1.2 The inverse of subtraction _______________________
1.3 In the sum 5 676 – 231 = 5 445, the 5 676 is known as the ______________(3)
2. Complete the following number patterns:
2.1 175 ; 140 ; 105; _______________________; 35
2.2 _______________________; _______________________; 240 ; 120 (2)
3. Complete the following flow diagram:
Figure 1.7.
(2)
4. Calculate the difference, first rounding off to the nearest 1 000:
4.1 45 679 – 23 499
__________________________________________________________________ (3)
5. Complete:
6 775 – 1 448 = 6 777 - ______________________________________________ (1)
6. Seko had to calculate the following: 56 123 – 23 569. He started off by
23 569 + 31 = 23 600
Complete the sum.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_______________________________________________________________ (3)
7. Nomsa forgot to complete her sum. Please do it for her:
Figure 1.8.
(4)
8. Mr Muruvan had R500 000. After he had paid in cash for a house, he had R13 401 left over.
What was the price of his house?
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_______________________________________________________________ (4)
TOTAL: 20
Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.6: We know this when the learner solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights,
social, economic and environmental issues such as:
1.6.1 financial (including buying and selling, profit and loss, and simple budgets);
1.6. To be able to do mental arithmetic*
MATHEMATICS
Number Concept, Addition and Subtraction
EDUCATOR SECTION
Memorandum
1.1 20
1.2 28
1.3 25
1.4 24
1.5 6
1.6 76
1.7 9
1.8 7
1.9 48
1.10 11
1.11 30
1.12 8
1.13 9
1.14 12
1.15 9
1.16 108
1.17 45
1.18 81
1.19 7
1.20 12
Leaner Section
Content
ACTIVITY: To be able to do mental arithmetic [LO 1.9]
In Mathematics it is very important that you must be able to think quickly. Let us see how you
COPE! Complete the following mental arithmetic test as quickly and accurately as possible.
1.1 5 × 4 = ___________________
1.2 14 + 9 + 5 = ___________________
1.3 32 − 7 + ___________________
1.4 8 × 3 = ___________________
1.5 7 × ___________________ = 42
1.6 Double 38: ___________________
1.7 ___________________ × 8 = 72
1.8 8 × ___________________ = 56
1.9 4 × 12 = ___________________
1.10 ___________________ × 12 = 132
1.11 126 ÷ 6 + 9 = ___________________
1.12 48 ÷ ___________________ = 6
1.13 12 × ___________________ = 108
1.14 ___________________ × 6 = 72
1.15 54 ÷ 6 = ___________________
1.16 Halve 216: ___________________
1.17 ___________________ ÷ 5 = 9
1.18 ___________________ ÷ 9 = 9
1.19 63 ÷ 9 = ___________________
1.20 144 ÷ 12 = ___________________
Complete: I have __________________________ correct.
DID YOU KNOW?
We use the Hindu-Arabic number system!
The ancient Romans developed their counting system more than 2 000 years ago. Some of their
figures look like these:
I ; II ; III ; IV ; V
Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.9: We know this when the learner performs mental calculations.
1.7. To count and calculate correctly without using a
1.7. To count and calculate correctly without using a
pencil and paper*
MATHEMATICS
Number Concept, Addition and Subtraction
EDUCATOR SECTION
Memorandum
2.
2.1 add 12
2.2 less 40
2.3 less 12
2.4 add 12
2.5 add 28
3.
3.1 9; 11; 28; 100; 456
3.2 9; 1; 30; 82
3.3 2; 8; 11; 17
4.
4.1 99
4.2 36
Leaner Section
Content
ACTIVITY: To count and calculate correctly without using a pencil and paper
[LO 1.1, LO 1.8]
1. In the previous activity you worked with small numbers. Now let us work with greater numbers.
Team up with a friend and count:
1.1 in ones from 985 tot 1 005
1.2 in twos from 640 backwards to 596
1.3 in fives from 2 035 to 2 095
1.4 in tens from 1 890 backwards to 1 760
1.5 in hundreds from 800 to 2 600
1.6 in thousands from 4 300 to 9 300
2. Sometimes one does addition and/or subtraction unwittingly (without being aware that that is what you are doing) to get the right answer. Can you tell your friend what to do to each of these numbers in order to change it into the new number?
