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Divide with Place Value Strategies and Models

Students use place value understanding, rectangular arrays, area models, and the relationship between multiplication and division to find whole-number quotients for up to four-digit dividends divided by one-digit divisors. They build conceptual understanding before applying algorithms.

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Divide with Place Value Strategies and Models

Grade 4 · Division with Multi-Digit Dividends · question 1 of 3

0 of 20

20 rungs. A star at the top.

24 ÷ = 12

How it is taught

0:00 of 5:03

Break the dividend into friendly place-value parts.

Divide each part, then add the quotients.

Division undoes multiplication.

Read it: Divide in big pieces

What is 96 ÷ 6? Take out 10 sixes, which is 60, and 36 are left. Take out 6 more sixes, and nothing is left. 10 + 6 = 16.

  1. Share the places: tens and hundreds share out just like ones.
  2. Or take out easy chunks of the divisor, and add the chunks.
  3. Or go place by place, the biggest place first, and write a digit for each place.

Dividing asks how many groups of the divisor fit. Places, chunks and digits all count those groups.

Each way gives the same quotient, so you can check one way with another.

Every place gets a digit, even a 0: 412 ÷ 4 is 103, not 13.

Share the places, take out chunks, or go place by place. Each way gives the same quotient.

Dropping the 0 from the middle: 412 ÷ 4 written as 13.

1 ten ÷ 4 is 0 tens, and the 0 holds the tens place. 412 ÷ 4 = 103.

320 ÷ 4 = ___ — 80. 320 is 32 tens, and 32 tens ÷ 4 = 8 tens, which is 80.

96 ÷ 4

Imagine ninety-six stickers shared equally between four friends. How many does each friend get?

We can write this as ninety-six divided by four.

Let's break ninety-six into friendly numbers — eighty plus sixteen. Both of these divide by four easily.

Now we'll draw a rectangle. One side is four, our divisor.

Inside, we put eighty on the left and sixteen on the right. Together they still make ninety-six.

How many fours fit inside eighty?

Twenty! Write twenty above the eighty box.

How many fours fit inside sixteen?

Four! Write four above the sixteen box.

Now we add our partial quotients: twenty plus four.

96 stickers, 4 friends — how many each?96 ÷ 4 = ?96 = 80 + 1648016204Partial quotients20 + 4 = 2496 ÷ 4 = 24ANSWER24stickers each
Grade 4 · Break apart by place value to divide

Ninety-six divided by four is twenty-four. Each friend gets twenty-four stickers. Nice work!

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
Climbing now
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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