Lesson 14

This warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved. In the next activity, students will see three different ways the amount of beans in a cup are counted.

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

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

• “¿Se imaginan contar tantos frijoles? ¿Cómo lo harían?” // “Can you imagine counting out so many beans? How would you do it?”
• “Hoy vamos a seguir pensando sobre estas ideas de conteo en nuestra primera actividad” // “We are going to keep thinking about those counting ideas in our first activity today.”

The purpose of this activity is for students to compare methods that can be used to count numbers between 100 and 999. Students see images of beans that are put in groups of 5 and another in groups of 10. A third image uses groups of 100, groups of 10, and single beans. Students make connections to place value and their understanding of the base-ten structure (MP2, MP7). They also consider opportunities for accuracy and efficiency when they articulate pros and cons for each method.

• Groups of 2
• Display image of a cup of beans or display a cup of beans.
• Read the context aloud.

• 1 minute: quiet think time
• 5 minutes: small-group discussion
• Monitor for students who:
  • describe the organization and group sizes in each method
  • describe Clare’s method in terms of hundreds, tens, and ones
  • discuss ideas such as efficiency (how long it takes) and accuracy (chances of mistakes)

• Invite previously selected students to share their observations.
• “¿Cuál de estas estrategias creen que sería la más rápida o la más lenta? Expliquen” // “Which of these strategies do you believe would be the fastest or slowest? Explain.”
• “¿Piensan que sería más fácil cometer un error usando una de estas estrategias? ¿Cuál y por qué?” // “Do you think it would be easier to make a mistake using one of these strategies? Which one and why?”
• “¿Cuál estrategia prefieren? ¿Por qué?” // “Which strategy do you prefer? Why?”

The purpose of this activity for students to choose their own method to count between 100 and 999 objects accurately and efficiently. Students should be encouraged to use their understanding of place value.

• Each group of 2 to 4 students will need between one-half cup to one cup of beans or other small objects to count. If real-world objects are unavailable, centimeter cubes could be used instead.

• Groups of 2 or 4.
• Give students each group \(\frac{1}{2}\) to 1 cup of beans and a sticky note.
• “Van a usar el método que prefieran para contar los frijoles y después van a escribir su resultado en una nota adhesiva. Dóblenla para esconder su resultado” // “You will use any method you prefer to count the beans and then write your result on one sticky note and then fold it to hide your result.”

• 5–10 minutes: small-group work time
• Monitor for students who make groups of 5, groups of 10, or groups of 100.
• Display and read the gallery walk questions.
• “Piensen sobre estas preguntas mientras caminan” // “Think about these questions as you walk around.”
• 10 minutes: gallery walk

If students double count beans or groups of beans ask, “¿Cómo puedes organizar tus montones para asegurarte de no contar dos veces algunos de los montones?” // “How can you organize your piles to make sure you did not double count some of the piles?”

• “Cuando organizaron sus frijoles y los contaron, ¿se sintieron seguros de sus resultados? ¿Por qué?” // “When you organized your beans and counted them, did you feel confident about your results? Why?”
• Invite students to share answers to the gallery walk questions.