Emma thought of a math challenge for her classmates to solve. Then Emma asked her classmates the following question:

Transcription

1 Emma thought of a math challenge for her classmates to solve. She gave them the following directions: Draw a square on your paper. Draw in the lines of symmetry. Then Emma asked her classmates the following question: If the square is worth $24.00, what are the fair values of at least 2 shapes you discover in your square? 1 of 11

2 Suggested Grade Span 3 5 Grade(s) in Which Task Was Piloted 3 and 4 Task Emma thought of a math challenge for her classmates to solve. She gave them the following directions: Draw a square on your paper. Draw in the lines of symmetry. Then Emma asked her classmates the following question: If the square is worth $24.00, what are the fair values of at least 2 shapes you discover in your square? Alternative Versions of Task More Accessible Version: Emma thought of a math challenge for her classmates to solve. She gave them the following directions: Draw a square on your paper. Draw in the lines of symmetry. Then Emma asked her classmates the following question: If the square is worth $8.00, what are the fair values of at least 2 shapes you discover in your square? 2 of 11

3 More Challenging Version: Emma thought of a math challenge for her classmates to solve. She gave them the following directions: Draw a square on your paper. Draw in the lines of symmetry. Then Emma asked her classmates the following question: If the square is worth $24.00, what are the fair values of at least 3 shapes you discover in your square? What fractional part of the whole square is each of your 3 or more shapes? NCTM Content Standards and Evidence Geometry Standard for Grades 3 5: Instructional programs from pre-kindergarten through grade 12 should enable students to... Apply transformation and use symmetry to analyze mathematical situations. NCTM Evidence: Identify and describe line and rotational symmetry in two- and threedimensional shapes and designs. Exemplars Task-Specific Evidence: This task requires students to find and draw all the lines of symmetry of a square. Number and Operations Standard for Grades 3 5: Instructional programs from prekindergarten through grade 12 should enable students to... Compute fluently and make reasonable estimates. NCTM Evidence: Develop fluency in adding, subtracting, multiplying and dividing whole numbers. Exemplars Task-Specific Evidence: This task requires students to find the worth of a fraction of a square by dividing $24.00 into equal parts. Time/Context/Qualifiers/Tip(s) From Piloting Teacher This is a short- to medium-length task done in one class period. Students need to be familiar with finding lines of symmetry. Students should have pattern blocks available to use with this task. 3 of 11

4 Links This task may be used along with an art lesson on what makes a picture pleasing to the eye. Common Strategies Used to Solve This Task Most students drew a square and were able to draw some or all the lines of symmetry. The students found the second part of the task more challenging. In trying to find the worth of the shapes in their squares, some students had difficulty coming up with a strategy that would get them started. Possible Solutions The square has four lines of symmetry. The worth of the shapes inside the square will vary depending on the shapes students choose; however, each of the triangles formed by the lines of symmetry is worth $24.00/8 = $3.00. More Accessible Version Solution: The square has four lines of symmetry. The worth of the shapes inside the square will vary depending on the shapes students choose; however, each of the triangles formed by the lines of symmetry is worth $8.00/8 = $1.00. More Challenging Version Solution: The square has four lines of symmetry. The worth of the shapes inside the square will vary depending on the shapes students choose; however, each of the triangles formed by the lines of symmetry is worth $24.00/8 = $3.00. The fractional part of the whole square that each shape represents also depends on what shapes they choose; however, each triangle formed by the lines of symmetry is one-eighth of the whole square. Task-Specific Assessment Notes General Notes Students need to know the definition of lines of symmetry and have some experience finding lines of symmetry. Novice The Novice may or may not draw a square. The student will not be able to find all the lines of symmetry. The Novice will not be able to engage in the second part of the task, finding the value of shapes in the square. Apprentice The Apprentice will be able to find a solution to one of the two parts of the task. The student will be able to find all the lines of symmetry of the square but will not be able to determine the worth 4 of 11

5 of shapes inside the square. The students may understand parts of the task but will not be able to come to a complete solution. Practitioner The Practitioner will be able to find all the lines of symmetry and will be able to find the worth of at least two shapes in the square. Evidence of a strategy and reasons for the solutions will be communicated through a methodical, organized, coherent, sequenced and labeled response. Expert The Expert will have a complete solution. Evidence of analyzing the situation in mathematical terms and of extending prior knowledge will be present. The student may discuss the shapes in the square using fractions or percents. The Expert may solve the problem with another, more complicated, shape. 5 of 11

6 Novice 6 of 11

7 Apprentice 7 of 11

8 Practitioner 8 of 11

9 Practitioner 9 of 11

10 Expert 10 of 11

11 Expert 11 of 11