In this activity, students use base-ten blocks or base-ten diagrams to represent large numbers in the ten-thousands and hundred-thousands. They learn that when they assign a new value, 10, to the small cube, larger numbers are more accessible and can be represented with fewer blocks. The limitation of blocks in the classroom will create a need to represent large numbers in a different way. Blocks should be made available and students should be invited to use them if needed. Students should also be encouraged to represent base-ten blocks in diagrams in ways that make sense to them.

When students interpret and use Lin's strategy, they state the meaning of each base-ten block or part of their diagram in a strategic way allowing them to represent large numbers (MP6).

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

• 2–3 minutes: gallery walk
• “What connections do you see between the representations you made using Lin's strategy?” (I see 15 of the large squares for 15,000 and in another drawing. I see 1 large cube and 5 large squares.)
• Collect student responses and highlight connections between groups of ten that are equivalent to other units.
• “Which blocks would we use to represent 100,000?” (100 large squares or ten large cubes. We could also create a new block to represent 100,000.)

In this activity, students interpret a collection of blocks in which a small cube represents different values. They notice a pattern in the value of the digits when the small cube represents 1 and then represents 10. Although students are not required to articulate this relationship until the next lesson, the reasoning elicits observations about the relationship between the digits in the multi-digit number and the number of each type of block (MP7, MP8).

If students say that the value of the collection of blocks remains the same even when the small cube has changed in value, consider asking:

• “How did you find the value of the blocks after the small cube changed from a value of 1 to 10?”
• “If each small cube is now worth 10, what is the value of the long rectangle? How can you use this to find the value of the other blocks?”

• Invite students to share their answers to the last problem.
• Create a chart of statements students make when comparing the two numbers for reference in a future lesson.

The purpose of this activity is to review the meaning of expanded form so students can write numbers to the ten-thousands in expanded form.

• Select 1–2 students to share equations for the second problem.
• “120,450: Let’s practice saying this number together as a class.”
• “What digit is in the thousands place in this number?” (zero)
• “How did Lin end up with a 0 in the thousands place, when she had 20 blocks with a value of 1,000?” (Each group of 10 thousands makes 1 unit of ten-thousand. Since there are 2 groups of 10 thousands, there are 2 ten-thousands.)
• “How can we explain the number represented by 10 blocks with the value of 10,000 each?” (Ten groups of 10,000 is 100,000. We can also count by 10,000. Nine blocks with a value of 10,000 is 90,000, so 10 blocks would be 10,000 more than that, or 100,000.)
• Record the reasoning about the value of the blocks using equations: