Working WWith Numbers in Various Contexts - · PDF fileWorking WWith Numbers in Various Contexts ... 56 005 is 5 tens of thousands 6 thousands 0 hundreds 0 tens 5 units l. 10 090 is

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WWoorrkkiinngg WWiitthhNNuummbbeerrss iinn

VVaarriioouuss CCoonntteexxttss

NQF Level: 1 US No: 7447

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

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

Class Group: . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . . . .

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

Version: 01 Version Date: July 2006

22Working with numbers in various contexts

Primary Agriculture NQF Level 1 Unit Standard No: 7447

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, names Policies and Procedures for Assessment, 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 the following unit standard:

Title: Working with numbers in various contexts

US No: 7447 NQF Level: 1 Credits: 6

This unit standard is one of the building blocks in the qualifications 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 48970 1 120

National Certificate in Mixed Farming Systems 48971 1 120

National Certificate in Pant Production 48972 1 120

Please mark the learning program the learners are enrolled in:

Are you assessing a: Yes No

Learnership?

Skills Program?

Short Course?

TT PPlleeaassee NNoottee::

This Unit Standard 7447 Assessment Guide must be read in conjunction with the generic Assessor Guide as prescribed and published by the AgriSETA.

Note to Assessor: If you are assessing this module as part of a full qualification or learnership, please ensure that you have familiarised yourself with the content of the qualification.




Instructions to Learner(s):

Brainstorm as a group, and write down keywords for yourself. Think of examples of as many as possible things that we might use numbers for.

11..11 SSOO 55 AACC 22--33

Learner Workbook: Page 3 Facilitator Guide: Page 10 - 11

Model Answer(s): Stock control; measuring orchards; planning irrigation scheduling; missing agro-chemicals, etc..

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

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Instructions to Learner:

Change Base Ten Numerals into Base Two Numerals

11..22 SSOO 55 AACC 11


Model Answers:

1. 81 a) None of these

2. 1001 d) 1111101001

3. 51 c) 110011

4. 1210 c) 1010111001

5. 36 c) 10100

6. 25 c) 11001

7. 49 b) 110001

8. 9 d) 1010

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

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1. Fill in the numbers showing the value of each figure. The first one is done for you.

a. 23 is 2 tens 3 units

b. 765 is 7_ hundreds 6 tens 5 units

c. 809 is 8 hundreds 0 tens 9 units

d. 832 is 8 hundreds 3 tens 2 units

e. 2 934 is 2 thousands 9 hundreds 3 tens 4 units

f. 6 203 is 6 thousands 2 hundreds 0 tens 3 units

g. 7 042 is 7 thousands 0 hundreds 4 tens 2 units

h. 23 934 is 2 tens of thousands 3 thousands 9 hundreds 3 tens 4 units

i. 90 462 is 9 tens of thousands 0 thousands 4 hundreds 6 tens 2 units

j. 72 895 is 7 tens of thousands 2 thousands 8 hundreds 9 tens 5 units

k. 56 005 is 5 tens of thousands 6 thousands 0 hundreds 0 tens 5 units

l. 10 090 is 1 tens of thousands 0 thousands 0 hundreds 9 tens 0 units

2. Use the place value table to write the following numbers in figures:

M Hth Tth Th H T U

a. Two hundred and four 2 0 4

b. One thousand 1 0 0 0

c. Six thousand five hundred and six 6 5 0 6

d. Two thousand and nine 2 0 0 9

e. Forty five thousand 4 5 0 0 0

f. Sixty four thousand and twenty nine 6 4 0 2 9

g. One hundred thousand 1 0 0 0 0 0

h. Two hundred and six thousand 2 0 6 0 0 0

i Six hundred and nineteen thousand 6 1 9 0 0 0

j. Seventy four thousand six hundred and four 7 4 6 0 4

k. One hundred and nineteen thousand 1 1 9 0 0 0

l. Nine hundred and nine thousand six hundred and two 9 0 9 6 0 2

m. One million 1 0 0 0 0 0 0


Complete these exercises. Place value (1) and numbers in words (2).

22..11

SSOO 66 AACC 11--44





1. You are working in a packing store, where apples are packed. You are asked to count the number of apples that are packed in an hour. Give a detailed account of the following:

a. Where would you start?

At place where apples enter the packaging.

b. If you were told to estimate the number of apples packed in the hour, how would you go about it?

Multiply the amount of boxes packed in an hour with the average amount of apples per box.

c. If you were told to count the exact number of apples packed in an hour, how would you go about it?

