THE PROOF SET IN STONE

Size: px
Start display at page:

Download "THE PROOF SET IN STONE"

Transcription

1 373 6 THE PROOF SET IN STONE π e & MATHEMATICAL EVIDENCE FOR INTELLIGENT DESIGN IN THE FIRST WORDS OF THE BIBLE By Peter Bluer 1

2 16 July 2009 Printed 17 May

3 The Two Universal Constants encoded in Gen 1.1 and John 1.1 The two universal constants known to science and mathematics are the well known one called Pi - π: /7 and the not so well known one of Exponentiation called e : π first appears as the ratio of the diameter of a circle to its circumference C = πd or 2πr. This constant is used to calculate the Area of Circle and the Surface Area and the Volume of a Sphere. Its use is truly universal in Physics and other branches of Science. For example, a few formulae are, 0 = e iπ + 1 Pure Maths ƒ 0 = 1 / 2π LC Force on a Planet = 4π 2 m r / T 2 Electrical Theory Gravitation theory Any Science that involves 2 or 3 dimensional space or solid materials, which is virtually everything, will always involve π. The other universal constant is involved throughout Science and Mathematics. It was first discovered in the 16th century and is associated with exponential growth. It is found in quantitative science and technology obeying the law of the form y = Ae kt. It is not always realised by both teachers and students just how important this constant is. Here are some formulae that uses e. x = Ae kt A(x) = x / Loge x Wave Equation Distribution of Prime numbers Q (t) = Qe -t/rc Electrical theory e x é = Cos x + ésin x Pure Mathematics é = -1 Now why are we discussing these constants as regards the issue of Creation and Evolution? Special Creation by God is the answer given by the Bible of why we are here on Earth. First we have to establish the true value of both these constants. 1. This paper is taken from the book A Proof Set in Stone obtainable from the author Dr Peter Bluer, 15 Patchcroft Rd, Wythenshawe, Manchester, M22 5JG. The Author is indebted to Vernon Jenkins, Bevan Williams and Ian Strachan for their discovery of some of these symmetries and the numerical constants. 3

4 à 1 á 1 á 2 â 2 â 3 ã 3 ã 4 ä 4 ä 5 å 5 å 6 6 æ 7 æ 7 ç 8 ç 8 è 9 è 9 é 10 é 10 ë 20 ê 20 ì 30 ë 30 î 40 ì 40 ð 50 í 50 ñ 60 î 60 ò 70 ï 70 ô 80 ð 80 ö ñ 100 ø 200 ó 200 ù 300 ô 300 ú 400 õ 400 ö ø 700 ù 800 The ancients did not know that e existed and had difficulty arriving at a true value of π, but today we know the true value of π to many millions of places of decimals. We know the value of e from the time when it was first discovered. Now what does the Bible say about these two constants? Quite a lot and the values will be shown to be within 0.001% of the true values in both cases. Because these Constants are Irrational Numbers in the same way as 2 is, it is not possible that the Biblical method of calculating the values can be exact. This is even true for the mathematical formulae that mathematicians use.. Firstly both the Hebrew and Greek alphabets have an unusual phenomena in that not only are they letters that spell words but each letter has a numerical value that was decided in about 200 BC. The Table shows the values. The Scripture in Gen 1.1 says In the beginning God created the Heavens and the Earth and John 1.1 says In the beginning was the Word and the Word was with God and the Word was God It is the numeric values of these two sentences that provide the answer. Below is Gen 1.1 with the necessary values applied from the table of values. It must be remembered that Gen 1.1 was written thousands of years ago at the very dawn of history. The following analysis is truly amazing. It is hardly believable, but I must say the facts are written in Scripture in the same manner as a name engraved in Stone. Now for the formula! = ,200,1,5 400,1,6 40,10,40,300,5 400,1 40,10,5,30,1 1,200,2 400,10,300,1,200,2 õøàä úàåt íéîùä úà íéäìà àøá úéùàøá Earth the and Heavens the God created beginning the In 4

5 Applying this most intriguing formula to the Gen 1.1 and John 1.1 π = Gen 1.1 The number of letters x the product of the letters The number of words x the product of the words π = 28 x = x Standard form format 28 ( letters ) x 90 x 200 x 1 x 5 x 400 x 1 x 6 x 40 x 10 x 40 x 300 x 5 x 400 x 1 x 40 x 10 x 5 x 30 x 1 x 1 x 200 x 2 x 400 x 10 x 300 x 1 x 200 x 2 we have the following value 28 x ,000,000,000,000,000,000,000,000,000 This can be expressed as 28 x x Then 7 ( words ) x 913 x 203 x 86 x 401 x 395 x 407 x 296 which gives 7 x 304,153,525,784,175,760 This can be expressed as 7 x x This is the same string of digits as We now apply the same formula to John 1.1 π e = John 1.1 The number of letters x the product of the letters The number of words x the product of the words ,50 1,100,600,8,10 8, ,70,3,70,200 20,1, ,70,3,70,200 8,50 In [the] beginning was the Word and the Word was Åí áñ çí ï ëïãïò 5 êáé ï ëïãïò çí ,100,70, ,70,50 9,5,70,50 20,1,10 9,5,70,200 8, ,70,3,70,200 with the God and God was the Word, ðñïò ôïí èåïí, êáé èåïò çí ï ëïãïò

6 e = 52 x = x Standard form format 52 ( letters ) x 5 x 50 x 1 x 100 x 600 x 8 x 10 x 8 x 50 x 70 x 30 x 70 x 3 x 70 x 200 x 20 x 1 x 10 x 70 x 30 x 70 x 3 x 70 x 200 x 8 x 50 x 80 x 100 x 70 x 200 x 300 x 70 x 50 x 9 x 5 x 70 x 50 x 20 x 1 x 10 x 9 x 5 x 70 x 200 x 8 x 50 x 70 x 30 x 70 x 3 x 70 x 200 We have the following calculation: 52_x_843,625,145,625,911,083,008,0000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000 This can be expressed as 52 x x ( words ) x 55 x 719 x 58 x 70 x 373 x 31 x 70 x 373 x 58 x 450 x 420 x 134 x 31 x 284 x 58 x 70 x 373 which gives 17 x Expressed as 17 x x This value of e is derived in the same way as for π after stripping the constants of their surplus zeroes and using the constants in their standard form format: This string of digits are the same as the constant e This is one thousandth of 1% accuracy. [ and the scripture cannot be broken John ], To now consider the accuracy to 7 millionths of a unit we will take the sum of both π and e Mathematical value Biblical value π = e = Total sum = The absolute error = or 1 Ten Thousandths of 1% That these two major constants that appear throughout the Creation and they are both derived from Gen 1.1 and John 1.1 These two verses contain the major truths of Creation from Judaism and Christianity. I cannot emphasize too much just how this Exponential Constant and its inverse the logarithm describes the physical Universe in which we live. This constant has only being discovered and developed in the last 4 centuries, the Ancients new nothing of it yet it is explicit in John 1.1, written 2000 years ago by the same format as Gen

