Measure, estimate aand calculate - Home Page- … Guide Primary Agriculture Measure, estimate aand calculate NQF Level: 2 US No: 12444 The availability of this product is due to the

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NQF Level: 2 US No: 12444

The availability of this product is due to the financial support of the National Department of Agriculture and the AgriSETA.

Assessor: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Workplace / Company: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Commodity: . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . . . . .

Measure, Estimate and Calculate Physical quantities, and Explore, Describe and Represent geometrical relationships in 2-dimensions, in different life or workplace

contexts.

Primary Agriculture NQF Level 2 Unit Standard No: 12444 22

Version: 01 Version Date: July 2006

BBeeffoorree wwee ssttaarrtt…… his assessment guide contains all necessary activities and instructions that will enable the assessor and

learner to gather evidence of the learner’s competence as required by the unit standard. This guide was designed to be used by a trained and accredited assessor whom is registered to assess this specific unit standard as per the requirements of the AgriSETA ETQA.

Prior to the delivery of the program the facilitator and assessor must familiarise themselves with content of this guide, as well as the content of the relevant Learner Workbook.

The assessor, facilitator and learner must plan the assessment process together, in order to offer the learner the maximum support, and the opportunity to reflect competence.

The policies and procedures that are required during the application of this assessment are available on the website of the AgriSETA and should be strictly adhered to. The assessor must familiarise him/herself with this document before proceeding.

This guide provides step-by-step instructions for the assessment process of:

This unit standard is one of the building blocks in the qualification listed below. Please mark the qualification you are currently assessing, because that will be determined by the context of application:

Title ID Number NQF Level Credits Mark

National Certificate in Animal Production 48976 2 120

National Certificate in Mixed Farming Systems 48977 2 120

National Certificate in Plant Production 48975 2 120

Please mark the learning program you are enrolled in:

Are you enrolled in a: Y N

Learnership?

Skills Program?

Short Course?

TT

Title:Measure, Estimate and Calculate Physical quantities, and Explore, Describe and Represent geometrical relationships in 2-dimensions, in different life or workplace contexts.

US No: 12444 NQF Level: 2 Credits: 3

PPlleeaassee NNoottee::

This Unit Standard 12444 Assessment Guide must be read in conjunction with the generic Assessor Guide as prescribed and published by the AgriSETA.

NNoottee ttoo AAsssseessssoorr::

If you are assessing this module as part of a full qualification or learnership, please ensure that you have familiarized yourself with the


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1. Write down the measurement in millimeters, centimeters and meters of the following lines:

Model Answer(s): a. 113mm, 11,3cm, 0,113m b. 54mm, 5,4cm, 0,054m c. 75mm, 7,5cm 0,075m d. 144mm, 14,4cm, 0,144m e. 54mm, 5,4cm, 0,054m

2. Draw straight lines in your workbook that are of the following lengths:

Model Answer(s): a) 150mm b) 0,025m c) 8,75cm d) 0,00019km e) 4mm The assessor must determine the accuracy of the drawings by measuring with a ruler

3. Convert the following units from SI to Imperial:

Model Answer(s): a)34cm to inches 34x0,3937 = 13,3858 inches b) 22 litres to gallons 22x0,22=4,84gallons c)70 kilometres to miles 70x0,6214=43,498miles d)78 kilograms to pounds 78x2,205=171,99pounds e)144 square metres to square yards 144x1,196=172,224square yards f)56 metres to feet and yards 56x3,281=183,736feet 56x1,094=61,264yards

4. Convert the following units from Imperial to SI

Model Answer(s): a. 16 ounces to grams 16x28,35=453,6g b. 34 yards to meters 34x0,9144=31,0896m c. 6,5 gallons to liters 6,5x4,456=28,964litres d. 487 feet to meters 487x0,3048=148,4376m

Instructions to learner:

Complete the following tasks: 11 SSOO 11

Learner Workbook: Page 25 Facilitator Guide: Page 11


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e. 19 acres to hectares 19x0,4047=7,6893ha f. 56 tons to kilograms 56x1016=56896kg g. 45 inches to centimeters 45x2,54=114,3cm h. 321 cubic inches to cubic meters 321x0,02832=9,09072m3 i. 1092 miles to kilometers 1092x1,609=1757028km j. 12 pounds to kilograms 12x0,4536=5,4432kg

5. Estimate the length, breadth and height of the classroom.

Model Answer(s): Answers will depend on the size of the classroom. The assessor must measure the sizes before the lesson.

