Lesson 6

The purpose of this True or False is to elicit the strategies and understandings students have for explaining why an equation is true based on place value. These understandings will be helpful later when students need to find ways to make equations true by attending to place value.

• 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 strategies.
• Repeat with each statement.

• “¿De qué otras maneras podemos escribir una expresión que tenga un valor de 527?” // “What other ways could we write an expression that has a value of 527?”

The purpose of this activity is for students to use their understanding of place value to find the number that makes each equation true. Students must consider how units may be composed or decomposed to find the unknown number (MP7). The number choices intentionally emphasize the types of compositions and decompositions students may use to add and subtract within 1,000. The synthesis focuses on the equations that involve composing or decomposing two units.

• Groups of 2
• Give students access to base-ten blocks.

• 5 minutes: independent work time
• “Por turnos, compartan con su compañero cómo pensaron. Muestren o expliquen cómo saben que su ecuación es verdadera” // “Take turns sharing your thinking with your partner. Show or explain how you know your equation is true.”
• 3 minutes: partner discussion
• For finding the number that makes 2 hundreds + 9 tens + 17 ones true, monitor for students who:
  • explain by using base-ten blocks or place value diagrams
  • explain how they noticed when they would need to compose or decompose more than one unit

If students create equations that are not true, prompt students to make the known side of the equation with base-ten blocks, consider asking:

• “¿Cómo puedes componer o descomponer unidades en base diez para mostrar que la ecuación es verdadera?” // “How can you compose or decompose units to show the equation is true?”

• Invite previously identified students to share their method for finding the unknown number for 2 hundreds + 9 tens + 17 ones = _____ hundreds + 7 ones.
• For students who use base-ten blocks, draw place value diagrams to record their explanation.
• Consider asking:
  • “¿Cómo saben que ambos lados de la ecuación son iguales?” // “How do you know both sides of the equation are equal?”
  • “¿Compusieron o descompusieron unidades en base diez? ¿Compusieron o descompusieron más de una vez?” // “Did you compose or decompose units? Did you compose or decompose more than one time?”

The purpose of this activity is for students to use their understanding of place value to find and create matching expressions. The activity encourages students to write expressions that show the same value by composing or decomposing hundreds, tens, and ones. Although students may find the value of each expression to find matches, monitor for the ways they reason why two expression match or do not match by using what they know about hundreds, tens, and ones (MP7).

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

• Groups of 2
• Give each group a set of cards.

• “Con su compañero, encuentren tres expresiones que tengan el mismo valor” // “Work with your partner to find three expressions that have the same value.”
• “Anoten las letras de las tarjetas que queden en el mismo grupo y escriban su propia expresión que tenga el mismo valor” // “Record the letters of the matching cards and write your own expression that has the same value.”
• 10 minutes: partner work time

If students find matches that are not equivalent or do not explain their matches, consider asking:

• “¿Cómo podrías usar bloques en base diez o diagramas para mostrar cómo pensaste?” // “How could you use base-ten blocks or diagrams to show your thinking?”

• Display cards C, H, and J.
• “¿Estas expresiones quedaron en el mismo grupo? Expliquen sus ideas” // “Do these expressions match? Explain.”
• “¿Qué otras expresiones escribieron que tuvieran el mismo valor que estas expresiones?” // “What other expressions did you write that match these expressions?”
• If time, consider asking:
  • “¿Qué otras expresiones podrían escribir que tengan el mismo valor que estas expresiones?” // “What other expressions could you write to match these expressions?”