7 How did John in his gospel know this 2000 years ago? Did he study Genesis and realised that π was encoded and then he secretly knew this exponential constant and decided to encode this in his writings? This whole notion is preposterous and the real truth is that God inspired him to write these profound words! If we drop one letter the constants are destroyed so it shows that the actual text has been preserved by the providence of God. Gen 1.1 can be displayed in Numerical Geometry % %% %%% %%%% The sum of the 3 %%%%% %%%%%% black Equilateral %%%%%%% %%%%%%%% 2701 %%%%%%%%% Triangles is 1998 %%%%%%%%%% %%%%%%%%%%% %%%%%%%%%%%% which is the phrase: %%%%%%%%%%%%% %%%%%%%%%%%%%% %%%%%%%%%%%%%%% %%%%%%%%%%%%%%%% In the beginning %%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%% God created %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%% the Heavens %%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% The smaller triangle %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%% is 703 the phrase: %%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%% and the Earth %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 73 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 73 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% And %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% the Earth %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 703 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 73 The triangle above has 2701 elements with side lengths of 73 elements, 2701 is the value of Gen 1.1, 2701 is the 73 rd Triangular Number. The inscribed triangle has 703 elements the value of and the Earth with side lengths of 37 elements, which is 37 th Triangular number. This triangle fits neatly in such a way as to section off 3 more Triangles that have 666 elements and side lengths of 36 elements = 1998 Notice the threeness of the Symmetry, a sign of the Triune God. 7

8 Here are some further Symmetries of Gen 1.1 which are outstanding. If we add together the odd positional values of the words, 913 (1) + 86 (3) (5) (7) = 1690 = 10 x 169 The even positional values, 203 (2) (4) (6) = 1011 = 3 x 337 First the value 1690 is 10 times the 8 th Hexagon number ( 169 ) = 10 x 169. Also the second value 1011 is 3 times the 8 th Hexagram number ( 337 ) 1011 = 3 x 337. & && & && & && & & && & && & && & && & && & & && & && & & & & && & && & && & && && & && & & && & & & && & & && && & & && & && 337 & && The Value of 169 this Structure is 2701 = 37 x 73 && && && Gen 1.1 && && && && & && && & && & *& *& & && && & & & && & & && && & && && && && & && && & && & & && && & & && & & && & & && & & && & & & && & && && & && && & & && & && & && & & & && & & & & && & & None of this design is a 337 product of chance but of && & & divine origin. && & By Dr Peter Bluer PhD, BSc [hons] && &

9 Many people ask me why 373? The number 373 is a very interesting value. From the look of it you can see it is a palindrome - that is, it reads the same value backwards as well as forwards. Looking again it will separate into (37)3 or into 3(73). And 73 is the reflection of is the 74 th prime number. You might ask why is that so relevant? The value 74 is 2 x 37 and 74 is the neighbour of 73. Now it gets interesting!. On investigation 37 is the 12 th prime number and 73 is the 21 st prime number and we can now observe that 12 and 21 are the reflections of each other in just the same way that 37 and 73 are reflections. The neighbour of the value 373 is the number 374 which when separated gives (37)4 and 3(74) which is of course 3( 2 x 37 ). Let us now find the product of 37 x 73 = Is this unusual? Yes! Finding the sum of 2701 and its reflection 1072 gives Now 3773 = 7 x 7 x 7 x 11 = 7 3 x 11 [ 3 & 7 ] All this from 373 is a strange phenomenon! Upon examination of 2701 it is the 73 rd triangular number i.e. the sum of all the values of = There many more results concerning these numbers 3 & 7 and it can be shown by algebra that only 3, 7 have these remarkable properties. The question is where on earth did I get this starting number 373? The answer is from the Bible is the value of Gen 1.1 and 373 is the value of Word the name of Jesus Christ. Now Jesus has the value 888 = 3 x 8 x 37 and Christ has the value of 1480 = 3 x 5 x 37 Both multiples of 37 The value of π can also be given as The Name of the Messiah (Christ) Word ( ëïãïò ) = 30,70,3,70,200 = 373 ëïãïò 9

10 These words of Genesis were written by Moses before the numeration of the letters were known!! The numeration of the Hebrew came into existence in about 200 BC. John 1.1 is in Greek, Gen 1.1 is in Hebrew a different language. The Star of David has a history only from about 1000 BC. It is very intriguing that a Mathematic structure such as the Hexagram was chosen as Israel s national emblem. ** Therein lies the clue that we have all missed! ** The structure of the Hexagon and the Hexagram was discovered while proving by algebra that 37 x 73 = 2701 and also is the 73 rd triangular number with reflective digits. This is unique solution which uses the values of 3 and 7. Gen 1.1 is 37 x 73 = 2701 ( ) John 1.1 is 39 x 93 = 3627 Please note, both scriptures have reflective factors = 6328 the 112 th Triangular number. 112 is the value of LORD ( 26 ) + GOD ( 86 ) Hebrew. JESUS = (888 = 3 x 8 x 37) + CHRIST = (1480 = 5 x 8 x 37) = 2368 ' ' ' '''' ' '''' '''' ' ' ' 6328 is an anagram of 2368 = 4 3 x 37 ( ) Gen 1.1 with the 5 words 1998 = 2 x 3 3 x 37 Now the Hexagon can be viewed also as a cube. The cubes shown are 3 3 and 4 3 To recall, the value of The God íéäìàä is 91. Exploring the factor 91 = 7 x 13 we have '''' ''''' '''''' ''''''' '''''' ''''' '''' = = 37 and its Reflection 73 and 73 x 37 = = = 91 and its Reflection 19 and 19 x 37 = 703 The value 703 = and the Earth is composed of = 703 if we now calculate 3 3 / 91 = and = 3 3 x 3 3 x 407. with also 4 3 / 91 = and = 3 3 x 4 3 x 407. The value 407 (11 x 37) is the value of the sixth word of Gen 1.1 These Structures show an origin not of man, but of God because when Gen 1.1 was written the numeric assignments were unknown. 10

