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Recognise, classify, represent and describe numbers

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 5

ORDINARY AND DECIMAL FRACTIONS

Module 48

RECOGNISE, CLASSIFY, REPRESENT AND COMPARE NUMBERS

Activity 1:

To recognise, classify, represent and compare numbers [LO 1.3.3]

To recognise and use equivalent forms of numbers [LO 1.5.2]

1. You have just completed a learning unit on ordinary fractions. Let us do some revision.

What fraction in each of the following figures is coloured in?

1.1

Figure 1
Figure 1 (Picture 1.png)

1.2

Figure 2
Figure 2 (Picture 2.png)

1.3

Figure 3
Figure 3 (Picture 3.png)

2. Write the answers above as decimal fractions.

TENTHS

Refresh your memory!

We read 0,3 as nought comma three and we call it a decimal fraction.

The comma is called the decimal sign and it separates the whole numbers from the fractions.

Do you still remember?

1 10 1 10 size 12{ { {1} over {"10"} } } {}

Figure 4
Figure 4 (Picture 4.png)

3. Look at the number line and fill in the missing numbers.

Figure 5
Figure 5 (graphics1.png)

4. Work together with a friend. Count aloud and complete the following:

4.1 0,2 ; 0,4 ; 0,6 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.2 4,7 ; 4,5 ; 4,3 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.3 0,5 ; 1,5 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.4 3,6 ; 3,2 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.5 9,2 ; 9,1 ; .............. ; .............. ; .............. ; .............. ; .............. ;

Do you still remember?

If I want to add 0,3 to the previous number repeatedly I can programme my calculator in this way: Number+ 0,3 + = = =

Activity 2 :

To use a series of techniques to do mental arithmetic [LO 1.10.5]

By now you know that we can use the pocket calculator very effectively to find or check answers. Now that you have seen how to programme your pocket calculator or to add on, try to complete the following activity without making any mistakes. Programme your pocket calculator and write the first 10 answers to the following:

1.1 Start at 3,7 and add 0,6 each time:

1.2 Start at 9,3 and subtract 0,4 each time:

Activity 3:

  • To recognise, classify and represent numbers in order to describe and compare them [LO 1.3.3]
  • To recognise and use equivalent forms of numbers [LO 1.5.2]
  • To use a series of techniques to do mental arithmetic [LO 1.10.5]

In this activity we would like to see whether you can determine which ordinary fractions (mixed numbers) fit in with which decimal fractions. It is important for you to be able to see that 0,2kg is actually exactly the same as 210210 size 12{ { {2} over {"10"} } } {} kg !

1. Link the ordinary fractions to their decimal fraction partners. Connect column A to the correct answer in column B.

Table 1
  A   B
E.g. 0,2 kg   1 510510 size 12{ { {5} over {"10"} } } {} / 1 1212 size 12{ { {1} over {2} } } {} km
1.1 0,5 m   152 710710 size 12{ { {7} over {"10"} } } {} km
1.2 17,6 litre   210210 size 12{ { {2} over {"10"} } } {} kg
1.3 8,4 seconds   8 410410 size 12{ { {4} over {"10"} } } {} sec
1.4 152,7 km   17 610610 size 12{ { {6} over {"10"} } } {}
1.5 1,5 km   510510 size 12{ { {5} over {"10"} } } {} / 1212 size 12{ { {1} over {2} } } {} m

Challenge!

2.Work with a friend. Write the following fractions as decimal fractions:

2.1 4545 size 12{ { {4} over {5} } } {} 2.2 220220 size 12{ { {2} over {"20"} } } {}

2.3 3535 size 12{ { {3} over {5} } } {} 2.4 720720 size 12{ { {7} over {"20"} } } {}

2.5 18301830 size 12{ { {"18"} over {"30"} } } {} 2.6 48604860 size 12{ { {"48"} over {"60"} } } {}

3. Explain what must be done to get the above answers.

4. How can you check your answers with a calculator?

5. Now use a calculator to check your answers in no. 2.

Activity 4:

To be capable of doing mental arithmetic [LO 1.9]

1. You now have the opportunity of improving your mental arithmetic skills and applying your newly acquired knowledge. Complete the following mental arithmetic test as quickly and as accurately as possible:

Table 2
   
1.1 19 + 21 + 17 = ............ 1.11 ............ ÷ 5 = 8
1.2 125 + 175 = ............ 1.12 45 ÷ ............ = 5
1.3 1 004 – 9 = ............ 1.13 ............ ÷ 9 = 8
1.4 Halve 196 : ............ Write as a decimal fraction:
1.5 Double 225 : ............ 1.14 13 410410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {} : ............
1.6 7 × 4 = ............ 1.15 124 710710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {} : ............
1.7 3 × 8 = ............ 1.16 1 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {} : ............
1.8 ............ × 5 = 45 1.17 2 14201420 size 12{ { { size 8{"14"} } over { size 8{"20"} } } } {} : ............
1.9 ............ × 6 = 42 Write as a decimal fraction:
1.10 24 ÷ 4 = ............ 1.18 4,9 : ............
  1.19 12,8 : ............
  1.20 109,2 : ............
   

