Sample work Mathematics Standard 1 Year 12: planning to build a house
In this task, students use scale drawings to calculate measurements for building a house and apply financial concepts to determine costs. See how examples have been graded, including the intended outcomes and criteria for the assessment.
Nature of the task
This task involves the use of mathematical processes to solve a real world problem. Students use scale drawings to calculate measurements related to building a house and apply financial mathematics concepts to determine the costs involved.
Context
Students have engaged in learning for the subtopics, Measurement and Investment. They have participated in activities to solve problems related to two-dimensional and three-dimensional models and representations and have worked with a variety of rates and ratios. They have developed knowledge of financial mathematics to analyse different financial situations, to calculate the best options for given circumstances, and to solve financial problems.
Outcomes assessed
MS1-12-3 interprets the results of measurements and calculations and makes judgements about their reasonableness
MS1-12-4 analyses simple two-dimensional and three-dimensional models to solve practical problems
MS1-12-5 makes informed decisions about financial situations likely to be encountered post-school
MS1-12-9 chooses and uses appropriate technology effectively and recognises appropriate times for such use
MS1-12-10 uses mathematical argument and reasoning to evaluate conclusions, communicating a position clearly to others
Criteria for assessment
Students will be assessed on their ability to:
- solve problems based on a scenario
- select and use appropriate mathematical processes and language to investigate problems
- provide reasoning and justification for conclusions.
Scenario
Amanda is building a house on a block of land. She has a number of questions that need resolving.
Use the plans and elevation provided to assist you in answering the questions.
- Amanda needs to know the height of the tree on the block of land to ensure that it will not interfere with power lines. The tree casts a shadow 4.74 m long. At the same time, a one metre ruler casts a shadow 0.95 m long.
- Draw a labelled diagram using all of the above information.
- What is the height of the tree?
- If the power lines are 4.5 metres above ground level, discuss whether this will be an issue for Amanda?
- Amanda has been given two elevations of the house but needs to determine if they are the south, north, west or east elevations. Use the plans and elevations to identify Elevation A and Elevation B.
- Amanda wants to place floorboards in the study but needs more information.
- Calculate the actual dimensions of the study
- Use your answer from part a) to calculate the floor area of the study
- To allow for wastage when laying the floorboards, 10% additional materials are required. How many square metres of flooring, to the nearest square metre, does Amanda require?
- If the cost of the floorboards is $65 per square metre, how much will the floorboards for the study cost Amanda?
Amanda received an inheritance of $200 000 and invested this at 4% per annum compounded quarterly for 10 years. The construction cost of the house will be $340 000. Will Amanda have enough money to build her dream home? Justify your answer with calculations.
6. Amanda has made a few changes to the plan and will need $350 000. What amount would need to have been invested 10 years ago at an interest rate of 4% p.a. compounded quarterly to cover this build?
Scale 1 : 150
Elevation A
Elevation B
Graded student work samples
This is a sample of work relevant to Mathematics Standard 1 Stage 6 (2017).
Alex
Commentary
This response demonstrates accuracy in reading and interpreting diagrams, including the use of scale, and in performing relevant calculations. Appropriate formulae have been selected and used to solve a problem in financial mathematics. Thorough and correct reasoning has been used to construct mathematical arguments and justify responses. This response demonstrates characteristics of work typically produced by a student performing at grade A standard at the end of the course.
Sam
Commentary
This response demonstrates skills in applying a given formula to solve a financial mathematics problem but simple errors in the calculation of area and percentage increase have been made. Correct diagrams and scale calculations have been used but the elevations are incorrect. Reasoning has been applied to explain why the tree is too tall and the amount of money is insufficient. The future value has been correctly identified but the present value calculation is incorrect. This response demonstrates characteristics of work typically produced by a student performing at grade B standard at the end of the course.
Sasha
Commentary
This response demonstrates some understanding of ratios and basic area, and elementary skills in substituting into a formula. One step in a mathematical process has been identified, but responses to other questions are incorrect or missing. Incorrect measurement units have been used, and there is no evidence of the ability to correctly interpret elevations. This response demonstrates characteristics of work typically produced by a student performing at grade E standard at the end of the course.