Inside Collection (Course): Mathematics Grade 5
1. Use your existing knowledge to complete the following table:
T  U  t  h  
E.g.  5  9  8  =  5

=  5,98  
1.1  3  6  =  _____  =  _____  
1.2  1  7  =  _____  =  _____  
1.3  3  6  =  _____  =  _____  
1.4  4  2  8  5  =  _____  =  _____ 
1.5  4  7  0  3  =  _____  =  _____ 
Brainteaser!
What will the following fractions look like if written as decimal fractions on the calculator?
1.
2.
3.
4.
5.
6.
How do the answers of 3 and 4 differ from the rest?
Why is this?
Did you know?
Normally we don’t write the noughts at the end of decimal fractions, but in the following cases we do:
a) When we work with money: R8,60 (shows how many cents there are).
b) When we time an athlete with a stopwatch: 7,30 seconds. This is how we give results to the hundredth of a second.
1. It is sometimes difficult to determine exactly where a decimal number fits into the greater whole. A number line is a handy way of helping you to determine this, because it helps you to “see” the sequence of the numbers. Draw arrows and label with the letters given to indicate more or less where the following numbers will be on the number line:
A : 5,82
B : 5,99
C : 6,09
D : 6,24
1. Let us play a game!
Work with a friend. Take turns. Close your eyes and press on any number in the diagram on the next page with the back of your pencil. Open your eyes and tell your friend what the number consists of:
e.g. 14,38 = 14 +
Colour in every number you get right green. Your friend colours all his / her correct numbers blue. The one who has something wrong misses a turn. The one who has coloured in the most blocks, wins.
1. By now you know how to write tenths and hundredths as decimal fractions. Look very carefully at the following numbers. Replace the * with < , > or =.
Hint: You should break the numbers up as in the game above if you have any doubts about the correct answer.
1.1 1,7 * 1,07 _____
1.2 0,6 * 0,06 _____
1.3 0,58 * 0,9 _____
1.4 0,34 * 0,4 _____
1.5 2,05 * 2,5 _____
1.6 1,8 * 1,80 _____
Brainteaser!
What does one quarter (
Can you write the following as decimal fractions?
a)
b)
c)
d)
1. Challenge!
Take a measuring tape and measure the height of five of your class mates (to 2 digits after the decimal comma). List your results in a table and number your friends from the shortest to the tallest.
Name  Height  Numbered:short to tall  
1.1  
1.2  
1.3  
1.4  
1.5 
Did you know?
When I write one thousandth
The noughts are place holders for the units, tenths and hundredths and may not be left out.
E.g.
U  t  h  th 
X  
X  X  
X  X  X  
X  X  X  X 
1.1
U  t  h  th 
X  
X  X  
X  X  
X  X  
X  X  X  
X  X  X 
1.2
U  t  h  th 
x  
x  
x  
x  x  
x  x  x  
x  x  x 
1.3
U  t  h  th 
x  
x  
x  x  
x  x  
x  x  x  
x  x  x  
x  x  x 
1. Colour in only the bags that are heavier than 1,5 kg:
2. In Module 1 we spoke a lot about the value and place value of numbers. (Do you remember?) Look carefully at the following numbers and then write down the value of each number that has been underlined:
E.g. 3,768 :
2.1 4,231 : _____
2.2 8,923 : _____
2.3 289,7 : _____
2.4 21,38 : _____
2.5 57,236 : _____
2.6 9,897 : _____
3. Compare the following numbers. Draw a circle around the smallest one.
Hint: You may change them to ordinary fractions / mixed numbers if you like – this may help you to get the answer more easily!
3.1 0,6 ; 0.06 ; 0,006
3.2 3,2 ; 0,32 ; 0,032
3.3 1,101 ; 1,111 ; 1,110
Brainteaser!
What does one eighth (
And
Can your write
What does
Explain how you got these answers WITHOUT using the calculator!
Learning outcomes(LOs) 
LO 1 
Numbers, Operations and RelationshipsThe learner is 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 standards(ASs) 
We know this when the learner: 
1.3 recognises and represents the following numbers in order to describe and compare them: 
1.3.3 decimal fractions of the form 0,5; 1,5; 2,5, and so on, in the context of measurement; 
1.5 recognises and uses equivalent forms of the numbers listed above, including: 
1.5.2 decimal fractions of the form 0,5, 1,5 and 2,5, and so on, in the context of measurement; 
1.6 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:

1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.9 performs mental calculations involving:1.9.1 addition and subtraction;1.9.2 multiplication of whole numbers to at least 10 x 10; 
1.10 uses a range of techniques to perform written and mental calculations with whole numbers including:

1.11 uses a range of strategies to check solutions and judge the reasonableness of solutions; 
LO 2 
Patterns, functions and algebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. 
We know this when the learner: 
2.6 determines, through discussion and comparison, the equivalence of different descriptions of the same relationship of rule presented 
2.6.3 by number sentences. 
We know this when the learner: 
2.6 determines, through discussion and comparison, the equivalence of different descriptions of the same relationship of rule presented 
2.6.3 by number sentences. 
We know this when the learner: 
5.3 organises and records data using tallies and tables; 
1. 1.1
1.2
1.3
1.4
1.5
BRAINTEASER!
1. 0,03
2. 0,09
3. 0,4
4. 0,8
5. 0,37
6. 0,59
Only one digit after the comma.
Pocket calculator does not show the last nought.
ACTIVITY 2
1.
A B C D
ACTIVITY 4
1. 1.1 >
1.2 >
1.3 <
1.4 <
1.5 <
1.6 =
BRAINTEASER!
a) 0,75
ACTIVITY 6
1. 1.1: 5,026
2. 2.1: 5
2.2: 2
2.3:
ACTIVITY 7
1. 1,523; 1,52; 2,5; 2,146; 1,7; 1,510; 3,5
2. 2.1
2.2
2.3
2.4 20
2.5
2.6
3. 3.1 0,006
3.2 0,032
3.3 1,101
BRAINTEASER!
0,125; 0,375; 0,625; 0,875
0,448
0,7
Change denominator to 1 000 (equivalent fractions)