) = 1000 grams (g)

0.5 kg = 500 g

0.25 kg = 250 g

Convert to same units before comparing

Multiply by 1000 to go from kg to g

Divide by 1000 to go from g to kg

Benchmark Objects

Light objects in grams:

• Paperclip ≈ 1 g

• Small coin ≈ 5 g

• Pencil ≈ 10 g

Heavy objects in kilograms:

• Textbook ≈ 1 kg

• Bag of flour ≈ 2 kg

Comparison Strategy

1. Convert to same units

2. Compare the numbers

3. Subtract to find difference

4. State which is heavier/lighter

Problem-Solving Steps

1. Read the problem carefully

2. Identify what you need to find

3. Note given information

4. Convert units if needed

5. Perform calculations

6. Check your answer

Questions & Answers

Question: I get confused when converting between grams and kilograms. How do I remember which way to move the decimal point?

Answer: Here's a helpful way to remember:

  • Kilograms to grams: Multiply by 1000 (move decimal point 3 places to the right)
  • Grams to kilograms: Divide by 1000 (move decimal point 3 places to the left)

Think about it this way: There are 1000 grams in 1 kilogram, so converting from the larger unit (kg) to the smaller unit (g) means you get a bigger number. When you convert from the smaller unit (g) to the larger unit (kg), you get a smaller number.

Example: 2.5 kg = 2500 g (decimal moved 3 places right), and 3000 g = 3 kg (decimal moved 3 places left).

Practice with different numbers until it becomes automatic!

Question: What's the difference between mass and weight? Our teacher sometimes says "weight" and sometimes says "mass".

Answer: Great question! In simple terms:

  • Mass: How much matter is in an object. It stays the same no matter where you are.
  • Weight: The force of gravity pulling on an object. It changes depending on where you are (like on Earth vs. Moon).

In elementary school, teachers often use "weight" and "mass" interchangeably because for practical purposes on Earth, they're proportional. An object with more mass also weighs more.

For your grade 3 studies, focus on understanding that mass tells us how heavy something is, and we measure it in grams and kilograms using scales.

Example: A 1 kg bag of flour has the same mass everywhere, but it would weigh less on the moon due to lower gravity.

Question: When I'm solving word problems about mass, I don't know whether to add, subtract, multiply, or divide. How do I decide?

Answer: Look for clue words in the problem that tell you what to do:

  • Addition (+): "total", "altogether", "combined", "sum", "in all", "how much altogether"
  • Subtraction (-): "left", "remaining", "difference", "less", "take away", "how much more"
  • Multiplication (×): "groups of", "each", "times", "product", "total for all"
  • Division (÷): "shared equally", "divided among", "each person gets", "how many in each group"

Example: "A teacher has 2.4 kg of clay and divides it equally among 8 students." The words "divides equally among" tell you to divide: 2.4 kg ÷ 8 = 0.3 kg per student.

Always read the problem slowly and identify what the question is asking before deciding on the operation!