Dictionary Day (Oct. 16) Meeting (Multiple Topics)
|
|
- Alexandra Harris
- 7 years ago
- Views:
Transcription
1 Dictionary Day (Oct. 16) Meeting (Multiple Topics) Topic This meeting s topics cover a wide range of math topics, though every problem is word- or letterrelated. The majority of the problems use general math or logic, with some counting, symmetry and number theory included. Materials Needed Copies of the Dictionary Day problem set (Problems and answers can be viewed here, but a more student-friendly version in larger font is available for download from on the MCP Members Only page of the Club Program section.) Calculators Meeting Plan This meeting is perfect for Dictionary Day (Oct. 16) because, though it involves a lot of math, every problem is related to words or letters. The first eight problems in the problem set are relatively straightforward; students should be able to successfully attempt/tackle them if working in pairs or individually. Problem #9 could require more explanation from the coach, and problem #10 is designed to be a nice wrap-up activity for the entire club to do together. 1. The letters of the alphabet are each assigned a random integer value, and H = 10. The value of a word comes from the sum of its letters values. If MATH is 35 points, TEAM is 42 points and MEET is 38 points, what is the value of A? 2006 School Competition, Team Round #6 2. The word-sum of a word is determined by adding together the value of each letter. In the alphabet, letters A through H each have a value of 5 cents; letters I through R each have a value of 7 cents; and letters S through Z each have a value of 8 cents. What is the word-sum of the word MATHCOUNTS? 2005 School Competition, Sprint Round #1 3. How many letters of the alphabet shown below have a vertical line of symmetry? 2005 School Competition, Sprint Round #7 ABCDEFGHIJKLMNOPQRSTUVWXYZ 4. A set of magnetic letters contains two of each consonant and three of each vowel. Only a complete set of letters may be purchased. How many complete sets of magnetic letters must be purchased to make a sign that reads: MATHCOUNTS COMPETITION TODAY? 2002 School Competition, Team Round #1 5. The sequence below is formed by repeating the letters of the alphabet, in order, the same number of times as the letter s ordinal position in the alphabet. After 26 Zs, the sequence starts over with ABBCCC. What is the 2005th letter in the sequence? A B B C C C D D D D E E E E E 2005 School Competition, Team Round #8 6. If all of the letters of the word BEEP are used, in how many different ways can the four letters be arranged in a four-letter sequence? The two Es are indistinguishable, so EEPB should be counted only once since we would not be able to tell a difference if the two Es were swapped School Handbook, Volume I, Warm-Up 4-3 (For #7, #8) A value is assigned to each letter of the alphabet such that A = 1, B = 2, C = 3,..., Z = 26. The wordproduct of a word is the product of the values of each letter in the word. For example, the word-product of NAME is = What is Carrie s favorite breakfast food if its word-product is 4655? 8. What is her favorite dessert if its word-product is 165? MATHCOUNTS Club Resource Guide 25 Club Resource Guide.pdf 25 8/18/08 11:24:15 AM
2 9. A value is assigned to each letter of the alphabet such that A = 1, B = 2, C = 3,..., Z = 26. A nine-digit code is then created for each letter using the prime factorization of its assigned value. The first digit of a letter s code is the number of times 2 is used as a factor, the second digit is the number of times 3 is used as a factor, the third digit is the number of times 5 is used as a factor and so on. For example, since N is the 14 th letter of the alphabet and N = 14 = , the code for the letter N is with 1s in the first and fourth positions because its prime factorization has one 2 (the first prime number) and one 7 (the fourth prime number). What 6-letter word does the following sequence of six codes represent? The first row is the code for the first letter of the word, the second row is the code for the second letter of the word and so on Chapter Competition, Target Round # There are many words that can be made from the 10 letters in the word DICTIONARY. According to the definition of word-product given for #7 and #8, what word can you make with the highest word-product? Answers: 21 points; 68 cents; 11 letters; 3 sets; V; 12 ways; EGGS; CAKE; EQUALS; multiple answers the word TRY has a word-product of = 9000, so incorporating these three letters