Lesson 5

The purpose of this True or False is to elicit insights students have about the value of the digits in a three-digit number. The reasoning students express in the task helps students deepen their understanding that numbers can be represented in different ways. This will be helpful later when students represent numbers in multiple ways in the lesson activities.

In this activity, when students describe how they use the value of each digit to determine if the equation is true, they look for and make use of the base-ten structure when they look for the value of each digit in a 3-digit number (MP7).

• Display one statement.
• “Hagan una señal cuando sepan si la afirmación es verdadera o no, y puedan explicar cómo lo saben” // “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

• Share and record answers and strategy.
• Repeat with each statement.

• “¿En qué se diferencia la última ecuación?” // “What is different about the last equation?” (It’s not decomposed into hundreds, tens, and ones. 22 shows some tens and some ones and 10 shows another ten.)

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).

• Groups of 2
• Display Andre, Tyler, and Mai’s situation and the image of their blocks.
• “¿Cómo se vería la expresión?” // “What would the expression look like?”
• 1 minute: independent work time
• 1 minutes: partner discussion
• Share responses.
• Display 357 and \(300 + 50 + 7\).
• “Podemos representar el valor de los bloques escribiendo un número de tres dígitos” // “We can represent the value of the blocks by writing a three-digit number.”
• “Un número también se puede representar como la suma del valor de cada uno de sus dígitos. Se le llama forma desarrollada” // “A number can also be represented as a sum of the value of each of its digits. This is called expanded form.”
• “Al igual que en un número de tres dígitos, en la forma desarrollada se muestra la suma comenzando con la posición que tiene el mayor valor a la izquierda y se continúa hacia la posición que tiene el menor valor a la derecha” // “Like a three-digit number, expanded form shows the sum starting with the place that has the greatest value on the left to the place with the least value on the right.”
• As needed, discuss reasons why any expressions generated in the launch would or would not be examples of expanded form.

• “Ahora van a practicar la escritura del valor de los diagramas en base diez en forma desarrollada y como números de tres dígitos” // “Now you will practice writing the value of the base-ten diagrams in expanded form and as a three-digit number.”
• 7 minutes: partner work time

• “¿Cuál es el valor de \(40 + 100 + 3\)? Expliquen cómo lo saben” // “What is the value of \(40 + 100 + 3\)? Explain how you know.” (143. 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?” (\(100 + 40 + 3\))

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.

• Each group of 2 needs 3 number cubes.

• Groups of 2
• Give each group 3 number cubes.
• “Su compañero y ustedes van a formar números de tres dígitos” // “You and your partner will be making three-digit numbers.”
• “Lancen los dados numéricos. Usen los dígitos que obtuvieron para formar números de tres dígitos que coincidan con las instrucciones de cada problema” // “Roll the number cubes. Use the digits you roll to make three-digit number that matches the directions for each problem.”
• “Intentemos 1 juntos” // “Let’s try 1 together.”
• Roll three number cubes.
• “Obtuve un _____, un _____ y un _____” // “I rolled a _____, a _____, and a _____.”
• “¿Cuál es el menor número de tres dígitos que puedo formar con estos dígitos?” // “What is the smallest three-digit number I could make with these digits?”
• 30 seconds: quiet think time
• Share responses
• “Después de que su compañero y ustedes lleguen a un acuerdo sobre cómo organizar sus dígitos, escriban los números como números de tres dígitos y en forma desarrollada” // “After you and your partner agree on how to arrange your digits, write the number as a three-digit number and in expanded form.”
• Write the number as a three-digit number and in expanded form on the board.

• 7 minutes: partner work time
• As students work, consider asking:
  • “¿Observaron un patrón en los dígitos cuando formaron el menor número o el mayor número?” // “Do you notice a pattern in the digits when you made the smallest or largest number?”
• Monitor for students who recognize that in order to make the largest number possible they need to order the number cubes from greatest to least.

• 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.