FACULTY OF EDUCATION AND ARTS

FACULTY OF EDUCATION AND ARTS

National School of EducationSEMESTER 1, 2023

EDMA163: Exploring Mathematics and Numeracy

Problem-Solving Folio Questions

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ASSESSMENT TASK 2: Problem Solving Folio

Assessment Task 2 is a problem solving folio which enables you to demonstrate your understanding and learning of the mathematical content within this unit. You will be provided with a series of problems to solve which draw on your learnings from but not limited to lectures, readings, tutorial content, whole class tasks, task sheets from this unit.

Due date: 14 May 2023 by 11:59pm Weighting:40%Length and/or format:The folio will consist of fully worked and annotated problems and critical reflection on personal mathematics learning. (Equivalent to 1200 words)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. How to submit:Problem-solving tasks - scanned copy of handwritten worked solutions uploaded to LEO; Critical reflection word processed and submitted via LEO.

Marking Rubric will be made available on LEO.

Problem Solutions

For the submitted part of this component of your folio you will present full written and annotated solutions to the problems. You will both solve the problems and explain and justify your problem-solving process and mathematical thinking and reasoning (NB. much of the focus of this unit is learning how to do this).

You need to convince the audience that your solution is correct, or at least reasonable. You can demonstrate this by including evidence of:

Your interpretation of the problem (including any assumptions you may have made);

Where you chose to start, and why;

Which strategy you adopted to get started, and why (e.g., drew a diagram, acted it out, used concrete materials, etc);

Your mathematical reasoning throughout the solution process (e.g., did your initial strategy work, or did you need to change direction? how did you know to what to do next? etc.);

Any difficulties you encountered, and how you overcame these (e.g., collaboration with others, looked up similar problems online, etc.).

You may also discuss how you explored the mathematics further, for further clarification and/or for further extension of your own mathematical knowledge and understanding.

Critical Reflection of mathematics learning (500 words)

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.

Understand the problem

Devise a plan

Carry out the plan

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

For more information go to your Reading List (in the Information and resources tile) and look for the following in the References section:

Melvin. (n.d.).Polyas Problem Solving Techniques. University of California Berkeley. https://math.berkeley.edu/~gmelvin/polya.pdf

Walle, J. V. D., Karp, K., & Bay-Williams, J. (2017).Elementary and middle school mathematics. P.Ed Custom Books. (available as ebook read pages 57 59)

Attempt all Problems

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

6 3 = 0 4

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.

The restaurant bill for 7 friends came to $245.

Work out how much each person paid.

Michaela $

Neil $

Oliver $

Peta $

Quentin $

Robert $

Sasha $

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.

38563551460500Matraville 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).How many connections are there?

-1270000A 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.31215182733455166758490

Jim buys enough cartons and trades with friends so he has one of each number.

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?

-558804254500 River valley land is valued more highly than rolling hills in estimating the sale price of a farm. Paulas farm is a rectangle with an area of 40 square kilometres (40 km2). 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?

A

B

C

A

B

C

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?

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).What cuboids are possible?

(Hint: 1 mL = 1 cm3)

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

Canary travels 243 km on 14 litres of petrol

Brit travels 315 kilometres on 17 litres

VeeDub travels 220 km on 12 litres

Which car had the best fuel economy?

How far would you expect Canary to travel on 7 litres of petrol?

You drive Veedub for 100 kilometres. How much petrol do you expect to use?

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

131889549530A

400000A

In responding to this question remember your focus is on trying to demonstrate and develop fractional thinking. Explain your thinking when answering each question.

If figure A is one-quarter of a bar B, show bar B.

If figure A is five-fourths of a bar C, show bar C.

If figure A is two-thirds of bar D, show bar D.

If figure A is one and half the length of a bar E, show bar E.

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?

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

Johns journey is graphed in RED and Bills in GREEN.

2413016764000 Who travelled fastest in the first hour?

When are Bill and John the same distance from A?

When is John stationary?

What distance did John travel in the first 5 hours?

302704513525500The spinner on the right is spun. Find the probabilities of obtaining each of the following events:

A: the number is a factor of 35

B: the number is a multiple of 2

C: the number is a prime number

D: the number is a square number

E: the number is more than 5

191389053086000The staircase show is made from squares. It is 3 steps high. How many squares will be needed to make a staircase that is 6 steps high, 10 steps high, 55 steps high, a staircase of any height? [Hint: Be systematic]

A large bowl of punch is made with the following ingredients:

32 cups of lemonade

24 cups of apple juice

16 cups of orange and mango juiceHow many cups of each ingredient would you use to make a smaller bowl of punch that has exactly the same flavour as the large bowl?

Farmer Jim plants apple trees in a square pattern. To protect the apple trees against wind, he plants conifers or pine trees all around the orchard. The diagram shows the pattern of plantings for any number of rows (n) of apple trees. How many apple and conifers or pine trees are needed for n = 5?