11 As we investigate further, these Signatures 37 & 73 will keep re-occuring in these numerical structures. For example concatenate the values 37 & 73 in this way as Arranged as follows (37)3 or 3(73). What do we find? 373 is the 74 th Prime Number. 74 is 2 x 37 and the neighbour of 73. Add the last two words [6,7] = 703 (7, 3) and 703 = gives the digits [37x3] [373] [3x73] Previously we had 3773 revealing 7 3 = 7 x 7 x 7 = also encodes 37 and 73. How? 3(43) = = 37 (34)3 = = 73 (7) (7) This value 343 equals the sum of two Hebrew words Myhla rmayv In summary this number 2701 and its Prime Number product of 37 x 73 is most definitely a very remarkable number. It is time, I think, that you should know what is the translation of these 7 Hebrew words. It is the sentence that the Astronauts read out from their Space Module. It is the most famous sentence known to man and it comes from the most ancient document we have. It is from the first words of the Bible in Gen 1.1 In the beginning God created the Heaven and the Earth The 2 nd object the 1 st object Subject and verb Xrah 7 tav 6 MymDh 5 ta 4 Myhla 3 arb 2 tydarb Earth the **and Heavens the ** God created beginning the In Each day of Creation begins And God said 343 = 7 3 as above Gen 1.3,6,9,14,20,24, **Untranslatable Participle - the sign of the direct object 11 Myhla rmayv God said and

12 Outstanding All these the values are define by the Decimal System i.e. Radix 10. In Appendix A, it is proved examining the other possible Radices of the form r = 3a + 1, that the only viable Radix for Bible Numerics is Radix 10. Multiples of 37 n th Prime Number 1 Position in π ( Pi ) 1 1 x 3 x 37 = th Prime no occurs at position x 3 x 37 = nd Prime no occurs at position x 3 x 37 = rd Prime no occurs at position x 3 x 37 = th Prime no occurs at position x 3 x 37 = th Prime no occurs at position x 3 x 37 = th Prime no occurs at position x 3 x 37 = th Prime no occurs at position x 3 x 37 = th Prime no occurs at position x 3 x 37 = th Prime no occurs at position 762 Totals Sums to Sums to Remember Gen 1.1 with its value of 2701 and its Reflection of = 3773 Proof-Evidence Reflect <> = Can you believe the above! These properties of 37 & 73 = 2701 are phenomenal and that is why The Lord has chosen base 10 and the Symmetries of the Prime Number 37. It is only in this age of computers that it has been possible to calculate these large number positions in π and Prime Numbers. This Prime Number 37 is found in the Bible Gen 1.1 and in DNA. After Gen 1.1 we will examine Gen 1.2b says And the Spirit of God moved upon the face of the waters This phrase about Creation has the remarkable value of 1369 = 37 x 37 Creation: 20 Amino Acids: The Atomic weight DNA 2738 = 2 x 37 x This program finds the position of any numeric string in Pi - π The position of any Prime Number. The knowledge of Primes Numbers up to was unknown to Moses. 12

13 Atheism Remember the 7 values of Gen 1.1 Xrah tav MymDh ta Myhla arb tydarb Earth the and Heavens the _ God created beginning the In Previously we learnt that these values sum to = 2701 = 37 x 73 Just as 37 is the reflection of is the reflection of 1072, then = 3773 Next index the 7 values to Primes in this way. What is the 913 th Prime? The Final result of the indexing of the 7 words of Gen 1.1 to Prime numbers with the result seems to me beyond Miraculous. I find this hard to believe every time I study this. It is like a Thunderbolt from Heaven 913 th Prime No. = rd Prime No. = th Prime No. = st Prime No. = th Prime No. = th Prime No. = th Prime No. = 1949 The Total Sum = Now is the 2161 st Prime Number. We Reflect & add = 3773 Just as = = 2 x 2 x [13 x 31] The Signatures of John 1.1 = 3 x 3 x [13 x 31] Remember these values are from Gen 1.1 Wow!!! This incredible result is the work of the Master Mathematician our Father The connection between Prime numbers and the values of Gen 1.1 is truly phenomenal. Prime numbers are studied by Mathematicians as Primes are fundamental to Mathematics. This analysis shows the absolute Proof Set in Stone of the divine origin of the 7 words which Moses had written. He had NO KNOWLEDGE of the values of 7 words in Gen 1.1. In the beginning God created the Heaven and the Earth He [Jesus] is the reflection of God's glory and the exact likeness of his being Heb 1.3 As 37 reflects 73 Finally the total of in Rev 1.1 The Revelation from Jesus Christ, which God gave him... has the value and 2 x = 3773 x 10!! 13 Vanquished This next item, Unbelievable. 703 rd Prime No. is st Prime No. is And between 5303 and there are exactly integers

14 You should now watch the DVD or read the Seven Unusual Numbers booklet. This will give you the unassailable evidence that you need which proves that the Bible is indeed the true revelation to Mankind. It shows by Prime Numbers that the words in Hebrew of Genesis 1.1 and the Greek words of John 1.1 are the exactly the right number of words and letters that there should be. No more and no less! Now what can we say about the Messiah - Jesus Christ? The Religions of Ancient Rome could not compete with the promise of the God of Israel - the promise of Eternal life in the Kingdom of God and with the entrance into his Kingdom having been paid for by the blood of His Christ - His own Son. The Promise is the free gift of eternal life. You cannot work for it. John 6.29 They said to Jesus, What must we do, to do the works of God?" Jesus answered them, This is the work of God, that you believe in him whom He has sent. All the Prophets from Moses, Isaiah, Jeremiah never spoke like this Man! The Prophets all confessed their Sins but this man never gave the slightest hint that he was a sinner, for in Christ the whole fullness of the Deity dwells bodily Col 2.9 Also He made the most amazing statements that no Prophet had ever uttered: Jesus said to them you will die in your sins unless you believe that I am He I say to you, If any one may keep my word, by no means will he taste death in the [ coming ] age John 8.24, 51 I am the Resurrection and the life; he who believes in me, though he die, yet shall he live, [ at the resurrection of the dead ] and whoever lives [ again, in this resurrection ] and believes in me shall never die John To see the Evidence for why the Bible is True watch the DVD. 14

15 This small booklet is part of a book. Contents 460 Pages 373 A Proof Set in Stone by Dr Peter Bluer, PhD, BSc [hons] Section 1 The Fundamental Doctrine of Christianity. The exposition of John 1.1 More evidence from the New Testament. The Plural of God in the Old Testament. Who is the Angel of the Covenant?. The Glory of the LORD. The Doctrine of the Holy Spirit. Section 2 Mathematical proof for an unbelieving age that Genesis Investigation of Gen 1.1. Evidence in the New Testament. Numerical Geometry. Algebraic Analysis. The Shema. Other Languages, English, French and German. Numerical analysis of John 1.1. The analysis of Pi, π, 22/7, e, Section 3 Clear evidence that Jesus Christ is the prophesied Messiah sent to Israel at the time of the Roman Empire. The exact time of his appearance as prophesied by Daniel the Prophet and a New assessment of the Second Advent. A verse by verse exposition of 70 Weeks of Daniel 9:24-25 The book is obtainable from the Author for incl. P & 15 Patchcroft Rd, Peel Hall,Wythenshawe, Manchester, M22 5JG, Peter Bluer PhD, BSc [hons] 15

