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**__Introduction__** Your task is to design, and price, a water and grain storage facility for a village of 50 families. The facility will store enough grain and water to supply the village for one month. The walls and roof of the facility will be made out of metal sheet that costs $15 per square metre. The facility must be placed on a 23cm thick concrete floor. The concrete costs $630 per cubic metre. You must make every effort to keep the cost as low as possible. You will be assessed on criteria C (Communication in Mathematics) and D (Reflection in Mathematics).

**__ Group Work: RESEARCH __** **// Class time: //** // One double lesson on Monday October 11 and one single lesson on Friday October 15 // **// Checkpoint: //**// Monday October 18 //  1. Size of an average family in your allocated country.  2. Food and water needs for an average family in your country.  3. Political/military/geographical realities of the country.  4. Designs of water and grain storage facilities. // You should collect your research, including sources, on your group’s wikispaces page. Your information must be well organised, not just cut and paste. You must comment on your research and summarise your findings. //

**__ Group Work: DESIGN __** **// Class time: //** // One double lessons on Wednesday October 27 and two single lessons on Friday October 29 and Monday November 1. // **// Checkpoint: //**// Tuesday November 2 //  1. Calculate how much space is needed to store the grain and water.  2. Design your storage spaces. Decide on shape and materials.  It is important that you consider a few options and make an informed decision regarding which one to choose.  3. Calculate the total cost of the building materials.  4. Write your proposal, clearly communicating your process, design and justifications.

**__ Group Work: PRESENTATION __** **// Class time: //** // One double lesson on Tuesday November 2 and one single lesson on Monday November 8. // **// Due: //**// Wednesday November 10. // All four members of the group will present the proposal. Members will be assessed individually on their ability to communicate mathematically. The proposal will be broken down into four parts. The presentation must consist of both audio and visual components. For example your group could present verbally using a slideshow or you could use a poster, a video, a model of your proposal or a combination of all of these. **Part One**: Results of research. Introduction to the task. Calculations for space needed to store grain and water. **Part Two:** Chosen design, dimensions and volume. **Part Three**: Chosen design, Surface Area, Total cost. **Part Four:** Other options – why were they rejected as designs. If there are three members in a group then Part One must be shared equally between the members.

**__ VOCABULARY __** // The following table contains some mathematical terms and representations that you might need to include in your presentation and reflection. // Width Height Radius Area Surface Area Volume Capacity Cost ||= Rectangle Circle Triangle Square Prism Cylinder Sphere Hemisphere Pyrimid Cone ||= metre (m) millimetre (mm) centimetre (cm) square metre (m 2 ) cubic metre (m 3 ) Litre (L) Mega Litre (ML) Giga Litre (GL) gram (g) kilogram (kg) Tonne (T) Dollar ($) ||= Convert Maximise Minimise Approximate Estimate Uncertainty Error Multiply Divide Add Subtract ||
 * = ** Measurements ** ||= ** Shapes ** ||= ** Units ** ||= ** Other ** ||
 * = Length

**__ INDIVIDUAL: REFLECTION __** **// Class time: //** // One double lesson on Friday November 12. // **// Due: //**// Monday November 15. //  a. Is the cost that you came up with in your proposal likely to be the real cost of the project? Why or why not?  b. How do you think the work you have done could benefit a real community?  c. To what degree of accuracy did you give your calculated lengths (nearest metre, centimetre, millimetre, micrometre) surface areas (nearest square metre, centimetre, millimetre, micrometre) volumes (nearest cubic metre, centimetre, millimetre, micrometre OR Litre, millilitre, MegaLitre) and costs (nearest dollar, nearest 100 dollars, nearest $0.01).  d. Why did you use this degree of accuracy? (Consider the effect of measurement uncertainties in building your facility)  e. How would you improve your design and method for determining costs if you were set a similar task again?


