Place value: how to help your child practice

What is place value?

Place value is the idea that the same digit is worth different amounts in different spots. In 47, the 4 means 4 tens, or 40. In 74, the same 4 means just 4 ones.

Each place is worth ten times the place to its right: ones, then tens, then hundreds, then thousands. That's why 10 ones make 1 ten and 10 tens make 1 hundred, and it's the reason regrouping, rounding and lining up numbers all work.

In most US schools, 1st graders work with tens and ones up to about 120, 2nd graders add hundreds and read, write and compare numbers to 1,000, and 3rd graders use place value to round and to add and subtract within 1,000. The math topic guide shows how place value connects to the rest of elementary math, and the 2nd grade guide covers what else comes up that year.

How do you find the value of a digit, step by step?

Teach one routine and use it for every place-value question:

1. Name the places from the right. Point to each digit and say "ones, tens, hundreds." In 352, the 2 is in the ones, the 5 in the tens, the 3 in the hundreds.
2. Say the digit and its place together. "5 tens."
3. Turn it into a number. 5 tens is 50. That's the value of the 5.
4. Put it back together to check. 300 + 50 + 2 = 352. Writing a number this way is called expanded form.

For comparing, start at the biggest place. To compare 409 and 490, both have 4 hundreds, so look at the tens: 0 tens versus 9 tens. So 490 is greater.

A zero holds a place even when it's worth nothing: 604 means 6 hundreds, 0 tens and 4 ones, and without the zero it would be 64.

What place value mistakes do kids make most?

Mixing up the digit and its value

Asked for the value of the 4 in 47, a child answers 4. The digit is 4, but its value is 40. Have them say the place out loud ("4 tens") before answering.

Dropping the zero

For 6 hundreds, 0 tens and 4 ones, a child writes 64. Without the zero, the 6 slides into the tens place. Use a three-column chart labeled H, T, O so every place gets a digit, even when it's 0.

Writing numbers the way they sound

A child hears "three hundred twenty-five" and writes 30025, putting down 300, then 20, then 5. Show that the 3 goes in the hundreds place of a three-digit number: 325 = 300 + 20 + 5.

How can you practice place value at home in 10 minutes?

Place value sticks best when kids can see and touch the groups.

• Minutes 1–3: bundle it. Give your child 34 dry pasta pieces or toothpicks and have them make bundles of 10. They should find 3 bundles and 4 left over, which is exactly what 34 means.
• Minutes 4–8: five mixed problems. One "value of the digit" question (the 6 in 362), one expanded form (518), one "build the number" (2 hundreds, 0 tens, 7 ones), one comparison (381 or 318?), and one "what's 10 more?" (245).
• Minutes 9–10: make the biggest number. Write three digits on scraps of paper, such as 5, 1 and 8. Your child arranges them into the biggest number (851) and the smallest (158) and explains why.

Over the week, swap in new digits each night so the practice stays fresh.

How can Easy Twin help with place value?

Scan your child's place value worksheet and Easy Twin makes a twin with the same kinds of questions and new numbers. Every question comes with two hints and worked steps, visuals like number lines and tables are redrawn with new data, and your child can play the twin as a quest or you can print it with an answer key.

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