Place value: teaching tens and ones with things at home

Place value means a digit’s position tells you what it is worth. In 14, the 1 sits in the tens place and means one ten, and the 4 sits in the ones place and means four ones. Teach it with real bundles: ten sticks tied together is one ten, and loose sticks are ones.

What is place value?

We write every number with just ten digits, 0 to 9. The same digit can mean different amounts depending on where it stands. The 3 in 32 means three tens, which is 30. The 3 in 23 means three ones.

The US Grade 1 standards ask children to “understand that the two digits of a two-digit number represent amounts of tens and ones.” Two ideas sit under it: ten ones can be bundled into one ten, and every two-digit number is some tens and some ones. Grade 2 adds hundreds, with a hundred described as a bundle of ten tens.

The IES practice guide on teaching math to young children recommends teaching number “using a developmental progression.” We follow that idea here: counting first, then grouping, then written digits. If counting past 20 is shaky, start with our guide on how to teach a child to count.

What do children learn about place value in each grade?

In the US Common Core standards, place value builds over three school years:

• Kindergarten: the numbers 11 to 19 as ten ones and some more ones, built with objects or drawings and recorded with a drawing or an equation such as 18 = 10 + 8.
• Grade 1: counting to 120 from any number; two-digit numbers as tens and ones; comparing two-digit numbers; finding 10 more or 10 less than a number in their head “without having to count”; and adding within 100.
• Grade 2: hundreds, tens and ones; counting within 1,000 and skip-counting by 5s, 10s and 100s; reading and writing numbers to 1,000 as numerals, number names and expanded form; and adding or taking away 10 or 100 in their head.

These are goals for a whole school year, and children reach them at different speeds. Use the list to see what comes next for your child.

Why is 14 “ten and four”?

The teen numbers are the first place where a child sees tens and ones together. The Grade 1 standards state that the numbers 11 to 19 are composed of a ten and some ones. So 14 is one ten and four ones, and 17 is one ten and seven ones.

The words can hide this. Fourteen is a squashed “four and ten,” with the ones said first, while the written number puts the ten first. Twenty-four, in contrast, says the tens first. Eleven and twelve have names of their own that do not sound like “one ten and one” at all. A child who finds teens hard may be reacting to the words, and bundles show what the words leave out.

The IES practice guide lists thirteen and fifteen as numbers children commonly skip when counting, because the words are irregular, and suggests practicing those exceptions on purpose. Say them slowly with bundles in front of you: “fif-teen” is five and ten. From twenty on, the names follow a pattern the same guide suggests pointing out: twenty, twenty-one, twenty-two, with the decade word first and the ones after it.

How do I teach tens and ones with bundles?

You need about 30 craft sticks or straws, and rubber bands or yarn. Dry pasta or buttons can stand for ones for children over 3 when you are watching. To build numbers on a screen instead, try our free place value chart.

1. Count out 10 sticks and put a rubber band around them. Say, “This is one ten. It has ten ones inside.”
2. Add 4 loose sticks. Ask, “How many sticks are there?” Let your child count the loose ones and say, “Ten and four. Fourteen.”
3. Write 14. Point to the 1: “This says one ten.” Point to the 4: “This says four ones.”
4. Build another number, such as 23. Make 2 bundles and 3 loose sticks. Ask your child to write it.
5. Reverse it. Write 31 and ask your child to build it with bundles.
6. Try 40. Make 4 bundles and no loose sticks. This is a good moment to see what the zero does.

A ten-frame works the same way. It is a box with two rows of five squares. Fill one frame with 10 counters, then put 4 on a second frame. One full frame and four more make 14. The ten-frame also helps with number bonds; see our guide to number bonds to 10.

Draw this chart on paper with two columns. Children put bundles in the tens column and loose sticks in the ones column, then write the digits under each.

How does the zero work?

The zero is a placeholder. In 40, it says “no ones,” which keeps the 4 in the tens place. The Grade 1 standards cover this: the numbers 10, 20, up to 90 mean one ten, two tens, up to nine tens, “and 0 ones.”

