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Tables and checks to arrange and record data

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 5

ORDINARY AND DECIMAL FRACTIONS

Module 49

TABLES AND CHECKS TO ARRANGE AND RECORD DATA

Activity 1:

To use tables and checks to arrange and record data [LO 5.3]

1. Use your existing knowledge to complete the following table:

Table 1
  T U t h        
E.g.   5 9 8 = 5 9810098100 size 12{ { { size 8{"98"} } over { size 8{"100"} } } } {} = 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 = _____ = _____

Brain-teaser!

What will the following fractions look like if written as decimal fractions on the calculator?

1. 31003100 size 12{ { {3} over {"100"} } } {} ______

2. 91009100 size 12{ { {9} over {"100"} } } {} ______

3. 4010040100 size 12{ { {"40"} over {"100"} } } {} ______

4. 8010080100 size 12{ { {"80"} over {"100"} } } {} ______

5. 3710037100 size 12{ { {"37"} over {"100"} } } {} ______

6. 5910059100 size 12{ { {"59"} over {"100"} } } {} ______

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 stop-watch: 7,30 seconds. This is how we give results to the hundredth of a second.

  1. a) When Mom buys material: 1,70 m (so that the saleslady knows exactly how many cm to cut).

Activity 2:

To recognise and represent numbers [LO 1.3.3]

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:

Figure 1
Figure 1 (Picture 10.png)

A : 5,82

B : 5,99

C : 6,09

D : 6,24

Activity 3:

To use a series of techniques to do mental arithmetic [LO 1.10.2]

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 + 310310 size 12{ { {3} over {"10"} } } {} + 81008100 size 12{ { {8} over {"100"} } } {}

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.

Figure 2
Figure 2 (Picture 13.png)

Activity 4:

To recognise and classify numbers in order to compare them [LO 1.3.3]

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 _____

Brain-teaser!

What does one quarter ( 1414 size 12{ { { size 8{1} } over { size 8{4} } } } {}) look like as a decimal fraction?

Can you write the following as decimal fractions?

a) 3434 size 12{ { {3} over {4} } } {} : _____

b) 125125 size 12{ { {1} over {"25"} } } {} : _____

c) 320320 size 12{ { {3} over {"20"} } } {} : _____

d) 17501750 size 12{ { {"17"} over {"50"} } } {} : _____

Activity 5:

To use tables and checks in order to arrange and record data [LO 5.3]

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.

Table 2
  Name Height Numbered:short to tall
1.1      
1.2      
1.3      
1.4      
1.5      

THOUSANDTHS

Did you know?

When I write one thousandth 1100011000 size 12{ { {1} over {"1000"} } } {} as a decimal fraction, it will be 0,001.

The noughts are place holders for the units, tenths and hundredths and may not be left out.

1 1000 1 1000 size 12{ { {1} over {"1000"} } } {} 1 100 1 100 size 12{ { {1} over {"100"} } } {}

Figure 3
Figure 3 (Picture 41.png)

Activity 6:

To recognise, classify and represent numbers in order to describe and compare them [LO 1.3.3]

  1. Look carefully at the representations below. Which decimal numbers are represented in each one?

E.g.

Table 3
U t h th
       
       
      X
X     X
X   X X
X X X X

1.1

Table 4
U t h th
      X
X     X
X     X
X     X
X   X X
X   X X

1.2

Table 5
U t h th
       
  x    
  x    
  x    
  x   x
x x   x
x x   x

1.3

Table 6
U t h th
      x
      x
    x x
    x x
  x x x
  x x x
  x x x
  1. Can you write the above as mixed numbers / common fractions?

Activity 7:

To recognise, classify and represent numbers in order to describe and compare them [LO 1.3.3]

1. Colour in only the bags that are heavier than 1,5 kg:

Figure 4
Figure 4 (Picture 42.png)

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 : 8100081000 size 12{ { {8} over {"1000"} } } {}

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

Brain-teaser!

What does one eighth ( 1818 size 12{ { {1} over {8} } } {} ) look like as a decimal fraction?

And 3838 size 12{ { {3} over {8} } } {} ?_____ And 5858 size 12{ { {5} over {8} } } {} ? _____ And 7878 size 12{ { {7} over {8} } } {} ?._____

Can your write 112250112250 size 12{ { {"112"} over {"250"} } } {} as a decimal fraction? .

What does 350500350500 size 12{ { {"350"} over {"500"} } } {} look like as a decimal fraction?

Explain how you got these answers WITHOUT using the calculator!

Assessment

Table 7
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:
  • measurements in Natural Sciences and Technology contexts;
1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve:
  • (additional) addition of positive decimals with 2 decimal places;
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:
  • building up and breaking down numbers;
  • using a calculator;
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;

Memorandum

ACTIVITY 1

1. 1.1 3610036100 size 12{ { { size 8{"36"} } over { size 8{"100"} } } } {} = 0,36

1.2 1710017100 size 12{1 { { size 8{7} } over { size 8{"100"} } } } {} = 1,07

1.3 36103610 size 12{3 { { size 8{6} } over { size 8{"10"} } } } {} = 3,6 / 3,60

1.4 42851004285100 size 12{"42" { { size 8{"85"} } over { size 8{"100"} } } } {} = 42,85

1.5 473100473100 size 12{"47" { { size 8{3} } over { size 8{"100"} } } } {} = 47,03

BRAIN-TEASER!

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

Figure 5
Figure 5 (Picture 33.png)

ACTIVITY 4

1. 1.1 >

1.2 >

1.3 <

1.4 <

1.5 <

1.6 =

BRAIN-TEASER!

a) 0,75

  1. a) 0,04
  2. b) 0,15
  3. c) 0,34

ACTIVITY 6

1. 1.1: 5,026

  • :2,603
  • :0,359

2. 2.1: 5 261000261000 size 12{ { { size 8{"26"} } over { size 8{"1000"} } } } {}

2.2: 2 60310006031000 size 12{ { { size 8{"603"} } over { size 8{"1000"} } } } {}

2.3: 35910003591000 size 12{ { { size 8{"359"} } over { size 8{"1000"} } } } {}

ACTIVITY 7

1. 1,523; 1,52; 2,5; 2,146; 1,7; 1,510; 3,5

2. 2.1 31003100 size 12{ { { size 8{3} } over { size 8{"100"} } } } {}

2.2 910910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {}

2.3 710710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {}

2.4 20

2.5 6100061000 size 12{ { { size 8{6} } over { size 8{"1000"} } } } {}

2.6 91009100 size 12{ { { size 8{9} } over { size 8{"100"} } } } {}

3. 3.1 0,006

3.2 0,032

3.3 1,101

BRAIN-TEASER!

0,125; 0,375; 0,625; 0,875

0,448

0,7

Change denominator to 1 000 (equivalent fractions)

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