Lesson 12

The purpose of this True or False is to elicit strategies and understandings students have for making it easier to find the value of expressions by making a ten. These understandings help students deepen their understanding of the properties of operations and will be helpful later when students will need to fluently add within 100.

• 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.

• “¿Cómo podemos cambiar la segunda ecuación para hacer que sea verdadera?” // “How could we change the second equation to make it true?” (We could change the 10 to 17 or the 20 to 27 because we need 7 more.)

The purpose of this activity is for students to solve addition and subtraction problems within 100 with the unknown in all positions. Students write equations with a ? for the unknown and find the number that makes the equations true. The mathematical context of each problem encourages students to use the number line to reason about what is unknown and how they may represent the problem with an equation (MP2).

• Groups of 2
• Give each student a copy of the blackline master.
• Display an image of a blank number line or draw a number line.
• “Hoy van a resolver acertijos para encontrar un número secreto” // “Today you will be solving riddles to find a mystery number.”
• “En cada caso, van a escribir una ecuación que le corresponda al acertijo. Usen el signo ? para representar el número desconocido” // “For each riddle, you will write an equation that represents the riddle, and write a ? for the unknown.”
• “Luego, van a representar la ecuación en la recta numérica” // “Then you will represent the equation on the number line.”
• “Intentemos un acertijo juntos” // “Let’s try one together.”
• Demonstrate on a number line with input from the students.
• “Empecé en un número, salté 10 hacia la izquierda. Mi salto terminó en el 42. ¿Qué ecuación puedo escribir usando el signo ? para representar el número desconocido?” // “I started on a number, jumped 10 to the left. My jump ended at 42. What equation could I write with a ? for the unknown?” (? - 10 = 42)
• “¿Cómo puedo encontrar el valor del número secreto?” // “How could I find the value of the mystery number?” (Do the opposite. Start at 42 and move 10 to the right.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Share responses and record on the number line.

• “Ahora tendrán la oportunidad de resolver acertijos para encontrar un número desconocido. Luego, van a usar una recta numérica para representar cómo pensaron. Su compañero y ustedes pueden tomar turnos para leer el acertijo mientras la otra persona lo sigue a lo largo de la recta numérica” // “Now you will have a chance to solve riddles to find a missing number, and then represent your thinking on a number line. You and your partner can take turns reading the riddle, while the other person follows along on the number line.”
• 12 minutes: partner work time

If students write equations other than those represented by the riddle or number line representation, consider asking:

• “¿Cómo decidiste dónde poner tu punto inicial o tu punto final?” // “How do you decide where to put your starting or ending points?”
• “¿Qué parte del acertijo te puede ayudar a escoger la dirección de tus flechas y tus saltos?” // “What part of the riddle could help you choose the direction for your arrows and jumps?”

• Invite students to share the answer to each riddle and display their number line.
• “¿Cuáles acertijos les parecieron los más retadores a su compañero y a ustedes? Expliquen” // “Which riddles did you and your partner find to be most challenging? Explain.”

The purpose of this activity is for students to find the value of an unknown in addition and subtraction equations. Students can choose to find the unknown number using either operation and represent their thinking on a number line. Listen for the ways students use the number line to make sense of the relationship between the numbers in each equation and use methods that show they are thinking about ways to use the structure of the number line and their understanding of place value (MP7).

• Groups of 2
• Give each student a copy of the blackline master.

• “Encuentren, de una manera que tenga sentido para ustedes, el número que hace que cada ecuación sea verdadera” // “Find the number that makes each equation true in a way that makes sense to you.”
• “Usen una recta numérica para mostrar cómo pensaron” // “Represent your thinking on the number line.”
• Monitor for a student who finds the value for \({?} + 57 = 72\) by:
  • starting at 57, drawing a jump to 72, and counting each length unit in between
  • staring at 57, drawing a jump of 3 and a jump of 12 to 72
  • starting at 72 and jumping back 57 in one jump or multiple jumps

• Invite previously selected students to share how they found the number that makes \(? + 57 =72\) true.
• Consider asking:
  • “¿De qué manera la recta numérica de ______ muestra los números que conocíamos? ¿De qué manera muestra el número desconocido?” // “How does ______'s number line show the numbers that we knew? How does it show the unknown number?”
  • “¿En qué se parecen estos métodos? ¿En qué son diferentes?” // “How are these methods the same? How are they different?”
• As time permits, continue with other equations.