will give multiples of Possible Next Steps Using the definition of word-product, students can work on #10 individually for a little while and then as a group try to figure out the highest-scoring word they can think of. **Please send us the highest-scoring word your club finds, and we will share some of the top-scoring words online. Be sure to give us your school name when you submit your high-scoring word and send it to info@mathcounts.org with subject line MATHCOUNTS Club Program. Similarly, students can come up with riddles like #7 and #8. Discuss why some words would be much more difficult to guess (many non-prime factors) and others would be much easier to figure out (only prime factors). Perhaps give students some words and ask them to provide their respective codes using the instructions for problem # MATHCOUNTS Club Resource Guide Club Resource Guide.pdf 26 8/18/08 11:24:15 AM
3 A = 1 Dictionary Day Meeting Problem Set A = 1 1. The letters of the alphabet are each assigned a random integer value, and H = 10. The value of a word comes from the sum of its letters values. If MATH is 35 points, TEAM is 42 points and MEET is 38 points, what is the point value of A? 2006 School Competition, Team Round #6 2. The word-sum of a word is determined by adding together the value of each letter. In the alphabet, letters A through H each have a value of 5 cents; letters I through R each have a value of 7 cents; and letters S through Z each have a value of 8 cents. What is the wordsum of the word MATHCOUNTS, in cents? 2005 School Competition, Sprint Round #1 3. How many letters of the alphabet shown below have a vertical line of symmetry? 2005 School Competition, Sprint Round #7 ABCDEFGHIJKLMNOPQRSTUVWXYZ 4. A set of magnetic letters contains two of each consonant and three of each vowel. Only a complete set of letters may be purchased. How many complete sets of magnetic letters must be purchased to make a sign that reads: MATHCOUNTS COMPETITION TODAY? 2002 School Competition, Team Round #1 5. The sequence below is formed by repeating the letters of the alphabet, in order, the same number of times as the letter s ordinal position in the alphabet. After 26 Zs, the sequence starts over with ABBCCC. What is the 2005th letter in the sequence? A B B C C C D D D D E E E E E 2005 School Competition, Team Round #8 6. If all of the letters of the word BEEP are used, in how many different ways can the four letters be arranged in a four-letter sequence? The two Es are indistinguishable, so EEPB should be counted only once since we would not be able to tell a difference if the two Es were swapped School Handbook, Volume I, Warm-Up 4-3 (For #7, #8) A value is assigned to each letter of the alphabet such that A = 1, B = 2, C = 3,..., Z = 26. The word-product of a word is the product of the values of each letter in the word. For example, the word-product of NAME is = What is Carrie s favorite breakfast food if its word-product is 4655? Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Problem Set
4 8. What is her favorite dessert if its word-product is 165? 9. A value is assigned to each letter of the alphabet such that A = 1, B = 2, C = 3,..., Z = 26. A nine-digit code is then created for each letter using the prime factorization of its assigned value. The first digit of a letter s code is the number of times 2 is used as a factor, the second digit is the number of times 3 is used as a factor, the third digit is the number of times 5 is used as a factor and so on. For example, since N is the 14 th letter of the alphabet and N = 14 = , the code for the letter N is with 1s in the first and fourth positions because its prime factorization has one 2 (the first prime number) and one 7 (the fourth prime number). What 6-letter word does the following sequence of six codes represent? The first row is the code for the first letter of the word, the second row is the code for the second letter of the word and so on Chapter Competition, Target Round #6 10. There are many words that can be made from the 10 letters in the word DICTIONARY. According to the definition of word-product given for #7 and #8, what word can you make with the highest word-product? **Answers to these problems are on page 26 of the Club Resource Guide.** Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Problem Set
5 Dictionary Day Solutions ( MCP Club Resource Guide) Problem 1. Since H = 10, from MATH = 35 points, we know MAT = = 25 points. From TEAM being 42 points, we can see that the E = = 17 points. Notice that MEET and TEAM only have one letter different. Since MEET is 38 points and TEAM is 42 points, the difference in their points is = 4 points. This means an A is 4 points more than an E. Since we know E = 17 points, then A = = 21 points. Problem 2. According to the values given, MATHCOUNTS will have a word-sum of = 68 cents. Problem 3. In the alphabet shown, the letters A, H, I, M, O, T, U, V, W, X and Y have vertical lines of symmetry. This is 11 letters. Problem 4. In the sign MATHCOUNTS COMPETITION TODAY, there are multiple copies of many letters. Here is our total tally: M 2; A 2; T 5; H 1; C 2; O 4; U 1; N 2; S 1; P 1; E 1; I 2; D 1; Y 1. The consonant with the highest total is T. We would need 3 complete sets to get our 5 Ts. The vowel with the highest total is O, but we would only need 2 complete sets to get our 4 Os. Therefore, we will need 3 complete sets of letters to make the sign. Problem 5. Let s determine how many letters are written when we do one complete cycle of the alphabet. Notice there will be 1 A and 26 Zs, there will be 2 Bs and 25 Ys, etc. Each pairing adds to 27 letters, and there will be 13 pairings. This is a total of 351 letters. Dividing 2005 by 351, we see that we will have written 5.7 cycles of the alphabet. Six cycles of the alphabet will put us at = 2106 letters. Subtracting off 26 Zs we have = 2080 letters with the last being Y. Subtracting off 25 Ys we have = 2055 letters with the last being X. Subtracting off 24 Xs we have = 2031 letters with the last being W. Subtracting off 23 Ws we have = 2008 Vs. Since there are 22 Vs, we can see that the 2005th letter will be a V. Problem 6. Since our Es are indistinguishable, we can easily list out the possibilities for the placement of our Es in a four-letter sequence: EE E E E E E E E E EE With each of these six sequences, we can place the B and P in two ways. For instance EE can become either EEBP or EEPB. Therefore, there are a total of 6 2 = 12 ways to arrange the four letters if the Es are indistinguishable. Problem 7. The word-product 4655 can be factored down to The letters corresponding with 5, 7 and 19 are E, G and S, respectively. Notice that multiplying any of these factors together will give us more factors of 4655, but they will be greater than 26 and not correspond to a letter. Since 1 is a factor of every number, it s possible we can use an A. However, at this point we have E, G, G and S, and without needing to rearrange these, we gets EGGS, which is a well-known breakfast food. Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Solution Set
6 Problem 8. The word-product 165 can be factored down to The letters that correspond with these values are E, C and K. Again, remember that A can always be added. It s possible to break 165 into 11 15, but this only allows us to work with K and O, and possibly A. Using E, C, K and A we can get the popular dessert of CAKE. Problem 9. The values 1 through 26 are assigned to A through Z, respectively. A 9-digit code is created for each letter using prime factorization. The first digit of a letter s code is the number of times 2 is used as a factor; the second digit is the number of times 3 is used as a factor and so on. We are given six 9-digit codes and asked to determine what word this set of codes spells. The first 9-digit code is: The only 1 is in the 3rd column where the 3rd prime, 5, is used as the factor, so 5 is the first value or E. The second 9-digit code is: The only 1 is in the 7th column where the 7th prime, 17, is used as the factor, so 17 is the second value or Q. The third 9-digit code is: The 1s are the second and fourth prime, or 3 and = 21 or U. The fourth 9-digit code is: The only number with no prime factors is 1 or A. The fifth 9-digit code is: = 4 3 = 12 or L. The sixth 9-digit code is: The only 1 is in the 8th column where the 8th prime, 19, is used as the factor so 19 is the value or S. Our word is EQUALS. Problem 10. Answers will vary. Copyright MATHCOUNTS, Inc MATHCOUNTS Club Resource Guide Solution Set
Halloween (Oct. 31) Meeting (Multiple Topics)
Halloween (Oct. 31) Meeting (Multiple Topics) Topic There are a variety of math topics covered in the problems used for this meeting. Materials Needed Copies of the Halloween problem set (Problems and
More informationKenken For Teachers. Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles June 27, 2010. Abstract
Kenken For Teachers Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles June 7, 00 Abstract Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic skills.
More information3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
More informationBake Cookies Day (Dec. 18) Meeting (Multiple Topics)
Bake Cookies Day (Dec. 18) Meeting (Multiple Topics) Topic This meeting s problems cover a variety of topics. However, there is a heavy emphasis on proportional reasoning. Materials Needed Copies of the
More informationContents. Sample worksheet from www.mathmammoth.com
Contents Introduction... 4 Warmup: Mental Math 1... 8 Warmup: Mental Math 2... 10 Review: Addition and Subtraction... 12 Review: Multiplication and Division... 15 Balance Problems and Equations... 19 More
More informationJust the Factors, Ma am
1 Introduction Just the Factors, Ma am The purpose of this note is to find and study a method for determining and counting all the positive integer divisors of a positive integer Let N be a given positive
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material
More informationEE6-5 Solving Equations with Balances Pages 77 78
EE6-5 Solving Equations with Balances Pages 77 78 STANDARDS 6.EE.B.5, 6.EE.B.6 Goals Students will use pictures to model and solve equations. Vocabulary balance equation expression sides (of an equation)
More information1. When the least common multiple of 8 and 20 is multiplied by the greatest common factor of 8 and 20, what is the result?
Black Equivalent Fractions and LCM 1. When the least common multiple of 8 and 20 is multiplied by the greatest common factor of 8 and 20, what is the result? 2. The sum of three consecutive integers is
More informationA permutation can also be represented by describing its cycles. What do you suppose is meant by this?
Shuffling, Cycles, and Matrices Warm up problem. Eight people stand in a line. From left to right their positions are numbered,,,... 8. The eight people then change places according to THE RULE which directs
More informationPigeonhole Principle Solutions
Pigeonhole Principle Solutions 1. Show that if we take n + 1 numbers from the set {1, 2,..., 2n}, then some pair of numbers will have no factors in common. Solution: Note that consecutive numbers (such
More informationMath Journal HMH Mega Math. itools Number
Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and
More informationPrime Time: Homework Examples from ACE
Prime Time: Homework Examples from ACE Investigation 1: Building on Factors and Multiples, ACE #8, 28 Investigation 2: Common Multiples and Common Factors, ACE #11, 16, 17, 28 Investigation 3: Factorizations:
More informationSection 4.1 Rules of Exponents
Section 4.1 Rules of Exponents THE MEANING OF THE EXPONENT The exponent is an abbreviation for repeated multiplication. The repeated number is called a factor. x n means n factors of x. The exponent tells
More informationALGEBRA. sequence, term, nth term, consecutive, rule, relationship, generate, predict, continue increase, decrease finite, infinite
ALGEBRA Pupils should be taught to: Generate and describe sequences As outcomes, Year 7 pupils should, for example: Use, read and write, spelling correctly: sequence, term, nth term, consecutive, rule,
More informationSession 7 Fractions and Decimals
Key Terms in This Session Session 7 Fractions and Decimals Previously Introduced prime number rational numbers New in This Session period repeating decimal terminating decimal Introduction In this session,
More informationCategory 3 Number Theory Meet #1, October, 2000
Category 3 Meet #1, October, 2000 1. For how many positive integral values of n will 168 n be a whole number? 2. What is the greatest integer that will always divide the product of four consecutive integers?
More informationRegions in a circle. 7 points 57 regions
Regions in a circle 1 point 1 region points regions 3 points 4 regions 4 points 8 regions 5 points 16 regions The question is, what is the next picture? How many regions will 6 points give? There's an
More information. 0 1 10 2 100 11 1000 3 20 1 2 3 4 5 6 7 8 9
Introduction The purpose of this note is to find and study a method for determining and counting all the positive integer divisors of a positive integer Let N be a given positive integer We say d is a
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
More informationGrade 6 Math Circles March 10/11, 2015 Prime Time Solutions
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Lights, Camera, Primes! Grade 6 Math Circles March 10/11, 2015 Prime Time Solutions Today, we re going
More informationMATHEMATICS. Y5 Multiplication and Division 5330 Square numbers, prime numbers, factors and multiples. Equipment. MathSphere
MATHEMATICS Y5 Multiplication and Division 5330 Square numbers, prime numbers, factors and multiples Paper, pencil, ruler. Equipment MathSphere 5330 Square numbers, prime numbers, factors and multiples
More informationFactoring Whole Numbers
2.2 Factoring Whole Numbers 2.2 OBJECTIVES 1. Find the factors of a whole number 2. Find the prime factorization for any number 3. Find the greatest common factor (GCF) of two numbers 4. Find the GCF for
More information3 Some Integer Functions
3 Some Integer Functions A Pair of Fundamental Integer Functions The integer function that is the heart of this section is the modulo function. However, before getting to it, let us look at some very simple
More informationMATH 140 Lab 4: Probability and the Standard Normal Distribution
MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes
More informationFive Ways to Solve Proportion Problems
Five Ways to Solve Proportion Problems Understanding ratios and using proportional thinking is the most important set of math concepts we teach in middle school. Ratios grow out of fractions and lead into
More informationFractions. If the top and bottom numbers of a fraction are the same then you have a whole one.
What do fractions mean? Fractions Academic Skills Advice Look at the bottom of the fraction first this tells you how many pieces the shape (or number) has been cut into. Then look at the top of the fraction
More informationHomework Activities for Kindergarten
Homework Activities for Kindergarten Listed below are several learning activities for your child to complete at home to reinforce skills being taught in school. The sight words are on the last page. Reading
More informationCommission Formula. Value If True Parameter Value If False Parameter. Logical Test Parameter
Excel Review This review uses material and questions from Practice Excel Exam 1 found on the Lab Exam 2 Study Guide webpage. Print out a copy of Practice Excel Exam 1. Download the Practice Excel Exam
More informationIf A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
More informationWelcome to Harcourt Mega Math: The Number Games
Welcome to Harcourt Mega Math: The Number Games Harcourt Mega Math In The Number Games, students take on a math challenge in a lively insect stadium. Introduced by our host Penny and a number of sporting
More informationWhen I think about using an advanced scientific or graphing calculator, I feel:
Slide 2.11, 2.14 & 3.2 MATH HISTORY QUESTION EXERCISE ONE My last math course was (course, year, and school): I would say that my experience in that course was: A math course I especially remember was:
More informationMATHS ACTIVITIES FOR REGISTRATION TIME
MATHS ACTIVITIES FOR REGISTRATION TIME At the beginning of the year, pair children as partners. You could match different ability children for support. Target Number Write a target number on the board.
More informationWe can express this in decimal notation (in contrast to the underline notation we have been using) as follows: 9081 + 900b + 90c = 9001 + 100c + 10b
In this session, we ll learn how to solve problems related to place value. This is one of the fundamental concepts in arithmetic, something every elementary and middle school mathematics teacher should
More informationGreatest Common Factor and Least Common Multiple
Greatest Common Factor and Least Common Multiple Intro In order to understand the concepts of Greatest Common Factor (GCF) and Least Common Multiple (LCM), we need to define two key terms: Multiple: Multiples
More informationExponential Notation and the Order of Operations
1.7 Exponential Notation and the Order of Operations 1.7 OBJECTIVES 1. Use exponent notation 2. Evaluate expressions containing powers of whole numbers 3. Know the order of operations 4. Evaluate expressions
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A3d,e Time allotted for this Lesson: 4 Hours Essential Question: LESSON 4 FINITE ARITHMETIC SERIES AND RELATIONSHIP TO QUADRATIC
More informationCurrent California Math Standards Balanced Equations
Balanced Equations Current California Math Standards Balanced Equations Grade Three Number Sense 1.0 Students understand the place value of whole numbers: 1.1 Count, read, and write whole numbers to 10,000.
