Lesson 7

The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students find factor pairs of numbers.

• 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 for each expression.

• “¿Cómo les ayuda conocer el primer y el tercer cociente a encontrar el último cociente?” // “How does knowing the first and third quotients help you find the last quotient?” (Since \(12 + 60=72\) , we can add the answers to those quotients to get the answer to the last problem.)
• Consider asking:
  • “¿Alguien puede expresar el razonamiento de _____ de otra forma?” // “Who can restate _____’s reasoning in a different way?”
  • “¿Alguien usó la misma estrategia, pero la explicaría de otra forma?” // “Did anyone have the same strategy but would explain it differently?”
  • “¿Alguien pensó en esa expresión de otra forma?” // “Did anyone approach the expression in a different way?”
  • “¿Alguien quiere agregar algo a la estrategia de _____?” // “Does anyone want to add on to_____’s strategy?”

The purpose of this activity is for students to find factors and multiples of a given number and make statements that use the terms “factors” and “multiples.” This work prompts students to use language precisely (MP6).

Students can generate many different statements for each number and use the given number in either of the two blanks in the sentence stem. They then share their statements with their partner and explain why their sentences make sense. As they do so, students practice constructing viable arguments and attending to the reasoning of others (MP3).

• Groups of 2
• “Vamos a practicar cómo usar las palabras ‘factor’ y ‘múltiplo’ como preparación para un juego que vamos a jugar. Dediquen un momento a completar las afirmaciones individualmente” // “We are going to practice using the words ‘factor’ and ‘multiple’ in preparation for a game we’ll play. Take some time to complete the statements on your own.”
• 3–5 minutes: independent work time

• “Ahora compartan sus afirmaciones con su pareja. Asegúrense de hacerle preguntas al otro mientras explica sus afirmaciones” // “Now share your statements with your partner. Be sure to ask each other questions as you explain your statements.”
• 3–5 minutes: partner discussion

• “Entre las afirmaciones que se inventaron, ¿cuál fue su favorita? ¿Por qué fue su favorita?” // “What was your favorite statement you came up with? Why was it your favorite?”
• “¿Qué observaron y qué se preguntaron con su pareja sobre esta actividad?” // “What did you and your partner notice and wonder about this activity?”

The purpose of this activity is for students to practice finding factors and multiples of numbers and using the vocabulary. Students can play multiple rounds of the game as time allows and should be encouraged to use the ideas from the previous activity, if needed. This game is Stage 2 of the center Find the Number. In this stage, students find factors and multiples for a given number. The gameboard is a square grid with the numbers 1–100.

To start, one player chooses an even number less than 50. The other player covers either a factor or multiple of that number. Students take turns covering either a multiple or factor of the previous number. When there are no factors or multiples left to cover, the player who covered the last number gets a point. Students take turns choosing the starting number. Students play 10 rounds, or as many rounds as time allows. The player with the most points wins.

• Groups of 2
• Give each group of 2 students the blackline master and centimeter cubes.
• “Vamos a jugar un juego llamado ‘Encuentra el número’. Tómense unos minutos para leer las instrucciones” // “We are going to play a game called Find the Number. Take a few minutes to read the directions.”
• 2 minutes: independent work time
• “¿Qué preguntas tienen sobre el juego?” // “What questions do you have about the game?”
• If needed, play an example round.

• 10–15 minutes: partner game time
• Monitor for students who strategically choose numbers to win the round.

• “¿Cuál fue su estrategia para escoger los números mientras jugaban el juego?” // “What was your strategy for choosing numbers as you played the game?” (I wanted to keep the round going as long as possible, so I liked choosing numbers that I knew had a lot of factors. I tried to find a number that was prime that I could use so that my partner would have a harder time choosing a number.)