Assessment for learning activity Stage 4 or 5 (linked to the Mathematics and steel rolling unit) Activity name: Mathematics and steel rolling Context This assessment activity is embedded in the Stage 4 or 5 enrichment unit Mathematics and steel rolling Students have been engaged in learning relating to the use of Pythagoras theorem and the circumference of a circle to calculate the length of steel (both sheet steel and steel plate) required to roll cylinders, bends and conical pieces (frustums) to specified dimensions. Description of activity The class is divided into groups of 3 5 students. Students work in their groups to complete the tasks contained in the document Mathematics and steel rolling assessment. (included below) Each student is to submit their individual answers to tasks 1 to 9. (i.e. you may work together as a group to solve the questions, but you must then write up your own solution). The group is to submit a video recording of their calculations of the dimensions and the marking out of the steel plate as specified in task 10. Use of digital technologies Digital technologies appropriate for use in the preparation of the solutions and recording of the video include: a spreadsheet application (such as Excel) (optional) a word processor application which facilitates the use of mathematical synbols (such as Equation Editor or MathType in Word) hardware (video camera or tablet computer or mobile phone) to record video and save in an appropriate file format. Areas for assessment Working Mathematically: Communicating, Problem Solving, Reasoning Stage 4 Measurement and Geometry: Pythagoras, circles, similar triangles Outcomes MA4-1WM communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-2WM applies appropriate mathematical techniques to solve problems MA4-3WM recognises and explains mathematical relationships using reasoning MA5.1-1WM uses appropriate terminology, diagrams and symbols in mathematical contexts MA5.1-2WM selects and uses appropriate strategies to solve problems MA5.2-2WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems MA4-12MG calculates the circumferences of circles and the lengths of arcs MA4-16MG applies Pythagoras theorem to calculate side lengths in right-angled triangles, and solves related problems MA5.1-10MG applies trigonometry, given diagrams, to solve problems, including problems involving 1
angles of elevation and depression MA5.2-13MG applies trigonometry to solve problems, including problems involving bearings MA5.1-11MG describes and applies the properties of similar figures and scale drawings Criteria for assessing learning Students will be assessed on their ability to: interpret the information given choose and apply the appropriate mathematical reasoning and processes accurately perform the calculations communicate the results in a way that explicitly answers the question work in and contribute to a group situation (as a group), produce a video which explains the solution and shows the marking out of an imagined steel plate. 2
Feedback Teacher feedback will be provided orally in relation to the criteria, including at these key intervals in the development of the response: preparation of solutions to tasks 1-9 preparation and recording of video for task 10. At the completion of the activity, teacher feedback in relation to the criteria will be provided in written form. Peer- and self-assessment in relation to the way in which each member of the group participated in the various processes required can be provided in written form using a feedback form. Students consider the feedback from their teacher, peers and themselves to determine the steps that they will take to improve: their knowledge, skills and understanding in the aspects of content identified as relative weaknesses the effectiveness of group situations. Sample feedback forms are provided on the following pages. 3
Sample teacher feedback form* Calculating dimensions for steel rolling Use of spreadsheet The student: cylinder made from steel sheet N/A conical frustum made from steel sheet The student: Creates a spreadsheet which calculates the length to roll a cylinder from sheet steel Creates a spreadsheet which calculates the length to roll a conical frustum from sheet steel cylinder made from steel plate bend made from steel plate conical frustum made from steel plate Creates a spreadsheet which calculates the length to roll a cylinder from steel plate Creates a spreadsheet which calculates the length to roll a conical frustum from steel plate 4
Video recording The group: Records a presentation which shows how to calculate the dimensions of the steel plate to make a conical frustum Records a presentation which shows how to mark out the steel plate to make a conical frustum * Teachers identify (circle statement, tick within cell) each of the feedback statements in the table that apply for components of the activity completed by the student individually or as a team member. If desired, teachers could assign one or more marks to each of the feedback statements identified. 5
Sample self-assessment form for learning of the content I know what these are/look like: Not at all Sometimes Often Always cylinder, cone, frustum I can: Not at all Sometimes Often Always calculate the length of steel (sheet or plate) required to make a cylinder calculate the dimensions of steel (sheet or plate) required to make a conical frustum calculate the length of steel plate required to make a bend use a spreadsheet to make a dimensions calculator for cylinders rolled from steel use a spreadsheet to make a dimensions calculator for conical pieces rolled from steel 6
Sample peer- and self-assessment form for participation in the team The team member/i: Never Sometimes Often Always participated constructively in the activity listened carefully to the ideas of others provided helpful feedback to keep the team on task when needed contributed equally to the team s work completed assigned tasks on time treated others in the team with respect 7
Mathematics and steel rolling assessment task You are to work in groups to complete this assessment, but you must hand in individual answers to questions 1 to 9. Submit a group response to question 10. 1. What are the dimensions of sheet steel needed to make a cylindrical tank of height 1200 mm and diameter 800 mm? 2. What are the dimensions of 50 mm plate steel needed to make a cylinder of height 1200 mm and diameter 800 mm? 3. Use the dimensions given on the picture to find the length of steel plate required to make one of these structural supports. 90 0 bend at 100 mm radius 200 mm 50 mm 900 mm 90 0 bend at 300 mm radius 50 0 bend at 100 mm radius 1200 mm 1000 mm 8
4. Find the dimensions of the shape that has to be rolled to make the curved surface of this waste bin. 250 mm 180mm 170 mm 5. Find the dimensions of the shape that has to be rolled to make a conical frustum of height 600 mm, diameters of 700 mm and 300 mm. The piece is to be made from 40 mm steel plate. 6. Make a suitably formatted spreadsheet which takes in the height and radius of a cylinder, then displays the dimensions of sheet steel needed. 7. Make a suitably formatted spreadsheet which takes in the height, external diameter and wall thickness of a cylinder, then displays the dimensions of steel plate needed. 8. Make a suitably formatted spreadsheet which takes in the height and top and bottom radius of a frustum of a cone, then displays the dimensions of sheet steel required. 9. Make a suitably formatted spreadsheet which takes in the height, wall thickness, top and bottom radius of a frustum of a cone, then displays the dimensions of steel plate required. 10. A conical frustum is to be made from 60 mm steel plate. The frustum is to be 1200 mm high, and have diameters of 800 mm and 700 mm. Record a video (just use ipad or mobile phone to record) in which your group: (a) explains how to calculate the dimensions (b) shows how to mark out the figure to cut and roll to make the frustum (use chalk to mark out on a suitable hard outdoor surface). The video should be no longer than 5 minutes in duration. 9