6. Convert the following:

Model Answer(s): a. Convert 600C to Fahrenheit 60 x 9/5 + 32= 140F b. Convert 1000F to degrees Celcius (5[100 – 32]) � 9 = 37,780C c. Calculate the area of a field of 50m length and 15m breadth. A = 50x15=750m2 d. Tractor drives 48 km in 2 hours. What is its velocity? v=48/2=24km/hr e. A train travels at 120km/hr for 3 hours. How far did it travel? D=120x3=360km

7. Convert the following:

Model Answer(s): a. 10g to kg 0,01g b. 5cm to m 0,05m c. 6km to m 60000m d. 10km to m 10000m e. 2l to ml 2000ml f. 150ml to l 0,15l g. 455kg to g 455000g

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Identify the following triangles:

Model Answer(s): a) scalene b) right c) isosceles d) equilateral

2. Calculate the sizes of the angles marked a-h

Model Answer(s): a)

a = 600

b)

b=450

c)

c=d=500

d)

e=800

e)

f=500

f)

g=400 h=1000





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1. Identify each of the following quadrilaterals.

Model Answer(s): a) rectangle b) square c) parallelogram d) kite e) rhombus f) trapezium g) trapezoid h) general quadrilateral

2. Determine the sizes of the sides and angles labeled of a-k.

Model Answer(s): a)

a = 25mm b = 1200

b)

c = 400 d = 10mm e = 500





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c)

f = 900 g = 450

h = 15cm

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Draw the following figures with the correct tools and describe their characteristics:

Model Answer(s): a. rectangle with measurements 40mm x 50mm b. square with one side 35mm c. triangle with sides 25mm x 35mm x 50mm d. circle with a radius of 5mm The assessor should measure the drawings of the students to assess accuracy.

2. Calculate the unknown angles in each case.

Model Answer(s): 1.

a = 1300 b = 500 c = 500 d = 500

2.

e = 470 f = 470 g = 470 h = 1330

3.

j = 500 k = 600 l = 700

4.

m = 830 n = 320





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5.

o = 500 p = 500 q = 1300 r = 950 s = 350

6.

t = 450 u = 700 v = 650 w = 650 x = 700

7.

y= 540 z = 540 aa = 540 bb = 540

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Calculate the value of the unknown side in each of the following right-angled triangles, by using the Theorem of Pythagoras. (A calculator may be used).

Model Answer(s): a) P 30 cm Q 40cm R PR2 = 302 + 402 PR2 = 900 + 1600 PR2 = 2500 PR = 50cm b) D 120 cm 150 cm E F ? EF2 = DF2-DE2 EF2 = 1502 - 1202 EF2 = 22500 – 14400 EF2 = 8100 EF2 = 90





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2. A farmer has a field of 70x110m. Work out the length of the diagonal of the field.

Model Answer(s):

Diag2 = 1102 + 702 Diag2 = 12100 + 4900 Diag2 = 17000 Diag = 130,38m

3. A farmer needs to secure a pole of 6m with a rope. The rope needs to be tied to the top of the pole and to a hook 3m from the base of the pole. How long must the rope be? Draw a diagram to help you.

Model Answer(s):

Rope2 = 62 + 32 Rope2 = 36 + 9 Rope2 = 45 Rope = 6,708m

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. A field is 30m long and 15 m wide. Calculate

a. the perimeter

b. the area of the field.

Model Answer(s): a. Perimeter = 30m + 15m+30m + 15m = 90m b. Area = 30m x 15m = 450m2

2. A circular irrigator has a diameter of 50m. Calculate

a. the perimeter/circumference of the irrigated area

b. the surface area of the irrigated part of the field.

Model Answer(s): a) Circumference = πx diameter = π x 50m = 157,08m b) Area = πr2 = π x 25 x 25 = 1963,50m2

3. A sheep dipping tank on a farm has the following dimensions: length = 5m, breadth=2m and depth = 1,2m. Calculate the volume of water that this tank can hold.

Model Answer(s): Volume = lxbxh = 5m x 2m x 1,2m = 12m3


Complete the following tasks: 66



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4. A farmer wants to fence off a piece of land as a paddock for his horses.

There are, however, certain problems. One side of the land is cut off due to overhead power lines. On another side there is a very dangerous hole. See the diagram below to visualize the land. The shaded area represents the paddock that he can create.

Calculate:

a. the length of wire he will need for the perimeter

b. the surface area of the paddock.

