The purpose of this activity is for students to interpret a partial-quotients calculation with a two-digit divisor. Before interpreting the partial-products calculation, students find the value of the quotient in a way that makes sense to them. This will help them understand the partial-quotients calculation by familiarizing themselves with the numbers, and likely some of the steps, in the calculation. In explaining both their answers and strategies as well as Elena's, students need to be precise in their word choice and use of language (MP6), and they also have an opportunity to improve their argument and critique the reasoning of others (MP3).

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

MLR1 Stronger and Clearer Each Time

• “Compartan con su compañero su descripción de la forma en que Elena encontró el valor de . Por turnos, uno habla y el otro escucha. Si es su turno de hablar, compartan sus ideas y lo que han escrito hasta ese momento. Si es su turno de escuchar, hagan preguntas y comentarios que ayuden a su compañero a mejorar su trabajo” // “Share your description of how Elena found the value of , 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 work.”
• 3–5 minutes: structured partner discussion
• Repeat with 2–3 different partners.
• (Optional) If needed, display question starters and prompts for feedback.
  • “¿Puedes dar un ejemplo que ayude a mostrar... ?” // “Can you give an example to help show . . . ?”
  • “¿Puedes usar la palabra _____ en tu explicación?” // “Can you use the word _____ in your explanation?”
• “Ajusten su borrador inicial basándose en los comentarios que les hicieron sus compañeros” // “Revise your initial draft, based on the feedback you got from your partners.”
• 2–3 minutes: independent work time
• “¿En qué se parece la estrategia de Elena a su estrategia? ¿En qué es diferente?” // “How was Elena’s strategy the same as and different from your strategy?” (She used the same calculations, but organized her work differently.)
• “¿Cómo le ayuda el método que usó Elena a organizar su trabajo?” // “How does the method Elena used help her organize her work?” (She records the multiples of 16 in one place and subtracts them in another.)

The purpose of this activity is for students to deepen their understanding of a partial-quotients algorithm and to practice using it. Students use a partial-quotients algorithm to find quotients of a three-digit dividend divided by a two-digit divisor. One of the quotients here involves a remainder, prompting students to interpret it. In the Activity Synthesis, students are reminded that the term “remainder” is used to describe “leftovers” when dividing. Different levels of scaffolding are provided, with some of the calculations partly completed. If students struggle to decide what multiple of the divisor to subtract, encourage them to pick a multiple they can calculate easily and that is less than or equal to what remains of the dividend.

• Ask previously identified students to share their work for .
• “¿368 es un múltiplo de 14? ¿Cómo lo saben?” // “Is 368 a multiple of 14? How do you know?” (No, because there is a remainder of 4, and we cannot make another group of 14 with only 4 left).
• Display the expression . “¿De qué manera la expresión representa ?” // “How does the expression represent ? (It shows that there are 26 groups of 14, with 4 left over. Dividing 368 by 14 gives 26 and a remainder of 4.)
• “Este problema tenía un residuo. Cuando dividimos y nos sobra una parte de un grupo, lo llamamos un ‘residuo’, porque representa lo que queda después de dividir en grupos iguales” // “This problem had a remainder. When we divide and end up with part of a group left over, we call it a ‘remainder,’ because it represents what is remaining after we divide into equal groups.”