Sparrow Research and Industrial Consultants © January 2006

A Mathematical Skills Fundamental for the Pulp and Paper Industry

NUMBERS & NUMBER SYSTEMS 2

Assessor Guide

NQF Level 2
Credits: 3
Unit Standard 7480

Compiled by:

Amanda Gilfillan
Bredenkamp Bruwer

for

FIETA

US 7480 Number and number systems 2Assessor Guide1

Sparrow Research and Industrial Consultants © January 2006

ASSESSOR GUIDE

US 7480: Demonstrate understanding of rational and irrational numbers and number systems

Learner / Assessor
ID No / ID No
Tel. Work / Tel Work
Cell No / Cell No
Job Title / Job Title
Date / Date
Qualification: / National Certificate in Metal and Engineering Manufacturing / National Certificate in Construction Material Manufacturing
ID and Title of Unit Standard / 7480 / Demonstrate understanding of rational and irrational numbers and number systems
NQF / 2 / Credits / 3

ASSESSMENT SCHEDULE FOR US 7480

Assessment Method / Theoretical Written / Theoretical
Oral / Practical / Feedback
session
Date
Time
Location
Resources required
Candidate signature / Assessor signature / Moderator / Manager signature

RECOGNITION OF PRIOR LEARNING

Use the assignments indicated by the  icon for RPL

US 7480: ASSESSMENT PLAN

Unit Standard Number: 7480 / Unit Standard Title: Demonstrate understanding of rational and irrational numbers and number systems
NQF Level: 2 / Credits: 3
No / Specific outcomes / Learning Outcomes /

Assessment Criteria

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Assessment Methods

/

Assessment Responses

/

Instruments Required by Learner

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Assessment Instruments

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US 7480 T1: Distinguish between number systems
1.1 / SO1 AC1-7
SO2 AC1-5 / Be able to distinguish between natural and whole numbers and integers / Distinguish between natural and whole numbers and integers / Test / Arrange numbers in correct order / Test to be completed / Memorandum
Be able to distinguish between rational and irrational numbers / Distinguish between rational and irrational numbers
US 7480 T2: Understanding conversion between improper and mixed fractions
2.1 / SO1 AC1-7
SO2 AC1-5 / Be able to write mixed numbers as improper fractions / Write mixed numbers as improper fractions / Test / Do various calculations / Test to be completed / Memorandum
Be able to write improper fractions as mixed fractions / Write improper fractions as mixed fractions
US7480 T3: Understanding the conversion between decimals and common fractions
3.1 / SO1 AC1-7
SO2 AC1-5 / Be able to write fractions as decimal numbers and round it off / Write fractions as decimal numbers and round it off / Test / Do various calculations / Test to be completed / Memorandum
Be able to convert decimals to common fractions / Convert decimals to common fractions
Be able to express recurring decimals to common fractions / Express recurring decimals to common fractions
US: 7480 T4: Understanding the method of rounding off, estimation and approximation
4.1 / SO1 AC1-7
SO2 AC1-5 / Be able to apply the method of rounding off, estimation and approximation / Apply the method of rounding off, estimation and approximation / Test / Do various calculations / Test to be completed / Memorandum
US: 7480 T5: Understand scientific notation
5.1 / SO1 AC1-7
SO2 AC1-5 / Be able to write numbers in scientific notation / Write numbers in scientific notation / Test / Do various calculations / Test to be completed / Memorandum
Be able to use exponents laws to do calculations with scientific notation / Do calculations with scientific numbers
US: 7480 T6: Understanding order of operations and usage of computational tools
6.1 / SO1 AC1-7
SO2 AC1-5 / Be able to perform calculations with a calculator / Do calculations with a calculator / Test / Do various calculations / Test to be completed / Memorandum
Be able to use algorithms to do calculations / Use algorithms to do calculations

