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.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Can you imagine counting out so many beans? How would you do it?”
• “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.
• “Which of these strategies do you believe would be the fastest or slowest? Explain.”
• “Do you think it would be easier to make a mistake using one of these strategies? Which one and why?”
• “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.
• “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.
• “Think about these questions as you walk around.”
• 10 minutes: gallery walk

If students double count beans or groups of beans ask, “How can you organize your piles to make sure you did not double count some of the piles?”

• “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.