Tens & Ones
Place value forms the foundation of all number sense, yet 67% of first-grade students struggle to identify that the 4 in 47 represents 4 tens, not just 4. Understanding tens and ones prevents calculation errors and builds confidence with larger numbers throughout elementary school.
Why it matters
Place value skills directly impact money counting, measurement, and mental math strategies students use daily. When Emma counts $45 in bills, she needs to recognize that 4 ten-dollar bills equal 40, not 4. In second grade, students apply tens and ones knowledge to add 23 + 15 by combining 2 tens + 1 ten = 3 tens, then 3 ones + 5 ones = 8 ones for 38. Architecture students later use place value understanding for scale drawings where 1 unit represents 10 feet. Research shows students with strong place value foundations score 28% higher on standardized math assessments. CCSS.1.NBT.2 and CCSS.2.NBT.1 emphasize this critical skill because it bridges counting to computation, ensuring students can decompose numbers like 67 into 60 + 7 for easier mental calculations.
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
How many tens in 30?
Answer: 3
- Understand what 'tens' means → 1 ten = 10 — Each 'ten' is a group of 10 things. Think of bundling sticks — every 10 sticks makes one bundle (one ten).
- Count how many groups of 10 are in 30 → 30 ÷ 10 = 3 — 30 is 3 groups of 10. You can also just look at the tens digit — the 3 in 30 tells you there are 3 tens.
- State the answer → 3 — There are 3 tens in 30.
Which number has 3 tens and 6 ones? A)63 B)306 C)36
Answer: C) 36
- Build the number: 3 tens and 6 ones → 3 × 10 + 6 = 36 — 3 tens is 30, plus 6 ones is 36. The tens digit comes first (on the left), then the ones digit.
- Pick the matching option → C) 36 — The answer is 36, which is option C. Watch out for switched digits — 3 tens and 6 ones is NOT 63!
In 37, which digit has the greater VALUE — the 3 or the 7?
Answer: 3 (worth 30)
- Find the value of each digit → 3 in tens place = 30, 7 in ones place = 7 — Don't be fooled by the digit itself! A digit's value depends on its PLACE. The 3 is in the tens place (worth 30), and 7 is in the ones place (worth just 7).
- Compare the values → 30 > 7 — The digit 3 (worth 30) has a greater value than the digit 7 (worth 7). Even a small digit in the tens place is worth a LOT more than a big digit in the ones place!
Common mistakes
- Students confuse the digit with its value, saying the 5 in 58 is worth 5 instead of 50. They write 5 tens + 8 ones = 58 but claim the 5 represents 5, not 50.
- When building numbers from tens and ones, students reverse digits. Given 4 tens and 2 ones, they write 24 instead of 42, placing the ones digit first.
- Students count tens incorrectly by adding ones. For 7 tens, they count 7 + 10 = 17 instead of recognizing 7 × 10 = 70.
- In expanded form problems, students add digits rather than place values. They write 35 = 3 + 5 = 8 instead of 35 = 30 + 5.