To see it, build 4 bundles, count by tens (“10, 20, 30, 40”), and write 40. Then take one bundle apart into ten loose sticks and count again. The total is the same; only the arrangement changed.

With hundreds, a zero can sit in the middle. The Grade 2 standards use 706 as an example: 7 hundreds, 0 tens and 6 ones. Without the zero, 706 would read as 76.

What is expanded form?

Expanded form writes a number as the sum of what each digit is worth: 346 = 300 + 40 + 6. The US Grade 2 standards ask children to read and write numbers to 1,000 in three ways: as numerals (346), as number names (three hundred forty-six) and in expanded form. Start smaller, with two-digit numbers: 14 = 10 + 4 and 23 = 20 + 3.

You can make place value cards from paper strips:

1. Write 300, 40 and 6 on three paper strips. Give every digit the same width, so the 300 strip is three digits long and the 6 strip is one.
2. Lay them out side by side and read them as a sum: “three hundred, plus forty, plus six.”
3. Stack them with their right edges lined up. The 40 covers the last two zeros of 300, and the 6 covers the last zero of 40, so the stack reads 346.
4. Pull the strips apart again and ask, “What is the 4 worth?”

Strips for 10 to 90 and 1 to 9 are enough for every two-digit number, so make those first.

Why might my child write 104 for 14?

A child who writes numbers as they sound may write 41 for fourteen, because the four is heard first. Or the child may write 10 and 4 side by side and get 104. This is our own reasoning from how the words sound, and we found no study that measures how often it happens.

1. Ask your child to build the number with bundles first.
2. Count the bundles and the loose sticks aloud.
3. Write one digit for the bundles and one for the loose sticks. The tens digit goes on the left.
4. Compare with what they wrote. Say, “What do you see? Does your number show one ten and four ones?”

Skip correcting each slip and let the bundles show the answer.

How does place value help with other math?

Place value comes up in much of the math that follows. To compare 38 and 83, look at the tens first. 3 tens is less than 8 tens, so 38 is less than 83. Our guide on greater than and less than shows how to teach that comparison.

It also helps with adding. To add 10 to 23, add one bundle: the tens change from 2 to 3, and the ones stay the same. Take a bundle away and you get 13. The Grade 1 standards ask children to find 10 more and 10 less like this, in their head. A hundred chart, the numbers 1 to 100 in rows of ten, shows the same thing: one row down is 10 more, and one row up is 10 less.

Bigger sums work the same way. For 27 + 15, put the bundles together (2 tens and 1 ten make 3 tens) and the loose sticks together (7 and 5 make 12). Twelve loose sticks are enough for a new bundle with 2 left over, so the answer is 4 tens and 2 ones, which is 42. The Grade 1 standards describe exactly this: you add tens and tens, ones and ones, and “sometimes it is necessary to compose a ten.” Our guide to how to teach addition covers other strategies.

Which place value games help?

Two games need only sticks, a die and a deck of cards. Keep dice, pasta and buttons away from children under 3.

• Roll and bundle: take turns rolling a die and taking that many sticks. Whenever you have 10 loose sticks, band them into a bundle. Say your number after each turn: “2 tens and 3 ones, 23.” The first to 5 bundles, which is 50, wins.
• Make the biggest number: take out the tens and picture cards and count aces as 1. Each player draws two cards and makes the biggest two-digit number they can. A 7 and a 4 make 74, which beats 47. Compare the tens first to see who wins the round.

Two free games on this site practice the same ideas:

• River Race: add and subtract two-digit numbers, a good use of tens and ones.
• Make Ten Match: find two cards that make 10, which practices the pairs inside a ten.

Play beside your child and ask, “How many tens? How many ones?” The Grade 1 curriculum page shows where tens and ones sit among the other topics, and the Grade 2 page covers hundreds. Short sessions are enough. If your child is still stuck after weeks of calm practice with bundles, talk to their teacher.