Lesson 15

The purpose of this warm-up is to invite students to share what they know about people’s ages and to elicit the idea that ages are numbers that can be put on a number line. While students may notice and wonder many things in this context, it is important to highlight the candles correspond to ages and that the ages can be represented on a number line.

• Create a number line from 0–100, marking intervals of 5, to display during the synthesis.

• Groups of 2
• Display the images.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Sin intentar contar todas las velas, ¿tienen alguna idea sobre las edades que pueden tener la primera y la segunda persona?” // “Without trying to count all the candles, do you have an idea about how old the first and second person might be?”
• “¿Qué edad tienen algunas de las personas que conocen, incluyendo a los adultos?” // “How old are some of the people that you know, including adults?”
• Select a few responses to locate and label on the number line.
• “Hoy vamos a pensar en las edades de diferentes personas e inventaremos problemas de suma y resta sobre edades. Usaremos nuestra recta numérica para representar nuestros problemas y como ayuda para resolverlos” // “Today, we are going to think about different people’s ages and make up addition and subtraction problems about ages.  We’ll use our number line to represent and help us solve our problems.”

The purpose of this activity is for students to leverage their previous work representing addition and subtraction problems on the number line to solve problems about the differences in family members’ ages. For each riddle, the previous answer is needed to solve. Students may use any strategy that helps them make sense of the problems in context.

• Groups of 2
• “Kiran escribió algunos acertijos basándose en las edades de personas de su familia. Vamos a resolverlos” // “Kiran wrote some riddles based on the ages of people in his family.  Let’s solve them.” 
• Give each student a copy of the blackline master.

• “Con su compañero, lean cada acertijo con detenimiento. Si les ayuda, pueden usar una recta numérica” // “Work with your partner to read each riddle carefully. You may use a number line if it is helpful.”
• “Mientras trabajan, piensen en si están usando la suma o la resta” // “As you work, think about whether you are using addition or subtraction.”
• 10 minutes: partner work time
• Monitor for students who use a number line or write an expression or equation to show their thinking.
• Monitor for students who locate and label each family member's age and name on the number line.

• Invite previously selected students to share.
• “Cuando leyeron el acertijo, ¿cómo supieron cuál estrategia usar?” // “How did you know which strategy to use when you read a riddle?” (I thought about if the person was older or younger than the person before. That helped me decide if I should count on or count backwards.)
• “¿Qué otras preguntas matemáticas podemos hacer que estén relacionadas con las edades de personas de la familia de Kiran?” // “What other mathematical questions can we ask related to Kiran’s family’s ages?”
• Share and record responses. Keep them displayed for the next activity.
• Suggest a few of the following if needed: 
  • “Si la hermana y el hermano de Kiran celebran juntos su fiesta de cumpleaños, ¿cuántas velas necesitan?” // “If Kiran’s sister and brother have their birthday party together, how many candles do they need?” (27: \(12 + 15\)) 
  • “¿Cuántos años más tiene la abuela de Kiran que su abuelo?” // “How much older is Kiran’s grandma than his grandpa?” (4: \(68-64\))
  • “¿Hace cuántos años la mamá de Kiran tenía la edad que Kiran tiene ahora?” // “How many years ago was his mom Kiran’s age?” (32: \(39-7\))

The purpose of this activity is for students to write their own number riddles involving people’s ages. Keep the mathematical questions from the synthesis displayed for students if they need ideas for riddles.

• Groups of 2
• Give each student a copy of the blackline master. 
• “Vamos a inventar nuestros propios acertijos sobre edades y a compartirlos con los demás. ¿Pueden pensar en alguien que tenga entre 1 y 9 años, en alguien que tenga entre 10 y 19 años, y en alguien que tenga entre 20 y 39 años? ¿Y en alguien que tenga más de 40 años?” // “We’re going to make up our own age riddles to share with each other. Can you think of someone between 1–9 years old, someone between 10–19 years old, and someone who is 20–39 years old? Older than 40?” 
• 30 seconds: quiet think time
• 1 minute: partner discussion 

• “Van a usar el nombre y la edad de personas que conocen para inventar preguntas matemáticas que le harán a su compañero. Si no están seguros de la edad de alguna persona, pueden hacer una buena estimación y usarla” // “You will use people you know and their ages to come up with mathematical questions to ask your partner. If you don’t know the person’s age for sure, make a good estimate to use.”
• “Pueden usar los acertijos de Kiran como ayuda. Si les ayuda a planear sus preguntas, pueden ubicar en la recta numérica la edad de cada persona que planean usar” // “You can use Kiran's riddles to help. You can locate the age of each person you plan to use on your number line if it helps you plan your questions.”
• 5 minutes: independent work time
• 30 seconds: quiet think time
• “Tomen turnos para hacer preguntas. Cuando su compañero les haga una pregunta, usen una recta numérica o una ecuación para mostrar lo que piensan” // “Take turns asking questions. When your partner asks you a question, record your thinking using a number line or equation.”
• 10 minutes: partner work time.
• Monitor for students who come up with something different than the questions presented in the previous activity.

• Invite previously selected students to share.
• “¿Encontraron algunos problemas que fueran un reto para resolver? ¿Qué los hacía retadores?” // “Did you find any problems that were challenging to solve? What made it challenging?”