The purpose of this activity is for students to find quotients using base-ten blocks and represent their methods. Students solve two problems, one where decomposing a hundred or ten is not necessary and one where it is. Students use base-ten blocks to represent the problem and find the quotient, then they work in small groups to create a visual display of how they used the base-ten blocks. This builds on work students have done in previous grades representing operations with base-ten representations.

The base-ten blocks help highlight the important role place value plays in division (MP7). There are not enough hundreds in 104 to divide into 8 equal groups but there are enough tens to put 1 ten in 8 equal groups. Then the 2 remaining tens can be broken into ones to complete the division.

• “What is the same and what is different between the representations?”
• 30 seconds quiet think time
• 1 minute: partner discussion

The purpose of this activity is for students to find quotients and represent their thinking with base-ten blocks. The numbers in the expressions are designed to encourage students to think about when the base-ten blocks may be helpful and when they become cumbersome. In future lessons, students will be asked to interpret base-ten representations but may use any method or representation that makes sense to them.

• “Tell me more about how you found the value of  ______.“
• “How might you use the blocks to check your mental math?”

• “In the Lesson Synthesis, let’s compare some different representations for a division problem.”