m30946 Recognise, classify, represent and describe numbers 1.1 2009/08/03 01:29:52.018 GMT-5 2009/08/03 01:38:24.328 GMT-5 gert bezuidenhout gert bezuidenhout gertb@mweb.co.za gert bezuidenhout gert bezuidenhout gertb@mweb.co.za gert bezuidenhout gert bezuidenhout gertb@mweb.co.za Mathematics and Statistics en

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

1.2

1.3

2. Write the answers above as decimal fractions.

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

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

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 + = = =

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:

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 210 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. A B E.g. 0,2 kg 1 510 size 12{ { {5} over {"10"} } } {} / 1 12 size 12{ { {1} over {2} } } {} km 1.1 0,5 m 152 710 size 12{ { {7} over {"10"} } } {} km 1.2 17,6 litre 210 size 12{ { {2} over {"10"} } } {} kg 1.3 8,4 seconds 8 410 size 12{ { {4} over {"10"} } } {} sec 1.4 152,7 km 17 610 size 12{ { {6} over {"10"} } } {} ℓ 1.5 1,5 km 510 size 12{ { {5} over {"10"} } } {} / 12 size 12{ { {1} over {2} } } {} m Challenge! 2.Work with a friend. Write the following fractions as decimal fractions: 2.1 45 size 12{ { {4} over {5} } } {} 2.2 220 size 12{ { {2} over {"20"} } } {} 2.3 35 size 12{ { {3} over {5} } } {} 2.4 720 size 12{ { {7} over {"20"} } } {} 2.5 1830 size 12{ { {"18"} over {"30"} } } {} 2.6 4860 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.

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: 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 13 410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {} : ............ 1.6 7 × 4 = ............ 1.15 124 710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {} : ............ 1.7 3 × 8 = ............ 1.16 1 45 size 12{ { { size 8{4} } over { size 8{5} } } } {} : ............ 1.8 ............ × 5 = 45 1.17 2 1420 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 : ............

Look carefully at the following: 100 c = R1,00 1c = 1100 size 12{ { {1} over {"100"} } } {} of a rand 1c = R 1100 size 12{ { {1} over {"100"} } } {} R0,01

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? 1100 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 10100 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 size 12{ { {1} over {"100"} } } {}

2. What fraction of the following is NOT coloured in? Write it also as a decimal fraction. 2.1

2.2

2.3

2.4

2.5

2.6

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;

ACTIVITY 1 1. 1.1: 310 size 12{ { { size 8{3} } over { size 8{"10"} } } } {} 1.2: 610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {} 1.3: 910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {} 2. 2.1: 0,03 :0,6 2.3: 0,9 3. 410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {}; 510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {}; 610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {}; 810 size 12{ { { size 8{8} } over { size 8{"10"} } } } {}; 1110 size 12{1 { { size 8{1} } over { size 8{"10"} } } } {}; 1310 size 12{1 { { size 8{3} } over { size 8{"10"} } } } {}; 1410 size 12{1 { { size 8{4} } over { size 8{"10"} } } } {}; 1510 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: 510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} / 12 size 12{ { { size 8{1} } over { size 8{2} } } } {} :17 610 size 12{ { { size 8{6} } over { size 8{"10"} } } } {} :8 410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {} :152 710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {} :1 510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {} / 1 12 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: 4 910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {} : 7; 1.19: 12 810 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} : 6; 1.20 : 09 210 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: 86100 size 12{ { { size 8{"86"} } over { size 8{"100"} } } } {} = 0,86 2.2 72100 size 12{ { { size 8{"72"} } over { size 8{"100"} } } } {} = 0,72 2.3 44100 size 12{ { { size 8{"44"} } over { size 8{"100"} } } } {} = 0,44 2.4 : 3100 size 12{ { { size 8{3} } over { size 8{"100"} } } } {} = 0,03 2.5: 10100 size 12{ { { size 8{"10"} } over { size 8{"100"} } } } {} = 0,10 2.6 : 70100 size 12{ { { size 8{"70"} } over { size 8{"100"} } } } {} = 0,70