Lesson 14
Hundreds of Objects (optional)
Warmup: Notice and Wonder: Jar of Beans (10 minutes)
Narrative
This warmup 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.
Launch
 Groups of 2
 Display the image.
 “What do you notice? What do you wonder?”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Share and record responses.
Student Facing
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
 “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.”
Activity 1: Cup of Beans (10 minutes)
Narrative
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 baseten structure (MP2, MP7). They also consider opportunities for accuracy and efficiency when they articulate pros and cons for each method.
Launch
 Groups of 2
 Display image of a cup of beans or display a cup of beans.
 Read the context aloud.
Activity
 1 minute: quiet think time
 5 minutes: smallgroup 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)
Student Facing
Clare, Noah, and Jada counted a cup of dried beans. They each came up with 529 beans. The following pictures show how each of them counted.
Jada’s counting strategy:
Noah’s counting strategy:
Clare’s counting strategy:

What do you notice about each of their strategies?

What is helpful about each strategy?

What is challenging about each strategy?
Student Response
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Activity Synthesis
 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?”
Activity 2: Lots of Beans (25 minutes)
Narrative
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.
Supports accessibility for: Organization, Memory
Advances: Representing, Conversing
Required Materials
Materials to Gather
Required Preparation
 Each group of 2 to 4 students will need between onehalf cup to one cup of beans or other small objects to count. If realworld objects are unavailable, centimeter cubes could be used instead.
Launch
 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.”
Activity
 5–10 minutes: smallgroup 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
Student Facing
Organize and count your beans. Use the space to record your thinking.
Gallery walk questions:
 How does this strategy help you count their beans?
 How can this be made clearer?
 How is this strategy the same as your strategy? How is it different?
 Does your group have more or fewer beans? Explain your reasoning.
Student Response
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Advancing Student Thinking
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?”
Activity Synthesis
 “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.
Lesson Synthesis
Lesson Synthesis
“Today, we used strategies we have been studying about numbers between 100 and 999 to count a large amount of beans.”
“What are important things to remember when you count a large number of objects? What is important when you represent your strategy so that it is clear to others?”