16 This book provides full Scientific Evidence for the Truth of the Bible and the Proof of he fundamental Teaching of Christianity, called The Deity of Christ with full Analysis of the Event called the Second Coming of Christ. 373 A Proof Set in Stone by Dr Peter Bluer, PhD, BSc (hons) 373 A Proof Set in Stone incl P & P DVD (3 booklets included) 5.99 incl P & P DVD has 5 videos - 70 weeks, Bible Numerics, Running time 4 hours Book obtainable from Peter Bluer or and Ebay under Creation. 15 Patchcroft Road, Peel Hall, Wythenshawe Manchester, M22 5JG, U.K. Tel peter@biblemaths.com Please make cheque payable to Dr Peter Bluer Air mail, Europe, U.S.A and the The Rest of the World - See Web site for Overseas Prices 16

7 th GRADE PLANNER Mathematics. Lesson Plan # QTR. 3 QTR. 1 QTR. 2 QTR 4. Objective

7 th GRADE PLANNER Mathematics. Lesson Plan # QTR. 3 QTR. 1 QTR. 2 QTR 4. Objective Standard : Number and Computation Benchmark : Number Sense M7-..K The student knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers,

More information

Ancient System of Operations: Computing with Mathematical Devices. By: Calvin L. Fitts Jr. History of Mathematics. Ms.

Ancient System of Operations: Computing with Mathematical Devices. By: Calvin L. Fitts Jr. History of Mathematics. Ms. Ancient System of Operations 1 Running head: ANCIENT SYSTEMS OF OPERATIONS Ancient System of Operations: Computing with Mathematical Devices By: Calvin L. Fitts Jr. History of Mathematics Ms. Jennifer

More information

Name Period Date. REAL NUMBER SYSTEM Student Pages for Packet 3: Operations with Real Numbers

Name Period Date. REAL NUMBER SYSTEM Student Pages for Packet 3: Operations with Real Numbers Name Period Date REAL NUMBER SYSTEM Student Pages for Packet : Operations with Real Numbers RNS. Rational Numbers Review concepts of experimental and theoretical probability. a Understand why all quotients

More information

5.1 to 5.3 P4.ink. Carnegie Unit 3 Examples & Class Notes

5.1 to 5.3 P4.ink. Carnegie Unit 3 Examples & Class Notes Carnegie Unit 3 Examples & Class Notes 1 2 3 This number is called the index. 1 Only multiply the numbers inside radical symbols, if and only if, they have the same index. 4 5 1 Use the times tables &

More information

Rene Descartes (left) and Pierre de Fermat (right) developed analytical geometry independently of each other in the 1600 s.

Rene Descartes (left) and Pierre de Fermat (right) developed analytical geometry independently of each other in the 1600 s. Lesson 14 Analtical Geometr, Part I Rene Descartes (left) and Pierre de Fermat (right) developed analtical geometr independentl of each other in the 1600 s. Rules and Definitions Rules No new rules for

More information

Prentice Hall Mathematics: Pre-Algebra 2004 Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 8)

Prentice Hall Mathematics: Pre-Algebra 2004 Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 8) Colorado Model Content Standards and Grade Level Expectations (Grade 8) Standard 1: Students develop number sense and use numbers and number relationships in problemsolving situations and communicate the

More information

Montana City School GRADE 5

Montana City School GRADE 5 Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate

More information

Tier 2: GEOMETRY INTRODUCTION TO GEOMETRY Lessons Abbreviation Key Table... 7 G1 LESSON: WHAT IS GEOMETRY?... 8 G1E... 9 G1EA...

Tier 2: GEOMETRY INTRODUCTION TO GEOMETRY Lessons Abbreviation Key Table... 7 G1 LESSON: WHAT IS GEOMETRY?... 8 G1E... 9 G1EA... Craig Hane, Ph.D., Founder Tier 2: GEOMETRY INTRODUCTION TO GEOMETRY... 6 1.1 Lessons Abbreviation Key Table... 7 G1 LESSON: WHAT IS GEOMETRY?... 8 G1E... 9 G1EA... 10 G2 LESSON: STRAIGHT LINES AND ANGLES...

More information

Precalculus, Quarter 2, Unit 2.1. Trigonometry Graphs. Overview

Precalculus, Quarter 2, Unit 2.1. Trigonometry Graphs. Overview 13 Precalculus, Quarter 2, Unit 2.1 Trigonometry Graphs Overview Number of instructional days: 12 (1 day = 45 minutes) Content to be learned Convert between radian and degree measure. Determine the usefulness

More information

Mathematics - Grade 7: Introduction Math 7

Mathematics - Grade 7: Introduction Math 7 Mathematics - Grade 7: Introduction Math 7 In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding

More information

Table of Contents. Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1

Table of Contents. Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1 Table of Contents Table of Contents Introduction to the Math Practice Series...iv Common Mathematics Symbols and Terms...1 Chapter 1: Real Numbers...5 Real Numbers...5 Checking Progress: Real Numbers...8

More information

How to get the most out of the e-sword free software

How to get the most out of the e-sword free software 1. Who is the writer and/or speaker? 2. When was it written and/or said? 3. To whom was it written and/or spoken? 4. What are the major natural divisions? 5. What is the repeated key word? 6. What simple

More information

Middle School Math Course 2

Middle School Math Course 2 Middle School Math Course 2 Correlation of the ALEKS course Middle School Math Course 2 to the Indiana Academic Standards for Mathematics Grade 7 (2014) 1: NUMBER SENSE = ALEKS course topic that addresses

More information

8 th Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the

8 th Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 8 th Grade Mathematics Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13. This document is designed to help North Carolina educators

More information

Using the Best of Both!

Using the Best of Both! Using the Best of Both! A Guide to Using Connected Mathematics 2 with Prentice Hall Mathematics Courses 1, 2, 3 2012, and Algebra Readiness MatBro111707BestOfBothPH10&CMP2.indd 1 6/7/11 11:59 AM Using

More information

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 5-8

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 5-8 NUMBER SENSE & OPERATIONS 5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents. Fractions 1/2, 1/3, 1/4, 1/5, 1/10 and equivalent decimals

More information

Big Mathematical Ideas and Understandings

Big Mathematical Ideas and Understandings Big Mathematical Ideas and Understandings A Big Idea is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole.