Model Answer(s): a) Perimeter = (30m – 5m) + perimeter of quarter circle + (50m – 5m) + (30m –

10m) + length of power line + (50m – 20m) (Length of power line)2 = 202 + 102 (by Pythagoras) (Length of power line)2 = 400+100 (Length of power line)2 = 500 Length of power line = 22,36m Perimeter = (25m) + (¼ x2 x π x 10) + (45m) + (20m) + (22,36m) + (30m) =

158,07m b) Area = Area of rectangle – area of ¼ circle – area of triangle Area = (50 x 30) – (¼ x π x 5 x 5) – (½ x 10 x 20) Area = 1500m2 – 19,63m2 – 100m2 Area = 1380,36m2


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5. Below is a diagram of a shed. The roof of the shed needs to be waterproofed with a certain type of paint called KeepDri.

a. Calculate the surface area of the roof (remember that there are two halves to the roof!).

b. If 5l of KeepDri paint coats 15m2 of roof, how many 5l tins of paint must he buy?

c. If one 5l tin of KeepDri paint costs R150, how much will it cost him to paint the roof?

Model Answer(s): a. Surface Area = 2 x 7m x 35m = 490m2 b. No. of tins = 490m2 / 15m2 = 32,67 tins. One cannot buy 0,67 of a tin, thus he

must thus buy at least 33 tins. c. Total cost = no of tins x cost per tin = 33 x R150 = R4950

MMyy NNootteess ……

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1. In the diagram below two scales are shown, Scale A and Scale B, both scales recording kilograms:

80

70 10

60 20

50 30

40

Scale A Scale B Model Answer(s): a) What mass is indicated on Scale A? 14kg b) Scale B must be calibrated to record a mass of 120 kg and must have 10 kg

intervals. Redraw the diagram above and indicate with an arrow a mass of 100 kg.


Complete the following tasks: 77



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2. The diagram below represents a feeding trough with dimensions as shown.

b

h y

x

a. Determine a formula for the volume (V) of the trough in terms of x, b, y and h.

Model Answer(s): Volume = area of base x height The triangle must be used as a base because it is the only surface at which all the other

sides are at a right angle. Volume = ½xbxh xx

V = bhx/2

b. A formula for the surface area (A) of the trough in terms of x, b, y and h.

Model Answer(s):

A = ½bh + xy + xb + xh

c. Calculate the surface area if h = 30mm ; b = 40mm and x = 80mm

Model Answer(s): Y2 = 302 + 402 Y = 50 A = ½ x40 x 30 + 80 x50 + 80x40 + 80x30 A = 600 + 4000 + 3200 + 2400 = 10200m2


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3. In the diagram below calculate the length of BC and hence the area of the quadrilateral ABCD.

D

60mm

A E 80mm

44mm 44mm

B C

Model Answer(s): DE=80-44=36m AE2=602 -362 = 2304 AE = BC = 48m Area = area of rectangle + area of triangle = 44m x 48m + ½ x 48 x 36 = 2112 + 864 = 2976m2

4. Match the scale drawing that will best suit the reproduction of the object:

Model Answer(s): Scale Object a) 1:10 South Africa h b) 1:2 Ant e c) 1cm:1m House c d) 1:10 000 Pen b e) 10:1 Your place of work c f) 1000:1 Telephone a g) 100 000:1 h) 1cm:200km


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5. In the diagram below AB // CF and AE and BD are straight lines. Calculate, giving reasons,

Model Answer(s): (a)

(b)

(c)

a) C3 = 700 alt. angles, AB parallel to CF b) C1 = 500 angles on a straight line c) A = 600 angles of triangle

6. Look at the three angles drawn below:

P

A

Q R B C D

a) Estimate the size of each angle.

Model Answer(s): ∠PQR 750 ∠ACB 270 ∠ACD 1530


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b) Measure each angle with a protractor.

Model Answer(s): ∠PQR 750 ∠ACB 270 ∠ACD 1530

c) Say whether each angle is acute, obtuse, right, straight or reflex angle.

Model Answer(s): ∠PQR acute ∠ACB acute ∠ACD obtuse


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1. Draw the following two-dimensional shapes and transform them to three- dimensional shapes by adding a height or depth of 3cm.

a) Square with dimensions 250mm

b) Rectangle with dimensions 300mm by 200mm

c) Right-angled triangle with an adjacent side of 3cm and an opposite side of 2cm

d) Circle with a diameter of 400mm

e) Semi-circle with a radius of 1cm.

Model Answer(s): The Assessor should draw these on a transparency and measure the students accuracy by overlaying the transparency

2. Redraw these objects as if you are looking from the top:

a) b)

c) d)





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Model Answer(s): a)

b)

c)

d)

3. Find at least 3 objects (not discussed in this learning guide) that are symmetrical. Redraw them in your workbook and indicate the lines of symmetry.

