Volume and Mass

Grade 3 ยท geometry ยท 85 practice problems ยท read aloud

๐Ÿ”Š Listen to this explanation

๐Ÿ“ฆ Volume and Mass

What Are Volume and Mass?

Volume is how much space something takes up. Think about how much water fits in a water bottle.

Mass is how much matter or "stuff" is in an object. It tells us how heavy something is.

We use them to compare objects! Which box can hold more toys? Which bag of apples is heavier?

How Do We Measure Them?

  1. For Volume (Liquids): We use liters (L) and milliliters (mL). A water bottle holds about 500 mL. A large milk jug holds about 4 L.
  2. For Mass (Heaviness): We use grams (g) and kilograms (kg). A paperclip has a mass of about 1 gram. A textbook has a mass of about 1 kilogram.

Let's Look at Some Examples

Example 1: Volume

Jada has a 2-liter juice bottle and a 300-milliliter cup. How much juice is there in all?

Step 1: Remember, 1 liter = 1,000 milliliters. So, 2 liters = 2,000 mL.

Step 2: Add the volumes: 2,000 mL + 300 mL = 2,300 mL.

Example 2: Mass

Liam's bag of oranges has a mass of 3 kg. How many grams is that?

Step 1: Remember, 1 kilogram = 1,000 grams.

Step 2: Multiply: 3 kg ร— 1,000 = 3,000 grams.

โš ๏ธ Common Mistakes to Avoid

  • Mixing up Volume and Mass: Remember, volume is for space (like in a container), mass is for weight (like on a scale).
  • Forgetting to Convert Units: Always check if your units are the same before you add or subtract! You can't add liters and milliliters directly.

๐Ÿ’ก Tips & Tricks

  • Memory Aid: "Liters for Liquids" โ€“ both words start with L!
  • Kilograms are Heavy: A kitten has a mass of about 1 kg. A gram is very light, like a raisin.
  • When converting kg to g, just add three zeros! (2 kg = 2,000 g).

How to Practice

  • Help in the kitchen! Read labels on bottles and containers to see their volume (mL or L).
  • At the grocery store, look at the mass on packages of fruit, pasta, or cereal.
  • Create your own problems: "If I have a 1 L bottle and drink 200 mL, how much is left?"

Practice problems

6 of the 85, worked through step by step โ€” try them before opening the answer.

1 24 ร— 3 = ?

Hint: Think about breaking the multiplication into smaller parts. For example, 12 ร— 2 means adding 12 two times.

Show the answer

Answer: 72

  1. Break 24 into tens and ones. 24 = 20 + 4.
  2. Multiply each part by 3. First, 20 ร— 3 = 60. Second, 4 ร— 3 = 12.
  3. Add the results together. 60 + 12 = 72. So, 24 ร— 3 = 72.

We are multiplying 24 by 3.

2 75 ร— 4 = ?

Hint: Think about how you can break down the multiplication into smaller, easier steps. What is another way to think about multiplying by 4?

Show the answer

Answer: 300

  1. Break down 75 into parts that are easier to multiply. 75 = 70 + 5.
  2. Multiply each part by 4. First, 70 ร— 4 = 280. Second, 5 ร— 4 = 20.
  3. Add the results together. 280 + 20 = 300. So, 75 ร— 4 = 300.

Let's solve 75 ร— 4 step by step.

3 75 ร— 6 = ?

Hint: Break the multiplication into easier parts. For example, to calculate 40 ร— 3, you could think of 40 ร— 2 = 80, then add another 40 to get 120.

Show the answer

Answer: 450

  1. Set up the multiplication: 75 ร— 6
  2. Multiply the ones place: 5 ร— 6 = 30. Write down 0 and carry over the 3.
  3. Multiply the tens place: 7 ร— 6 = 42.
  4. Add the carried over 3: 42 + 3 = 45.
  5. Write the 45 in the tens and hundreds places, resulting in 450.

The answer is 450.

4 72 ร— 6 = ?

Hint: Break the multiplication into smaller parts to make it easier to calculate.

Show the answer

Answer: 432

  1. Multiply the ones digit of the first number by the second number: 2 ร— 6 = 12. Write down the 2 and carry over the 1.
  2. Multiply the tens digit of the first number by the second number: 7 ร— 6 = 42.
  3. Add the carried-over 1 to the result: 42 + 1 = 43.
  4. Write this result in front of the ones digit we wrote earlier: 432. The final answer is 432.

5 84 ร— 7 = ?

Hint: Break the multiplication into smaller, easier steps. Think about multiplying each part separately and then combining the results.

Show the answer

Answer: 588

  1. Multiply 80 by 7. 80 ร— 7 = 560.
  2. Multiply 4 by 7. 4 ร— 7 = 28.
  3. Add the two results together. 560 + 28 = 588.

The answer is 588.

6 84 รท 4 = ?

Hint: Think about how to break a larger number into equal groups.

Show the answer

Answer: 21

  1. We are dividing 84 by 4. This means we are splitting 84 into 4 equal groups.
  2. First, divide the tens place. 8 tens divided by 4 is 2 tens (20).
  3. Next, divide the ones place. 4 ones divided by 4 is 1 one (1).
  4. Add the results together: 20 + 1 = 21.
  5. Check: 4 ร— 21 = 84.

The answer is 21.

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