Tens & Ones
When second-grader Emma counts 43 jellybeans, she needs to understand that the 4 represents 40 jellybeans, not just 4. Place value with tens and ones forms the foundation for all multi-digit arithmetic in elementary mathematics. CCSS.1.NBT.2 and CCSS.2.NBT.1 emphasize building this critical number sense through concrete representations and abstract understanding.
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Why it matters
Place value understanding directly impacts students' ability to perform addition with regrouping, subtraction with borrowing, and multiplication algorithms. When students grasp that 67 means 6 tens plus 7 ones, they can mentally calculate 67 + 20 by adding 2 more tens to get 87. This concept appears in real-world scenarios like counting money (3 dimes and 4 pennies equals 34 cents), measuring distances (42 inches means 4 groups of 10 inches plus 2 more), and organizing classroom supplies (5 boxes of 10 crayons plus 8 loose crayons equals 58 total crayons). Without solid place value foundations, students struggle with regrouping in 47 + 36, often writing incorrect sums like 713 instead of 83 because they don't understand that 13 ones must regroup into 1 ten and 3 ones.
How to solve tens & ones
Place Value — Tens & Ones
- In a two-digit number, the left digit = tens, the right digit = ones.
- 34 = 3 tens + 4 ones = 30 + 4.
- The value of a digit depends on its position.
- Hundreds are to the left of tens: 245 = 2 hundreds + 4 tens + 5 ones.
Example: In 72: the 7 is worth 70 (7 tens), the 2 is worth 2 (2 ones).
Worked examples
You have 4 bundles of 10 sticks. How many sticks in total?
Answer: 40
- Each bundle has 10 sticks → 1 bundle = 10 sticks — A bundle is a group of 10 sticks tied together. Each bundle represents one 'ten'.
- Multiply: 4 bundles × 10 → 4 × 10 = 40 — 4 bundles of 10 is 40 sticks total. You can also count by tens: 10, 20, 30, 40.
What number has 9 tens and 9 ones?
Answer: 99
- Each position has a value → tens place = ×10, ones place = ×1 — In our number system, each spot has a different value. The tens place is worth 10 times more than the ones place. Think of it like: tens are 'big' coins worth 10, and ones are 'small' coins worth 1.
- Multiply the tens: 9 × 10 → 9 × 10 = 90 — 9 tens means 9 groups of 10, which is 90.
- The ones are just themselves → 9 × 1 = 9 — The ones digit is 9. Each one is worth just 1.
- Add them together → 90 + 9 = 99 — Combine the tens and ones: 90 + 9 = 99. The number is 99!
Which digit is in the tens place of 68?
Answer: 6
- Look at the digits of 68 → 68 → 6 and 8 — The number 68 has two digits. In a two-digit number, the LEFT digit is always the tens and the RIGHT digit is always the ones.
- Identify the tens digit → 6 — The tens digit is 6 (the left digit). It's worth 60. The ones digit is 8 (the right digit), worth just 8.
Common mistakes
- ✗Students confuse digit identity with digit value, saying the 5 in 52 equals 5 instead of 50. They might write 52 as 5 + 2 = 7 rather than 50 + 2 = 52.
- ✗When building numbers with manipulatives, students count individual objects instead of recognizing groups. Given 3 ten-blocks and 7 unit cubes, they count 10 objects instead of identifying 37.
- ✗Students reverse place value positions, writing 34 when asked for 4 tens and 3 ones, creating 43 instead of the correct answer of 34.
- ✗In expanded form problems, students add digits rather than place values, writing 25 = 2 + 5 = 7 instead of 25 = 20 + 5.
Practice on your own
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