ASSESSMENT MEMORANDUM - US: 7480

Unit standard: Demonstrate understanding of rational and irrational numbers and number systems / US: 7480 / NQF level: 2 / Credits: 3
Assessment Criteria : T1 Distinguish between number systems / T2 Understanding conversion between improper and mixed fractions
T3 Understanding the conversion between decimals and common fractions / T4 Understanding the method of rounding off, estimation and approximation
T5 Understand scientific notation / T6 Understanding order of operations and usage of computational tools
MEMORANDUM FOR QUESTION 1
Complete the following test. Study the following list of numbers and arrange them in the columns below: (numbers can be used more than once) / 
1) Natural Numbers / 2) Integers / 3) Rational numbers / 4) Irrational Numbers
-5 / 0 / / / 1,5 / 2 / / 3,14 / / 10
Question / Answer
1 / Natural Numbers / ,10 / 1
2 / Integers / -5 ; 0 ; ; 10 / 4
3 / Rational numbers / -5 ; 0 ; ; ; 1,5 ; 2 ; ; 3,14 ; 10 / 9
4 / Irrational Numbers / / 1
Total / 15
MEMORANDUM FOR QUESTION 2 / 
Write the following mixed numbers as improper fractions
Question / Answer
1 / 2 / / 2
2 / 1 / / 2
3 / 4 / / 2
4 / 3 / / 2
Total / 8
MEMORANDUM FOR QUESTION 3 / 
Write the following improper fractions as mixed numbers
Question / Answer
1 / / 2 / 2
2 / / 5 / 2
3 / / 3 or / 2
4 / / 3 / 2
Total / 8
MEMORANDUM FOR QUESTION 4 / 
Write the following fractions as decimal numbers
Question / Answer
1 / / 0,75 / 1
2 / / 0,625 / 1
3 / / 0,012 / 1
4 / 2 / 2,6 / 1
Total / 4
MEMORANDUM FOR QUESTION 5 / 
Convert the following decimal numbers to mixed numbers or proper fractions
Question / Answer
1 / 2,37 / 2 / 1
2 / / / 1
3 / 0,25 / / 1
4 / 0,875 / / 1
5 / / / 2
6 / / / 2
Total / 8
MEMORANDUM FOR QUESTION 6 / 
Write the following numbers in scientific notation
Question / Answer
1 / 680 000 / / 1
2 / 0,000367 / / 1
3 / 0,0046 / / 1
Write in expanded form
4 / / 25 700 / 1
5 / / 0,000000536 / 1
Calculate and give your answer in scientific notation
6 / / / 2
7 / / / 2
8 / / / 1
Total / 10
MEMORANDUM FOR QUESTION 7 / 
Question / Answer
1 / What is the meaning of the mathematical symbol“≈” / It means approximately equal to / 1
2 / Estimate the answer of the following expression without using a calculator:
/ (any other answer is wrong) / 2
Total / 3
MEMORANDUM FOR QUESTION 8 / 
Round off the following decimal numbers to two decimal places
Question / Answer
1 / 0,765 / 0,77 / 1
2 / 5,863 / 5,86 / 1
3 / 2,432 / 2,43 / 1
Round off the following decimal numbers to the nearest thousands
4 / 2,7899 / 2,790 / 1
5 / 0,4643 / 0,464 / 1
6 / 89,3656 / 89,366 / 1
Round off the following numbers to the nearest hundred
7 / 78 059 / 78 100 / 1
8 / 1 684 / 1 700 / 1
Total / 8
MEMORANDUM FOR QUESTION 9 / 
Use your calculator to solve the following problem.
Question / Answer
1 / The following items were bought at a supermarket. Calculate the total cost.
3 Cold drinks @ R3,50
6 Chocolates @ R 5,50
2 Hamburgers @ R 10,65 / / 6
Total / 6
MEMORANDUM FOR QUESTION 10 / 
Use a calculator to do the following calculations. Write down all the necessary steps and round off as indicated.
Question / Answer
1 / (3 dec) / / 3
0,167
2 / (2 dec) / / 3
3 / (1 dec) / / 3
4 / / / 3
(2 dec) /
5 / / / 3
Total / 15
INFORMAL ASSESSMENT: CRITICAL CROSSFIELD OUTCOMES
Critical outcomes / Level 1
Code 1 Not yet achieved
(NA) / Level 2
Code 2 Partially achieved (PA) / Level 3
Code 3 Achieved
(A) / Level 4
Code 4 Outstanding achievement (O)
Identify and solve problems / Learner experiences difficulty with problem solving activities. / Learner can identify and solve only basic problems that require recall of knowledge. / Learner is able to recall, interpret and apply knowledge to solve problems. / Learner is able to interpret, apply, analyse, synthesise and evaluate knowledge to solve problems.
Communicate effectively / Learner cannot communicate effectively, and lacks basic vocabulary or confidence. / Learner communicates when necessary but uses only basic vocabulary. / Learner communicates well, good command of language, confident. / Learner communicates clearly and effectively by using sophisticated vocabulary. Very confident.
SUMMARY OF RESULTS US 7480
Name: / ID No:
No / Assessment / Marks / Marks / Descriptor
1 / Question 1 / 15
2 / Question 2 / 8
3 / Question 3 / 8
4 / Question 4 / 4
5 / Question 5 / 8
6 / Question 6 / 10
7 / Question 7 / 3
8 / Question 8 / 8
9 / Question 9 / 6
10 / Question 10 / 15
Total / 85
MARKS / DESCRIPTORS
0-33 / 0-39% / Not yet competent (NC)
34-41 / 40-49% / Partially competent (PC)
42-63 / 50-74% / Competent (C)
64-85 / 75-100% / Outstandingly competent (OC)
Comments
Further Actions
Signature Learner / Date
Signature Assessor / Date
Signature Moderator / Date

ASSESSMENT CHECKLIST

Complete the following checklist after each assessment and hand it over to the Learnership / Training Coordinator for further action. Use the given definitions to clarify the meaning of each criterion. The learner can also be asked for his / her evaluation.

Name / Date
Rating scale / 1 = Inappropriate / 2 = Needs small changes / 3 = Appropriate / 4 = Excellent
Assessment / Fairness / Validity / Reliability & consistency / Practical / Transparent / Comments
1 / Question 1
2 / Question 2
3 / Question 3
4 / Question 4
5 / Question 5
6 / Question 6
7 / Question 7
8 / Question 8
9 / Question 9
10 / Question 10

ASSESSMENT CHECKLIST DEFINITIONS

Criteria / Definitions
Review assessment / Did I observe all the principles of assessment?
1 / Fairness / Was the assessment instrument fair to the learner without disadvantaging anyone?
2 / Validity / Does the assessment instrument measure what it is intended to measure?
3 / Reliability and consistency / Is the instrument consistent (always the same) in the same or similar context each time a particular assessment is made
4 / Practicability / Doe the assessment take into account available financial resources, facilities, equipment and time
5 / Transparency / Is the assessment transparent (clear and open) to everyone making use of it.

Assessor GuideUS 7480 – Numbers & Number Systems 21