More information

3.D. The Platonic solids

3.D. The Platonic solids 3.D. The Platonic solids The purpose of this addendum to the course notes is to provide more information about regular solid figures, which played an important role in Greek mathematics and philosophy.

More information

A trigonometric ratio is a,

A trigonometric ratio is a, ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric

More information

Counting shapes 1.4.6

Counting shapes 1.4.6 GRADE R_TERM 1 WEEK TOPIC CONTENT CAMI KEYSTROKE CAMI Program Count in ones 1.1.1.1; 1.1.1.2; 1.1.1.3 1.1.1.4 Cami Math Count pictures 1.1.3.1; 1.1.3.2; 1 & 2 Counting 1.1.3.3; 1.1.3.4; Counting in units

More information

Correlation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11

Correlation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11 Correlation of the ALEKS courses Algebra 1 and High School Geometry to the Wyoming Mathematics Content Standards for Grade 11 1: Number Operations and Concepts Students use numbers, number sense, and number

More information

Alaska Mathematics Standards Vocabulary Word List Grade 7

Alaska Mathematics Standards Vocabulary Word List Grade 7 1 estimate proportion proportional relationship rate ratio rational coefficient rational number scale Ratios and Proportional Relationships To find a number close to an exact amount; an estimate tells

More information

SFU CMPT Lecture: Week 8

SFU CMPT Lecture: Week 8 SFU CMPT-307 2008-2 1 Lecture: Week 8 SFU CMPT-307 2008-2 Lecture: Week 8 Ján Maňuch E-mail: jmanuch@sfu.ca Lecture on June 24, 2008, 5.30pm-8.20pm SFU CMPT-307 2008-2 2 Lecture: Week 8 Universal hashing

More information

Encryption à la Mod Name

Encryption à la Mod Name Rock Around the Clock Part Encryption à la Mod Let s call the integers,, 3,, 5, and the mod 7 encryption numbers and define a new mod 7 multiplication operation, denoted by, in the following manner: a

More information

Alabama State Standards correlated to Merit Software Math Programs

Alabama State Standards correlated to Merit Software Math Programs Alabama State Standards correlated to Merit Software Math Programs The Classroom Improvement Section is responsible for the development, implementation, and assessment of the minimum curriculum content

More information

Lecture 3: Some Strange Properties of Fractal Curves

Lecture 3: Some Strange Properties of Fractal Curves Lecture 3: Some Strange Properties of Fractal Curves I have been a stranger in a strange land. Exodus 2:22 1. Fractal Strangeness Fractals have a look and feel that is very different from ordinary curves.

More information

Scope and Sequence for the New Jersey Core Curriculum Content Standards

Scope and Sequence for the New Jersey Core Curriculum Content Standards Scope and Sequence for the New Jersey Core Curriculum Content Standards The following chart provides an overview of where within Prentice Hall Course 3 Mathematics each of the Cumulative Progress Indicators

More information

Anadarko Public Schools MATH Power Standards

Anadarko Public Schools MATH Power Standards Anadarko Public Schools MATH Power Standards Kindergarten 1. Say the number name sequence forward and backward beginning from a given number within the known sequence (counting on, spiral) 2. Write numbers

More information

Mathematics LV 5 (with QuickTables)

Mathematics LV 5 (with QuickTables) Mathematics LV 5 (with QuickTables) This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence

More information

Section 1.1 Definitions and Properties

Section 1.1 Definitions and Properties Section 1.1 Definitions and Properties Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Abbreviate repeated addition using Exponents and Square

More information

8.B. The result of Regiomontanus on tetrahedra

8.B. The result of Regiomontanus on tetrahedra 8.B. The result of Regiomontanus on tetrahedra We have already mentioned that Plato s theory that the five regular polyhedra represent the fundamental elements of nature, and in supplement (3.D) to the

More information

Maths: Phase 5 (Y12-13) Outcomes

Maths: Phase 5 (Y12-13) Outcomes Maths: Phase 5 (Y12-13) Outcomes I know numbers are beautiful. If they aren t beautiful nothing is. Paul Erdose Maths is discovered it doesn t just exist. Maths is a tool to understand, question and criticise

More information

Mathematics (JUN11MPC201) General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core TOTAL

Mathematics (JUN11MPC201) General Certificate of Education Advanced Subsidiary Examination June Unit Pure Core TOTAL Centre Number Candidate Number For Examiner s Use Surname Other Names Candidate Signature Examiner s Initials Mathematics Unit Pure Core 2 Wednesday 18 May 2011 General Certificate of Education Advanced

More information

Course Outlines. Elementary Mathematics (Grades K-5) Kids and Numbers (Recommended for K-1 students)

Course Outlines. Elementary Mathematics (Grades K-5) Kids and Numbers (Recommended for K-1 students) Course Outlines Elementary Mathematics (Grades K-5) Kids and Numbers (Recommended for K-1 students) Shapes and Patterns. Grouping objects by similar properties. Identifying simple figures within a complex

More information

A theme park charges $12 entry to visitors. Find the money taken if 1296 people visit the park.

A theme park charges $12 entry to visitors. Find the money taken if 1296 people visit the park. Write an Equation An equation is a term used to describe a collection of numbers and variables related through mathematical operators. An algebraic equation will contain letters that relate to real quantities

More information

Lesson/Unit Plan Name: Platonic Solids Using geometric nets to explore Platonic solids and discovering Euler s formula.

Lesson/Unit Plan Name: Platonic Solids Using geometric nets to explore Platonic solids and discovering Euler s formula. Grade Level/Course: Grade 6 Lesson/Unit Plan Name: Platonic Solids Using geometric nets to explore Platonic solids and discovering Euler s formula. Rationale/Lesson Abstract: An activity where the students

More information

Sample tasks from: Geometry Assessments Through the Common Core (Grades 6-12)

Sample tasks from: Geometry Assessments Through the Common Core (Grades 6-12) Sample tasks from: Geometry Assessments Through the Common Core (Grades 6-12) A resource from The Charles A Dana Center at The University of Texas at Austin 2011 About the Dana Center Assessments More

More information

Dulwich College. SAMPLE PAPER Mathematics

Dulwich College. SAMPLE PAPER Mathematics 1+ Dulwich College YEAR 9 ENTRANCE AND SCHOLARSHIP EXAMINATION SAMPLE PAPER Mathematics 1 HOUR 0 MINUTES Use a calculator where appropriate. Answer all the questions. Show all your working. Marks for parts

More information

Planar Graphs, Solids, and Surfaces. Planar Graphs 1/28

Planar Graphs, Solids, and Surfaces. Planar Graphs 1/28 Planar Graphs, Solids, and Surfaces Planar Graphs 1/28 Last time we discussed the Four Color Theorem, which says that any map can be colored with at most 4 colors and not have two regions that share a

