MATHEMATICAL LITERACY US 9016: REPRESENT ANALYSE …

Portfolio of Evidence: Project Management NQF 4: SAQA ID 50080

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Project Management - US 9016– Issue 3 – 01-01-2021

MATHEMATICAL LITERACY

US 9016: REPRESENT ANALYSE AND CALCULATE SHAPE AND MOTION IN 2 AND 3 DIMENSIONAL

SPACE IN DIFFERENT CONTEXTS; NQF LEVEL 4, 4 CREDITS

Learner Name: Learner ID #: Learner Student Number:

Formative Assessment

Class Activities

During and after the initial training the learner will be required to complete a number of activities. These activities will be both individual and group activities (class activities formative activities). The activities are numbered and are to be included in the learner’s portfolio of evidence. These activities will measure the progress of the learner through the programme. For authenticity reasons these activities must be handwritten.

Class Activity 1: Estimate or measure quantities

Complete the following in small groups / individually as per the instructions from your facilitator:

9016.1.1 9016.1.2 9016.1.3 9016.1.4

1. When you are working on a project then you would need to know about measuring instruments and computational tools used to measure various items and quantities. What instruments and/or computational tools will you use to measure or calculate the following? Complete the table:

Width of a page

Temperature

To calculate a percentage

2 x 4

Adding 45 numbers


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Time

The floor area of a room

Mass

Distance between two towns

Sugar in a sugar pot

2. The measuring cylinder is used to measure volumes of liquid accurately. What does the following picture show / illustrate?


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3. Estimate the following measurements:

The length of the room you are in now

The distance to the nearest airport

The temperature today

The number of people in your organisation

4. Identify and list at least 3 things that you can do to ensure that your measurements are accurate:

5. What is the difference between Accuracy and Precision?


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Place any extra evidence after this page, clearly marked for easy reference.

Class Activity 2: Select and use appropriate formulae and units in measurement and calculation


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1. If you wanted to carpet the training room you are kitting out as part of your project, what size carpet would you need to buy? Show your calculations (using estimations)

2. If you wanted to tile the training room walls, and each box of tiles= 1,2m², how many boxes would you require? Show your calculations (using estimations)


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3. At a cost of R55 per box, how much would it cost to tile the training room?

4. There are specific situations at home or at work/during a project where one has to be absolutely accurate (correct) in measurement. Name 3 such situations and explain why accuracy is important in each case


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5. Calculate the following (show your calculations):

27% of 333

¾ + (2/5 x 4/7),

One third of 96 plus three quarters of 44 minus 20% of 110

The average of 16, 22, 24, 18 and 21


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6. In what units will you express the following readings/measurements?

Cooldrink in a tin

Distance to the stars

Mass of a packet of sugar

Speed of a bullet

Temperature

Water in a drum

Breadth of a room

Size of a farm

Capacity of a truck

Distance between two towns

7. Write the following in scientific notation:

45 000

0.00000074

304 million

123/10 000 000 000

6000 x 74000000

24 mg + 14.664 g

0.00000006 x 0.000054

8. When you are working on a project then you would need to how to read product specifications. Read the Audi A6 specifications and then answer the questions that follow


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a. Find three examples of specifications regarding volume

b. If the diameter of the Audi’s wheels is 17 inches, calculate the circumference of the wheel


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c. If you travel to Durban from Johannesburg (650 km) in your new Audi A6, how much petrol will you use on average

d. How long will it take you to get to Durban from Johannesburg at an average speed of 120 km/h?


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e. Give the dimensions of the Audi A6 in metres

Length:

Width:

Height:

9. You want to tile the bathroom as part of your building project. The bathroom dimensions are shown below with the shaded area indicating the bath. What is the size of the area that must be tiled?