Model Answer(s): e.g. a leaf

Check that: a. object is recognizable b. drawing is neat c. line of symmetry is placed correctly


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1. Peter has a piece of land. He has put a fence around it so that his sheep can stay inside. The land is 300m x 800m. How large is the area that his sheep can use?

Model Answer(s): Area = 300m x 800m = 240000m2

2. Thandi lives in a rondawel. She wants to paint the walls of the rondawel. The man at the paint shop told her that she would use about 5l of paint per ten square meters. She wants to work out how many litres of paint she needs to buy. The diameter of the rondawel is 5m. The walls are 2 meters high. She needs to paint the inside and the outside of the rondawel.

Model Answer(s): The rondawel represents a cylinder. If you flatten out a cylinder it becomes a rectangle. The breadth of the rectangle represents the height of the rondawel, i.e. 2m. The length of the rectangle represents the circumference of the circle, i.e. πd

surface area for the outside of the rondawel = 2 x π x 5 = 31,42m2 Total surface area for inside and outside = 2 x 31,42m2 = 62,84m2 One tin of paint covers 10m2, thus she needs 62,84m2/10-m2 = 6,284 tins of paint. 93 per square meter, how much will it cost him to carpet out the whole area?

Total cost = 30m2 x R 39.93 = R1197.9

She must buy at least 7 tins of paint, since you cannot buy half full tins.

There are 5 litres per tin, thus she must buy 7 x 5 = 35 litres


Complete the following tasks: SSeellff CChheecckk



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3. Martin wants to lay a carpet in his lounge, dining room and passage. His wife Martha writes down the measurements.

Lounge 3m x 4,5m

Dining Room 3,5m x 3m

Passage 1,5m x 4m

a. How much carpeting will Martin have to buy to cover all three areas?

Model Answer(s): Total surface area = 3m x 4,5m + 3,5m x 3m + 1,5m x 4m Total surface area = 13,5m2 + 10,5 m2+ 6m2 = 30m2

b. If the carpet he buys costs R39, 93 per square meter, how much will it cost him to carpet out the whole area?

Model Answer(s): Total cost = 30m2 x R 39.93 = R1197.9

4. Sheila brews beer. She has a tank in which she keeps the beer. The tank is 3 metres high and has a diameter of 2m. How much beer can she hold in such a tank?

Model Answer(s): Volume = area of base x height, = πr2xh = π x 1m x 1m x 3m = 9,42m3

5. Thabo wants to build a rectangular container for water. This is for his cattle to drink water from. He wants the container to measure 2m x 0,75m x 1m. How much water will this container hold?

Model Answer(s): Volume = area of base x height = 2m x 0,75m x 1 m = 1,5m3

6. The dimensions of a carton box are 56cm x 340mm x 0,75m. How many small boxes that are 10cm3 can you fit into the big box?

Model Answer(s): Volume = area of base x height = 56cm x 34 cm x 75cm = 142800cm3 No. of boxes = 142 800cm3 / 10cm3 = 14280 boxes


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7. Kevin works on the production line of a factory that produces steel drums. The drums he makes have a radius of 50cm and a height of 1m. What is the volume of such a drum?

Model Answer(s): Volume = area of base x height = π x 0,5m x 0,5m x 1m = 0,785m3

8. The floor plan of a factory is shown in the diagram below. The grey area is the stand on which the factory stands.

a Calculate the entire area of the factory, without the parking and loading bays.

Model Answer(s): Total area = area of store room + workshop + admin office + reception Total area = 12mx12m + 31m x16m + 9mx8m + 5mx6m Total area = 144m2 + 496m2 + 72m2 + 30m2 Total area = 742m2


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b The stand is twice as long as it is wide. Calculate the area of the stand.

Model Answer(s): Area of stand = 50m x 100m = 50000m2

9. In the figure below, line PR is extended at both ends. Calculate the size of each of the angles of °PQR, giving reasons for your calculations:

155° P

Q 80° R

Model Answer(s): <QPR = 250 angles on a straight line <QRP = 1000 angles on a straight line <RQP = 550 angles of a triangle

MMyy NNootteess …… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10. Jabu has to do deliveries at all the points marked on the map below. The scale is 1cm:1km. He has to work out the shortest distance so that he can do all the deliveries. He needs to start and end at point A.

Model Answer(s): A to F to H to J to I to G to E to B to D to C. Or students can give the same order backwards. Any other answer must be checked by actual measurement.