Table 1.4.
NUMBER
NEW NUMBER
2.1 126
??? 138
2.2 868
??? 828
2.3 943
??? 931
2.4 9 987
??? 9 999
2.5 6 472
??? 6 500
3. If we know the multiples of 10, 100 and 1 000 well, we can divide by them by doing mental
arithmetic (without pencil and paper). Can you give the following answers faster than your friend?
3.1 How many tens are there in: 90 ; 110 ; 280 ; 1 000 ; 4 560 ?
3.2 How many hundreds are there in: 900 ; 1 100 ; 3 000 ; 8 200 ?
3.3 How many thousands are there in: 2 000 ; 8 000 ; 11 000 ; 17 000 ?
Do you see the pattern in the answers? What is the secret of calculating the answers so easily?
÷ 10:
÷ 100:
÷ 1 000:
DO YOU STILL REMEMBER THE FOLLOWING?
An EVEN number is exactly divisible by 2 (can be shared equally amongst 2). An ODD number
cannot be divided exactly by 2 without a remainder or without having a fraction in the answer, e.g.
3 can be divided by 2, but the answer is 1 .
4. Now use your knowledge of even and odd numbers to see whether you can solve the following
riddles
Figure 1.9.
4.1
Figure 1.10.
4.2
Now look at the following diagram.
Figure 1.11.
The number that is represented here is 5 243.
We read it as:
five thousand, two hundred and forty-three.
1. We can also write it like this:
5 243 = 5 000 + 200 + 40 + 3
= (5 × 1 000) + (2 × 100) + (4 × 10) + (3 × 1)
This way of writing is called expanded notation.
Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.1: We know this when the learner counts forwards and backwards in
whole number intervals and fractions;
Assessment Standard 1.8: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems.
1.8. To recognise numbers and represent them
1.8. To recognise numbers and represent them
correctly*
MATHEMATICS
Number Concept, Addition and Subtraction
EDUCATOR SECTION
Memorandum
1.
1.1 A: 2 613
B: 4 871
1.2 A: 2 613 = 2 000 + 600 + 10 + 3
= (2 × 1 000) + (6 × 100) + (1 × 10) + (3 × 1)
B: 4 871 = 4 000 + 800 + 70 + 1
= (4 × 1 000) + (8 × 100) + (7 × 10) + (1 × 1)
3.
3.1 800; 6
(8 × 100); (6 × 1)
3.2 4 000; 90
(4 × 1 000); (9 × 10); (8 × 1)
4.
4.1 20
4.2 8
4.3 5 000
4.4 600
BRAIN TEASERS!
a) 7 846
b) 7 740
c) 3 251
d) 8 292
e) 10
f) 100
Leaner Section
Content
Activity: To recognise numbers and represent them correctly [LO 1.3]
To recognise the place value of digits [LO 1.4]
1. Every digit in every number has a certain value and meaning. Have you ever considered what
the 3 in 435 819 means? Let us see.
Figure 1.12.
1.1 Which number is represented in:
A: __________________________________________________________________
B: __________________________________________________________________
1.2 Write the number in expanded notation:
A: __________________________________________________________________
_____________________________________________________________________
B: __________________________________________________________________
_____________________________________________________________________
2. For the next exercise you must know the place value of every digit. If you can determine this, represent the numbers 6 038 and 4 792 on the diagrams below.
Figure 1.13.
3. It is easier to recognise and represent numbers if we write them in expanded notation. By doing this we know the value of every digit. Fill in the missing numbers.
3.1 9 826 = 9 000 + ....................... + 20 + .......................
= (9 × 1 000) + (......... × .........) + (2 × 10) + (......... × .........)
3.2 4 198 = ................... + 100 + ................... + 8
= (......... × .........) + (1 × 100) + (......... × .........) + (......... × .........)
DO YOU UNDERSTAND?
The VALUE of the 7 in 8 427 is 7.
The VALUE of the 7 in 8 724 = 700.
4. Let us review the difference between value and place value. Can you tell a friend the place
value of every digit below? Then write down the value of every digit in bold print.