HUNDREDTHS

Look carefully at the following:

100 c = R1,00

1c = 11001100 size 12{ { {1} over {"100"} } } {} of a rand

1c = R 11001100 size 12{ { {1} over {"100"} } } {} R0,01

Activity 5:

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

To recognise and use equivalent forms of numbers [LO 1.5.2]

1. By now you have probably discovered that when we work with rand and cents we are actually working with hundredths! Look carefully at the example above and than write the following in rand:

1.1 4 c .........................

1.2 38 c .........................

1.3 2 c .........................

1.4 303 c .........................

1.5 460 c .........................

Did you know?

11001100 size 12{ { { size 8{1} } over { size 8{"100"} } } } {} is written like this as a decimal fraction: 0,01. We read it as nought comma nought one. If we have less than 1010010100 size 12{ { { size 8{"10"} } over { size 8{"100"} } } } {} we must write 0 (nought) as a place-holder after the decimal comma, in the place of the tenths.

Let us look again at our number system:

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

Figure 6
Figure 6 (Picture 31.png)

2. What fraction of the following is NOT coloured in? Write it also as a decimal fraction.

2.1

Figure 7
Figure 7 (Picture 32.png)

2.2

Figure 8
Figure 8 (Picture 33.png)

2.3

Figure 9
Figure 9 (Picture 34.png)

2.4

Figure 10
Figure 10 (Picture 35.png)

2.5

Figure 11
Figure 11 (Picture 36.png)

2.6

Figure 12
Figure 12 (Picture 37.png)

Assessment

Table 3
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;

Memorandum

ACTIVITY 1

1. 1.1: 310310 size 12{ { { size 8{3} } over { size 8{"10"} } } } {}

1.2: 610610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}

1.3: 910910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {}

2. 2.1: 0,03

  • :0,6

2.3: 0,9

3. 410410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {}; 510510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {}; 610610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}; 810810 size 12{ { { size 8{8} } over { size 8{"10"} } } } {}; 11101110 size 12{1 { { size 8{1} } over { size 8{"10"} } } } {}; 13101310 size 12{1 { { size 8{3} } over { size 8{"10"} } } } {}; 14101410 size 12{1 { { size 8{4} } over { size 8{"10"} } } } {}; 15101510 size 12{1 { { size 8{5} } over { size 8{"10"} } } } {}

0,3; 0,7; 0,9; 1,2; 1,3

4. 4.1: 31,5

  • :312,4
  • :402,6
  • :650,2

5. 5.1: 0,8; 1; 1,2; 1,4; 1,6

5.2: 4,1; 3,9; 3,7; 3,5; 3,3

5.3: 2,5; 3,5; 4,5; 5,5; 6,5

5.4: 2,8; 2,4; 2; 1,6; 1,2

5.5: 9; 8,9; 8,8; 8,7; 8,6

ACTIVITY 2

1.1: 4,3; 4,9; 5,5; 6,1; 6,7; 7,3; 7,9; 8,5; 9,1; 9,7

1.2: 8,9; 8,5; 8,1; 7,7; 7,3; 6,9; 6,5; 6,1; 5,7; 5,3

ACTIVITY 3

1. 1.1: 510510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} / 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

  • :17 610610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}
  • :8 410410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {}
  • :152 710710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {}
  • :1 510510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} / 1 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

2. 2.1: 0,8

  • : 0,1
  • : 0,6
  • :0,35
  • : 0,6
  • : 0,8

3. Change denominator to 10 or 100 (equivalent fractions)

4. Numerator + denominator =

ACTIVITY 4

12. 1.1: 57; 1.11: 40

  • :300; 1.12: 9
  • :995; 1.13: 72
  • : 98; 1.14: 13,4
  • :510; 1.15: 124,7
  • : 28; 1.16: 1,8
  • : 24; 1.17: 2,7
  • : 9; 1.18: 4 910910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {}
  • : 7; 1.19: 12 810810 size 12{ { { size 8{8} } over { size 8{"10"} } } } {}
  • : 6; 1.20 : 09 210210 size 12{ { { size 8{2} } over { size 8{"10"} } } } {}

ACTIVITY 5

1. 1.1: R0,04

  • :R0,38
  • :R0,02
  • :R3,03
  • :R4,60

2. 2.1: 8610086100 size 12{ { { size 8{"86"} } over { size 8{"100"} } } } {} = 0,86

2.2 7210072100 size 12{ { { size 8{"72"} } over { size 8{"100"} } } } {} = 0,72

2.3 4410044100 size 12{ { { size 8{"44"} } over { size 8{"100"} } } } {} = 0,44

2.4 : 31003100 size 12{ { { size 8{3} } over { size 8{"100"} } } } {} = 0,03

2.5: 1010010100 size 12{ { { size 8{"10"} } over { size 8{"100"} } } } {} = 0,10

2.6 : 7010070100 size 12{ { { size 8{"70"} } over { size 8{"100"} } } } {} = 0,70

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