Lesson 12

The purpose of this Number Talk is to elicit strategies and understandings students have for mentally subtracting a multiple of 10 from a number. Building on their understanding of place value, students subtract tens from tens. These understandings help students develop fluency and will be helpful in later lessons when students will need to be able to subtract using strategies based on place value.

• 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 strategies.
• Keep expressions and work displayed.
• Repeat with each expression.

• “¿Cómo les puede ayudar la tercera expresión a encontrar el valor de la última expresión?” // “How could the third expression help you find the value of the last expression?” (76 is 10 more than 66 and 30 is 10 less than 40, so the difference between the two numbers is the same.)

The purpose of this activity is for students to analyze a mistake in ordering numbers (MP3). When placing numbers in order from least to greatest, students can compare using their understanding of place value. However, they see that, unlike comparing just two numbers, when comparing sets of numbers, there is more to keep track of. Students learn that a number line provides a linear representation to help organize numbers in sequence and visualize the relative distance between numbers.

• Groups of 2

• “Kiran y Andre ordenaron algunos números de menor a mayor” // “Kiran and Andre put some numbers in order from least to greatest.”
• “Andre estaba en desacuerdo con Kiran, así que usó una recta numérica para justificar su respuesta. ¿Con quién están de acuerdo?” // “Andre disagreed with Kiran, so he used a number line to justify his answer. Whom do you agree with?”
• “Individualmente, piensen sobre esto y prepárense para explicar cómo pensaron” // “Think about this on your own and be prepared to explain your thinking.”
• 3 minutes: independent work time
• “Discutan con un compañero. Usen todo lo que saben sobre el valor posicional o la recta numérica para justificar su razonamiento” // “Discuss with a partner using what you know about place value or the number line to justify your reasoning.”
• 5 minutes: partner work time
• Monitor for students who:
  • use precise place value language to describe the correct placement of 269 and 272 in the list
  • use the number line to explain that a list of numbers from least to greatest should match the placement of the numbers on the number line from left to right

• Invite previously selected students to share using precise place value language.
• Invite a student to explain using the number line.
• “Cuando ordenamos números, podemos usar lo que sabemos sobre el valor posicional. También podemos pensar sobre la secuencia de conteo y usar una recta numérica para ayudarnos a ver los números en orden” // “When we order numbers, we can use what we know about place value. We can also think about the counting sequence and use a number line to help us see the numbers in order.”

The purpose of this activity is for students to order numbers. Students estimate the location and label numbers on a number line, and then write them in order from least to greatest or greatest to least. For the third set of numbers, students may order the numbers using any method that makes sense to them. Students reflect on how the number line can help us organize numbers (MP5). Throughout the activity, monitor for the way students explain their reasoning based on place value and the relative position of numbers on the number line.

• Groups of 2

• “Ahora van a tener la oportunidad de ordenar números” // “Now you will have a chance to order numbers.”
• “Algunas veces los van a ordenar de menor a mayor y algunas veces lo harán de mayor a menor” // “Sometimes you will put them in order from least to greatest, and sometimes it will be from greatest to least.”
• 10 minutes: independent work time
• “Comparen con un compañero. Expliquen cómo pensaron” // “Compare with a partner. Explain your thinking.”
• 5 minutes: partner discussion
• Monitor for students who order the last set of numbers by:
  • explaining their reasoning using precise place value language
  • placing each number on the number line before ordering the numbers

If students locate the numbers on the number line, but reverse the order given in the problem, consider asking:

• “¿Cómo decidiste el orden de tus números?” // “How did you decide the order of your numbers?”
• “¿Tu lista muestra los números en orden de menor a mayor o de mayor a menor?” // “Does your list show the numbers in order from least to greatest or greatest to least?”

• Invite previously identified students to share their reasoning.
• “¿En qué se parecen los números que marcaron en la recta numérica a la lista de números que escribieron? ¿En qué son diferentes?” // “How are the numbers you labeled on the number line the same as the list of numbers you wrote? How are they different?” (For least to greatest, its the same. The difference is the number line shows the distance between each number, but the list of numbers shows them right next to each other.)