The purpose of this activity is for students to write three-digit numbers as the sum of the value of each digit, expanded form. Students connect the order and values of the addends in expanded form to the order and value of each place in a three-digit number. Use expanded form and its definition interchangeably throughout the activity so that students feel comfortable with the new vocabulary. When students represent numbers as sums by place value, they interpret the three-digit numbers in terms of its digits and the operation of addition (MP7).

• “¿Cuál es el valor de ? Expliquen cómo lo saben” // “What is the value of ? Explain how you know.” (143, because I saw there was 1 hundred, 4 tens, and 3 ones. I just rearranged it in my head like expanded form.)
• “Sabemos que cuando encontramos el valor de una suma, podemos reorganizar los sumandos para sumar en cualquier orden. Cuando un número está escrito en forma desarrollada, los valores se escriben en el orden del valor posicional” // “We know we can rearrange the addends to add in any order when we find the value of a sum. When a number is written in expanded form the values are written in place value order.”
• “¿Cómo escribiríamos 143 en forma desarrollada?” // “How would we write 143 in expanded form?” ()

In this activity, students represent numbers using base-ten numerals and expanded form. Students work with a partner to arrange number cubes to create the largest or smallest three-digit number. This gives students the opportunity to reason together about place value. Students recognize that placing the number cubes in order from least to greatest creates the smallest number and ordering them from greatest to least will yield the largest possible number. This reasoning will be helpful in later lessons when students compare and order three-digit numbers.

• Invite 2–3 previously selected students to share the largest numbers they made.
• “¿Cómo sabían si estaban formando el mayor número posible?” // “How did you know if you were making the largest number possible?” (The largest digit rolled needed to be the hundreds. The next largest digit needed to be in the tens.)
• As time permits, repeat with the smallest number.