More informationUnit 6 Number and Operations in Base Ten: Decimals
Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationLearn Unifon Spell the Sounds!
Learn Unifon Spell the Sounds! By Kenneth C. Anderson Are you tired of feeling stupid because you spell words wrong all the time? Me, too. But I m doing something about it. English is an easy language
More informationChapter 11 Number Theory
Chapter 11 Number Theory Number theory is one of the oldest branches of mathematics. For many years people who studied number theory delighted in its pure nature because there were few practical applications
More information4/1/2017. PS. Sequences and Series FROM 9.2 AND 9.3 IN THE BOOK AS WELL AS FROM OTHER SOURCES. TODAY IS NATIONAL MANATEE APPRECIATION DAY
PS. Sequences and Series FROM 9.2 AND 9.3 IN THE BOOK AS WELL AS FROM OTHER SOURCES. TODAY IS NATIONAL MANATEE APPRECIATION DAY 1 Oh the things you should learn How to recognize and write arithmetic sequences
More informationAnnotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.
Work sample portfolio summary WORK SAMPLE PORTFOLIO Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Each portfolio is an example
More informationSubtracting Negative Integers
Subtracting Negative Integers Notes: Comparison of CST questions to the skill of subtracting negative integers. 5 th Grade/65 NS2.1 Add, subtract, multiply and divide with decimals; add with negative integers;
More informationIntegers (pages 294 298)
A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write
More informationLesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations)
Lesson Plans for (9 th Grade Main Lesson) Possibility & Probability (including Permutations and Combinations) Note: At my school, there is only room for one math main lesson block in ninth grade. Therefore,
More informationMercer County Schools
Mercer County Schools PRIORITIZED CURRICULUM Mathematics Content Maps Second Grade Mercer County Schools PRIORITIZED CURRICULUM The Mercer County Schools Prioritized Curriculum is composed of West Virginia
More informationNF5-12 Flexibility with Equivalent Fractions and Pages 110 112
NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.
More informationTom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
More informationAccentuate the Negative: Homework Examples from ACE
Accentuate the Negative: Homework Examples from ACE Investigation 1: Extending the Number System, ACE #6, 7, 12-15, 47, 49-52 Investigation 2: Adding and Subtracting Rational Numbers, ACE 18-22, 38(a),
More informationDay One: Least Common Multiple
Grade Level/Course: 5 th /6 th Grade Math Lesson/Unit Plan Name: Using Prime Factors to find LCM and GCF. Rationale/Lesson Abstract: The objective of this two- part lesson is to give students a clear understanding
More information6 3 4 9 = 6 10 + 3 10 + 4 10 + 9 10
Lesson The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base- system. When you
More informationWelcome to Basic Math Skills!
Basic Math Skills Welcome to Basic Math Skills! Most students find the math sections to be the most difficult. Basic Math Skills was designed to give you a refresher on the basics of math. There are lots
More informationIB Math Research Problem
Vincent Chu Block F IB Math Research Problem The product of all factors of 2000 can be found using several methods. One of the methods I employed in the beginning is a primitive one I wrote a computer
More informationCalculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1
Calculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1 What are the multiples of 5? The multiples are in the five times table What are the factors of 90? Each of these is a pair of factors.
More informationPrime Factorization 0.1. Overcoming Math Anxiety
0.1 Prime Factorization 0.1 OBJECTIVES 1. Find the factors of a natural number 2. Determine whether a number is prime, composite, or neither 3. Find the prime factorization for a number 4. Find the GCF
More informationPlanning Guide. Grade 6 Factors and Multiples. Number Specific Outcome 3
Mathematics Planning Guide Grade 6 Factors and Multiples Number Specific Outcome 3 This Planning Guide can be accessed online at: http://www.learnalberta.ca/content/mepg6/html/pg6_factorsmultiples/index.html
More information2015 School Competition Target Round Problems 1 & 2
2015 School Competition Target Round Problems 1 & 2 Name DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO. This section of the competition consists of eight problems, which will be presented in pairs. Work
More informationACTIVITY: Identifying Common Multiples
1.6 Least Common Multiple of two numbers? How can you find the least common multiple 1 ACTIVITY: Identifying Common Work with a partner. Using the first several multiples of each number, copy and complete
More informationINTERSECTION MATH And more! James Tanton
INTERSECTION MATH And more! James Tanton www.jamestanton.com The following represents a sample activity based on the December 2006 newsletter of the St. Mark s Institute of Mathematics (www.stmarksschool.org/math).
