Lesson 1.1.3
Place Value (Ones & Tens)
About 12 minutes
From the hundred square to columns
In the last lesson you saw that numbers in the same column of the hundred square share the same ones digit: 4, 14, 24, 34 … That pattern is the first hint of place value: the digit on the right counts single steps (ones); the digit to its left counts whole groups of ten (tens).
For numbers up to 99 we use two places: tens and ones. The number 37 means three tens and seven ones — not “three and seven” smooshed together, but 30 plus 7.
Same digit, different worth
In 44, both digits are “4,” but they do not mean the same thing. The 4 on the left is four tens (40). The 4 on the right is four ones (4). So 44 is 40 + 4.
We write numerals in a fixed order so everyone agrees which digit is counting tens and which is counting ones. Swap the digits in 37 and you get 73 — a different number. (When both digits are the same, like 44, swapping does not change how the number looks — but each 4 still has a different job: tens vs ones.)
Build the number with blocks
Below, each tall stack is one ten. Each small square is a one. Slide the tens and ones to match a number in your head, then read the chart: the tens digit counts how many stacks, the ones digit counts the loose squares.
Change the sliders. Each full column of ten small blocks is one ten. The single squares are ones. Together they show the same number as the digits in the chart.
Base-ten blocks
| Tens | Ones |
|---|---|
| 3 | 7 |
- The number
- 37
- Expanded form
- 30 + 7 = 37
When the ones digit is 0, you only see tens blocks — for example 50 is five tens and zero ones. When the tens digit is 0, you are below ten: 6 is zero tens and six ones (we usually write just “6,” but the idea still helps when we extend to larger numbers later).
Try it
Answer in your head or on paper, then open “Show answer” to check.
In 62, what does the digit 6 stand for? What does the digit 2 stand for?
Show answer
6 stands for six tens (60). 2 stands for two ones (2). So 62 = 60 + 2.
What number is four tens and five ones?
Show answer
45. Four tens is 40, plus five ones gives 45.
You have 3 tens blocks and 9 ones blocks. What number is that? Add one more one — what number do you get?
Show answer
39. Adding one more one gives ten ones, which regroup as another ten: 39 + 1 = 40 (four tens and zero ones).
Which is larger, 58 or 85? Explain using tens and ones.
Show answer
85 is larger. It has eight tens (80) while 58 has only five tens (50). The larger tens digit wins here.
Write 70 as tens plus ones.
Show answer
Seven tens and zero ones. In expanded form that is 70 + 0 — seven tens (70) plus no extra ones.
What is next?
You can split two-digit numbers into tens and ones and see why digit order matters. Next, in lesson 1.1.4, we extend the same idea to hundreds and thousands — same columns, bigger groups.