Lesson 1

This warm-up prompts students to compare numbers represented in different ways. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. During the synthesis, ask students to explain the meaning of any terminology they use, such as place value, hundreds, tens, ones, sum, or base-ten diagram.

• Groups of 2
• Display the image and expressions.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2-3 minutes: partner discussion
• Share and record responses.

• “What do all of these ways of showing numbers have in common?” (The parts of the number have been separated into hundreds, tens, and ones.)
• “Remember that expanded form is a specific way of writing a number as a sum of hundreds, tens, and ones. It is written as a sum of the value of each digit like in B.”
• “How would we write 482 in expanded form?” \((400 + 80 + 2)\)

The purpose of this activity is for students to revisit numbers that are written in different forms. Students match numbers represented in different forms: base-ten numerals, base-ten diagrams, number names, and expanded form. As they make matches, students use their understanding of base-ten structure represented in many different ways (MP7).

• Create a set of cards from the blackline master for each group of 2. 

• Groups of 2
• Distribute one set of pre-cut cards to each group of students.
• Give students access to base-ten blocks.

• “This set of cards includes numbers in different forms. Find the cards that match. Work with your partner to explain your matches.”
• 8 minutes: partner work time

If students don't match base-ten numerals to the other representations, consider asking:

• “What does each digit in the number represent?”
• “How could we use what each digit represents to match it to another representation?”

• Invite students to share the matches they made and how they know those cards go together.
• Attend to the language that students use to describe their matches and numbers in different forms, giving them opportunities to describe the numbers in different forms more precisely.
• Highlight the use of terms like hundreds, tens, ones, word form, expanded form, base-ten blocks, and base-ten diagrams.

The purpose of this activity is for students to use place value understanding from grade 2 to decompose numbers in different ways. In small groups, students start by writing a three-digit number, and then pass their number to the group member to their right. Each time students receive the number, they decompose it in a different way. In the synthesis, students look for connections in the ways their number was decomposed, and in all the recording sheets in their group. Highlight connections that show that place value can be used to represent a number as different combinations of hundreds, tens, and ones. This will be helpful later in the unit when students add and subtract using strategies and algorithms based on place value.

• Groups of 4
• Display: 365
• “What are some ways you could decompose this number?”
• 30 seconds: quiet think time
• Share and record responses.
• Give each student a copy of the blackline master.
• “Take a minute and think of a three-digit number that you will use for this activity.“
• 30 seconds: quiet think time.
• “Now write your number in the first box on your sheet.”

• “Pass your paper to your right and receive the paper from your left. The paper has a number in Box 1. In Box 2, show one way the number you were just passed can be decomposed.”
• 1-2 minutes: independent work time
• “Pass your paper to your right and receive the paper from your left. The paper has a number in Box 1 and one way of decomposing that number in Box 2. In Box 3, show another way the number you were just passed can be decomposed.”
• 1-2 minutes: independent work time
• “Pass your paper to your right and receive the paper from your left. The paper shows two ways of decomposing a number. In Box 4, show another way to decompose that number.”
• 1-2 minutes: independent work time
• “Pass your paper one more time. You should have your original number back.”
• “Talk to your group about which box was the most difficult for you to fill in. Share ideas about what helped you most during this activity.”
• 2-3 minutes: group discussion
• Share responses.

• “Look at what was written to represent your number. Write down any connections you notice between the different ways the number was represented.”
• 3 minutes: independent work time
• “Now, look at the recording sheets of everyone in your group. What patterns do you notice in the ways the numbers are decomposed?”
• 2-3 minutes: group discussion

If students don't generate decompositions based on place value, consider asking:

• “How did you decompose the number?”
• “How could you use base-ten blocks to come up with other ways to decompose the number?”

• Have groups share the connections they saw across the sheets.