Student Name Date: Tuesday 28 March 2017 Teacher Mathematics Assessment Item Year 9 – Assignment Topics Guidelines RESULTS Criteria Communication and justification Knowledge and procedures Modelling and problem solving Grade 7-9 MATHS Criterion Standard A Q Standard B Q Standard C Q Standard D Q Standard E Q Knowledge and procedures Connection and description of mathematical concepts and relationships# in a range of situations, including some that are complex unfamiliar C1 Connection and description of mathematical concepts and relationships in complex familiar or simple unfamiliar situations A3a* Recognition and identification of mathematical concepts and relationships in simple familiar situations A2a A2b Some identification of simple mathematical concepts Statements about obvious mathematical concepts Recall and use of facts, definitions, technologies and procedures to find solutions# in a range of situations including some that are complex unfamiliar B2* Recall and use of facts, definitions, technologies and procedures to find solutions in complex familiar or simple unfamiliar situations Recall and use of facts, definitions, technologies and procedures to find solutions in simple familiar situations B3b Some recall and use of facts, definitions, technologies and simple procedures Partial recall of facts, definitions or simple procedures Criterion Standard A Q Standard B Q Standard C Q Standard D Q Standard E Q Modelling and problem solving Systematic application of problem-solving approaches# to investigate a range of situations, including some that are complex unfamiliar B3a* Application of problem-solving approaches to investigate complex familiar or simple unfamiliar situations A3b B5 C2 Application of problem-solving approaches to investigate simple familiar situations B4 Some selection and application of problem-solving approaches in simple-familiar situations. Partial selection of problem-solving approaches Development of mathematical models and representations in a range of situations, including some that are complex unfamiliar B1* Development of mathematical models and representations in complex familiar or simple unfamiliar situations Development of mathematical models and representations in simple familiar situations Statements about simple mathematical models and representations A1 Isolated statements about given mathematical models and representations Criterion Standard A Standard B Standard C Standard D Standard E Communication and justification Effective and clear use of appropriate mathematical terminology, diagrams, conventions and symbols Consistent use of appropriate mathematical terminology, diagrams, conventions and symbols Satisfactory use of appropriate mathematical terminology, diagrams, conventions and symbols Use of aspects of mathematical terminology, diagrams and symbols Use of everyday language Clear explanation of mathematical thinking and reasoning#, including logical justification of choices made, evaluation of strategies used and conclusions reached, Explanation of mathematical thinking and reasoning, including reasons for choices made, strategies used and conclusions reached Description of mathematical thinking and reasoning, including discussion of choices made, strategies used and conclusions reached Statements about choices made, strategies used and conclusions reached Isolated statements about given strategies or conclusions * Standard awarded depends on the complexity of the design. Declaration: In preparing this assessment, it is assumed you will use your own notes and any books – all referenced as per the referencing guide in your diary. It is your responsibility to keep a file copy of this assessment. • I declare that this assessment is my own work. • No part of this assessment was written by another person, nor was any part copied from another person either by hand or electronically. • Any advice given to me by a parent, tutor or other person was of a general nature only, and the solutions shown are my own solutions. • In the event of any question regarding my ownership or authenticity of this assessment, I can explain clearly the process by which I obtained the solutions. Signed: _____________________________ Date: ________________________ BRIEF Bill and Susan live up on Mount Tamborine. They are looking to do some renovations to their property, redesigning their backyard with a garden and a pool. Bill and Susan's backyard would benefit from a small attractive garden, as so far their backyard is just lawn, with no other features. Hence, their first task is to put together a garden design. When designing a pool, Bill and Susan will have to consider their water supply. People living on the mountain have water tanks. Rain falls on the surface of the roof, flows into the gutters and from there into pipes that lead into the water tanks. At times, when insufficient rain falls, the mountain people have to order water that is delivered by water trucks and pumped into the tanks. PART A The following diagram shows some approximate dimensions of their backyard. This diagram is NOT drawn to scale. 1. Design a garden to go in Bill and Susan's backyard. Sketch your garden design with clearly labelled dimensions on the diagram of the backyard provided on page 7. You will need to consider how the garden from Part A will fit in the backyard with your chosen pool design for Part B. 2. Bill and Susan find out from a landscaping company that they need to order one cubic metre of mulch per 12m2 of garden area. The company will deliver in multiples of half a cubic metre of mulch. a. What is the area of your garden? b. How many cubic metres of mulch will they need to order? Show full working and justify your answer. 3. Bill and Susan want to put in a wooden border around the garden edges. The wood edging they are buying from the landscaping company is sold in 5m rolls. a. Determine how many rolls they need to buy, giving mathematical justification for your answer. b. State any assumptions made. PART B 1. Design a small but reasonably sized pool for Bill and Susan. There needs to be a deep end and a shallow end. Draw two sketches of the pool, showing all dimensions. The bird's eye view must be drawn onto the provided diagram of the backyard on page 7 along with the garden from Part A, and you must also provide a separate sketch of the cross-section of the pool. 2. Bill and Susan will be tiling the inner walls of the pool. Calculate the surface area they need to tile. 3. a. Calculate the volume of water that would fill the pool. b. Determine the capacity of the pool and justify the units used. 4. Bill and Susan will not fill the pool from their tank but will have to get the water truck to fill their pool. The water truck can pump water into the pool at a flow rate of 890 L/min. How long it would take to fill the pool to the brim? Express your answer in appropriate units. 5. State any assumptions made and any limitations to your solutions to Part B. PART C The roof of Bill and Susan's house has a surface area of m2. They have a cylindrical water tank with a diameter of 4180 mm and a height of 3050 mm. As a guide to collection capacity, consider that each 1 mm of rain = 1 Litre (L) of water per square metres (m2) of roof area, then allow 15% wastage factor. (Water sometimes gushes over the side of the gutters if Bill does not clean the gutters). 1. Use the information above to determine the height the water in their tank will rise by, if they receive 30mm of rain in a particular day. 2. State any assumptions made and any limitations to your solutions to part C. Sketch your garden design in Part A Question 1 and pool design in Part 2 Question 1