Using the Partial Quotients Method

Grade 6 Unit 5: Arithmetic in Base Ten Using the Partial Quotients Method

Warmup

Get as many problems correct out of 30 problems as you can! Try to go as fast as you can! Then try it again to beat your best number of correct problems and best time!

Activity #1

Division by Partial Quotients Method.

Enter any two numbers to divide. The Dividend must be greater than the Divisor.
Adjust in the app below, to a suggested quotient using the triangular slider. The value will appear on the right.
Enter the product of the divisor and the suggested quotient in the first box at the top.
Do the subtraction and fill in the value in the second box.
Adjust to a second suggested quotient.
Enter the product of the divisor and the suggested quotient in the third box.
Do the subtraction and fill in the value in the fourth box.
Adjust to a fourth suggested quotient.
Enter the product of the divisor and the suggested quotient in the fifth box.
Enter the difference in the last box.
Add up the suggested quotients and fill the answer in the Quotient box.
Fill in the remainder in the Remainder box. You should have check marks to confirm your answer or you look through your steps. Naturally, any division process stops as soon as the remainder is less than the divisor.
To have new numbers to divide, click the reset button.

Activity #2

Use the Partial Quotients Method.

(A). Elena used base-ten diagrams to find 372 ÷ 3. She started by representing 372.

She made 3 groups, each with 1 hundred. Then, she put the tens and ones in each of the 3 groups. Here below is her diagram for 372 ÷ 3.

(1). Elena’s diagram for 372 has 7 tens. The one for 372 ÷ 3 has only 6 tens. Why?

(2). Where did the extra ones (small squares) come from?

(B). Andre calculated 657 ÷ 3 using a method that was different from Elena’s.

(1). Andre subtracted 600 from 657. What does the 600 represent?

(2). Andre wrote 10 above the 200, and then subtracted 30 from 57. How is the 30 related to the 10?

(3). What do the numbers 200, 10, and 9 represent?

(4). What is the meaning of the 0 at the bottom of Andre’s work?

(5). How might Andre calculate 896 ÷ 4? Explain your reasoning.

Activity #3

Practice Partial Quotient Method.

(1). Here is an incomplete calculation of 534 ÷ 6. Write the missing numbers (marked with “?”) that would make the calculation complete.

(2). Use the partial quotients method to find the quotient.

(3). Use the partial quotients method to find 1,115 ÷ 5.

(4). Use the partial quotients method to find 6655 ÷ 7.

(5). Use the partial quotients method to find 432 ÷ 16.

Challenge #1

Here is one way to find using partial quotients.

Show or explain a different way of using partial quotients to divide 2,105 by 5.

Challenge #2

Here is an incomplete calculation of 534 : 6. Write the missing numbers (marked with “?”) that would make the calculation complete.

Challenge #3

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