Numbers up to ten thousand

How Big is One Thousand?

A thousand is much larger than the numbers we use every day. To imagine its size, consider these real-world examples:

• 10 single unit cubes snap together to make 1 Ten rod.
• 10 Ten rods line up to form 1 Hundred flat ($10 \times 10 = 100$).
• 10 Hundred flats stack together to make 1 Thousand cube ($10 \times 100 = 1,000$).

Key Idea: Every time we move one place to the left in a number, the value becomes 10 times bigger.

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Building Numbers with Base-Ten Blocks

We can combine thousands, hundreds, tens, and ones blocks to represent any 4-digit number.

• Combine the values: $1,000 + 200 + 30 + 4 = 1,234$.
• Read out loud: "One thousand, two hundred thirty-four."

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Worked Example: Identifying a 4-Digit Number

Problem: What number is represented by the base-ten blocks shown below? Write it in standard form.

Solution Steps (Part 1):

• Step 1 (Thousands): Count 2 large cubes $\rightarrow 2 \times 1,000 = \mathbf{2,000}$.
• Step 2 (Hundreds): There are no hundred flats $\rightarrow 0 \times 100 = \mathbf{0}$.

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Worked Example: Completing the Number

Solution Steps (Part 2):

• Step 3 (Tens): Count 3 rods $\rightarrow 3 \times 10 = \mathbf{30}$.
• Step 4 (Ones): Count 5 unit cubes $\rightarrow 5 \times 1 = \mathbf{5}$.
• Expanded Form: $2,000 + 0 + 30 + 5 = \mathbf{2,035}$

⚠️ Common Pitfall: Never skip empty places! Writing $235$ instead of $2,035$ changes the value completely. The digit $0$ acts as a required placeholder for the hundreds place.