The purpose of this activity is for students to use strategies based on place value to find quotients greater than 10. Students use base-ten blocks to represent quotients with single-digit divisors, for which it is intuitive to think of the divisor as the number of groups. In a later activity, students will be reminded that the divisor can also be interpreted as the size of each group. 

Working with base-ten blocks encourages students to divide out the tens and then the ones, and to see that sometimes it is necessary to decompose one or more tens to finish putting the dividend into equal groups. When students represent a quotient using base-ten blocks, they reason abstractly and quantitatively (MP2).

• Invite students to share their responses and reasoning for the last set of quotients.
• Ask students who used base-ten blocks or drew diagrams, “Was it necessary to decompose any of the tens into ones to divide?” (It wasn’t necessary for because there was already the right number of tens and ones to put into 3 groups. It wasn’t necessary for because I started with 10 tens and there was already the right number of tens to put into 5 groups.)
• “Why was it necessary or helpful to decompose the tens in 84?” (After putting 7 tens in 7 groups, there’s still 1 ten and 4 ones. The 1 ten couldn’t be split into 7 groups.)

The purpose of this activity is to show that the two meanings of division still apply when dividing greater numbers and that, in some cases, one interpretation may be more helpful than the other.

Students first analyze two ways of using base-ten blocks to represent  and see that the divisor, 5, can be interpreted to mean the number of groups or the size of one group. Students then consider how they might interpret and represent the divisor in other quotients. The reasoning here prepares students to reason more strategically as they divide greater numbers. 

• Invite students to share their responses and reasoning for the last set of problems.
• “How did you decide whether the divisor, the number we’re dividing by, is the number of groups or the amount in each group?” (It depends on the number. In the first two problems, the divisor was 4 and 6, so it was easier to think about 4 groups and 6 groups. In the last problem, the divisor was 15. It was easier to think about how many groups of 15 are in 75 than to think about making 15 groups from 75.)