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10. A rectangular swimming pool is 11, 5 m long and 5 m wide. How many metres of fencing are needed to enclose the pool if you erect the fencing 2m from the edge? Show the sketch and your calculations:

11. At R48.50 a square metre, what is the cost of laying a cement floor in a room that is 6m long and 4 m wide?


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12. You want to share the following recipe with your friends in Britain. Convert the recipe to their relevant units:

Classic Crème Caramel 940 ml milk 375 ml vanilla sugar 5 eggs 4 egg yolks 15 ml vanilla

SERVES 6

Scald the milk and allow to cool 20 minutes. In a saucepan, melt 180 ml of sugar and cook until dark brown, stirring constantly. Take care not to scorch. Pour into a warm mould, covering the bottom and sides. Beat the eggs and egg yolks with the remaining sugar. Slowly whip in the milk and vanilla. Pour into the sugar-lined mould. Place mould in a second pan filled halfway with hot water. Bake for 45 minutes in a 160° oven. Cool, then chill. To serve, invert on to a rimmed serving platter.

Britain (Imperial)

Milk (940 ml)

Vanilla sugar (375 ml)

Vanilla (15 ml)

Oven (160°)

13. How far up on a wall of a building will a 10-meter ladder reach if the foot of the ladder is 1, 25 metres from the wall? Draw the situation and then explain your answer:


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14. Calculate the perimeter (circumference) and area of the following drawing:

20 cm

34 cm

15. Calculate the “external surface” area of a rectangular prism with dimensions: 20 cm, 25


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cm, 40cm

16. Provide the formula for the following measurement calculations:

Perimiter

Area of a square

Area of a Triangle

Area of a Circle

Surface Area of a Cylinder

Volume of a Rectangular Block

Volume of a Right Prism

Volume of a Cylinder

Speed

Acceleration

17. Jeannine has a bag with 3 CDs, 4 marbles, 7 books, and 1 orange.

a. What is the ratio of books to marbles?


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b. What is the ratio of CDs to the total number of items in the bag?

18. A rectangular swimming pool is 11,5 m long, 5 m wide and 3m deep throughout. Calculate its volume

19. Calculate the area of a triangle whose base is 13.9 m. and whose altitude is 7.8m

20. Calculate the area of parallelogram GDEF if the base is 5m and the altitude is 3,2m


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21. How many cubes were needed to build the design in this figure?

3,2m

5m G D


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22. Find the circumference and area of a circle with a diameter of 14 cm

Place any extra evidence after this page, clearly marked for easy reference


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.

Class Activity 3: Describe and represent 3-dimensional objects


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1. When you are working on a project then you would need to know about shapes such as polygons. How many sides do the following polygons have:

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Triangle

2. Are the following shapes symmetrical?


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3. The following is created using hexagons. What is this grouping an example of?

4. The following is a net of a shape / object. Which shape is represented?


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5. Name the following 2- and 3 dimensional shapes / objects:

6. Why do we use a scale in drawings and maps?


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7. When you are working on a project then you would need to know about making and interpreting drawings. Draw a front view of your house in the space below

8. Draw a rough floor plan (use an appropiate scale) for a house with the following rooms:

2 bedrooms; 1 bathroom; 1 kitchen; 1 living room; 1 passage



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Class Activity 4: Analyse relations and base conjectures on investigations of geometrical properties


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1. The following are representations of everyday items1. As a project manager, you often need to simplify things. You need to identify the 3-dimensionsl object / figure that is represented by each of the items – circle your answer in the column:

Christmas tree

cube

cone

rectangular prism

sphere

Trash can

sphere

cone

cylinder

cube

Candle

cube

cylinder

sphere

pyramid

Suitcase

rectangular prism

cube

sphere

pyramid

1 Adapted from: from: http://www.studyzone.org/testprep/math4/e/geometric3d3l.cfm

http://www.studyzone.org/testprep/math4/e/geometric3d3l.cfm


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These presents

cubes

cylinders

rectangular prisms

spheres

This tent

cube

cone

sphere

pyramid

The little boy’s books

cylinders

pyramids

rectangular prisms

cubes

Soccer ball

cylinder

cube

circle

sphere

Tissue box

sphere

rectangular prism

pyramid

cube


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2. Draw a top and side view of the tissue box:

3. Study the map and answer the questions below:

(Remember that, because roads twist and turn, the answers that you get will be estimates rather than accurate figures.)