Physically count each apple in each box & count each box packed in the hour.

d. If you asked the driver of the tractor and he told you that he arrived every hour with a load of 10 picking baskets that could always fit approximately 100 apples each, how would it make your estimate easier?

You’d be able to estimate that in an hour 10x100apples are packed (1000 apples).

e. If you know that there are 50 apples packed in a box, ready for distribution, and at the end of an hour you find that 70 boxes have been filled, how would that make you accurate calculation task easier?

70 boxes x 50 apples = 3500 apples packed in that hour.


Complete this exercise in your workbook.

22..22 SSOO 66 AACC 11--44





2. Explore different counting patterns using a calculator:

a. Use the numbers 2, 3, 5, 10, 20, 25, 30 and 50. Skip counting by what numbers will include 100 as part of the pattern?

b. What pattern do you see when you count by twos and begin with 2?

See even numbers emerge.

c. What do you notice when you count by twos and begin with 1? Why?

See uneven numbers emerge.

d. Will there be a pattern if you skip-count by fives and begin with 3? Why? Why not?

3,8,13,18,23,28…

Pattern emerging: repetition of 3’s and 8’s

e. What happens if you skip-count by tens and start with 37? What do you notice?

37,47,57,67,87…

7 stays constant, place value in front of 7 keeps increasing by 1

2,4,6,8,10…98,100

3,6,9,12,15…99

5,10,15,20…100

20,40,60,80,100

25,50,75,100

30,60,90

50,100

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

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Here are the answers – how did you do?

1. Draw a line to match each number to its equivalent value in words.

106.7

Fourteen point nine six

324

Thirty-two point four

5.09

One hundred and six point seven

14.96

Five hundred and nine

509

Three hundred and twenty-four

32.4

Five point zero nine

2. Write each number as digits, putting in decimal points where needed.

a. One thousand and sixty five point two four ______1065.24

b. Fifty-seven point nine two ______57.92

c. One hundred and one _____101

d. Ten point one ____10.1

e. Zero point five six _____0.56

3. Write each of these decimal numbers using digits.

a. Three and four tenths ____3.4

b. Sixteen and two hundredths _____16.02

c. Twenty five hundredth _____0.25


Complete these exercises in your workbook. Answer the questions about decimals.

22..33 SSOO 66 AACC 11--44





d. One and five thousandths ______1.005

e. Four hundred and five and three tenths _____405.3

f. Twenty six thousandths _____0.026

4. Tick ‘True’ or ‘False’ for each of these statements ( ):

True False

a. Four hundredths = 0.04

b. Five and six tenths = 50.6

c. 14.07 = fourteen and seven thousandths

d. Two point one six = two and six hundredths

e. 59.008 = fifty nine and eight thousandths

f. 9.019 = nine and nineteen thousandths

5. Try these questions and see how you do.

a. Which is greater, 5.7 or 5.18? _______5.7

b. Which is smaller, 2.19 or 2.6? _______2.19

c. 9.162 is more than 9.17 True or False? _______False

d. 0.175 is more than 0.2 True or False? ________False

e. Which is the largest, 96.145, 96.2 or 96.19? _______96.2

f. Which is the smallest, 25.62, 25.26 or 25.6? ________25.26

g. Put these in size order, largest first:

75.1, 25.7, 75.06, 25.008 _______________75.1, 75.06, 25.7, 25.008

h. Put these in size order, smallest first:

0.17, 0.8, 0.072, 0.06 _______________0.06, 0.072, 0.17, 0.8

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

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Now look up the same or equivalent word in a dictionary in your mother tongue. Write down in your own mother tongue what you understand about each word.

1. Key words for Addition

Word English Dictionary Meaning

What I understand it to mean in my mother tongue

Add

Sum

Altogether

Increase

Total

More

Plus

2. Key words for Subtraction



Subtract

Minus

Decrease

Difference

Less than

Take away

Fewer than

Reduce


Look up the meaning of each word in English, in the dictionary.

44..11

SSOO 11 AACC 11 -- 33

Learner Workbook: Page 10 Facilitator Guide: Page 14




3. Key words for Multiplication



Multiply

Multiple

Times

Sets of

Lots of

Groups of

Factors

Product

4. Key words for division



Divide

Divisible

Left over

Remainder

Share

Groups

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

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Complete these mathematical sentences:

1. 9 - (4 X 2) = 1

2. (9 - 4) X 2 = 10

3. (9 - 4) X (2 X 1) = 10

4. 48 - [42 - (3 X 9)] = 33

5. 63 - [8/2 + (14 - 10)] (Note: 8/2 is the same as 8 divided by 2, just like in fractions.)

