Lesson 11 Different Partial Quotients

- Let’s use what we know about multiplication and place value to find quotients.

Warm-up Notice and Wonder: Ways to Record

What do you notice? What do you wonder?

Clare’s strategy:

Jada’s strategy:

divide. three hundred sixty four divided by 13. With two image underneath.

$\begin{aligned} 130 \div 13 & = 10 \\ 130 \div 13 & = 10 \\ 65 \div 13 & = 5 \\ 39 \div 13 & = 3 \\ \overset{―}{364 \div 13} & \overset{―}{= 28} \end{aligned}$

Activity 1 Division Expressions

Take turns:

Choose a set of expressions that, when added together, is equal to $308 \div 14$ . Not all expressions will be used.
Explain to your partner how you know that your cards represent a sum that is equal to $308 \div 14$ .

(Pause for teacher directions.)
Choose one of the sets of expressions whose sum is equal to $308 \div 14$ and use it to find the value of $308 \div 14$ .

Activity 2 Choose Your Own Partial Quotients

For each expression, choose one of the partial quotients and, beginning with that expression, find the value of the quotient.

$360 \div 15$
- $150 \div 15$
- $300 \div 15$
- $60 \div 15$
$945 \div 45$
- $45 \div 45$
- $450 \div 45$
- $900 \div 45$
$992 \div 31$
- $165 \div 31$
- $341 \div 31$
- $310 \div 31$
How did you decide which partial quotient to use to begin finding the quotient? Did you change your mind with any of the problems?

Practice Problem

Problem 1

Explain why $256 \div 4$ is equivalent to $(200 \div 4) + (40 \div 4) + (16 \div 4)$ .
What is the value of $256 \div 4$ ? Explain your reasoning.