Lesson Plan

Number and Operations: Raul's Apples: Word Problem

Subject:	Math
Grade span:	6 to 8
Duration:	30 to 45 minutes

This lesson was excerpted from the Afterschool Training Toolkit under the promising practice: Math Tools

Description:

This sample is one example of how you can implement the Math Tools practice. In this lesson, students will use counters, such as pinto beans, and a variety of problem-solving techniques to estimate and determine the solution to Raul's Apples.

Learning Goals:

Use problem-solving strategies and manipulatives to solve a problem involving number sense
Find a solution to a real-world problem using manipulatives
Develop and use strategies to judge the reasonableness of results
Work together to problem solve

Materials:

Raul's Apples Problem (PDF) printed on small sheet of paper
Beans (about 100 per small group)

Preparation:

Ensure that each group has enough beans to allow them to explore different scenarios.
Think about the students in your group and determine whether using calculators may be necessary for them to access the problem-solving task. The use of calculators should be determined based on the goals for the students.

What to Do:

Organize students into small groups of three or four.
Hand out Raul's Apples problem, and allow students time to read and begin work on the problem.
Ask students to begin sharing their thinking in their small groups.
Provide them with beans to help them figure out the problem. Ask how the beans might help. Listen for a variety of ways in which students think about the beans. Help students see how the beans can be used to represent the apples in the problem.
As students find answers to the problem, ask them to justify their thinking to you. ("How did you use the beans? Were they helpful?" and "Why did you choose to start with that number of beans?") You can have them prepare a presentation for the entire group where they share their thinking about the problem.
Encourage students who have solved the problem in different ways to share their thinking, so that a variety of solution strategies are shown.

Teaching Tips:

To use manipulatives to explore Raul's Apples, work the problem in reverse using the beans to represent the apples Raul has.
Encourage students to begin at the end of the problem, where it states that "he discovers that there are only two left," using two beans to symbolize this.
When Raul encounters a friend he gives her "half of the remaining apples, plus two more." When working in reverse it is important to do every step in reverse. Therefore add two more beans to the two already on the table, this represents the reverse of "plus two more."
Then to find the reverse of "half the remaining apples" double the apples on the table, so that there are now eight (8) beans. Continue this process with each step of Raul's trip to find the number of apples in the bag at the beginning of the problem.

Evaluate (Outcomes to look for):

Listen for a variety of ways in which students think about using the beans to solve the problem (guess and check, working backwards, etc.)
Students should justify their use of manipulatives in the problem by how they helped find the solution
Comments and answers that indicate that students are listening to, monitoring, and applying the problem-solving strategies of their peers

Standards:
Click this link to see additional learning goals, grade-level benchmarks, and standards covered in this lesson.

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