The purpose of this activity is for students to represent numbers in different ways. The structure of the task encourages students to practice composing and decomposing units. Students also have opportunities to use and connect concrete and abstract representations of three-digit numbers (MP2).

• Display a picture or drawing of a group’s blocks before they composed or decomposed units, such as:

• “How could this group represent their number in another way?” (Exchange 1 of the tens for 10 ones, or exchange 10 tens for 1 hundred.)
• Display a picture or drawing of a group’s blocks that uses the fewest number of blocks, such as:

• “How could this group represent their number in another way?” (Exchange 1 of the hundreds for 10 tens, exchange 1 ten for 10 ones, or exchange all the tens for 40 ones.)

The purpose of this activity is for students to represent the same number in multiple ways. During the Gallery Walk, students are encouraged to connect different representations of a number that make use of structure in similar ways. (For example, a diagram and an equation might use the same hundreds, tens, and ones.) The Lesson Synthesis focuses on the different ways students represent 356 with expressions or equations. Students demonstrate their understanding of the structure of the base-ten system when they describe, compare, and connect different representations of the same three-digit number (MP7).

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

• “What ways of representing the number did your group discuss?”
• “How could you represent this number with equations, words, or digits?”

• Display:
  • 3 hundreds + 4 tens + 16 ones
• “Does this expression show 356? Explain.” (Yes, 16 ones is the same as 1 ten and 6 ones, so it’s the same as 3 hundreds + 5 tens + 6 ones.)
• “This is one way we could show 356 as an expression. What other ways did you see groups represent 356 as an expression?”
• Record responses.

• “How are the expressions the same? How are they different?” (They all show 356. Some expressions have different amounts of hundreds and tens. Some expressions use words.)
• 30 seconds: quiet think time
• 2 minute: partner discussion
• Share responses.