In this activity, students sort base-ten blocks and record the total number of blocks by the unit each block represents. Students work together to look for ways to compose larger units from smaller units in order to represent the same value with the fewest number of blocks (MP7). They represent composing a hundred by exchanging 10 ten blocks for a hundred block and represent composing a ten by exchanging 10 one blocks for a ten block. In the Synthesis, students compare different ways that groups represent the total value which may include representing the value as a three-digit number.

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• “How do you know that you have used the fewest number of blocks possible?”
• “How can you combine the tens or ones so you don’t use as many of the base-ten blocks?”

• Display previously identified students’ representations.
• “What is the same about the ways groups represent the total value of the blocks?” What is different? (They each show 4 hundreds, 9 tens, and 5 ones. Some just use diagrams, some use only digits, some use diagrams, numbers, and expressions.)

In this activity, students build on their work with base-ten blocks in previous activities to use base-ten diagrams to represent a value using the fewest number of each unit possible. They first interpret images of students’ representations of a number using base-ten blocks. When representing the same value, students may choose to draw the original representation and show composing units by circling groups of 10 tens or 10 ones. Others may choose other methods, such as circling or labeling the images to show ways to compose a larger unit or by using what they have learned about patterns in units from previous lessons. In the Synthesis, students connect the 3 digits in a three-digit numeral to their representations (MP7).

• “How many did Diego have in all? Explain how you know.”
• Select previously identified students to share.
• Write 283 while saying “2 hundreds, 8 tens, and 3 ones.”
• “This is a three-digit number. The digits represent amounts of hundreds, tens, and ones.”
• As needed, demonstrate reading the number left to right and gesture to emphasize the value of each digit.