FOM 11 Ch. 1 Practice Test Name: Inductive and Deductive Reasoning
|
|
- Albert Hawkins
- 5 years ago
- Views:
Transcription
1 FOM 11 Ch. 1 Practice Test Name: Inductive and Deductive Reasoning Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Justin gathered the following evidence. 17(22) = (22) = (22) = (22) = 396 Which conjecture, if any, is Justin most likely to make from this evidence? a. When you multiply a two-digit number by 22, the last and first digits of the product are the digits of the original number. b. When you multiply a two-digit number by 22, the first and last digits of the product are the digits of the original number. c. When you multiply a two-digit number by 22, the first and last digits of the product form a number that is twice the original number. d. None of the above conjectures can be made from this evidence. 2. Which conjecture, if any, could you make about the sum of two odd integers and one even integer? a. The sum will be an even integer. b. The sum will be an odd integer. c. The sum will be negative. d. It is not possible to make a conjecture. 3. Kerry created the following tables to show patterns. Multiples of Sum of the Digits In each case, the sum of the digits of a multiple of 3 is also a multiple of 3. Multiples of 3 3 = Sum of the Digits In each case, the sum of the digits of a multiple of 3 3, or 9, is also a multiple of 9. Based on this evidence, which conjecture might Kerry make? Is the conjecture valid? a. The sum of the digits of a multiple of 2 3, or 6, is also a multiple of 6; yes, this conjecture is valid. b. The sum of the digits of a multiple of 2 3, or 6, is also a multiple of 6; no, this conjecture is not valid. c. The sum of the digits of a multiple of 3 3 3, or 27, is also a multiple of 27; no, this conjecture is not valid. d. The sum of the digits of a multiple of 3 3 3, or 27, is also a multiple of 27; yes, this conjecture is valid.
2 4. Sasha made the following conjecture: All polygons with six equal sides are regular hexagons. Which figure, if either, is a counterexample to this conjecture? Explain. a. Figure A is a counterexample, because all six sides are equal and it is a regular hexagon. b. Figure B is a counterexample, because all six sides are equal and it is a regular hexagon. c. Figure B is a counterexample, because all six sides are equal and it is not a regular hexagon. d. Figure A is a counterexample, because all six sides are equal and it is not a regular hexagon. 5. Athena made the following conjecture. The sum of a multiple of 4 and a multiple of 8 must be a multiple of 8. Is the following equation a counterexample to this conjecture? Explain = 36 a. Yes, it is a counterexample, because 36 is a multiple of 8 b. No, it is not a counterexample, because 36 is a multiple of 8. c. No, it is not a counterexample, because 36 is not a multiple of 8. d. Yes, it is a counterexample, because 36 is not a multiple of All birds have backbones. Birds are the only animals that have feathers. Rosie is not a bird. What can be deduced about Rosie? 1. Rosie has a backbone. 2. Rosie does not have feathers. a. Neither Choice 1 nor Choice 2 b. Choice 1 only c. Choice 1 and Choice 2 d. Choice 2 only
3 7. Which of the following choices, if any, uses deductive reasoning to show that the sum of two odd integers is even? a = 8 and = 12 b. (2x + 1) + (2y + 1) = 2(x + y + 1) c. 2x + 2y + 1 = 2(x + y) + 1 d. None of the above choices 8. What type of error, if any, occurs in the following deduction? Saturday is not a school day for most students. Therefore, students should not wear red clothing on Saturdays. a. a false assumption or generalization b. an error in reasoning c. an error in calculation d. There is no error in the deduction. 9. Alison created a number trick in which she always ended with the original number. When Alison tried to prove her trick, however, it did not work. What type of error occurs in the proof? n Use n to represent any number. n + 4 Add 4. 2n + 4 Multiply by 2. 2n + 8 Add 4. n + 4 Divide by 2. n 1 Subtract 5. a. a false assumption or generalization b. an error in reasoning c. an error in calculation d. There is no error in the proof. 10. Which type of reasoning does the following statement demonstrate? Over the past 11 years, a tree has produced peaches each year. Therefore, the tree will produce peaches this year. a. inductive reasoning b. deductive reasoning c. neither inductive nor deductive reasoning 11. Determine the unknown term in this pattern. 8, 17, 14, 23,, 29, 26, 35 a. 21 b. 22 c. 20 d. 25
4 12. Which number should appear in the centre of Figure 4? a. 41 b. 24 c. 36 d. 11 Figure 1 Figure 2 Figure 3 Figure Which number should go in the grey square in this Sudoku puzzle? a. 5 b. 7 c. 1 d. 3 Short Answer 14. What conjecture could you make about the product of two odd integers and one even integer?