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a. Describe how you will get from West Gate to the Science Museum.


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b. Approximately how far is it if the scale is 1 cm= 5 km

4. Enter the coordinates of points B, C, D, F and G on the following figure:

5. Study the following map of South Africa depicting the main roads and then answer the questions that follow


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a. Express the scale used in this map as a ratio.


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b. Using your ruler, measure the shortest distance between Johannesburg and Cape Town and express it as kilometres.

c. How far (in kilometres) is Mmabatho from Johannesburg?

6. Identify and list the 5 simple machines that you would use in everyday life:



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Reflection

Individually complete the following:

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The purpose of reflection is for you to consider what you have learnt and how you will use it in the future. Answer the following questions as honestly as you can:

1. After the training programme, I can now (tick):

Measure, estimate, and calculate physical quantities in practical situations relevant to the adult with increasing responsibilities in life or the workplace

Explore analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems in two and three dimensional geometrical situations

2. How would you apply what you have learnt during this skills programme in the workplace?

3. What was the most significant thing you have learnt in this programme?

4. What do you think you still need to learn more about? (Action Plan)

5. What did you enjoy most about the training?

6. If there was something about the training that you could change, what would it be?

Portfolio of Evidence: Project Management NQF 4: SAQA ID 50080 US 7468 US 9016 US 9015

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Facilitator Observation Checklist

The facilitator needs to provide feedback on the participation of each learner in the class:

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The purpose of the facilitator observation checklist is to provide the learner with feedback about his/her participation during the formative class activities and also to highlight the observed strengths and perceived weaknesses that the learner displayed during the workshop and/or learning programme.

The facilitator is required to complete the Facilitator Observation checklist for each learner in his/her Learner Workbook. The learner needs to sign-off the document to confirm that he/she has received the observation feedback.

Learner Name Facilitator Name Date

Class Activity Group /

Individual Completed

Participation Comments on perceived strengths and weaknesses of the learner

1. Estimate or measure quantities

2. Select and use appropriate formulae and units in measurement and calculation

3. Describe and represent 3-dimensional objects

4. Analyse relations and base conjectures on investigations of geometrical properties

5. Reflection Individual

Portfolio of Evidence: Project Management NQF 4: SAQA ID 50080 US 7468 US 9016 US 9015

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Has the learner sufficiently demonstrated application of the following CCFO’s during the facilitated session?

CCFO1:

Identify and solve problems:

Use mathematics to analyse, describe and represent financial situations and to solve problems

based on data, statistics and probability

CCFO2:

Work effectively with others as a member of a team, group or organisation:

when monitoring cost budgets to ensure compliance

CCFO3:

N/A

CCFO4:

Collect, analyse, organise and critically evaluate information:

to plan and make provision for monitoring budgets and other financial situations

to make sense of situations

Yes / No Yes / No Yes / No Yes / No

CCFO5:

Communicate effectively:

regarding elements of the cost budget

to represent data, statistics and probability and effectively communicate or critique conclusions

CCFO6:

N/A

CCFO7:

N/A

CCFO8:

Use mathematics to critically analyse, describe and represent situations and to solve problems related to the life or work situations of the adult with increasing responsibilities

Yes / No Yes / No Yes / No Yes / No

Statement by the facilitator:

The learner has demonstrated sufficient knowledge and skill during class to proceed with the summative assessment (circle)

Yes No

Additional comments: (optional)

Learner Signature Facilitator Signature

Portfolio of Evidence: Project Management NQF 4: SAQA ID 50080 US 9016

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Summative Assessment

Knowledge Questions Please answer the following knowledge questions related to the unit standard embedded knowledge and assessment criteria and place it in your portfolio of evidence. Remember to number the answers according to the question numbers, should you need to attach a document.

You have to complete this Knowledge Questionnaire individually based on the theory that you covered in your Learner Guide and the formative assessments you completed in your Learner Workbook.

Note: The marks shown merely gives you an indication of how much to answer on the question.