11. Calculate the value of each of the unknown angle in each of the following:

a) B

X 60°

A D C ADC is a straight line

Model Answer(s): X = 1200 angles on a straight line


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b)

∠AXY = 50°

AB//CD//EF

Model Answer(s): a = 500 alt angles, AB//CD b = 500 vert opp angles, or corresp angles, AB//CD c = 1300 coint angles, CD//EF


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SSuummmmaattiivvee TTeesstt aanndd AAttttiittuuddee && AAttttrriibbuuttee EEvvaalluuaattiioonn

efore the knowledge test is undertaken, the learner must be reminded of what is expected from him / her in terms of summative and reflexive

competence. Read and explain to the learner, the Preparation for Your Final Assessment section in the learner workbook. Learners and assessor should sign off this section to acknowledge that this step was completed.

Please set up a knowledge test from the questions given as a guideline to learners and supply each learner with a test sheet.

Supply each report with the following heading:

BB

Unit Standard: 12444 NQF Level: 2

Learner Name:


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Questions

1. Identify the types of angles and triangles shown in the diagrams below: a)

b)

c)

d)

e)

f)

(6)

Model Answer a. acute b. right c. obtuse d. right angled triangle e. isosceles triangle f. scalene triangle


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2. Calculate the sizes of the angles indicated by the letters a – o. You must give reasons. a)

b)

c)

d)

e)

(15)

(15)

Model Answer a = 1150 angles on a str line b = 650 corr angles AB//CD c = 650 vert opp angles d = 420 alt angles BC//DE e = 830 angles on a str line f = 550

alt angles, AB//DE g = 600 alt angles MP//RQ h = 650 vert opp angles i = 650 corr angles, MP//RQ j+l = 1800 – 1360 corr angles, XY//VZ j = l = 220 diag bisect angles of rhombus M = 650 alt angles, AB//CE O = 650 iscosceles triangle N = 500 angles of triangle, OR angles on str line


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3. Identify the following shape and measure the sides and angles indicated by letters a – c

(4)

Model Answer The assessor must measure these and evaluate students answer.


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4. Use the table below to convert the following units:

To Convert From Multiply by To Convert From Multiply by

Inches to centimeters 2,540 Centimetres to inches 0,3937

Pounds to kilograms 0,4536 Kilograms to pounds 2,205

Pounds to grams 453,6 Grams to pounds 0,002205

Ounces to grams 28,35 Grams to ounces 15,43

Yards to metres 0,9144 Metres to yards 1,094

Feet to metres 0,3048 Metres to feet 3,281

Miles to kilometers 1,609 Kilometres to miles 0,6214

Tons to kilograms 1016 Kilograms to tons 0,0009842

Gallons to litres 4,456 Litres to gallons 0,22

a. 24cm to inches b. 100 kilometres to mile c. 15 yards to meters d. 78 kilograms to pounds e. 120 pounds to kilograms f. 150g to kg g. 1,5l to ml

(7)

Model Answer a. 24cm to inches 60,96 inches b. 100 kilometres to miles 62,14 miles c. 15 yards to meters 13,716 m d. 78 kilograms to pounds 171,99 pounds e. 120 pounds to kilograms 54,432 kg f. 150g to kg 0,15kg g. 1,5l to ml 1500ml


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5. For each of the following diagrams calculate the shaded area. a)

b)

(8)

(8)

Model Answer a. Shaded area = total area – white area = 15mx10m - ½ x 6m x 10m = 150m2 – 30m2 = 120m2

b. Shaded area = area of circle – area of square = πx3,535x3,535 – 5x5 = 39,258 – 25 =14,26cm2


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6. A farmhouse has a tank for the collection of rain water. The tank measures 5m in diameter and is 5 m high. Calculate the volume of the tank.

(4)

Model Answer Volume = area of base x height = πx2,5x2,5x5 = 98,17m3

7. A farmer has a tap in one corner of his shed. The tap needs to be moved to the opposite corner as shown on the diagram.

a) Calculate how much piping the farmer must order to complete the job. b) If the piping costs R54.50 per meter, calculate how much the pipes will cost.

(6)

Model Answer a. Length of pipe2 = 252 + 602 = 625 + 3600 = 4225 Length of pipe = 65m b. Total cost = 65m x R54.50 = R3542.50


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Assessment Feedback Form

Comments / Remarks

Feedback to learner on assessment and / or overall recommendations and action plan for competence:

Feedback from learner to assessor:

Assessment Judgement You have been found:

Competent

Not yet competent in this unit standard

Actions to follow:

Assessor report to ETQA

Learner results and attendance certification issued

Learner’s Signature:

Date:

Assessor’s Signature:

Date:

Moderator’s Signature:

Date:

Documents

Measure, estimate aand calculate - Home Page- … Guide Primary Agriculture Measure, estimate aand calculate NQF Level: 2 US No: 12444 The availability of this product is due to the