Professional Development SCMP November 2008
Crossing the River
1. Eight adults and two children need to cross a river, and they have one small boat available to help them. The boat can either hold one adult, or one or two children. Everyone in the group is able to row the boat. In the space below, show how you would get them all across the river.
How many one-way trips does it take for the eight adults and two children to cross the river?
2. How many one-way trips would it take to get the following groups across the river?
a. 6 adults and 2 children
b. 15 adults and 2 children
c. 3 adults and 2 children
3. How many trips would it take to get 100 adults and 2 children across the river? Describe how you find your answer.
4. Write a rule for finding the number of trips needed to get any number of adults (A) and 2 children across the river.
Crossing the River
Extra Challenges
5. What happens to your rule for finding the number of trips if there are different numbers of children? For example,
a. How many trips for 8 adults and 3 children?
b. 2 adults and 5 children?
c. A adults and 11 children?
6. One group of adults and children took 27 trips.
a. How many adults and children were in the group?
b. Is there more than one solution to part a?
c. If so, what is the rule that fits each solution?
Crossing the River
Follow-Up Homework
1. Adapt the “Crossing the River” math problem(s) so that it is appropriate for the grade level of your class. For example, you might change the number of adults. Just do not change the number of children! Also, you may want to make up your own story to present the problem rather than just giving it to them in a handout.
2. Before our next Professional Development Day (January 7), have your class work through your adapted “Crossing the River” math problem(s). When you present the problem, explain to your students that you are interested in their problem-solving process and that you want them to write down all of their thinking so that you can follow their ideas. They can draw pictures, make charts, or show their thinking in other ways.
3. Choose samples of your students’ work to bring to our January Professional Development Day. Make 6 photocopies of each piece you choose to share with your grade-level group. Be prepared to tell your group what intrigued you about the work you selected. Here are some guidelines for collecting and selecting student work:
· You might want to choose a piece in which the student thinking is not clear to you, and for which you would like to hear interpretations of the work from other group members.
· You might also want to choose a piece that shows a line of thinking that is out of the norm. It may be different from the way other students (and maybe even you) thought about the problem.
· You might want to choose a piece that you think is above and beyond. It may represent thinking that is explained clearly, neatly and/or logically.
The goal of doing these problems with your students is to look carefully at how students naturally work these problems. It would be great to see a good representation of how students think about the mathematical ideas that are embedded in the problems, and how they translate that thinking into words or pictures.
Adapted from: Education Development Center, Inc. from The Fostering Algebraic Thinking Toolkit
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SCMP Teacher Activity Log
November 2008
“Crossing the River”
Please provide the information requested below to verify at least 2.5 hours of planning, teaching, and analysis/reflection separate from the TLC planning/teaching days. This log will serve as confirmation of “Follow-up” hours to the grant CDE evaluator. Please indicate time in half hours, i.e., 1.5 = one and a half hours.
Activities / Total Time Required for each Type ActivityTime spent considering students’ learning styles, developmental levels, and ways to engage learners / .5 Hours
Teaching the lesson in the classroom / 1.5 Hours
Analysis of the results via reflective writing, discussion, lesson modification, etc. / .5 Hours
First Name / Last name
School / Grade(s)
Planning Date / Time
.5
Teaching Date / Time
1.5
Analysis Date / Time
.5
A brief description of the analysis: