m30951 Tables and checks to arrange and record data 1.1 2009/08/03 02:20:42.746 GMT-5 2009/08/03 02:51:33.685 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. Use your existing knowledge to complete the following table: T U t h E.g. 5 9 8 = 5 98100 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. 3100 size 12{ { {3} over {"100"} } } {} ______ 2. 9100 size 12{ { {9} over {"100"} } } {} ______ 3. 40100 size 12{ { {"40"} over {"100"} } } {} ______ 4. 80100 size 12{ { {"80"} over {"100"} } } {} ______ 5. 37100 size 12{ { {"37"} over {"100"} } } {} ______ 6. 59100 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. When Mom buys material: 1,70 m (so that the saleslady knows exactly how many cm to cut).

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 + 310 size 12{ { {3} over {"10"} } } {} + 8100 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.

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 ( 14 size 12{ { { size 8{1} } over { size 8{4} } } } {}) look like as a decimal fraction? Can you write the following as decimal fractions? a) 34 size 12{ { {3} over {4} } } {} : _____ b) 125 size 12{ { {1} over {"25"} } } {} : _____ c) 320 size 12{ { {3} over {"20"} } } {} : _____ d) 1750 size 12{ { {"17"} over {"50"} } } {} : _____

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 11000 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 size 12{ { {1} over {"1000"} } } {} 1 100 size 12{ { {1} over {"100"} } } {}

Look carefully at the representations below. Which decimal numbers are represented in each one? 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 Can you write the above as mixed numbers / common fractions?

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 : 81000 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 ( 18 size 12{ { {1} over {8} } } {} ) look like as a decimal fraction? And 38 size 12{ { {3} over {8} } } {} ?_____ And 58 size 12{ { {5} over {8} } } {} ? _____ And 78 size 12{ { {7} over {8} } } {} ?._____ Can your write 112250 size 12{ { {"112"} over {"250"} } } {} as a decimal fraction? . What does 350500 size 12{ { {"350"} over {"500"} } } {} look like as a decimal fraction? 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: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;

1. 1.1 36100 size 12{ { { size 8{"36"} } over { size 8{"100"} } } } {} = 0,36 1.2 17100 size 12{1 { { size 8{7} } over { size 8{"100"} } } } {} = 1,07 1.3 3610 size 12{3 { { size 8{6} } over { size 8{"10"} } } } {} = 3,6 / 3,60 1.4 4285100 size 12{"42" { { size 8{"85"} } over { size 8{"100"} } } } {} = 42,85 1.5 473100 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

ACTIVITY 4 1. 1.1 > 1.2 > 1.3 < 1.4 < 1.5 < 1.6 = BRAIN-TEASER! a) 0,75 0,04 0,15 0,34 ACTIVITY 6 1. 1.1: 5,026 :2,603 :0,359 2. 2.1: 5 261000 size 12{ { { size 8{"26"} } over { size 8{"1000"} } } } {} 2.2: 2 6031000 size 12{ { { size 8{"603"} } over { size 8{"1000"} } } } {} 2.3: 3591000 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 3100 size 12{ { { size 8{3} } over { size 8{"100"} } } } {} 2.2 910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {} 2.3 710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {} 2.4 20 2.5 61000 size 12{ { { size 8{6} } over { size 8{"1000"} } } } {} 2.6 9100 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)