Knowledge Questions Individually complete the following:

Unit Standard Reference

1. List any 3 measuring instruments and say what they are used to measure

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(3)

2. How does one ensure accuracy in measurement? 9016.1.2 9016.1.4

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(3)


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3. Explain the difference between mass and weight 9016.1.5

(2)

4. Calculate the perimeter of the rectangle, with sides of 30m and 15m. Show all your calculations

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9016 EEK1 9016 EEK 3

(5)


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5. Write down the formula to calculate the area of a triangle 9016.2.1

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(3)

6. Name the views for the following drawings (side, angled, top): 9016.2.3 9016.2.9

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(3)


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Practical Activities

Individually complete the following activities to show your ability to integrate and apply your knowledge and skills in the workplace.

Practical Activity 1: Mathematical Literacy

Individually complete the following:

9016 Related EEKs

CCFO1-8

You need to show that you can

Represent, analyse and calculate shape and motion in 2-and 3-dimensional space in different contexts

Complete the following in your workplace:

1. Measure, estimate, and calculate physical quantities in practical situations relevant to the adult with increasing responsibilities in life or the workplace. Complete the following tasks and provide evidence to show that you have done the following:

a. You need to demonstrate to your facilitator that you can measure, estimate and calculate physical quantities. Make sure that you demonstrate the following:

Basic instruments to include those readily available such as rulers, measuring tapes, measuring cylinders or jugs, thermometers, spring or kitchen balances, watches and clocks. In situations which necessitate it such as in the workplace, the use of more accurate instruments such as vernier callipers, micrometer screws, stop watches and chemical balances.

Quantities to estimate or measure to include length/distance, area, mass, time, speed acceleration and temperature.

Distinctions between mass and weight, speed and acceleration.

The quantities should range from the low or small to the high or large.

Mass, volume temperature, distance, and speed values are used in practical situations relevant to the young adult or the workplace.

Calculate heights and distances using Pythagoras' theorem.

Calculate surface areas and volumes of right prisms (i.e., end faces are polygons and the remaining faces are rectangles) cylinders, cones and spheres from measurements in practical situations relevant to the adult or in the workplace

b. Submit evidence of all of the above, e.g. photographs, documents showing calculations, etc. to substantiate your demonstration


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c. Request your facilitator to sign off the following observation sheet and provide comments (very important) about your knowledge and skills demonstrated

Learner Name Date

Measure, estimate, and calculate physical quantities in practical situations relevant to the adult with increasing responsibilities in life or the workplace

Did the learner:

Yes/No Comments

1. Read scales on the measuring instruments correctly?

2. Estimate quantities to a tolerance justified in the context of the need?

3. Choose the appropriate instrument to measure a particular quantity?

4. Measure quantities correctly to within the least step of the instrument?


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5. Select and use appropriate formulae?

6. Carry out calculations correctly and take the least steps of instruments used into account when reporting final values?

7. Use symbols and units in accordance with SI conventions and

as appropriate to the situation?

Facilitator Signature

Facilitator Name

2. Explore, analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems in two and three-dimensional geometrical situations. Complete the following tasks and provide evidence to show that you have done the following:

a. You need to demonstrate to your facilitator that you can explore, analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems. Make sure that you demonstrate the following:

Applications taken from different contexts such as packaging, arts, building construction, dressmaking. The operation of simple linkages and mechanisms such as car jacks.

Top, front and side views of objects are represented.

Use rough sketches to interpret, represent and describe situations.

The use of available technology (e.g., isometric paper, drawing instruments, software) to represent objects.

Use and interpret scale drawings of plans (e.g., plans of houses or factories; technical diagrams of simple mechanical household or work related devices).

Road maps relevant to the country.

World maps.

International time zones.

The use of the Cartesian co-ordinate system in determining location and describing relationships in at least two dimensions.


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c. Request your facilitator to sign off the following observation sheet and provide comments (very important) about your knowledge and skills demonstrated

Learner Name Date

Explore, analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems in two and three-dimensional geometrical situations

Did the learner:

Yes/No Comments

1. Base descriptions on a systematic analysis of the shapes and reflect the properties of the shapes accurately, clearly and completely?

