X.2 Make numbers using place value - up to 120
What is place value?
Place value is the value of a digit based on its position in a number. Each place in a number has a different value. Understanding place value helps us read, write, build, and compare numbers all the way up to 120.
- In the number 57, the digit '5' is in the tens place. Its value is 5 tens, or 50.
- In the number 57, the digit '7' is in the ones place. Its value is 7 ones, or 7.
- So, 57 means 5 tens plus 7 ones, which is 50 + 7.
Think of place value like a house address. The digit's "address" (ones, tens, hundreds) tells you its value. The digit itself tells you "how many" are at that address.
Understanding the ones and tens places
Numbers up to 120 have digits in the ones place and tens place. Some numbers also have a digit in the hundreds place. The rightmost digit is always the ones place. Moving left, the next place is the tens place. Moving left again, the next place is the hundreds place.
- In 84: The '4' is in the ones place. The '8' is in the tens place.
- In 120: The '0' is in the ones place. The '2' is in the tens place. The '1' is in the hundreds place.
- We say this as: "One hundred twenty." The zero in the ones place means zero ones.
Always start reading a number from the leftmost digit (the highest place value). For 120, start with the hundreds place: "one hundred."
The importance of the number 10
Our number system is a base-ten system. This means we group things in tens. When we have 10 single items (ones), we can group them together to make 1 group of ten. This is the foundation of place value.
- 10 ones = 1 ten
- 2 tens = 20 ones
- 11 is 1 ten and 1 one left over.
- 34 is 3 tens and 4 ones left over.
You use base-ten every day! Your fingers are a great example. Two full hands make 10 fingers, or 1 group of ten.
Making numbers with base-ten blocks
Base-ten blocks are math tools that help us see place value. A small cube represents 1 one. A long rod made of ten cubes represents 1 ten. A flat square made of one hundred cubes represents 1 hundred.
- To show 25: Use 2 ten rods and 5 unit cubes.
- To show 108: Use 1 hundred flat, 0 ten rods, and 8 unit cubes.
- To show 120: Use 1 hundred flat and 2 ten rods. The ones place is zero, so we use no unit cubes.
If you don't have blocks, you can draw them! A small square for a one, a line of ten squares for a ten, and a big square of 100 small squares for a hundred.
Writing numbers in expanded form
Expanded form is a way to write a number that shows the value of each digit. We write the number as the sum of the value of each digit in its place.
- Standard form: 63. Expanded form: 60 + 3
- Standard form: 91. Expanded form: 90 + 1
- Standard form: 115. Expanded form: 100 + 10 + 5
- Standard form: 120. Expanded form: 100 + 20 + 0 (or just 100 + 20)
Expanded form is like taking the number apart to see what it's made of. It clearly answers the question: "How many tens and ones?"
Building numbers from their parts
We can take the expanded form of a number and put it back together into standard form (the regular way we write numbers). This means combining the hundreds, tens, and ones.
- If you have 4 tens and 7 ones, you have 40 + 7 = 47.
- If you have 1 hundred, 0 tens, and 9 ones, you have 100 + 0 + 9 = 109.
- If you have 100 + 10 + 8, you put the digits in their places: 1 (hundreds), 1 (tens), 8 (ones) = 118.
When building a number, always fill the places from left to right. If there are no tens or ones, you must use a 0 as a placeholder. For example, 5 tens and 0 ones is 50, not 5.
Special patterns in numbers up to 120
Our number system has clear patterns that help us count and understand place value. Recognizing these patterns makes working with numbers easier.
- Counting by tens: 10, 20, 30, 40, 50... The ones digit is always 0, and the tens digit increases by 1.
- Decades: The numbers 21-29, 31-39, 41-49, etc., are called "decades." In the 20s, the tens digit is always 2. In the 30s, it's always 3.
- Moving to 100 and beyond: 99 is the last number with two digits. 100 is the first number with three digits: 1 hundred, 0 tens, 0 ones.
- Pattern after 100: 101, 102, 103... up to 109, then 110, 111, 112... up to 119, then 120.
A hundreds chart is the best tool to see these patterns visually. Look for the columns (ones digits are the same) and rows (tens digits are the same).
Comparing numbers using place value
We can use place value to decide which number is greater than (>), less than (<), or equal to (=) another number. Always start by comparing the digit in the highest place value.
- Compare 67 and 76.
- Look at the tens place first: 6 tens vs. 7 tens.
- Since 6 tens (60) is less than 7 tens (70), we know 67 < 76. We don't even need to check the ones.
- Compare 114 and 119.
- Hundreds place: Both are 1 (100 = 100).
- Tens place: Both are 1 (10 = 10).
- Ones place: 4 vs. 9. Since 4 is less than 9, 114 < 119.
- Compare 90 and 108.
- Highest place: 90 has 9 tens (no hundreds). 108 has 1 hundred.
- 1 hundred (100) is always greater than any amount of tens less than 100. So, 90 < 108.
Remember the alligator trick: The alligator's mouth (> or <) always opens toward the bigger number because it wants to eat more!
Real-world uses of place value
Place value isn't just for math class. We use it every day to understand numbers in our world.
- Money: $1.25 is 1 dollar (like a hundred), 2 dimes (like tens), and 5 pennies (like ones).
- Age: Understanding you are 7 years old means you have lived for 7 whole years. When someone is 112 years old, that is 1 hundred, 1 ten, and 2 ones.
- Sports scores: If the score is 120 to 98, you know 120 is greater because it has a hundreds digit (1 hundred) and 98 does not.
- Calendar: The year has 365 days. That's 3 hundreds, 6 tens, and 5 ones.
- Reading page numbers: Page 105 comes after page 99 because 105 has a hundreds digit.
Strong place value skills are the foundation for all future math, including adding, subtracting, and working with even larger numbers.
Common Core alignment: CCSS.MATH.CONTENT.1.NBT.B.2 – Understand that the two digits of a two-digit number represent amounts of tens and ones. CCSS.MATH.CONTENT.1.NBT.B.2.A – 10 can be thought of as a bundle of ten ones — called a "ten." CCSS.MATH.CONTENT.1.NBT.B.2.C – The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). CCSS.MATH.CONTENT.1.NBT.B.3 – Compare two two-digit numbers based on meanings of the tens and ones digits. CCSS.MATH.CONTENT.1.NBT.A.1 – Count to 120, starting at any number less than 120.
Notes for teachers
This lesson is aligned with CCSS.MATH.CONTENT.1.NBT.B.2, 1.NBT.B.3, and 1.NBT.A.1. Use it for whole-class instruction, independent practice, or homework.
The content emphasizes conceptual understanding through models (base-ten blocks), standard forms, and expanded forms. Key pedagogical focuses include the transition across 100 and the use of 0 as a placeholder. All activities are designed to build fluency with numbers within 120, a critical foundation for Grade 2.
All content is 100% free, student-safe, and designed for classroom and home use.