More information

NUMBERS AND NUMBER RELATIONSHIPS

NUMBERS AND NUMBER RELATIONSHIPS MODULE MODULE CHAPTERS Numbers and number patterns 2 Money matters KEY SKILLS writing rational numbers as terminating or recurring decimals identifying between which two integers any irrational number

More information

Class Book. Anita Straker, Tony Fisher, Rosalyn Hyde, Sue Jennings and Jonathan Longstaffe

Class Book. Anita Straker, Tony Fisher, Rosalyn Hyde, Sue Jennings and Jonathan Longstaffe Class Book Anita Straker, Tony Fisher, Rosalyn Hyde, Sue Jennings and Jonathan Longstaffe 5 Contents Tier 5 N5.1 Powers and roots 1 1 Integer powers of numbers 1 Estimating square roots 3 3 Prime factor

More information

Mathematical Reasoning. Lesson 47: Prisms and Cylinders. LESSON 47: Prisms and Cylinders. D. Legault, Minnesota Literacy Council,

Mathematical Reasoning. Lesson 47: Prisms and Cylinders. LESSON 47: Prisms and Cylinders. D. Legault, Minnesota Literacy Council, LESSON 47: Prisms and Cylinders Weekly Focus: prisms, cylinders Weekly Skill: calculate area and volume Lesson Summary: For the warm up, students will solve a problem about the earth and the moon. In Activity

More information

Perimeter and Area of Inscribed and Circumscribed Polygons

Perimeter and Area of Inscribed and Circumscribed Polygons University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln MAT Exam Expository Papers Math in the Middle Institute Partnership 7-007 Perimeter and Area of Inscribed and Circumscribed

More information

Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8

Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8 Middle School Math Course 3 Correlation of the ALEKS course Middle School Math 3 to the Illinois Assessment Framework for Grade 8 State Goal 6: Number Sense 6.8.01: 6.8.02: 6.8.03: 6.8.04: 6.8.05: = ALEKS

More information

3rd Quarter MATHEMATICS Pointers to Review S.Y

3rd Quarter MATHEMATICS Pointers to Review S.Y Grade 1 Grouping Count groups of equal quantity using concrete objects up to 50 and writes an equivalent expression. e.g. 2 groups of 5 Visualizes, represents, and separates objects into groups of equal

More information

The Real Number System

The Real Number System The Real Number System Pi is probably one of the most famous numbers in all of history. As a decimal, it goes on and on forever without repeating. Mathematicians have already calculated trillions of the

More information

PRE-ALGEBRA PREP. Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., 2002.

PRE-ALGEBRA PREP. Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., 2002. PRE-ALGEBRA PREP Textbook: The University of Chicago School Mathematics Project. Transition Mathematics, Second Edition, Prentice-Hall, Inc., 2002. Course Description: The students entering prep year have

More information

Mathematics: working hard together, achieving together, making every lesson count

Mathematics: working hard together, achieving together, making every lesson count Maths Mathematics: working hard together, achieving together, making every lesson count The Mathematics Department will provide students with exciting, relevant and challenging Mathematics, delivered by

More information

Prentice Hall Mathematics Course Correlated to: Archdiocese of Chicago (Illinois) Mathematics Curriculum Frameworks (2004) Grades 6-12

Prentice Hall Mathematics Course Correlated to: Archdiocese of Chicago (Illinois) Mathematics Curriculum Frameworks (2004) Grades 6-12 Archdiocese of Chicago (Illinois) Mathematics Curriculum Frameworks (2004) Grades 6-12 Goal Outcome Outcome Statement Priority Code Chapter Topic 6 6.01 6.06.01 - Represent place values from millionths

More information

Prentice Hall Mathematics: Course Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 8)

Prentice Hall Mathematics: Course Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 8) Colorado Model Content Standards and Grade Level Expectations (Grade 8) Standard 1: Students develop number sense and use numbers and number relationships in problemsolving situations and communicate the

More information

Reason with shapes and their attributes.

Reason with shapes and their attributes. Grade 3 Geometry and Perimeter SDadfa;sdklfjas;Unit Overview Reason with shapes and their attributes. 1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share

More information

APS Sixth Grade Math District Benchmark Assessment NM Math Standards Alignment

APS Sixth Grade Math District Benchmark Assessment NM Math Standards Alignment SIXTH GRADE NM STANDARDS Strand: NUMBER AND OPERATIONS Standard: Students will understand numerical concepts and mathematical operations. 5-8 Benchmark N.: Understand numbers, ways of representing numbers,

More information

Performance Level Descriptors. Mathematics

Performance Level Descriptors. Mathematics Performance Level Descriptors Grade 3 Well Students rarely, Understand that our number system is based on combinations of 1s, 10s, and 100s (place value, compare, order, decompose, and combine using addition)

More information

Grade Level Expectations for the Sunshine State Standards

Grade Level Expectations for the Sunshine State Standards for the Sunshine State Standards FLORIDA DEPARTMENT OF EDUCATION http://www.myfloridaeducation.com/ The seventh grade student: Number Sense, Concepts, and Operations knows word names and standard numerals

More information

Geometry and Gravitation

Geometry and Gravitation Chapter 15 Geometry and Gravitation 15.1 Introduction to Geometry Geometry is one of the oldest branches of mathematics, competing with number theory for historical primacy. Like all good science, its

More information

C -! F I? E! "#$ I%?... & '( )? I*+ ', -.? I* ', :;? I*+ <= ', -.? 8 >2? =B )? H. M. Baagill >K > 4L2 1

C -! F I? E! #$ I%?... & '( )? I*+ ', -.? I* ', :;? I*+ <= ', -.? 8 >2? =B )? H. M. Baagill >K > 4L2 1 - I? E I?...? I? I? I?? H. M. Baagill 1 ......3...3 4.. 6 1....7 2....17 3....22 4. - I...27 5. I -...32 6. I?...34 7. -...38 ( ) (40) 1. O...40 2....43 3. E...43 4....43 5....45 6....45 7....47 8. U...48

More information

CME Project, Algebra Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 11)

CME Project, Algebra Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 11) M11.A Numbers and Operations M11.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M11.A.1.1 Represent and/or use numbers in equivalent

More information

Middle School Math Course 3

Middle School Math Course 3 Middle School Math Course 3 Correlation of the ALEKS course Middle School Math Course 3 to the Texas Essential Knowledge and Skills (TEKS) for Mathematics Grade 8 (2012) (1) Mathematical process standards.