4.1 8 329 _________________________________________________________
4.2 4 238 _________________________________________________________
4.3 25 098 _________________________________________________________
4.4 89 641 _________________________________________________________
BRAIN TEASERS!
See if you are able to answer the following questions correctly:
a) 7 856 is 10 more than ____________________________________________
b) 7 640 is 100 less than ____________________________________________
c) ______________________________________ is the first odd number after 3 249
d) ____________________________________ is the even number just before 8 294
e) 8 000 is ______________________________________ times bigger than 800
f) 6 000 is ______________________________________ times bigger than 60
TIME FOR SELF-ASSESSMENT
Table 1.5.
Complete the following by placing a tick in the
Fairly
Altogether
Uncertain
Excellent
appropriate block:
certain
certain
I can count in hundreds, both forwards and
backwards (LO 1.1).
I can count forwards and backwards in thousands
(LO 1.1).
I know the difference between odd and even
numbers (LO 1.3).
I can write numbers in expanded notation (LO
1.3).
I can determine the value of digits in numbers
(LO 1.3).
Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.3: We know this when the learner recognises and represents numbers in order to describe and compare them:
Assessment Standard 1.4: We know this when the learner recognises the place value of digits in whole numbers to at least 6-digit numbers.
1.9. To improve your mental arithmetic skills*
MATHEMATICS
Number Concept, Addition and Subtraction
EDUCATOR SECTION
Memorandum
1. 11; 25; 6; 12; 11; 15; 27; 34
24; 8; 14; 9; 17; 13; 11; 12
2.
2.1 519; 527; 535; 543
2.2 825; 810; 795; 780
2.3 3 770; 3 779; 3 797; 3 806
2.4 99 800; 9 760; 9 640; 9 600
3.
3.1 3 003; 333; 330; 303; 33
3.2 6 666; 6 606; 6 600; 6 060; 6 006
Leaner Section
Content
ACTIVITY: To improve your mental arithmetic skills [LO 1.9]
To examine and extend numeric patterns [LO 2.1]
1. It happens often that one has to think quickly. That is why mental arithmetic skills are very important. Let us see whether you can work faster than your friend. Work in pairs and see who can give the answer first. Start at the arrow every time and work clockwise.
Figure 1.14.
DO YOU STILL REMEMBER?
Rows of numbers sometimes provide very interesting patterns. If we, for instance, begin at 350
and keep adding 15, we'll get the following pattern:
350 ; 365 ; 380 ; 395 ; 410
2. Rows of numbers always have some sort of numeric pattern. Examine the following patterns
and see whether you can complete the rows correctly (use your pocket calculator, if necessary, to check that you have worked correctly):
2.1 495 ; 503 ; 511 ; _________ ; _________ ; . _________ ; _________
2.2 870 ; 855 ; 840 ; _________ ; . _________ ; . _________ ; _________
2.3 3 752 ; 3 761 ; _________ ; _________ ; 3 788 ; _________ ; _______
2.4 _________ ; _________ ; 9 720 ; 9 680 : _________ ; _________
3. In our everyday life it is very important to be able to read and say numbers correctly. We also need to know which number is greater/smaller than the other. Just think of the number of times
per day you work with money. If you save R220, for instance, you would certainly not want R202
to be written in your savings booklet! Look at the following numbers and write them down in
order from the GREATEST to the SMALLEST (descending order).
3.1 303 ; 330 ; 333 ; 33 ; 3 003
_____________________________________________________________________
_____________________________________________________________________
3.2 6 006 ; 6 600 ; 6 666 ; 6 060 ; 6 606
_____________________________________________________________________
_____________________________________________________________________
Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.9: We know this when the learner performs mental calculations;
Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
Assessment Standard 2.1: We know this when the learner investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns.
1.10. To recognise numbers and compare them to one
another*
MATHEMATICS
Number Concept, Addition and Subtraction
EDUCATOR SECTION
Memorandum
1.
1.1 8 366
1.2 7 452
1.3 8 664
1.4 9 548
2.
2.1 6 750
2.2 8 260
2.3 3 516
2.4 9 379
3.