= 55

6. [800/ (200 X 4)] = 1

7. 28 + [ 10 - (4 + 2) ] = 32

8. (11-5) X (10 + 14) = 144

9. 125 / (5 X 5) (Remember from number 5? / = divided by.)

= 5

10. [28 - (4 X 5)] - 4 = 4


Complete this exercise.

55..11

SSOO 22 AACC 11--55


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

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Complete these mathematical sentences.

1. Write down the mathematical expression for each of the following every day situations or problems: (You don’t have to calculate the answer)

Samuel is 18 years of age. Zindsi is 4 years old. a. The sum of Samuel and Zindsi’s ages

Mathematical Sentence: 18 + 4 = x

b. Zindsi’s age in 6 years time

Mathematical Sentence: 4 + 6 = x

c. Samuel’s age 9 years ago

Mathematical Sentence: 18 – 9 = x

d. Double Zindsi’s age

Mathematical Sentence: 4 x 2 = x

e. The number of learners enrolled in the class are 40. How many are present if 8 are absent today


f. A train travels from Cape Town to Kayalitsha outside of peak hour. At the first station 6 people get on; 5 get on at the next station and 4 at the third station. How many people are on the train.

Mathematical Sentence: 6 + 5 + 4 = x

g. The number of passengers left on a bus if 20 out of 75 got off at the first stop.


h. The amount of money you spent if you bought mealy meal @ R 11.99; bread @ R3.49; Margarine @ R5.50 and Curry Powder @ R2.60

Mathematical Sentence: R 11.99 + R 3.49 + R 5.50 + R 2.60 = x

i. The amount of money you spent if you bought 6 new shirts at R25 each

Mathematical Sentence: R 25.00 x 6 = x



55..22 SSOO 22 AACC 11--55





2. Write down the mathematical expression for each of the following every day situations or problems: (You also have to calculate the answer)

a. Nine tourists book flights to visit South Africa. Their flight tickets cost them R 3500 each. What is the total amount of money paid by the tourists to the airline?

Mathematical Sentence: R 3500 x 9 = x

Answer : R 31 500.00

b. A learnership class of learners write a test. There are 14 learners in the class. The facilitator marks 70 questions in total. How many questions did each learner answer?

Mathematical Sentence: 70 ÷ 14 = x

Answer : 5

3. Make up your own examples of an everyday problem or situation that might be related to the following mathematical expressions.

1. Question:

24 / 4

What the problem could be: As per learner context

2. Question:

R100 – R40 – R55


3. Question:

6 x 4


4. Question:

22 + 55 + 68





1. Tick off whether you think the statement is true or false.

True False

a. "Pi" is a real number.

b. 2.52 is a real, rational number.

c. n + 5 is an expression for “the sum of a number and five.”

d. 3 is an irrational number.

e. “Twice a number divided by three” can be written as 2n - 3.

f. “Five decreased by twice a number” can be written as 5 - 2x.

g. “Ten less than a number” can be written as 10 n.

h. An integer is not a rational number.



77..11

SSOO 44 AACC 11--22


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Problem solving with +/- [answers]

Question 1

Step 1 Read the problem

You arrive at the bus stop at 10.30am. Your bus is due at 10.45am. How many minutes will you have to wait?

Step 2 Organize the calculation

The number of minutes from 10.30 to 10.45. You could count on from 10.30.

Step 3 Answer the calculation

10.30 to 10.40 is 10 minutes 10.40 to 10.45 is another 5 minutes 10 + 5 = 15 minutes

Step 4 Answer the problem

You will have to wait for 15 minutes

Question 2


Your puppy needs to have its inoculations before it can go out for a walk. If the puppy is 8 weeks old when it has its first inoculation, you have to wait 6 weeks for its booster and another 4 weeks for the booster to take effect. How old will the puppy be when it can go out?


I will start from the puppy’s age and add on all the weeks that it needs to stay in.


8 weeks old + 6 weeks + 4 weeks = 18


The puppy will be 18 weeks old.


Complete this exercise. Applying the problem solving skills that you have learnt.

77..33 SSOO 44 AACC 11--22





Question 3


You’re buying cable for your hi-fi. You need one piece 3m long and one piece 7m long. If you buy a 15m roll, how much will you have left ?


You could add together the 2 lengths you need, then take the amount from 15m.


Lengths needed: 3 + 7 = 10m Roll length id 15m so 15 – 5 = 5 metres


There would be 5m left.

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

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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

Working WWith Numbers in Various Contexts - · PDF fileWorking WWith Numbers in Various Contexts ... 56 005 is 5 tens of thousands 6 thousands 0 hundreds 0 tens 5 units l. 10 090 is