More information

Matija Gubec International School Zagreb MYP 0. Mathematics

Matija Gubec International School Zagreb MYP 0. Mathematics Matija Gubec International School Zagreb MYP 0 Mathematics 1 MYP0: Mathematics Unit 1: Natural numbers Through the activities students will do their own research on history of Natural numbers. Students

More information

UNIT 3 CIRCLES AND VOLUME Lesson 5: Explaining and Applying Area and Volume Formulas Instruction

UNIT 3 CIRCLES AND VOLUME Lesson 5: Explaining and Applying Area and Volume Formulas Instruction Prerequisite Skills This lesson requires the use of the following skills: using formulas for the surface areas of polygons and circles performing calculations with the angles in circles using the Pythagorean

More information

What You ll See in This Chapter. Word Cloud. René Descartes. Introduction. Ian Parberry University of North Texas. Fletcher Dunn

What You ll See in This Chapter. Word Cloud. René Descartes. Introduction. Ian Parberry University of North Texas. Fletcher Dunn What You ll See in This Chapter Chapter 1: Cartesian Coordinate Systems Fletcher Dunn Valve Software Ian Parberry University of North Texas This chapter describes the basic concepts of 3D math. It is divided

More information

Mathematics Background

Mathematics Background Finding Area and Distance Students work in this Unit develops a fundamentally important relationship connecting geometry and algebra: the Pythagorean Theorem. The presentation of ideas in the Unit reflects

More information

Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008

Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008 MATH-LITERACY MANUAL Dr. Relja Vulanovic Professor of Mathematics Kent State University at Stark c 2008 1 Real Numbers 1.1 Sets 1 1.2 Constants and Variables; Real Numbers 7 1.3 Operations with Numbers

More information

Moore Catholic High School Math Department

Moore Catholic High School Math Department Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during

More information

EDINBURGH PRIMARY SCHOOL

EDINBURGH PRIMARY SCHOOL EDINBURGH PRIMARY SCHOOL TARGETS FOR THE NEW MATHEMATICS CURRICULUM Parent Information Edinburgh Primary School Assessment MATHEMATICS TARGETS - A YEAR 1 MATHEMATICIAN Number and place value I can count

More information

Mathematics RIT Score:

Mathematics RIT Score: Mathematics RIT Score: 201-210 Number Sense and Operations Whole Numbers Understand the concept of division using pictorial representation Use front-end estimation strategy for multiplication and division

More information

y= sin( x) y= cos( x)

y= sin( x) y= cos( x) . The graphs of sin(x) and cos(x). Now I am going to define the two basic trig functions: sin(x) and cos(x). Study the diagram at the right. The circle has radius. The arm OP starts at the positive horizontal

More information

Mathematics - Grade 7: Introduction Math 7A

Mathematics - Grade 7: Introduction Math 7A Mathematics - Grade 7: Introduction Math 7A In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding

More information

Key Vocabulary Index. Key Vocabulary Index

Key Vocabulary Index. Key Vocabulary Index Key Vocabulary Index Mathematical terms are best understood when you see them used and defined in context. This index lists where you will find key vocabulary. A full glossary is available in your Record

More information

Geometry Honors Course Syllabus Middleboro High School, Ms. Miles

Geometry Honors Course Syllabus Middleboro High School, Ms. Miles Course Overview Geometry is a branch of mathematics that uses logic and reasoning to establish the mathematical relationships between points, lines, angles, figures, and solids. Honors Geometry introduces

More information

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6

Gateway Regional School District VERTICAL ALIGNMENT OF MATHEMATICS STANDARDS Grades 3-6 NUMBER SENSE & OPERATIONS 3.N.1 Exhibit an understanding of the values of the digits in the base ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999. Our

More information

CS3110 Spring 2017 Lecture 12: DRAFT: Constructive Real Numbers continued

CS3110 Spring 2017 Lecture 12: DRAFT: Constructive Real Numbers continued CS3110 Spring 2017 Lecture 12: DRAFT: Constructive Real Numbers continued Robert Constable Reminder: Prelim in class next Tuesday. It will not cover the real numbers beyond lecture 11 and comments on lecture

More information

Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the Massachusetts Curriculum Framework Learning Standards for Grade 5-6

Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the Massachusetts Curriculum Framework Learning Standards for Grade 5-6 Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the Massachusetts Curriculum Framework Learning Standards for Grade 5-6 Numbers Sense and Operations TD = Teacher Directed 6.N.1:

More information

1 Appendix to notes 2, on Hyperbolic geometry:

1 Appendix to notes 2, on Hyperbolic geometry: 1230, notes 3 1 Appendix to notes 2, on Hyperbolic geometry: The axioms of hyperbolic geometry are axioms 1-4 of Euclid, plus an alternative to axiom 5: Axiom 5-h: Given a line l and a point p not on l,

More information

Curriculum Design Template. Course Title: Math 8 Grade Level: 8

Curriculum Design Template. Course Title: Math 8 Grade Level: 8 Curriculum Design Template Content Area: Mathematics 8 Course Title: Math 8 Grade Level: 8 Equations Transformations Marking Period 1 Angles and Triangles Graphing and Writing Linear Equations Marking

More information

Section 1.2 Fractions

Section 1.2 Fractions Objectives Section 1.2 Fractions Factor and prime factor natural numbers Recognize special fraction forms Multiply and divide fractions Build equivalent fractions Simplify fractions Add and subtract fractions

More information

8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT

8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT 8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT ISAT test questions are derived from this checklist. Use as a curriculum guide.

More information

13-5. Pascal s Triangle. Vocabulary. Pascal s Triangle. Lesson. Mental Math

13-5. Pascal s Triangle. Vocabulary. Pascal s Triangle. Lesson. Mental Math Lesson 3-5 Pascal s Triangle Vocabulary Pascal s Triangle BIG IDEA The nth row of Pascal s Triangle contains the number of ways of choosing r objects out of n objects without regard to their order, that

More information

Year 1 End of Year Maths Targets. Pupil Name AUT 2 SPR 2 SPR 1 AUT 1 SUM 1 SUM 2 TARGETS

Year 1 End of Year Maths Targets. Pupil Name AUT 2 SPR 2 SPR 1 AUT 1 SUM 1 SUM 2 TARGETS Year End of Year Maths Targets Pupil Name Number and place value I can count to and across 00, forward and backwards,beginning with 0 or from any number. I can count in multiples of, 5 and 0. I can count,

More information

2 nd Grade Math Learning Targets. Algebra:

2 nd Grade Math Learning Targets. Algebra: 2 nd Grade Math Learning Targets Algebra: 2.A.2.1 Students are able to use concepts of equal to, greater than, and less than to compare numbers (0-100). - I can explain what equal to means. (2.A.2.1) I

More information

Prentice Hall Mathematics: Course Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 6)