3.1 <
3.2 <
3.3 <
3.4 <
Answer on p. 11-12
1. 46
2. 26
3. 39 337
4. 5 000 I)
5. 4 072 j)
6. 4 440
7. 7 739
8. =
9. 14; 5
10. 1 000; 8
Leaner Section
Content
Activity: To recognise numbers and compare them to one another [LO 1.3]
To be able to calculate correctly [LO 1.8]
MORE OR LESS?
Figure 1.15.
1. If you know where the tens and hundreds are in a number (place value) it is easy to add 10 or 100 (more than), or subtract 10 or 100 (less than). See whether you can write down the answer
immediately! Which number is:
1.1 10 more than 8 356?_____________________________________________
1.2 10 less than 7 462? ______________________________________________
1.3 100 more than 8 564? ____________________________________________
1.4 100 less than 9 648? _____________________________________________
2. In this activity you must read the question carefully and compare your answer to the given
number to ensure that you have worked correctly.
2.1 6 740 is 10 less than _____________________________________________
8 360 is 100 more than ____________________________________________
2.3 3 526 is 10 more than _____________________________________________
2.4 9 279 is 100 less than _____________________________________________
Note: "less than" now means that you must add to get the right answer, and "more than" means that you must subtract to calculate the answer!
COMPARING AND ARRANGING
DO YOU REMEMBER THIS?
> means "larger than"
< means "smaller than"
= means "equal to" or "the same as"
3. We can use the mathematical symbols < ; > and = when we compare answers. It is important that you calculate the answer correctly, or the symbol will be wrong! Now calculate the answer
where necessary, compare the answer left of the é wit the one right of the é and then complete: < ;
> or =:
3.1 (5 × 6) + 9 * 41
3.2 8 921 * 9 821
3.3 2 356 * 2 000 + 500 + 30 + 6
3.4 4 000 + 200 + 50 + 7 * 4 275
FUN WITH THE POCKET CALCULATOR!
Work with a friend. You will need one pocket calculator.
Figure 1.16.
Player A types in any four-digit number on the pocket calculator, e.g. 4 986.
Player B now "shoots down” any of the figures by means of subtraction, e.g. 4 986 − 80 = 4
906.
Take turns to "shoot down” figures. The winner is the player who gets 0 on the display screen.
ASSESS YOURSELF BEFORE GOING FURTHER!
Complete the following by marking the applicable column only:
Table 1.6.
Not
Almost Good Excellent
at all
I am able to see the patterns in rows of numbers and to
complete the number patterns (LO 2.1)
I am able to arrange numbers from large to small and vice
versa (LO 1.3)
I am able to insert the signs that show relationship (> ; < ; =
) correctly (LO 1.3)
LET US SEE HOW YOU ARE COPING.
Are you able to answer the following questions correctly?
1. How many hundreds are in 4 600?___________________________________
2. How many thousands are in 26 000? _________________________________
3. Encircle all the odd numbers in the following:
14 ; 39 ; 128 ; 337 ; 4 000
4. What is the value of the 5 in 5 713?__________________________________
5. Which number is represented in the following diagram?
Figure 1.17.
6. Encircle the largest number:
4 040 ; 4 404 ; 4 440 ; 4 004
7. Which number is 100 more than 7 639?_______________________________
8. Fill in > ; < of = :
40 + 200 + 3 000 + 6 ____________________ 3 246
9. Complete the pattern:
41 ; 32 ; 23 __________________ ; __________________
10. Complete:
2 386 = (2 × _________) + (3 × 100) + (_________ × 10) + (6 × 1)
Assessment
Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment Standard 1.3: We know this when the learner recognises and represents numbers in order to describe and compare them:
Assessment Standard 1.8: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems.
1.11. To represent, recognise and compare numbers*
MATHEMATICS
Number Concept, Addition and Subtraction
EDUCATOR SECTION
Memorandum
1.1 24; 48; 64; 32; 120; 16; 96; 88
1.2 36; 18; 45; 81; 54; 63; 108;
1.3 36; 24; 48; 144; 60; 120; 96; 108;
2.1 27
2.2 68,5
2.3 10
2.4 6
2.5 +
2.6 54
2.7 7