Lesson 15

The purpose of this Number Talk is to elicit strategies and understandings students have for adding and subtracting 10 from a two-digit number.

When students notice how the tens place changes while the ones place doesn’t, they are making sense of the base-ten structure of numbers (MP7).

• Display one expression.
• “Hagan una señal cuando tengan una respuesta y puedan explicar cómo la obtuvieron” // “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Cuál expresión tiene un valor mayor, \(52 + 10\) o \(52 - 10\)? ¿Pueden compararlas sin encontrar el valor de las expresiones?” // “Which expression has a greater value \(52 + 10\) or \(52 - 10\)? Can you compare without finding the value of the expressions?” (\(52 + 10\) will be greater than \(52 - 10\) because it is getting larger rather than having something taken away.)

The purpose of this activity is for students to interpret comparison symbols and compare two-digit numbers based on the value of the digits using drawings, numbers, or words. During the launch, students notice and wonder about two related comparison statements that use symbols rather than words. The teacher creates a chart with the comparison statements and what the symbols mean in words for students to refer to during the activity. Students may use connecting cubes to build each number, use the value of each number’s tens or ones place, or use expressions that show the value of tens and ones to justify their reasoning. Students then circle the true comparison statement.

• Write \(78 > 45\) and \(45 < 78\) on a piece of chart paper.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display \(78 > 45\) and \(45 < 78\).
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?” (The wider part of the symbol points toward the larger number. The point is toward the smaller number. Is this always true? Does the order you write the comparison matter? Does the order of the numbers matter?)
• 1 minute: quiet think time
• 2 minutes: partner discussion
• Record responses.
• “Estos son símbolos de comparación. Los usamos para mostrar que un valor es mayor que o menor que otro sin escribir las palabras. El lado abierto, o el lado del símbolo con la mayor cantidad de espacio entre la parte superior y la inferior, siempre mira hacia el número mayor” //  “These are comparison symbols. We can use them to show that one value is greater than or less than another without writing the words. The open side, or the side of the symbol with the greater amount of space between the top and bottom, always faces the greater number.”
• Record “78 es mayor que 45” // “78 is greater than 45” under \(78 > 45\). Consider writing “greater than” in a different color.
• “El lado puntiagudo, o el lado del símbolo con menos espacio entre las líneas, siempre mira hacia el número menor” // “The pointy side, or side of the symbol with less space between the lines, always faces the lesser number.”
• Record “45 es menor que 78” // “45 is less than 78” under \(45 < 78\). Consider writing “less than” in a different color.

• Read the task statement.
• 10 minutes: partner work time
• Monitor for students who:
  • verbally describe the relationship between two numbers using “greater than” and “less than”
  • compare numbers using their place value understanding

• Display \(21 < 12\) and \(21 > 12\).
• Invite previously identified students to share.
• “Sabemos que 21 es mayor que 12. ¿Cómo recuerdan qué símbolo representa mayor que?” // “We know that 21 is greater than 12. How do you remember which symbol represents greater than?” (I think about the part of the symbol with a greater amount of space being next to the greater number.)
• Display \(74 < 78\) and \(74 > 78\).
• Invite students to share their thinking.
• “74 es menor que 78. ¿Cómo saben qué símbolos muestran esto?” // “74 is less than 78. How do you know which symbols show this?” (The side of the symbols with less space between the lines needs to be closer to 74.)

The purpose of this activity is for students to determine if comparison statements are true or false and explain why. In the previous activity, students focused on using their understanding of place value to determine if the symbols were facing the appropriate numbers. In this activity, students are encouraged to read the statements from left to right before determining whether the statement is true or false. Encourage students to use the display created in the previous activity to help them interpret the symbols and read the statements.

• Groups of 2
• Give students access to connecting cubes in towers of 10 and singles.
• Display \(45 < 54\).
• “En la actividad anterior, decidimos que esta afirmación es verdadera. ¿Cómo se lee esta afirmación?” // “In the last activity, we decided that this statement is true. How would we read this statement?” (45 is less than 54.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• Display \(21 > 12\).
• “También decidimos que esta afirmación era verdadera. ¿Cómo se lee esta afirmación?” // “We also decided this statement was true. How would we read this statement?” (21 is greater than 12.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

• Read the task statement.
• “Van a trabajar con su pareja en esta actividad. Asegúrense de que cada uno tenga tiempo para pensar en el problema y darle sentido antes de compartir lo que pensaron” // “You are going to work with your partner on this activity. Make sure that each partner has time to think on their own and make sense of the problem before sharing your thinking.”
• 10 minutes: partner work time
• Monitor for students who determined \(58 = 53\) is false using the values of the tens or ones place to share during the synthesis.

If students discuss whether each statement is true or false, but do not read the statements, consider asking:

• “¿Cómo puedes usar la presentación que hicimos como ayuda para leer la afirmación?” // “How could you use the display we made to help you read the statement?”
• “Lee la afirmación. ¿Qué observaste sobre el símbolo que podría ayudarte a recordar cómo se dice la próxima vez que lo leas?” // “Read the statement. What did you notice about the symbol that could help you remember how to say it the next time you read it?”

• Display answers for students to check their work.
• Invite selected students to share their explanations for \(58 = 53\).
• “¿Cómo podemos cambiar esta afirmación para que sea verdadera?” // “How can we change this statement so it is true?” (\(58 > 53\))
• Read the new comparison statement.