Teacher Page
Introduction
Audience
Standards
Process
Materials
Evaluation
Conclusion
Resources
Student
Page 
Process
Procedures 
Notes 
• Provide participants with the concrete manipulatives and the graphical representations used in the number exploration activity from Section B of Day 2. Groups should receive one person sets of each assigned manipulative and one copy of each graphic representation. (Additional counters may be needed for the graphic representations.) 

• Assign problems to each group in the following way: There are six Problem Sets, A, B, C, D, E, and F. There are six problems in each set, numbered 1 6. Assign each group a number 1  6. The group will work that problem number from each set. For example, Group 1 will work Problem 1 from each of the six sets of problems. 

• Assign each group of four two concrete manipulatives and two graphical representations. Have eacl:1 person solve each of their group's assigned problems using one of the assigned manipulatives. For example, Participant A from Group I will solve problem I from each set of problems using baseten blocks. Participants should solve problems individually. Have each person use Chart 1 to record how effective the assigned manipulative was for solving the problem. 
Suggested assignments:
Groups I and 4: single counters, baseten blocks, partpartwhole mat with counters, ten frame mat with counters.
Groups 2 and 5: twocolor counters, straws and rubber bands, place value mat with baseten blocks, number line.
Groups 3 and 6: linking cubes, money, hundred chart, calculators.
Repeat assignments to other groups as necessary. 
• After individuals have completed the analysis, have each group of four 1 complete Chart 2, summarizing the effectiveness of each manipulative for solving each problem. Have each group determine the most effective and the least effective manipulative for each problem. Have groups share with each other: Group 1 with Group 2, Group 3 with Group 4, Group 5 with Group 6. 
Ask participants questions to encourage them to notice important mathematical characteristics of each type of representation. For example, Which model(s) seemed to work best for problems involving small numbers? Why? Which model(s) seemed to work best for problems involving larger numbers? Why? Why did this model NOT work well for larger numbers? What mathematical ideas to students already need to know to be able to use each model? 
• Have the participants brainstorm a list of issues that determines the difficulty level of word problems for students. In groups, have them examine Problem Sets A, B, and C and categorize the sets as to difficulty level. 
Problem Sets A, B, and C are subtraction problems. The problem sets were written so that Problem Set A is the easiest and Problem Set C is the most difficult. 
• In groups, have the participants analyze the similarities and differences between the three sets. Have them use the threecircle Venn diagram on Chart 3 to record their findings. As a whole group, compile the similarities and differences found. 
Similarities: all are subtraction; A and B are all single step problems; each set has two partitions, two comparisons, and two takeaway problems. Differences: number sizes are different in the three sets; sentence complexity is different; difficulty level is different. 
• Using Problems Sets A, B, and C, have participants brainstorm a list of Big Ideas for subtraction, recording them on the Analysis Chart. If time permits, a similar list for addition (Problem Sets D, E, and F) can be made. Participants may refer to the TEKS, if desired. 
This list willbeused with the Sampler activities. 
These pages were developed through TeacherTECH, the teacher professional development component of GirlTECH , which is sponsored by the Center for Excellence and Equity in Education (CEEE) with support from the National Science Foundation through EPIC .
Copyright © 1995 2005 by Ernesto Bautista 