Graphic Organizers: Using a Matrix to Help Solve Word Problems

1. Graphic Organizers:Using a Matrix to Help Solve Word Problems Learning Strategy Project By: Rachel Merren

2. What Are Graphic Organizers? See Reference Page

3. Benefits of Graphic Organizers • (Gregory & Chapman, 2007). • (Zemelman, Daniels, & Hyde, 2005). • Build • Help students • (Col, 1996). • (Hyerle, 1996).

4. Steps of Implementation • Give students a copy of the matrix with row and column labels filled in. • Have students anticipate how the matrix can be used. • Read the application problem twice. • Lead students through filling out the matrix. • Write the equation based on the “Total” column. • In the future, students will need to determine their own labels for the rows and columns. Lead them through this process: • Rows “What are you comparing?” • Columns “What do you know in general?”

5. Applications of Linear Equations Read the following problem twice. Write an equation that could be used to solve the problem. Ruth makes $5 an hour working after school and $6 an hour working on Saturdays. Last week she made $64.50 by working a total of 12 hours. How many hours did she work on Saturday? Total Saturday Earnings Total Weekday Earnings Total Amount Earned

6. Pre -Test • Read the following problem twice. Write an equation that could be used to find the correct solution. Tickets for the senior class play cost $6 for adults and $3 for students. A total of 846 tickets worth $3846 were sold. How many student tickets were sold?

7. Use a Matrix (Chart): • Thirty students bought pennants for the football game. Plain pennants cost $4 each and fancy ones cost $8 each. If the total bill was $168, how many students bought the fancy pennants?

8. Use a Matrix (Chart): • Adult tickets for the game cost $4 each and student tickets cost $2 each. A total of 920 tickets worth $2446 were sold. How many student tickets were sold? Number x Price = Cost a 4 2 4a Adult Student 920 - a 2 (920 – a) 4a + 2(920 – a) = 2446 Are you ready for the Post-Test? Yes No

9. Post -Test • Read the following problem twice. Write an equation that could be used to find the correct solution. Tickets for the senior class play cost $6 for adults and $3 for students. A total of 846 tickets worth $3846 were sold. How many student tickets were sold? Katie’s garden, which is 6 meters wide, has the same area as Courtney’s garden, which is 8 meters wide. Find the lengths of the two rectangular gardens if Katie’s garden is 3 meters longer than Courtney’s garden. (Remember: length x width = area)

10. References Col, J. (1996). Graphic Organizers. Retrieved June 7, 2008, from http://enchantedlearning.com Gregory, G., & Chapman, C. (2007). Differentiated Instructional Strategies: One Size Doesn’t Fit All. (2nded). Thousand Oaks, CA: Corwin Press. Hall, T., & Strangman, N. (2002). Graphic Organizers. Wakefield, MA: National Center of Accessing the General Curriculum. Retrieved June 7, 2008, from http://www.cast.org/publications/ncac/ncac_go.html Hyerle, D. (1996). Visual Tools for Constructing Knowledge. Alexandria, VA: Association for Supervision and Curriculum Development. Marzano, R., Pickering, D., & Pollock, J. (2001). Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement. Alexandria, VA: Association for Supervision and Curriculum Development. Zemelman, S., Daniels, H., & Hyde, A. (2005). Best Practices: Today’s Standards for Teaching & Learning in America’s Schools (3rd ed.). Portsmouth, NH: Heinemann.

11. Extra Example: • Gabriel worked 16 hours last week. He earned $5 per hour at a local restaurant and $5.50 per hour at a grocery store. If he earned a total of $82, how many hours did he work at the grocery store? # Hours x Wage = Income Restaurant Grocery Store r 5 5.5 5r 16 - r 5.5(16 – r) 5r + 5.5 (16 – r) = 82 Post-Test