Assignment Task

Purpose

The purpose of this assessment task is for students to reflect on their mathematics learning through problem-solving tasks undertaken, to demonstrate the development of efficient and effective problem-solving strategies and reflect on their learning. This provides students with the opportunity to demonstrate an understanding of the mathematical content, the use of appropriate technology in problem solving, and of how mathematics is a powerful thinking tool in making sense of the world.

Critical Reflection of mathematics learning

The assessed critical reflection component of your folio will be a personal, critical reflection of your own mathematics journey. The problem solving tasks should provide a stimulus for your reflection and should refer to. Whole Class Tasks, lecture content, readings, weekly task sheets, peer discussions and any further self-directed learning). 

The critical reflection should include (give specific examples):

• what you have learnt about mathematics and your own mathematical understandings
• preconceived ideas you had about mathematics and mathematics learning, prior to this unit, and discuss whether these preconceptions have been challenged, clarified or confirmed
• what you have learnt about the importance of your own understanding of mathematics for meaningful engagement in society
• describe how you will continue your learning
• make links to lecture content, prescribed readings, peer collaborations and/or any further reading, where appropriate, to support your reflection

The reflection is to be Word processed, typed in Times New Roman 12pt or Calibri 11pt, with at least 1.5 line spacing (this makes the assignment easier to read, and written feedback easier to insert). APA referencing is to be observed for both in-text citations and the reference list. Correct referencing is an extremely important part of academic writing (for academic honesty purposes); contact either the library or Academic Skills for help with this if necessary.

Problem Solving

To assist with developing a systematic method of approaching problem solving, George Polya developed a process which breaks down a problem into 4 steps. Each of these steps is described within a mathematical context in chosen references.

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Looking back

Devising a plan requires a toolbox of problem-solving strategies. Depending on your mathematical knowledge and understanding different strategies will be used, with some listed below:

• Visualise
• Look for patterns
• Predict and check for reasonableness
• Formulate conjectures and justify claims
• Create a list, table or chart
• Simplify the problem
• Write an equation
• Work backwards

Attempt all Problems

1. Place each of the digits 1, 2, 5, 7, 8, 9, in a different box to make this multiplication equation true.

2. A farmer went to market to buy different animals, with sheep costing $30, pigs $10 and hens $5. 

• He spent $50 and bought at least one of each animal. How many of each animal did the farmer buy?
• He wants to spend $100 to get exactly ten animals. Suggest three possible solutions.

3. The restaurant bill for 7 friends came to $245.

• Michaela paid the average of all the individual bills.
• Neil paid $8 more than Michaela, but $7 less than Oliver.
• Peta put in $60 but got $6 change.
• Quentin paid half of what Peta paid.
• Robert paid two-thirds of what Quentin paid.
• Sasha paid one third of what Peta paid.

5. Matraville Public School installs an intercom system. All 9 classrooms, a staffroom and the main office are connected to each other room individually (11 rooms in total).

5. A breakfast-food company have a contest. Each breakfast-food carton has a number in it. A prize of $1000 is awarded to anyone who can collect numbers with a sum of 100, made from any number of cards. The following numbers are used.

a. Does Jim have a winning combination using each card only once? Explain why or why not. 

If the company is going to add one more number to the list and so the contest has many more winners, what number would you suggest and why?

6. River valley land is valued more highly than rolling hills in estimating the sale price of a farm. Paula’s farm is a rectangle with an area of 40 square kilometres (40 km ² ). The river valley is shaded.

Points A and B are half-way along the longer boundaries of the farm and point C is half-way between B and the corner. What is the area of river valley land?

7. A wholesaler sells a dress for $80. The store marks it up to $160 – a mark-up of 100%. At the end of the season the dress is still there, so the store marks it down to 50% off. It is now $80 again. How can a 100% mark up and a 50% reduction result in the same amount?

8. The Juicy Company wants you to design a cuboid shaped carton to hold 240 mL of fruit juice. To make production easier the edges of the cuboid should be in whole numbers of centimetres, e.g. 24 cm × 10 cm × 1 cm (not a practical option).

9. Here are the results of NRMA open road tests on three different cars

10. Draw a rectangle in your problem book which represents figure A below. It does not need to be the exact length shown.

11. The ages of 8 teachers in Easter Hills primary school are 24, 33, 42, 40, 36, 40, 35 and 22. Calculate the mean age of the teachers. The school has employed four new teachers for 2018. The ages of these teachers are 51, 55, 49 and 53. Find the mean age for these new teachers. What is the mean age of all twelve teachers?

12. Use the graph below to answer the questions. Clearly explain your thinking.

John’s journey is graphed in RED and Bill’s in GREEN.