5 15. Make a conjecture about the relative size of the three figures. Check the validity of your conjecture. 16. Cheyenne told her little brother, Joseph, that horses, cats, and dogs are all mammals. As a result, Joseph made the following conjecture: All animals with four legs are mammals. Use a counterexample to show Joseph that his conjecture is not valid. 17. Kendra made the following conjecture: The sum of any three integers is greater than each integer. Do you agree or disagree? Briefly justify your decision with a counterexample if possible.
6 18. Try the following number trick with different numbers. Make a conjecture about the trick. Choose a number. Multiply by 3. Add 5. Multiply by 2. Subtract 10. Divide by In a Kakuro puzzle, you fill in the empty squares with the numbers from 1 to 9. Each row of squares must add up to the circled number to the left of it. Each column of squares must add up the circled number above it. A number cannot appear more than once in the same sum. Complete this Kakuro puzzle by filling in the grey squares.
7 Problem 20. Are d and e equal? Prove your answer. 21. Akilah, Barbara, Cathy, and Donna all go to the same high school. One likes history the best, one likes math the best, one likes computer science the best, and one likes English the best. Use the statements below to determine who likes computer science the best. Akilah and Cathy eat lunch with the student who likes computer science. Donna likes history the best.
8 Ch. 1 Practice Test - Inductive and Deductive Reasoning Answer Section SHORT ANSWER MULTIPLE CHOICE 1. D 2. A 3. C 4. D 5. D 6. D 7. B 8. B 9. C 10. A 11. C 12. B 13. B 14.For example, the product will be an even integer. 15.For example, I conjectured that the figures were different sizes, but when I measured them with a ruler, it turned out that they were the same size. 16.For example, lizards have four legs, and they are not mammals. 17.For example, disagree: 3 + ( 4) + 2 = 5, and 5 is less than each integer. 18.For example, the answer is always the original number. 19. PROBLEM 20. No, they are not equal. Angle d and the right angle are supplementary, so d must also be a right angle. If angle e is a right angle, then the side opposite to it will be a hypotenuse. Using the Pythagorean theorem: But the length of the side opposite e is 9 units, not 10, so e is not a right angle. Therefore, angle a and angle b are not equal. 21. Barbara likes computer science the best.
FOM 11 Ch. 1 Practice Test Name: Inductive and Deductive Reasoning
FOM 11 Ch. 1 Practice Test Name: Inductive and Deductive Reasoning Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Justin gathered the following evidence.
More informationInductive and Deductive Reasoning
Inductive and Deductive Reasoning Name General Outcome Develop algebraic and graphical reasoning through the study of relations Specific Outcomes it is expected that students will: Sample Question Student
More information2-1 Inductive Reasoning and Conjecture
Write a conjecture that describes the pattern in each sequence. Then use your conjecture to find the next item in the sequence. 18. 1, 4, 9, 16 1 = 1 2 4 = 2 2 9 = 3 2 16 = 4 2 Each element is the square
More information2.1 inductive reasoning and conjecture ink.notebook. September 07, Page 55. Ch 2. Reasoning. Page 56. and Proofs. 2.1 Inductive.
2.1 inductive reasoning and conjecture ink.notebook Page 55 Ch 2 Reasoning and Proofs Page 56 2.1 Inductive Reasoning Lesson Objectives Page 57 Standards Lesson Notes Page 58 2.1 Inductive Reasoning and
More informationGood Luck To. DIRECTIONS: Answer each question and show all work in the space provided. The next two terms of the sequence are,
Good Luck To Period Date DIRECTIONS: Answer each question and show all work in the space provided. 1. Find the next two terms of the sequence. 6, 36, 216, 1296, _?_, _?_ The next two terms of the sequence
More informationSet 6: Understanding the Pythagorean Theorem Instruction
Instruction Goal: To provide opportunities for students to develop concepts and skills related to understanding that the Pythagorean theorem is a statement about areas of squares on the sides of a right
More informationThe Pythagorean Theorem
. The Pythagorean Theorem Goals Draw squares on the legs of the triangle. Deduce the Pythagorean Theorem through exploration Use the Pythagorean Theorem to find unknown side lengths of right triangles
More informationGeometry Unit 2 Review Day 1 What to expect on the test:
Geometry Unit 2 Review Day 1 What to expect on the test: Conditional s Converse Inverse Contrapositive Bi-conditional statements Today we are going to do more work with Algebraic Proofs Counterexamples/Instances
More informationI followed the steps to work through four examples. Conjecture: It is 3 times. It worked.
