Lesson 13

The purpose of this True or False is to elicit the insights students have about the composition of multi-digit numbers in terms of place value. It also reinforces the idea that the same digit has different values depending on its place in a number—that is, digits cannot be viewed in isolation of their positions. The reasoning students do here will be helpful later when students compare and order numbers within 1,000,000.

• 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 corregirían las afirmaciones falsas para que sean verdaderas?” // “How would you correct the false statements so that they become true?”
  • \(3,\!291 = 1 + 90 + 200 + 3,\!000\)
  • \(190,\!023 = 100,\!000 + 90,\!000 + 20 +3\)

This activity prompts students to examine more closely how multi-digit numbers can be compared, and to use their insights to order several numbers. Students solidify their awareness that looking only at the first digit is not a definitive way of comparing numbers. They also practice constructing a logical argument and critiquing the reasoning of others (MP3) when they explain why the strategy of analyzing only one digit is not reliable. When students refine Tyler's statement about comparing numbers to include making sure to compare digits with the same place value, they attend to precision in the language they use (MP6).

This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing

• Groups of 2
• Read the first problem as a class.
• Ask 1–2 students to restate Tyler’s claim in their own words.

• “En silencio, trabajen unos minutos en los dos primeros problemas sobre la estrategia de Tyler. Luego, compartan sus respuestas con su compañero” // “Take a few quiet minutes to work on the first two problems about Tyler’s strategy. Then, share your responses with your partner.”
• 4–5 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for students who use place-value understanding to explain why Tyler’s strategy is not reliable.
• “Trabajen individualmente en los dos últimos problemas” // “Work on the last two problems independently.”
• 4–5 minutes: independent work time

Students may think that a number with larger digits is always greater than one with smaller digits, regardless of their place value and the number of the digits in each number. For instance, they consider 58,978 to be greater than 547,612 because the former has the digits 5, 7, 8, and 9, and the latter has smaller digits: 1, 2, 4, 5, 6, and 7. Urge students to read each number aloud and then ask which is greater: a number in the 58 thousands and one in the 547 thousands. Alternatively, ask students to identify in each 58,978 and 547,612 the digit in the place with the greatest value. Urge them to consider which is greater: 5 ten-thousand or 5 hundred-thousand.

• “Compartan con su compañero su estrategia para comparar números de varios dígitos. Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta el momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su explicación” // “Share your strategy for comparing multi-digit numbers with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their explanation.”
• 3–4 minutes: structured partner discussion
• Repeat with 1–2 other partners.
• “Ajusten su descripción inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial description based on the feedback you got from your partners.”
• 2–3 minutes: independent work time
• Invite students to briefly share their ordered sets of numbers from the last problem and their reasoning. Record and display their responses.
• If not mentioned in students’ explanations, point out that in the last set of numbers, the third digit (in the thousands place) in each 630,951 and 631,051 is what tells us how the two numbers compare. The third digit (in the hundreds place) also tells us how 63,591 and 63,951 compare.

In this activity, students apply their understanding of place value to order multi-digit whole numbers and solve problems in context. They also reason about the range of numbers whose values are between two given numbers. 

• “¿A quién le gusta jugar videojuegos? ¿Qué juegos les gusta jugar?” // “Who enjoys playing video games? What games do you enjoy playing?”
• “¿Alguien ha jugado un juego en el que los puntajes de los jugadores se acumulan o se suman a lo largo de varias rondas?” // “Who has played a game where the scores of the players get accumulated or added up over multiple rounds?”
• “Usemos lo que sabemos sobre los números grandes para comparar algunos puntajes de un videojuego y ordenar jugadores según su puntaje” // “Let’s use what we know about big numbers to compare some video game scores and rank some players.”

• “En silencio, trabajen en la actividad durante unos minutos. Luego, discutan sus respuestas con su compañero” // “Take a few quiet minutes to work on the activity. Then, discuss your responses with your partner.”
• 6–7 minutes: independent work time

• Invite students to share the ranking of the players and their reasoning. Record their responses.
• Invite students to share examples of what Andre's score could be.
• If not mentioned in students’ explanations, point out that 101,012 (the highest score) is 1,012 greater than the first six-digit number, 100,000. This means there are many six-digit numbers that could be the second-highest score.