Lesson 3

The purpose of this Number Talk is to elicit strategies and understandings students have for adding by place and composing a ten mentally. These understandings help students develop fluency and will be helpful later in this lesson when students describe base-ten representations by place and use the fewest number of base-ten blocks to represent a number.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “What did you notice about the sums?” (The expressions were all different, but all had a value of 84.)
• “How could you explain why the third and fourth expressions have the same value?” (You could take 2 ones from 36 and add it to 48 to make \(50+34\).)

In this activity, students sort base-ten blocks and record the total number of blocks they have 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

• Each group of 3–4 students will need a container with 2 hundreds, 28 tens, and 15 ones.
• Each group of 3–4 students will need access to additional base-ten blocks (hundred blocks and ten blocks).

• Groups of 3–4
• Give each group a container of blocks, access to base-ten blocks, and supplies for making a group display.

• “Your group has a container of base-ten blocks.”
• “Sort the blocks by the unit they represent and record the number of each type of block on your paper.”
• “Work together to figure out how to represent the same total value using the fewest number of blocks possible.”
• 6 minutes: small-group work time

MLR7 Compare and Connect

• “Create a visual display to show the total value of the blocks. Include details such as diagrams, labels, and numbers to help others understand your thinking.”
• 2–5 minutes: group work time
• “As you look at other groups’ representations, look for different ways groups show the value. Which ways are the same as your group’s representation? Which ways are different? How do you know they represent the same value?”
• 5 minutes: gallery walk
• “Discuss any revisions you would like to make to your representations with your group.”
• 1–2 minutes: small-group work time
• Monitor for students who:
  • create a base-ten diagram with the fewest amount of blocks represented
  • write 4 hundreds, 9 tens, 5 ones
  • write 495
  • use an expression such as \(400 + 95\) or \(400 + 90 + 5\)

If students represent their number with 10 or more of any unit, consider asking:

• “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 and what is different between the ways groups represented the total value of the blocks?” (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).

• Groups of 2
• Give students access to base-ten blocks.

• “Mai and Diego each used base-ten blocks to represent numbers.”
• “Record the number of hundreds, tens, and ones each student used.”
• “Find a way to represent the same value with the fewest number of each unit possible and represent it using a base-ten diagram.”
• “Use blocks if it helps.”
• “Together with your partner, figure out the total value of the blocks.”
• 8 minutes: partner work time
• Monitor for students who write the total as a three-digit number.

• “How many did Diego have in all? Explain how you knew.”
• 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.