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

• “¿Cómo decidiste cuál número es mayor?” // “How did you decide which number is greater?”
•  “¿Cómo nos ayuda pensar en el valor de los dígitos a comparar números?” // “How can thinking about the value of digits help us to compare numbers?”

• “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 the third digit (thousands place) in 630,951 and 631,051 is what tells us how these two numbers compare. The third digit (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. 

• 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.