Mrs. McKegney wants to tile her kitchen floor. The tiles are 3 inches on each side. The floor is 10' x 15'. How many tiles does she need? The tiles are sold in bundles of 10. Each bundle costs $3.50. How many bundles are needed? How much will she need to pay for the tiles? Write a letter to Mrs. McKegney clearly explaining your solution to her tile problem and how you went about solving the problem. Be sure to include a visual representation of your solution and observations that you made.
This task was given to students as an assessment piece for a measurement unit they had just completed. Students were provided with direct instruction and exploratory pieces, which centered around measurement before tackling this task. A menu approach was provided to students so they would have a choice about which tasks they wanted to solve. This enabled me to provide tasks appropriate for my higher performing students, as well as my special needs students. There is an adapted version on the next page. This task assesses several measurement areas including students' ability to manipulate and solve problems involving measurement and money. It also provides an opportunity for students to practice computation skills in a meaningful context. Most students will begin by finding how many three inch tiles are in a foot and then will find how many feet will be needed in all. Another strategy that a student used was to find the total area needed and then divide by nine (the total area of each tile). Students will then proceed to figuring the total bundles needed and the cost. 3 hours When studying pottery and/or tiles, this task would fit in nicely. Many South American countries are famous for their art of tile making. It is important to provide students with the concepts and skills they will need to solve this task through direct instruction and exploration of concepts. Students need a lot of experience in finding area with many different manipulatives, including tiles. Students should also have experience converting measurements, such as inches to feet. In order to address the diverse needs of my students, I adapted this task in the following way to meet the needs of my challenged students: Terrific Tiles (An Adapted Version) Mrs. McKegney wants to replace the rug in her classroom with tiles. The tiles are 6 inches on each side. The rug is 6' x 9'. How many tiles does she need? The tiles are sold in bundles of 5. Each bundle costs $1. How many bundles are needed? How much will she pay for the tiles? Some students who need this version of the task also may require several other accommodations in order to be successful. For instance, one student in my class worked with an instructional assistant to manipulate 6" x 6" pieces of construction paper on a rug that is located in the classroom. After placing the "tiles" directly on the rug, this student numbered them, as s/he counted them and then put the tiles in piles of five. S/he then counted how many $1 piles s/he had. His/her instructional assistant took dictation of his/her response and s/he created a visual representation of his/her solution on graph paper. For students who would not find the original task challenging, the task could be adapted so that students had to deal with fractional amounts, remainders and differing shapes of the area to be covered.
- Graph paper
- Tiles
- Rulers
- Calculators
2,400 tiles are needed.
240 bundles are needed. Cost of tiles will be $840.
This student was unable to make progress toward a solution. The student attempted to manipulate the numbers presented in the task, but really had no comprehension of the situation.
This student had a novel approach (finding the total area and then dividing the total area by nine, the area of the tiles). This worked for part of the problem, but the student failed to find the number of bundles needed and the total cost. The student's communication is poor; making it difficult to decipher what was done. The student uses math terminology incorrectly several times.
This student had an approach that worked, relying on diagrams to formulate understanding of the mathematical situation. The student was able to find the total number of tiles needed, the total number of bundles and the total cost. The student also attempted to make a mathematically relevant observation. The communication was mostly clear, but the reader must fill in some parts, for instance, how 240 bundles were obtained. Student language was varied and included terms, symbols and notation.
This student immediately recognized that this was an area problem. The student proceeds directly toward a solution by calculating tiles per square foot and correctly applying multiplication and division algorithms. The student used good math language and gives reasons for key decision making.
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