2. Ensure that descriptions include quantitative information appropriate to the situation and need?

3. Represent three-dimensional by top, front and side views?

4. Assimilate different views correctly to describe 3-dimensional objects?

5. Use available and appropriate technology in producing and analysing representations?


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6. Analyse relations of distance and positions between objects from different views?

7. Base conjectures as appropriate to the situation, on well-planned investigations of geometrical properties?

8. Ensure that the representations of the problems are consistent with and appropriate to the problem context - the problems are represented comprehensively and in mathematical terms?

9. Achieve results through efficient and correct analysis and manipulation of representations?

10. Present problem-solving methods clearly, logically and in mathematical terms?

11. Ensure that reflections on the chosen problem solving strategy reveal strengths and weaknesses of the strategy?

12. Identify alternative strategies to obtain the solution and compare it in terms of appropriateness and effectiveness?


Facilitator Name

Place your evidence after this page; clearly marked for easy reference.


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Practical Activity Checklist

Please tick that you have submitted the following evidence as per the instructions above:

Learner Name

Date

Practical Activity 1 Submitted

Yes/No

Name of my document / Comments

1. Measure, estimate, and calculate physical quantities in practical situations relevant to the adult with increasing responsibilities in life or the workplace

a. You need to demonstrate to your supervisor / qualified colleague that you can measure, estimate and calculate physical quantities

9016.1


9016.1

c. Request your supervisor / qualified colleague to sign off the observation sheet and provide comments (very important) about your knowledge and skills demonstrated

Signed off observation sheet

9016.1

2. Explore, analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems in two and three-dimensional geometrical situations

a. You need to demonstrate to your supervisor / qualified colleague that you can explore, analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems

9016.2


9016.2

c. Request your supervisor / qualified colleague to sign off the observation sheet and provide comments (very important) about your knowledge and skills demonstrated

Signed off observation sheet

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7. Critique and use techniques for collecting, organising and representing data

Learner Signature


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PERSONAL NARRATIVE

Answer the following questions based on your experience during the completion of this module. Discuss what you did well and what you would like to do differently.

What went well? What would I do differently?

1 I was able to identify and solve problems effectively throughout the various activities

completed in this module.

2 I was able to understand how different workplace activities have an impact on each other.

3 I was able to use new technology effectively in my daily tasks that I carried out.

4 I was able to communicate effectively with my team members and supervisors.

5 I was able to complete all my work in an organized and efficient manner.

6 Additional Comments

Learner Name: Signature

Facilitator Name: Signature

Date


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Witness Testimony

In the workplace, or in simulated classroom activities, you need to show your ability to integrate what you have learnt. This can be measured with the Specific Outcomes and the Critical Cross Field Outcomes of the Unit Standard.

Request your facilitator to complete the following form to show that you are able to integrate your learning into everyday workplace application. It is necessary that the supervisor also provides a short comment on the form:

Learner Name Date

Did the Learner: Yes No

1. Measure, estimate, and calculate physical quantities in practical situations relevant to the adult with increasing responsibilities in life or the workplace?

2. Explore analyse and critique, describe and represent, interpret and justify geometrical relationships and conjectures to solve problems in two and three dimensional geometrical situations?

3. Identify and solve problems in which responses demonstrate that responsible decisions using critical and creative thinking have been made?

4. Work effectively with others when monitoring cost budgets to ensure compliance?

5. Organise and manage oneself and one's activities responsibly and effectively?

6. Collect, analyse, organise and critically evaluate information?

7. Communicate effectively using visual, mathematical and/or language skills in the modes of oral and/or written presentation?

8. Use science and technology effectively and critically, showing responsibility towards the environment and health of others?

9. Demonstrate the world as a set of related systems where the accurate estimation and preparation of cost budgets impacts on the financial success of a project?

10. Be culturally sensitive across a range of social contexts so that all actions and decisions made are acceptable to all stakeholders with broad cultural backgrounds?

