Part C: Performance-Based Assessment Administration The performance task in Part C is designed to provide insight into how well students are able to perform in terms of the categories of the Ontario Achievement Chart: Knowledge and Understanding, Thinking, Communication, and Application. The task supplements the assessment of overall and specific expectations in the Grade 8 Measurement strand and the Grade 8 Geometry strand that relate to the Measurement and Geometry strand in Grade 9 Foundations of Mathematics (Applied) that have been assessed through the Concepts and Skills Assessment in Part B. Tell students that they should provide detailed answers to the problems, including how they solved the problems. Remind students that they may use pictures, numbers, words, diagrams, and/or tables to explain effectively how they solved the problem. Accommodating Students with Special Needs If individual students have difficulties explaining their thinking in writing, consider providing scribes to record for the students. You might provide opportunities to respond orally, or encourage students to show and explain their thinking using concrete materials. Some students may benefit from completing the assessment in a resource room. Scoring the Assessment A generic rubric based on the Ontario Achievement Chart for Mathematics is provided to assist with scoring student responses to the tasks. Spend some time reviewing the anchors and rationales provided for each level of achievement. The four categories should be considered as interrelated, reflecting the wholeness and interconnectedness of learning. Each student s performance should therefore be determined holistically by selecting the level that best describes the student s overall achievement. Sometimes a student will not achieve the same level for each criterion within a category or across categories. For example, a student may perform at Level 3 on Knowledge and Understanding, Thinking, and Application, but at Level 2 on Communication. Although you may determine that, overall, the student performed most consistently at Level 3, you may want to make a note that this student would benefit from additional instruction in the area of Communication. Note: When scoring student work on the performance tasks, it is appropriate to note what you observed and heard while the student worked on the task. After you have completed the scoring, you may record the results electronically using the ONAP 9 Tracking Sheet on the Nelson website, or using the Performance Task Class Tracking Sheet. Next Steps Strategies for improving performance in the four areas of the Achievement Chart are provided in the ONAP Introduction of the print resource, pages 16 to 19. Ontario Numeracy Assessment 1
Performance Task: Part A: Measurement What is the Best Juice Container? and Part B: Geometry Parallel or Not? Materials FOR THE TEACHER FOR EACH STUDENT OPTIONAL MATERIALS Performance Task Class Tracking Sheet Performance Task Rubric Anchors and Rationales ONAP 9 CD-ROM (optional) BLM C1: Performance Task 1: What is the Best Juice Container? Parallel or Not?: pp. 5 10 pencil eraser pencil crayons ruler protractor right cylinder cube right triangular prism Introducing the Task You might read the instructions with the students, or assign the task without discussion. Remind students to ensure that diagrams provide necessary dimensions. For Part A of this task, students apply their measurement skills to show whether a design team s packaging claim for three possible designs are correct. If students need concrete materials to help them visualize the three-dimensional figures, you might make right cylinders, cubes, and right triangular prisms available. For Part B of this task, students are given two optical illusions. Each optical illusion uses intersecting lines to make it appear that lines that are parallel are not. Students use geometry to show that lines which do not seem parallel actually are parallel. Have students use BLM C1: Performance Task: Part A: Measurement What is the Best Juice Container? Part B: Geometry Parallel or Not? to complete this task. Sample Answers 1. Cylinder: r = 6 cm, h = 19 cm V = πr 2 h V =& 31.4 (6 cm) 2 19 cm V =& 2148 cm 3 Cube: l = 13 cm, w = 13 cm, h = 13 cm V = area of base height V = 13 cm 13 cm 13 cm V = 2197 cm 3 Ontario Numeracy Assessment 2
Triangular right prism: triangle: b = 16 cm, h = 14 cm, prism: h = 17 cm V = area of base height V = 2 1 (16 cm)(14 cm) 17 cm V = 1904 cm 3 The cylinder and the cube meet the requirements but the triangular right prism does not. 2. Double the radius If the radius is doubled, r = 2 6 cm, or 12 cm V = πr 2 h V =& 3.14 (12 cm) 2 19 cm V =& 8591 cm 3 If the height is doubled, h = 2 19 cm, or 38 cm V = πr 2 h V =& 3.14 (6 cm) 2 38 cm V =& 4296 cm 3 The design team should double the radius since that would make the volume about 8591 cm 3, instead of 4296 cm 3 as it would be if the height were doubled. Doubling the radius results in about twice the volume as doubling the height. OR They should double the radius. The radius is squared in the formula for the volume of a cylinder but the height is not squared. So doubling the radius means the volume of the larger cylinder is about 4 times the volume of the original cylinder. Doubling the height means the volume of the larger cylinder is about 2 times the volume of the original cylinder. Ontario Numeracy Assessment 3
3. a) I traced two lines that I think are parallel but do not look parallel. I drew a transversal that intersects the two lines. I measured two corresponding angles, 1 and 2. 1 equals 134º and 2 equals 134º. The measures of the corresponding angles are equal, so the lines are parallel. b) I traced two lines that I think are parallel but do not look parallel. I drew a transversal that intersects the two lines that I traced. The measures of two interior angles on the same side of the transversal are 90º and 90º. Since 90º + 90º = 180º, the angles are supplementary. So the lines are parallel. Students may use other strategies to show that lines are parallel. Examples are: Equal alternate angles formed by a transversal Properties of a square Properties of a rectangle Equal distances between lines Ontario Numeracy Assessment 4
MG C-1.1 Name: Date: Performance Task Part A: Measurement What is the Best Juice Container? The Best Juice Company wants to sell orange juice in containers that hold 2 L of juice. The design team is making decisions about the container. The Best Juice Company design team has narrowed the choices to three possible designs a right cylinder a cube a right triangular prism (The base of the right triangular prism would be an equilateral triangle so all three sides are equal.) The design team wants the container to fit the following requirements: The container must hold 2 L of juice. (1 L = 1000 ml) The container will be a right cylinder, a cube, or a right triangular prism. The volume of the container must be less than 2200 cm 3. (1 ml = 1 cm 3 ) Volume of a right cylinder = area of base height, or V = π radius radius height, or V = πr 2 h Volume of a cube = area of base of prism height of prism, or Volume = length width height, or V = lwh, or Volume = side side side, or V = s 3 Volume of a right triangular prism = area of base of prism height of prism, or V = 2 1 base of triangle height of triangle height of prism
MG C-1.2 1. These are the three designs Best Juice has chosen for the containers. Determine whether each design meets the requirements. Design 1: right cylinder
MG C-1.3 Design 2: cube Design 3: right triangular prism
MG C-1.4 2. The design team at Best Juice wants a larger juice container. The container will be a cylinder. The design team will double the height or the radius of this cylinder. Which would result in a larger juice container: doubling the radius or doubling the height? How do you know? Check the change the design team should make to get the larger container. Double the height Double the radius I know the container would be larger because
MG C-1.5 Performance Task Part B: Geometry Parallel or Not? An optical illusion tricks your eyes into seeing an image differently than it really is. Many optical illusions are created using intersecting lines. 3. For each optical illusion: Choose a pair of lines that do not look parallel, but you think are parallel. Use a colour to trace the pair of lines. Show that the lines that you traced are parallel. Use a different strategy for each optical illusion. a) Explain how you know the lines that you traced are parallel.
MG C-1.6 b) Explain how you know the lines that you traced are parallel.