More informationRACE TO CLEAR THE MAT
RACE TO CLEAR THE MAT NUMBER Place Value Counting Addition Subtraction Getting Ready What You ll Need Base Ten Blocks, 1 set per group Base Ten Blocks Place-Value Mat, 1 per child Number cubes marked 1
More informationLesson 4: Convert Fractions, Review Order of Operations
Lesson 4: Convert Fractions, Review Order of Operations LESSON 4: Convert Fractions, Do Order of Operations Weekly Focus: fractions, decimals, percent, order of operations Weekly Skill: convert, compute
More informationLesson/Unit Plan Name: Patterns: Foundations of Functions
Grade Level/Course: 4 th and 5 th Lesson/Unit Plan Name: Patterns: Foundations of Functions Rationale/Lesson Abstract: In 4 th grade the students continue a sequence of numbers based on a rule such as
More informationThe Euclidean Algorithm
The Euclidean Algorithm A METHOD FOR FINDING THE GREATEST COMMON DIVISOR FOR TWO LARGE NUMBERS To be successful using this method you have got to know how to divide. If this is something that you have
More informationSection 1.5 Exponents, Square Roots, and the Order of Operations
Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.
More information+ = has become. has become. Maths in School. Fraction Calculations in School. by Kate Robinson
+ has become 0 Maths in School has become 0 Fraction Calculations in School by Kate Robinson Fractions Calculations in School Contents Introduction p. Simplifying fractions (cancelling down) p. Adding
More information6.4 Normal Distribution
Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under
More informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More informationSimplifying Square-Root Radicals Containing Perfect Square Factors
DETAILED SOLUTIONS AND CONCEPTS - OPERATIONS ON IRRATIONAL NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!
More informationFractions as Numbers INTENSIVE INTERVENTION. National Center on. at American Institutes for Research
National Center on INTENSIVE INTERVENTION at American Institutes for Research Fractions as Numbers 000 Thomas Jefferson Street, NW Washington, DC 0007 E-mail: NCII@air.org While permission to reprint this
More informationWhat Is Singapore Math?
What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has
More informationMath 319 Problem Set #3 Solution 21 February 2002
Math 319 Problem Set #3 Solution 21 February 2002 1. ( 2.1, problem 15) Find integers a 1, a 2, a 3, a 4, a 5 such that every integer x satisfies at least one of the congruences x a 1 (mod 2), x a 2 (mod
More informationBBC Learning English - Talk about English July 11, 2005
BBC Learning English - July 11, 2005 About this script Please note that this is not a word for word transcript of the programme as broadcast. In the recording and editing process changes may have been
More informationWorking with whole numbers
1 CHAPTER 1 Working with whole numbers In this chapter you will revise earlier work on: addition and subtraction without a calculator multiplication and division without a calculator using positive and
More information1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH
1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH Calendar The following tables show the CCSS focus of The Meeting activities, which appear at the beginning of each numbered lesson and are taught daily,
More informationMath Games For Skills and Concepts
Math Games p.1 Math Games For Skills and Concepts Original material 2001-2006, John Golden, GVSU permission granted for educational use Other material copyright: Investigations in Number, Data and Space,
More information1(a). How many ways are there to rearrange the letters in the word COMPUTER?
CS 280 Solution Guide Homework 5 by Tze Kiat Tan 1(a). How many ways are there to rearrange the letters in the word COMPUTER? There are 8 distinct letters in the word COMPUTER. Therefore, the number of
More informationMATH 10034 Fundamental Mathematics IV
MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.
