Tens and ones

What is this skill?

Tens and ones is first grade place value: understanding that a two-digit number such as 47 is made of 4 tens and 7 ones. The 4 does not mean four; it means four groups of ten, or forty. The 7 means seven single ones. Children practice this with bundles of sticks, base-ten blocks, ten frames and drawings of tens and ones.

Typical questions ask how many tens or ones are in a number, or what number is made from a given set of tens and ones. A key insight is that ten ones can be grouped into one ten, which is how our number system works.

Why it matters

Place value is arguably the most important idea in elementary math. It explains why we write numbers the way we do, why 52 is bigger than 25, and how adding, subtracting, rounding and later decimals work. Nearly every second and third grade skill, from adding with regrouping to rounding to the nearest ten, assumes a solid understanding of tens and ones.

Children who memorize "the left digit is the tens" without picturing actual groups of ten often struggle later, when regrouping asks them to break a ten into ten ones. Building numbers with real objects now prevents that.

Common mistakes

• Reading the tens digit as a number of ones, so 4 tens and 7 ones is thought of as 11 things. Building the number with bundles of ten makes the size of each digit visible.
• Mixing up the order when writing, such as writing 74 for 4 tens and 7 ones. Saying "tens first" and placing the tens on the left of a simple chart helps.
• Difficulty with zero in the ones place, as in 60. Show that 60 is 6 tens and no ones, which is why the 0 is needed.

How to help at home

• Bundle craft sticks, straws or pencils into tens with rubber bands. Build numbers like 34 (3 bundles and 4 singles) and ask your child to name them.
• Count a large pile of small items by making groups of ten in cups or bags, then counting the tens and the leftover ones. Write the number together.
• Use money: dimes are tens and pennies are ones. Show 5 dimes and 3 pennies and ask how many cents. Then ask for a number, like 42 cents, and let your child build it.
• Ask questions both ways: "How many tens are in 68?" and "What number has 3 tens and 9 ones?" Switching directions shows whether your child really understands.

Worked examples

These are real questions from the Tutorsaurus tens and ones practice, with the answers worked out.

1. Example 1

   7 tens and 9 ones is…

   Choices: 76, 78, 79, 81

   Answer: 79. 7 tens = 70, plus 9 ones = 79.

2. Example 2

   3 tens and 1 ones is…

   Choices: 34, 31, 33, 28

   Answer: 31. 3 tens = 30, plus 1 ones = 31.

3. Example 3

   9 tens and 5 ones is…

   Choices: 94, 97, 98, 95

   Answer: 95. 9 tens = 90, plus 5 ones = 95.