1.6 Reasoning to Solve Problems GOAL Solve problems using inductive or deductive reasoning. INVESTIGATE the Math Emma was given this math trick: Choose a number. Multiply by 6. Add 4. Divide by 2. Subtract
More informationRepresenting Square Numbers. Use materials to represent square numbers. A. Calculate the number of counters in this square array.
1.1 Student book page 4 Representing Square Numbers You will need counters a calculator Use materials to represent square numbers. A. Calculate the number of counters in this square array. 5 5 25 number
More information4.1 Patterns. Example 1 Find the patterns:
4.1 Patterns One definition of mathematics is the study of patterns. In this section, you will practice recognizing mathematical patterns in various problems. For each example, you will work with a partner
More informationIdeas beyond Number. Activity worksheets
Ideas beyond Number Activity sheet 1 Task 1 Some students started to solve this equation in different ways: For each statement tick True or False: = = = = Task 2: Counter-examples The exception disproves
More informationWarm Up Classify each angle. Holt McDougal Geometry
Warm Up Classify each angle. Objectives EQ: How do you use inductive reasoning to identify patterns and make conjectures? How do you find counterexamples to disprove conjectures? Unit 2A Day 4 inductive
More informationGeometry Benchmark Assessment #1
Geometry Benchmark Assessment #1 Multiple Choice Circle the letter of the choice that best completes the statement or answers the question. 1. When the net is folded into the rectangular prism shown beside
More informationIdeas beyond Number. Teacher s guide to Activity worksheets
Ideas beyond Number Teacher s guide to Activity worksheets Learning objectives To explore reasoning, logic and proof through practical, experimental, structured and formalised methods of communication
More informationSquare Roots and the Pythagorean Theorem
UNIT 1 Square Roots and the Pythagorean Theorem Just for Fun What Do You Notice? Follow the steps. An example is given. Example 1. Pick a 4-digit number with different digits. 3078 2. Find the greatest
More informationMt. Douglas Secondary
Foundations of Math 11 Section 4.1 Patterns 167 4.1 Patterns We have stated in chapter 2 that patterns are widely used in mathematics to reach logical conclusions. This type of reasoning is called inductive
More informationTHE ASSOCIATION OF MATHEMATICS TEACHERS OF NEW JERSEY 2018 ANNUAL WINTER CONFERENCE FOSTERING GROWTH MINDSETS IN EVERY MATH CLASSROOM
THE ASSOCIATION OF MATHEMATICS TEACHERS OF NEW JERSEY 2018 ANNUAL WINTER CONFERENCE FOSTERING GROWTH MINDSETS IN EVERY MATH CLASSROOM CREATING PRODUCTIVE LEARNING ENVIRONMENTS WEDNESDAY, FEBRUARY 7, 2018
More informationSample test questions All questions
Ma KEY STAGE 3 LEVELS 3 8 Sample test questions All questions 2003 Contents Question Level Attainment target Page Completing calculations 3 Number and algebra 3 Odd one out 3 Number and algebra 4 Hexagon
More information2 Reasoning and Proof
www.ck12.org CHAPTER 2 Reasoning and Proof Chapter Outline 2.1 INDUCTIVE REASONING 2.2 CONDITIONAL STATEMENTS 2.3 DEDUCTIVE REASONING 2.4 ALGEBRAIC AND CONGRUENCE PROPERTIES 2.5 PROOFS ABOUT ANGLE PAIRS
More informationFind the coordinates of the midpoint of a segment having the given endpoints.