More informationAdding and Subtracting Positive and Negative Numbers
Adding and Subtracting Positive and Negative Numbers Absolute Value For any real number, the distance from zero on the number line is the absolute value of the number. The absolute value of any real number
More informationDecimals Adding and Subtracting
1 Decimals Adding and Subtracting Decimals are a group of digits, which express numbers or measurements in units, tens, and multiples of 10. The digits for units and multiples of 10 are followed by a decimal
More informationAssessment Management
Facts Using Doubles Objective To provide opportunities for children to explore and practice doubles-plus-1 and doubles-plus-2 facts, as well as review strategies for solving other addition facts. www.everydaymathonline.com
More informationObjective To introduce the concept of square roots and the use of the square-root key on a calculator. Assessment Management
Unsquaring Numbers Objective To introduce the concept of square roots and the use of the square-root key on a calculator. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
More informationOA3-10 Patterns in Addition Tables
OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20
More informationPredicting the Ones Digit
. Predicting the Ones Digit Goals Eamine patterns in the eponential and standard forms of powers of whole numbers Use patterns in powers to estimate the ones digits for unknown powers In this problem,
More informationMinnesota Academic Standards
A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley
More informationMEP Pupil Text 12. A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued.
MEP Pupil Text Number Patterns. Simple Number Patterns A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued. Worked Example Write down the
More informationSquare Roots and Other Radicals
Radicals - Definition Radicals, or roots, are the opposite operation of applying exponents. A power can be undone with a radical and a radical can be undone with a power. For example, if you square 2,
More informationPre-Algebra Lecture 6
Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More informationThe Crescent Primary School Calculation Policy
The Crescent Primary School Calculation Policy Examples of calculation methods for each year group and the progression between each method. January 2015 Our Calculation Policy This calculation policy has
More informationNumber boards for mini mental sessions
Number boards for mini mental sessions Feel free to edit the document as you wish and customise boards and questions to suit your learners levels Print and laminate for extra sturdiness. Ideal for working
More informationCHAPTER 14 ORDINAL MEASURES OF CORRELATION: SPEARMAN'S RHO AND GAMMA
CHAPTER 14 ORDINAL MEASURES OF CORRELATION: SPEARMAN'S RHO AND GAMMA Chapter 13 introduced the concept of correlation statistics and explained the use of Pearson's Correlation Coefficient when working
More informationAn Introduction to Number Theory Prime Numbers and Their Applications.
East Tennessee State University Digital Commons @ East Tennessee State University Electronic Theses and Dissertations 8-2006 An Introduction to Number Theory Prime Numbers and Their Applications. Crystal
More informationMath BINGO MOST POPULAR. Do you have the lucky card? B I N G O
MOST POPULAR Math BINGO Do you have the lucky card? Your club members will love this MATHCOUNTS reboot of a classic game. With the perfect mix of luck and skill, this is a game that can be enjoyed by students
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationMATHCOUNTS TOOLBOX Facts, Formulas and Tricks
MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS Coaching Kit 40 I. PRIME NUMBERS from 1 through 100 (1 is not prime!) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 II.
More informationMental Maths module for the Foundation Phase
Mental Maths module for the Foundation Phase 1 CONTENTS 1. The importance of Mental Mathematics p 4 2. Benefits of Mental Maths p 6 3. Mental Maths games p 7 4. Mental Maths activities p 8 2 1. The importance
More information3.2 Methods of Addition
.2 Methods of Addition Objectives Relate addition stories to number bonds. Write two addition facts for a given number bond. Solve picture problems using addition. Learn addition facts through, and the
More informationSection 1.1 Linear Equations: Slope and Equations of Lines
Section. Linear Equations: Slope and Equations of Lines Slope The measure of the steepness of a line is called the slope of the line. It is the amount of change in y, the rise, divided by the amount of
More informationOrder of Operations More Essential Practice
Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure
More information