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Tens and ones to 120 Knowledge-Based Study

Math · Number Sense & Operations · Math · Counting & Place Value

Math topic explanations on Tens and ones to 120.

Study notes

  1. The Base-Ten System

    In our number system, we group objects into sets of ten to make counting and calculating easier.

    • One unit represents 1 one.
    • A group of 10 units forms 1 ten (10).

    For any two-digit number, the digit on the left represents the number of tens, and the digit on the right represents the number of remaining ones.

    For example, in the number 74:

    • There are 7 tens, which have a value of 70.
    • There are 4 ones, which have a value of 4.
    • Together, 70+4=7470 + 4 = 74.

    What Happens at 100?

    When you have 9 tens and add 1 more ten, you get 10 tens.

    Ten tens bundle together to make 1 hundred:

    10texttens=100textones=1texthundred10\\text{ tens} = 100\\text{ ones} = 1\\text{ hundred}

    When counting past 100 up to 120, numbers are written with three digits: the hundreds place, the tens place, and the ones place.

    • 100 has 1 hundred, 0 tens, and 0 ones.
    • 105 has 1 hundred, 0 tens, and 5 ones.
    • 110 has 1 hundred, 1 ten, and 0 ones.
    • 118 has 1 hundred, 1 ten, and 8 ones.

    Counting by Tens Past 100

    Numbers greater than 100 can also be viewed entirely in terms of tens and ones without separating out hundreds:

    • 100 is equal to 10 tens and 0 ones.
    • 106 is equal to 10 tens and 6 ones.
    • 114 is equal to 11 tens and 4 ones.
    • 120 is equal to 12 tens and 0 ones.

    Expressing numbers as total tens and ones reinforces place value connections:

    114=(11times10)+4=110+4=114114 = (11 \\times 10) + 4 = 110 + 4 = 114

    This flexible understanding helps when adding, subtracting, and comparing numbers up to 120.

    Watch Out for Zero as a Placeholder

    A frequent error occurs when writing numbers between 101 and 109. If a number has 0 tens, the digit 0 must still be written in the tens place.

    • Correct: 1 hundred, 0 tens, and 7 ones is written as 107.
    • Incorrect: Writing 17, which represents only 1 ten and 7 ones.

    Review Examples

    1. What number has 11 tens and 3 ones?
      11 tens = 110. Adding 3 ones gives 110+3=113110 + 3 = 113.
    2. How many tens and ones are in 108?
      108 contains 10 tens and 8 ones (or 1 hundred, 0 tens, and 8 ones).
    3. What number has 12 tens and 0 ones?
      12 tens = 120.