Prentice Hall Mathematics: Course Correlated to: Colorado Model Content Standards and Grade Level Expectations (Grade 6) Colorado Model Content Standards and Grade Level Expectations (Grade 6) Standard 1: Students develop number sense and use numbers and number relationships in problemsolving situations and communicate the

More information

Eighth Grade Math Assessment Framework Standard 6A Representations and Ordering

Eighth Grade Math Assessment Framework Standard 6A Representations and Ordering Eighth Grade Math Assessment Framework Standard 6A Representations and Ordering 6.8.01 Read, write, and recognize equivalent representations of integer powers of 10. Related Textbook pages Related Additional

More information

General Certificate of Secondary Education Higher Tier June 2014

General Certificate of Secondary Education Higher Tier June 2014 Centre Number Surname Candidate Number For Examiner s Use Other Names Candidate Signature Examiner s Initials Pages Mark Mathematics General Certificate of Secondary Education Higher Tier June 2014 43603H

More information

Year 9 Key Performance Indicators Maths (Number)

Year 9 Key Performance Indicators Maths (Number) Key Performance Indicators Maths (Number) M9.1 N1: I can apply the four operations to negative numbers. Raise negative numbers to a power Add and subtract negative numbers and know when the answer should

More information

Grade 7 Unit 1 at a Glance: Working With Rational Numbers

Grade 7 Unit 1 at a Glance: Working With Rational Numbers Grade 7 at a Glance: Working With Rational Numbers The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents

More information

Grades 7 & 8, Math Circles 20/21/22 February, D Geometry Solutions

Grades 7 & 8, Math Circles 20/21/22 February, D Geometry Solutions Faculty of Mathematics Waterloo, Ontario NL 3G1 Centre for Education in Mathematics and Computing D Geometry Review Grades 7 & 8, Math Circles 0/1/ February, 018 3D Geometry Solutions Two-dimensional shapes

More information

Prentice Hall Mathematics: Pre-Algebra 2004 Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 11)

Prentice Hall Mathematics: Pre-Algebra 2004 Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 11) AND M11.A Numbers and Operations M11.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. SE/TE: 2, 11, 18-22, 25, 27-29, 32-34, 44,

More information

Solving Linear Equations: Prentice Hall Lesson # 1-4; 3-1,2,3; 3-6; 5-1 thru 4; 6-1, 2. Graphing Linear Equations: PH Lesson 1-4

Solving Linear Equations: Prentice Hall Lesson # 1-4; 3-1,2,3; 3-6; 5-1 thru 4; 6-1, 2. Graphing Linear Equations: PH Lesson 1-4 9-12 Achievement/Math: Algebra I Goal A: Algebra I: [Student] will complete Algebra I assignments which address content with greater depth and higher levels of complexity as evidenced by mastery of [1/2/3/4/5/6/7/8/9/10]

More information

Grades 7 & 8 Pre-Algebra/Course 3,

Grades 7 & 8 Pre-Algebra/Course 3, Grades 7 & 8 Pre-Algebra/Course 3, TERM 1 - AUGUST/SEPTEMBER/OCTOBER Algebra Tools Solving Equations Integers Solving Multi-Step Equations and Inequalities TERM 2 NOVEMBER/DECEMBER/JANUARY Functions &

More information

Objective 1 : The student will demonstrate an understanding of numbers, operations, and quantitative reasoning.

Objective 1 : The student will demonstrate an understanding of numbers, operations, and quantitative reasoning. Essential Mathematics (with QuickTables) Correlation of the ALEKS course Essential Mathematics to the Texas Assessment of Knowledge and Skills (TAKS) for Grade 6 Objective 1 : The student will demonstrate

More information

5. Compare the volume of a three dimensional figure to surface area.

5. Compare the volume of a three dimensional figure to surface area. 5. Compare the volume of a three dimensional figure to surface area. 1. What are the inferences that can be drawn from sets of data points having a positive association and a negative association. 2. Why

More information

Introduction to Geometry

Introduction to Geometry Introduction to Geometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (211 topics + 6 additional topics)

More information

Written by Alaska Hults

Written by Alaska Hults Standards-Based Math Written by Alaska Hults Editor: Collene Dobelmann Illustrator: Corbin Hillam Designer/Production: Moonhee Pak/Rosa Gandara Cover Designer: Barbara Peterson Art Director: Tom Cochrane

More information

SE/TE: SE/TE: 80, N / A SE/TE: 3, 282 SE/TE: 3 4

SE/TE: SE/TE: 80, N / A SE/TE: 3, 282 SE/TE: 3 4 M11.A Numbers and Operations M11.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M11.A.1.1 Represent and/or use numbers in equivalent

More information

Note: Levels A-I respresent Grade Levels K-8; Florida - Grade 7 -Math Standards /Benchmarks PLATO Courseware Covering Florida - Grade 7 - Math

Note: Levels A-I respresent Grade Levels K-8; Florida - Grade 7 -Math Standards /Benchmarks PLATO Courseware Covering Florida - Grade 7 - Math Note: Levels A-I respresent Grade Levels K-8; - Grade 7 -Math Standards /Benchmarks 2005 PLATO Courseware Covering - Grade 7 - Math Number Sense, Concepts, and Operations Standard 1: The student understands

More information

Age Related Maths Expectations

Age Related Maths Expectations Step 1 Times Tables Addition Subtraction Multiplication Division Fractions Decimals Percentage & I can count in 2 s, 5 s and 10 s from 0 to 100 I can add in 1 s using practical resources I can add in 1

More information

Number/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9

Number/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative

More information

In this chapter, we will investigate what have become the standard applications of the integral:

In this chapter, we will investigate what have become the standard applications of the integral: Chapter 8 Overview: Applications of Integrals Calculus, like most mathematical fields, began with trying to solve everyday problems. The theory and operations were formalized later. As early as 70 BC,

More information

Area and Volume 2. Circles. Trapeziums. and Measures. Geometry. Key Point. Key Point. Key Point

Area and Volume 2. Circles. Trapeziums. and Measures. Geometry. Key Point. Key Point. Key Point Geometry and Measures Area and Volume 2 You must be able to: Recall and use the formulae for the circumference and area of a circle Recall and use the formula for the area of a trapezium Recall and use

More information

MERBEIN P-10 COLLEGE MATHS SCOPE & SEQUENCE

MERBEIN P-10 COLLEGE MATHS SCOPE & SEQUENCE MERBEIN P-10 COLLEGE MATHS SCOPE & SEQUENCE Year Number & Algebra Measurement & Geometry Statistics & Probability P Numbers to 20 Location Data collection Counting and comparing groups Length Ordinal numbers

More information