 * __ ASSESSMENT CRITERIA __**

Criterion C : Communication in Mathematics Uses some symbols for units (for example m, m2, $) Writes some formulas for Areas/Volumes/Costs etc using symbols. Uses some diagrams. Verbal and/or written work is disjointed and difficult to follow. || Verbal and written work is generally clear, though some links between information may be missing. Symbolic representations are used to represent formulae for areas, volumes, costs etc. Pronumerals are usually defined. Diagrams and pictures are included, clearly labeled and often supported by other work seen. Graphs and Tables (if used) are clearly labeled and explained. || Verbal and written work is easy to follow. Visual prompts and aids are used effectively to enhance the verbal presentation. Symbolic representations are effectively used. Diagrams and pictures, graphs and tables are clearly labeled, relevant and support proposal. || Criterion D: Reflection in mathematics
 * ** Achievement level ** ||  ** Descriptor **  ||  ** Clarifications **  ||
 * 1–2 || <span style="color: #221e1f; font-family: Cambria; font-size: 12pt; line-height: 115%; margin-bottom: 0cm;">The student shows basic use of mathematical language and/or forms of mathematical representation. The lines of reasoning are difficult to follow. || Uses some mathematical language, for example volume, area, metre, square metre.
 * <span style="color: #221e1f; display: block; font-family: Cambria; font-size: 12pt; line-height: 115%; text-align: center;">3–4 || <span style="color: #221e1f; font-family: Cambria; font-size: 12pt; line-height: 115%; margin-bottom: 0cm;">The student shows sufficient use of mathematical language and forms of mathematical representation. The lines of reasoning are clear though not always logical or complete. The student moves between different forms of representation with some success. || Uses mathematical language from the list given. Generally uses these terms appropriately. Units are used for calculated values.
 * <span style="color: #221e1f; display: block; font-family: Cambria; font-size: 12pt; line-height: 115%; text-align: center;">5–6 || <span style="color: #221e1f; font-family: Cambria; font-size: 12pt; line-height: 115%; margin-bottom: 0cm;">The student shows good use of mathematical language and forms of mathematical representation. The lines of reasoning are concise, logical and complete. The student moves effectively between different forms of representation. || Mathematical language and terminology used accurately throughout. Measurements are given using appropriate units (eg 2 ML instead of 2 000 000 L)

The student attempts to describe the importance of his or her findings in connection to real life. || <span style="font-family: Cambria; font-size: 12pt; line-height: normal; margin-bottom: 0cm; margin-left: 12.6pt; margin-right: 0cm; margin-top: 0cm;">Comments on whether cost is likely to be realistic
 * ** Achievement level ** ||  ** Descriptor **  ||  ** Indicator **  ||
 * <span style="color: #221e1f; display: block; font-family: Cambria; font-size: 12pt; line-height: 115%; text-align: center;">1–2 ||  The student attempts to explain whether his or her results make sense in the context of the problem.

<span style="font-family: Cambria; font-size: 12pt; line-height: normal; margin-bottom: 0cm; margin-left: 12.6pt; margin-right: 0cm; margin-top: 0cm;">Comments on use of storage facility by communities. || The student attempts to justify the degree of accuracy of his or her results where appropriate. || <span style="font-family: Cambria; font-size: 12pt; line-height: 115%; margin-bottom: 0cm; margin-left: 3.6pt; margin-right: 0cm; margin-top: 0cm;">Makes brief, valid comments about whether cost is likely to be realistic. <span style="font-family: Cambria; font-size: 12pt; line-height: 115%; margin-bottom: 0cm; margin-left: 3.6pt; margin-right: 0cm; margin-top: 0cm;">Makes brief, valid comments on usefulness of mathematics when designing storage facilities. <span style="font-family: Cambria; font-size: 12pt; line-height: 115%; margin-bottom: 0cm; margin-left: 3.6pt; margin-right: 0cm; margin-top: 0cm;">States degree of accuracy of at least two measurements and explains briefly why that degree of accuracy was chosen. || The student justifies the degree of accuracy of his or her results where appropriate. The student suggests improvements to the method when necessary. || Makes valid and detailed comments regarding whether cost is likely to be realistic, using both mathematical principals and real world factors to justify their answer.
 * <span style="color: #221e1f; display: block; font-family: Cambria; font-size: 12pt; line-height: 115%; text-align: center;">3–4 ||  The student correctly but briefly explains whether his or her results make sense in the context of the problem and describes the importance of his or her findings in connection to real life.
 * <span style="color: #221e1f; display: block; font-family: Cambria; font-size: 12pt; line-height: 115%; text-align: center;">5–6 ||  The student critically explains whether his or her results make sense in the context of the problem and provides a detailed explanation of the importance of his or her findings in connection to real life.

Makes valid and detailed comments regarding the usefulness of mathematics when designing facilities with reference to cost minimisation and volume maximisation. Details the effects that this type of work can have on a community.

Gives correct degree of accuracy for all calculations and explains using measurement uncertainties and other reasons why they have chosen this degree of accuracy.

Makes reasoned and useful suggestions regarding improvements to the design and/or costing process. ||