Place Value and Number Sense

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Concept Review

Topic Sentences: The Captain of Your Paragraph

Imagine a ship sailing without a captain. Where would it go? What would it do? Just like every ship needs a captain to guide it, every paragraph needs a topic sentence to lead the way.

A topic sentence is like a mathematical equation for writing. It tells your reader exactly what the paragraph will prove or explain. Just as 2 + 3 = 5 shows you the answer right away, a topic sentence shows your main idea right at the start.

The Topic Sentence Formula

Think of your topic sentence as having two important parts, just like a math problem:

WHAT

The subject you're writing about

WHY/HOW

Your main point about that subject

Let's see this formula in action. Here's a paragraph about soccer:

Topic Sentence: "Soccer is the most popular sport in the world for three main reasons."

Supporting detail 1: It's played in over 200 countries.

Supporting detail 2: You only need a ball to play.

Supporting detail 3: The World Cup has 3.5 billion viewers.

The "Promise Keeper" Rule

Here's something amazing: your topic sentence makes a promise to your reader. If you say "three main reasons," you must give exactly three reasons—not two, not four.

It's like saying "I have 5 apples." You can't then show someone 3 apples or 7 apples. Your paragraph must keep the promise your topic sentence makes!

Where Does the Captain Live?

Just like a ship's captain stands at the front to guide the crew, your topic sentence almost always comes first in your paragraph. It's the leader, so it goes in the leadership position—right at the beginning.

🔑 Key Takeaway

Without a captain, a ship drifts aimlessly. Without a topic sentence, your paragraph confuses readers. Make your topic sentence the strong captain that guides every other sentence exactly where it needs to go.

Sample questions

1. In the number 456,789, which digit is in the ten thousands place?

○ 6

○ 4

✓ 5

○ 7

Answer: 5 — The ten thousands place is the second digit from the left in a 6-digit number.

2. What is the value of the digit 3 in the number 324,501?

○ 30,000

○ 3,000

○ 300

✓ 300,000

Answer: 300,000 — The 3 is in the hundred thousands place, so its value represents 300,000.

3. If you increase the digit in the hundreds place of 12,345 by 2, what is the new number?

✓ 12,545

○ 14,345

○ 12,365

○ 32,345

Answer: 12,545 — The hundreds digit is 3. Adding 2 hundreds ($200$) changes it to 5.

Skills in this topic

Identify place value up to hundred thousands
Write numbers in expanded form
Convert between standard and expanded form
Compare numbers up to 100,000 using symbols
Order numbers from least to greatest up to 100,000

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