Samples of Evaluating Student Performance

Sample 8..........Grades 5, 6, and 7

Curriculum Organizer: Space and Shape (Measurement) (Transformations)

Learning Outcomes

It is expected that students will:

recognize motion as a slide, flip, or turn (Grade 5)
recognize tessellations created with regular and irregular shapes in the environment (Grade 5)
create, analyse, and describe designs using slides (Grade 5), flips (Grade 6), and turns (Grade 7)
use informal concepts of congruence to describe images of transformations (Grade 7)
connect reflections with lines and planes of symmetry (Grade 7)

Planning for Assessment

In this unit, students performed, analysed, and developed their understanding of transformations. Grade 5 students were expected to describe motion in terms of a slide, flip, or turn, while Grade 6 and 7 students were expected to create and describe linear patterns and tessellation designs that incorporate translations (slides), reflections (flips), and rotations (turns). The concepts of symmetry and congruence were used to help describe the simple motions and combinations of more than one motion. Students studied the graphic works of M.C. Escher to discover the beauty of tessellating patterns in art. They examined tessellation patterns in the environment: wallpaper patterns, flooring patterns, paving stone designs, designs on clothing.

The teacher taught a series of lessons that helped students understand the mathematics underlying tessellationsãwhy particular shapes tessellate a plane with no overlaps or gapsãand showed students how to create their own tessellation patterns. Students used pattern blocks to determine the angle measures of regular polygons. They hypothesized about which shapes would combine to cover the surface, and why they worked. From this exploration, students discovered that, in order to tessellate the plane, the sum of the angles around a given point must add up to 360ƒ. The teacher introduced the terms to describe motion: translation (slide), reflection (flip), and rotation (turn). Students analysed designs to determine which transformations were used to create them. The teacher taught students how to modify regular polygons (squares, rectangles, and equilateral triangles) to create more lifelike shapes, which could then be traced to create a tessellation.

Defining Criteria

The teacher and students developed a rating form to assess and evaluate student performance on the assessment task.

Attitudes

To what extent does the student:

persevere to find a solution
challenge him/herself to try increasingly difficult problems

Mathematical Thinking

To what extent does the student:

create, analyse, and describe designs using slides (Grade 5), flips (Grade 6), and turns (Grade 7)
use concepts of congruence to describe images of transformations (Grade 7)
modify the polygon's shape
create an effective aesthetic design (e.g., use of colour, detail)

Communication

To what extent does the student:

explain to others the modification of the polygon to create a design

Assessing and Evaluating Student Performance

Students were instructed to modify a regular polygon (square, rectangle, or equilateral triangle) to create a lifelike shape. They were also asked to tessellate the plane with their shapes to create a design, and finally to add colour and details to enhance the design.

This assessment task required students to integrate and apply their mathematical knowledge in order to create a new example of a modified polygon and to use it to create an Escher-like pattern. The evaluation was based on the specific criteria listed above. The degree of complexity and the overall effectiveness of the final design were taken into consideration. Students participated in creating a scale of difficulty that would be used for assessment purposes.

Level	Polygon	No. of Sides Modified	Transformations
1	rectangle	2	slide
2	rectangle	4	slide
3	rectangle	2	slide and flip
4	rectangle	4	slide and flip
5	triangle	2	rotation and slide
6	triangle	3	rotation and slide
7	rectangle	4	rotation and slide

Each student submitted a written paragraph that described his/her thinking and the process for creating the design (how the shape was created and which motion was used to tessellate the plane). They also completed self-assessments based on the criteria for attitudes towards mathematics and communication skills. The teacher used the Evaluating Mathematical Development Across Curriculum reference set as an assessment tool to further describe each student's learning and performance.

Evaluation for________________ Date____________

Portfolio	Evidence of work and thinking (4 points)	Student reflection (4 points)	Clarity/neatness (2 Points)	Total points
Practice exercises
Task 1
Task 2
Task 3
Task 4
Word Problem
Cover Letter
			Total points .......________

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Revised: October 20, 1997

BC Ministry of Education