Comments about how the learner applied the knowledge and skills in this programme:

Learner Name:

Learner Signature

Date

Facilitator Name:


Date


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PRACTICAL / WORKPLACE LOGBOOK

Complete this individually in your classroom / workplace. This logbook has been included to record all the time spent on learning and preparation for the assessment and other activities related to this programme:

Time spent in class (training)

Time spent completing an activity should be signed off by a facilitator / supervisor, mentor or witness where possible.

Time spent applying the new knowledge and skills

The logbook should show that the learner has spent at least 40 hours in acquiring the required knowledge and skills of this programme:

Learner Name:

Learner ID#:

Course ID: FETC Project Management NQF 4: SAQA ID 50080

Unit Standard ID US 9016: Represent, analyse and calculate shape and motion in 2-and 3-dimensional space in different contexts; NQF Level 4, 4 Credits

SAQA ID Number 9016 Credits 4 Notional Hours 40 Practical Hours

Practical / Workplace Activities Start Date

End Date

Total No of Hours

Sign Off by Facilitator / Supervisor / Manager / Mentor / Witness

Name & Surname

Relationship to Learner

Signature

Represent, analyse and calculate shape and motion in 2-and 3-dimensional space in different contexts

40 Hours

Activities Completed:

Classroom Training

Demonstrate to a colleague how to read scales on the measuring instruments correctly


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Explain to your supervisor how to estimate quantities to a tolerance justified in the context of the need while reading the above instruments.

Choose the appropriate instrument to measure a particular quantity

Demonstrate to a colleague how to measure quantities correctly to within the least step of the instrument

Select and use appropriate formulae

Carry out calculations correctly and take the least steps of instruments used into account when reporting final values

Use symbols and units in accordance with SI conventions and as appropriate to the situation

Show the properties of the shapes accurately, clearly and completely

Base written descriptions on a systematic analysis of the shapes

Include quantitative information appropriate to the situation and need in your descriptions

Represent 3-dimensional objects by top, front and side views

Adjust different views correctly to describe 3-dimensional objects

Produce and analyse representations, using available and appropriate technology

Do a written analysis on relations of distance and positions between objects from different views

Base written conjectures as appropriate to the situation, on well-planned investigations of geometrical properties

Confirm with your supervisor that the problems are represented comprehensively and in mathematical terms

Analyse and manipulate representations correctly to achieve


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results

Other related workplace activities:

FEEDBACK SECTION

Comments from Facilitator:

Comments from Student:


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Assessment Activities Checklist The learner needs to complete all the required activities that are guided by the Specific Outcomes and Assessment criteria of the Unit Standard(s) in this programme:

Programme LP3: Mathematical Literacy

Unit Standards US 9016: Represent, analyse and calculate shape and motion in 2-and 3-dimensional space in different contexts; NQF Level 4, 4 Credits

Once you have completed all the assessment activities, request your supervisor to check that you have completed all the required activities and that they have all been placed in your Portfolio of Evidence, in the following order:

Did the learner provide the required evidence:

Reference: Comments / Feedback Yes No

Formative – Class Activities

Class Activity 1

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Class Activity 2

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Class Activity 3

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Class Activity 4

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Reflection 9016

Facilitator Observation Checklist

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Summative - Knowledge Questions

Question 1 9016.1.1 9016.1.3

Question 2

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Did the learner provide the required evidence:

Reference: Comments / Feedback Yes No

Question 3 9016.1.5

Question 4

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Question 5 9016.2.1

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Question 6

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Summative – Practical Activities

Practical Activity

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CCFO1-8

As per the Practical Activity 1 Checklist:

Summative – Witness Testimony

Witness Testimony 9016

Summative – Logbook

Logbook 9016

Learner Name:

Learner Signature

Date

Facilitator Name:


Date


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FOR STUDENT This is to verify that the above work is my own / authentic. Learner Name: ___________________________Learner Student No:___________________ Learner Signature: ________________________ Date: _____________________________ FOR FACILITATOR File Checked:

This is to verify that the learner has completed all the above and is awaiting final assessment / moderation. Facilitator Name:__________________________ Facilitator Signature________________________Date:______________________________

Date Facilitator Signature

MATHEMATICAL LITERACY US 9016: REPRESENT ANALYSE …

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