Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Students first listen to The Doorbell Rang (Greenwillow Books, 1986) by Pat Hutchins, a story in which more people come to share Grandma1s wonderful cookies each time the doorbell rings. After the story is read, students investigate a problem situation that helps them develop meaning for the concept of division and leads to the use of fractions. Students first discuss the story1s plot and then are given the problem of how to share twelve cookies with eight children. Models are used to explore this operation and to generate fractional parts to create fair shares. Students work in groups with glue, scissors, and construction paper to investigate the problem. As the groups work, students are questioned about their problem-solving strategies. The groups show their answers with paper cookies and written explanations, and share their results with the class.
Topics for Discussion
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Using a Problem-Solving Approach
- How was problem solving the focus of this lesson? Identify the concepts and skills in the problem solving in this lesson. What were the important fraction ideas? How did Ms. Kincaid make sure that students addressed them?
- How did Ms. Kincaid engage students in the beginning of the lesson to ensure that they understood the problem?
- What strategies did you observe students using to share the cookies? How did students deal with remainders in this lesson?
- Ms. Kincaid stated, 3I want you to tell me how you know you are right. How can you prove to me that you have divided the cookies equally among those eight people?2 What is the purpose of this statement?
- Ms. Kincaid emphasized the use of words and pictures in the students1 explanations. How important is this approach and why?
- One group wrote, 3We know it is right because it is the only thing we could think of.2 What are ways to deal with this response?
- What were the characteristics of the task in this lesson that seemed to engage students and elicit their mathematical reasoning?
Using Literature in Mathematics
- Ms. Kincaid began the lesson by reading a children1s book. How did this book provide a context for the lesson? How did it stimulate the students1 thinking?
- Ms. Kincaid used the context of the story but created a problem that was more appropriate for her students. What other problems, based on the story, could be posed for students of different grade levels?
- Describe the benefits of using literature for learning mathematics.
- What mathematical concepts were illustrated in the story? How were these concepts extended to incorporate other mathematical ideas into the lesson?
- How did the story make connections to students1 daily lives? Cite examples of additional connections that could be made to students1 lives, to other subject areas, and to other mathematical topics.
Working with a group of teachers, divide into pairs. Each pair should write its own stories, appropriate to the grade level taught, in which some items must be cut into parts to complete the fair share. Each pair should use materials to solve its own problem. Then the problems can be exchanged for other teachers to solve. Compare characteristics of stories for different grade levels.
Solving Problems Consider these additional and more challenging problems. For each problem, use words and pictures to describe how you solved the problem and to explain how you know your solution is correct. Some possible problems are listed below in which you could use paper circles or paper strips to model the problem.
- Share 12 cookies among 9 people.
- Share 12 cookies among 10 people.
- Share 2 cookies among 8 people.
- Share 5 candy bars among 4 people.
- Share 11/2 candy bars among 4 people.