Roman Numbers-Journal # 16

Roman Numbers : Roman numerals were originated in Ancient Rome. It is based on certain letters which  are given values as numerals. Roman Numerals are widely used nowadays, in clocks, books, numberlists, etc.,. 1 I 2 II 3 III 4 IV 5 V 6 VI 7 VII 8 VIII 9 IX 10 X 11 XI 12 XII 13 XIII 14 XIV 15 XV 16 XVI 17 XVII 18 XVIII 19 XIX 20 XX 21 XXI 22 XXII 23 XXIII 24 XXIV 25 XXV 26 XXVI 27 XXVII 28 XXVIII 29 XXIX 30 XXX 31 XXXI 32 XXXII 33 XXXIII 34 XXXIV 35 XXXV 36 XXXVI 37 XXXVII 38 XXXVIII 39 XXXIX 40 XL 41 XLI 42 XLII 43 XLIII 44 XLIV 45 XLV 46 XLVI 47 XLVII 48 XLVIII 49 XLIX 50 L 51 LI 52 LII 53 LIII 54 LIV 55 LV 56 LVI 57 LVII 58 LVIII 59 LIX 60 LX 61 LXI 62 LXII 63 LXIII 64 LXIV 65 LXV 66 LXVI 67 LXVII 68 LXVIII 69 LXIX 70 LXX 71 LXXI 72 LXXII 73 LXXIII 74 LXXIV 75 LXXV 76 LXXVI 77 LXXVII 78 LXXVIII 79 LXXIX 80 LXXX 81 LXXXI 82 LXXXII 83 LXXXIII 84 LXXXIV 85 LXXXV 86 LXXXVI 87 LXXXVII 88 LXXXVIII 89 LXXXIX 90 XC 91 XCI 92 XCII 93 XCIII 94 XCIV 95 XCV 96 XCVI 97 XCVII 98 XCVIII 99 XCIX 100 C 200 CC ,300 CCC ,400 CD ,500 D,600 DC,700 DCC ,800 DCCC, 900 CM ,1000 M An accurate way to write the roman numbers is to first take the thousanda,hundreda, tens and units. Example: 1999, one thousand is M, nine hundred is CM, ninety is XC, nine is IX. Combine all these: MCMXCIX

Amazing Prime Numbers-Journal #15

Amazing Prime Numbers

Here are few amazing prime numbers,these prime numbers were proved by 18th century.
                                                                           

31
331
3331
33331
333331
3333331
33333331 The next number 333333331 is not a prime number .Whereas it is multiplied by 17x19607843=333333331

Examples of Manipulative -Journal#14

Examples of Manipulative

Elementary teachers who use manipulatives to help teach math can positively affect students learning .Students at all levels and of all abilities can benefit from manipulatives.

There are some kinds of munipulatives that teachers can prepare for students in the math class which they don't  cost too much for teacher or for the school .

1-Manipulative such as buttons, dried beans, cubes, and animal counters can help young people develop a rich understanding of “number” which forms the basis for counting, arithmetic, and real-world applications.

 They can be used for comparing as well as sorting and classifying. For example, children can use any of these objects to make, count, and order collections of objects. (E.g. Give me four buttons. How many beans are there? Put these groups in order from smallest to largest.)

These manipulatives mostly use for lower grades.

2-Sets of attribute logic blocks with their different shapes and colors are particularly effective for classifying, sorting, and ordering.

(E.g. Find all the pieces that belong in the set labelled “small and square.” Look at the three shapes in the loop. How are they alike? How are they different?) Attribute blocks can also be used to explore size, fractional relationships, and area.

3-Base ten blocks, Cuisenaire® rods, Unifix® cubes, and currency can be used to help children learn a wide range of number concepts, including place value, addition, subtraction, and multiplication.

With the base ten block manipulative, cubes represent ones, rods represent tens, flats represent hundreds, and blocks represent thousands; so a combination of manipulative can be used to represent “twenty-five” or “two groups of ten and five ones,” etc. (E.g. Can you trade ten cubes for a rod? Two rods and five cubes is the same as one rod and how many cubes?)These types of manipulatives can use for elemantry students grde 5 to 8.

Strategies for Asking Questions-Journal#13

     
    When planning questions, keep in mind your course goals

                                                       Avoid asking “leading questions.”

Follow a “yes-or- no” question with an additional question

                                                 Aim for direct, clear, specific questions

In class discussions, do not ask more than one question at once.

When you plan each class session, include notes of when you will pause to ask and answer questions.

Ask a mix of different types of questions

Zero Principle-Jornal#12

Zero Principle:


The zero principle says that the sum of two opposite integers is 0. Explain how the zero principle was used to find this sum.
(-5) + (+4) = (-1)


Answer:


This could be seen as -5 + 5 = 0;
                                   -5 + (4 + 1) = 0;
                                   -5 + 4 = -1.




Sovle the following using the principle of zer products
   

s^2+11s+28=0

s^2 + 4s + 7s +28=0


s(s+4) + 7(s+4)=0


(s+4)(s+7) = 0


using the principle of zero products:

s+4 = 0

OR

s+7 = 0


s = -7,-4

Use a variable ,Write an equation-Journal #11

Question :


Two apples weight the same as a banana and a cherry.A banana weights the same as nine cherries.How many cherries weight the same as one apple?




Solution:




1st .Understand the problem.
This is complicated since three quantities are being discuss.          


2nd.Devise a plan
We need to introduce three variables.

3rd.Carry out the plan
A=the weight of an apple                                                 
B=the weight of a banana
C=the weight of a cherry


     2A=B+C
      B=9C


Substituting: 2A=9C+C
                     2A=10C
                     A=5C
Answer :5 cherries weigh the same as one apple


4th.Look back
Without algebra,this was pretty tough.