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X.1 Understand place value up to 120

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Understanding Place Value

Place value tells us the value of each digit in a number. The position of the digit shows if it stands for ones, tens, or hundreds.

Examples:
  • In 47, the 4 means 4 tens (40) and the 7 means 7 ones.
  • In 82, the 8 means 8 tens (80) and the 2 means 2 ones.
  • In 109, the 1 means 1 hundred (100), the 0 means 0 tens, and the 9 means 9 ones.
Helpful Hint

The place of a digit decides its value. A “2” in the ones place is just 2, but a “2” in the tens place is 20.

Using Base-Ten Models

We can show numbers with base-ten blocks. A “cube” stands for 1 one, a “stick” or “long” stands for 1 ten, and a “flat” stands for 1 hundred.

Examples:
  • 34 is 3 tens (30) and 4 ones (4).
  • 76 is 7 tens (70) and 6 ones (6).
  • 112 is 1 hundred (100), 1 ten (10), and 2 ones (2).
Helpful Hint

Think of hundreds as “squares,” tens as “sticks,” and ones as “cubes.” This helps us picture numbers more clearly.

Writing Numbers in Different Forms

Numbers can be written in standard form, expanded form, and word form. Each form shows the value in a different way.

Examples:
  • 36: Standard form is 36. Expanded form is 30 + 6. Word form is “thirty-six.”
  • 105: Standard form is 105. Expanded form is 100 + 5. Word form is “one hundred five.”
  • 120: Standard form is 120. Expanded form is 100 + 20. Word form is “one hundred twenty.”
Helpful Hint

Expanded form shows the value of each digit. Word form helps us read numbers correctly.

Comparing Numbers with Place Value

We compare numbers by looking at the hundreds, tens, and ones. The place value of each digit tells us which number is greater, less, or equal.

Examples:
  • 42 < 56 because 4 tens (40) is less than 5 tens (50).
  • 89 > 75 because 8 tens (80) is more than 7 tens (70).
  • 64 = 64 because they have the same tens and ones.
Helpful Hint

Always compare the largest place first. If those are the same, then compare the next place value.

Counting with Place Value

We can count by tens and ones to build numbers up to 120. Place value helps us keep track as numbers grow larger.

Examples:
  • Counting tens: 10, 20, 30, 40, …, 120.
  • Counting ones: 115, 116, 117, 118, 119, 120.
  • Making 47: Start with 4 tens (40), then add 7 ones to reach 47.
Helpful Hint

Use tens to count faster, and ones to fill in the small steps between tens.