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Understand Ten-Times Place Value Relationships

Students recognize that moving one place to the left in a multi-digit number makes a digit worth ten times as much (e.g., the digit 4 in the thousands place is worth 10 times more than the same digit in the hundreds place). They use models such as base-ten blocks and place value charts to explore this relationship.

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Understand Ten-Times Place Value Relationships

Grade 4 · Place Value Understanding · question 1 of 3

0 of 20

20 rungs. A star at the top.

= 10 × 7

How it is taught

0:00 of 4:00

A digit's value depends on its place.

One place to the left multiplies that value by ten.

Read it: Move left, worth 10 times

Both numbers have a 4. In 400 the 4 is 4 hundreds; in 40 it is 4 tens. Same digit, different worth.

  1. Find the place the digit stands in, and say what it is worth: 4 tens is 40.
  2. Move it into the next place to the left: 4 tens become 4 hundreds.
  3. Compare the two worths: 400 = 10 × 40.

1 hundred is 10 tens, so 4 hundreds is 10 times as much as 4 tens.

Every pair of places side by side works the same way: 10 ones make 1 ten, 10 tens make 1 hundred, 10 hundreds make 1 thousand.

So you can read it either way: 400 is 10 times 40, and 400 ÷ 10 = 40.

A digit in the next place to the left is worth 10 times as much: 400 = 10 × 40, and 400 ÷ 10 = 40.

Saying the 4 in 400 and the 4 in 40 are worth the same, because the digit is the same.

Look at the place, not just the digit: 4 hundreds is 400, 4 tens is 40, and 400 = 10 × 40.

A 6 in the tens place is worth 60. In the next place to the left, the 6 is worth ___. — 600. 1 hundred is 10 tens, so the 6 is worth 10 times as much: 600.

The two 4s in 440

Look at the number four hundred forty. Both digits are 4 — but are they worth the same?

Let's drop it into a place value chart with hundreds, tens, and ones.

We write 4 in the hundreds, 4 in the tens, and 0 in the ones.

The 0 in the ones place is worth zero — easy.

The 4 in the tens place means four tens. That's forty.

The 4 in the hundreds place means four hundreds. That's four hundred.

So one 4 is worth forty, and the other 4 is worth four hundred. Same digit, very different value!

How do we get from forty to four hundred? We multiply by ten.

Every time we move one place to the left, the digit is worth ten times as much.

440 — are both 4s the same?440Let's find out how each digit is worth.HundredsTensOnes440= 0= 40= 400× 10One place left = 10× biggerRULE10×per place left400 = 10 × 40
Grade 4 · Each place to the left is 10 times bigger

The 4 in the hundreds place is ten times the 4 in the tens place. That's the ten-times rule!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
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Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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Understand Ten-Times Place Value Relationships — Grade 4 Mathematics