G.(2) Coordinate and transformational geometry. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to
More informationHANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273)
HANDS-ON TRANSFORMATIONS: DILATIONS AND SIMILARITY (Poll Code 44273) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.3 8.G.4
More information1. 1 Square Numbers and Area Models (pp. 6-10)
Math 8 Unit 1 Notes Name: 1. 1 Square Numbers and Area Models (pp. 6-10) square number: the product of a number multiplied by itself; for example, 25 is the square of 5 perfect square: a number that is
More informationClasswork Example 1: Exploring Subtraction with the Integer Game
7.2.5 Lesson Date Understanding Subtraction of Integers Student Objectives I can justify the rule for subtraction: Subtracting a number is the same as adding its opposite. I can relate the rule for subtraction
More informationUK JUNIOR MATHEMATICAL CHALLENGE. April 26th 2012
UK JUNIOR MATHEMATICAL CHALLENGE April 6th 0 SOLUTIONS These solutions augment the printed solutions that we send to schools. For convenience, the solutions sent to schools are confined to two sides of
More informationCRACKING THE 15 PUZZLE - PART 4: TYING EVERYTHING TOGETHER BEGINNERS 02/21/2016
CRACKING THE 15 PUZZLE - PART 4: TYING EVERYTHING TOGETHER BEGINNERS 02/21/2016 Review Recall from last time that we proved the following theorem: Theorem 1. The sign of any transposition is 1. Using this
More informationPuzzles to Play With
Puzzles to Play With Attached are some puzzles to occupy your mind. They are not arranged in order of difficulty. Some at the back are easier than some at the front. If you think you have a solution but
More informationEdge-disjoint tree representation of three tree degree sequences
Edge-disjoint tree representation of three tree degree sequences Ian Min Gyu Seong Carleton College seongi@carleton.edu October 2, 208 Ian Min Gyu Seong (Carleton College) Trees October 2, 208 / 65 Trees
More informationGeometry - Midterm Exam Review - Chapters 1, 2
Geometry - Midterm Exam Review - Chapters 1, 2 1. Name three points in the diagram that are not collinear. 2. Describe what the notation stands for. Illustrate with a sketch. 3. Draw four points, A, B,
More informationStudent Book SAMPLE CHAPTERS
Student Book SAMPLE CHAPTERS Nelson Student Book Nelson Math Focus... Eas Each lesson starts with a Lesson Goal. Chapter 6 You will need base ten blocks GOAL Multiply using a simpler, related question.
More informationConsecutive Numbers. Madhav Kaushish. November 23, Learning Outcomes: 1. Coming up with conjectures. 2. Coming up with proofs
Consecutive Numbers Madhav Kaushish November 23, 2017 Learning Outcomes: 1. Coming up with conjectures 2. Coming up with proofs 3. Generalising theorems The following is a dialogue between a teacher and
More information2Reasoning and Proof. Prerequisite Skills. Before VOCABULARY CHECK SKILLS AND ALGEBRA CHECK
2Reasoning and Proof 2.1 Use Inductive Reasoning 2.2 Analyze Conditional Statements 2.3 Apply Deductive Reasoning 2.4 Use Postulates and Diagrams 2.5 Reason Using Properties from Algebra 2.6 Prove Statements
More information1. Anthony and Bret have equal amounts of money. Each of them has at least 5 dollars. How much should Anthony give to Bret so that Bret has 10
1. Anthony and Bret have equal amounts of money. Each of them has at least 5 dollars. How much should Anthony give to Bret so that Bret has 10 dollars more than Anthony? 2. Ada, Bella and Cindy have some
More informationChapters 1-3, 5, Inductive and Deductive Reasoning, Fundamental Counting Principle
Math 137 Exam 1 Review Solutions Chapters 1-3, 5, Inductive and Deductive Reasoning, Fundamental Counting Principle NAMES: Solutions 1. (3) A costume contest was held at Maria s Halloween party. Out of
More informationA natural number is called a perfect cube if it is the cube of some. some natural number.
A natural number is called a perfect square if it is the square of some natural number. i.e., if m = n 2, then m is a perfect square where m and n are natural numbers. A natural number is called a perfect
More information2005 Galois Contest Wednesday, April 20, 2005
Canadian Mathematics Competition An activity of the Centre for Education in Mathematics and Computing, University of Waterloo, Waterloo, Ontario 2005 Galois Contest Wednesday, April 20, 2005 Solutions
More informationMeet # 1 October, Intermediate Mathematics League of Eastern Massachusetts
Meet # 1 October, 2000 Intermediate Mathematics League of Eastern Massachusetts Meet # 1 October, 2000 Category 1 Mystery 1. In the picture shown below, the top half of the clock is obstructed from view
More informationYour Task. Unit 3 (Chapter 1): Number Relationships. The 5 Goals of Chapter 1
Unit 3 (Chapter 1): Number Relationships The 5 Goals of Chapter 1 I will be able to: model perfect squares and square roots use a variety of strategies to recognize perfect squares use a variety of strategies
More informationWhat I can do for this unit:
Unit 1: Real Numbers Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 1-1 I can sort a set of numbers into irrationals and rationals,
More informationThe Real Number System and Pythagorean Theorem Unit 9 Part B
The Real Number System and Pythagorean Theorem Unit 9 Part B Standards: 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion;
More informationName: Date: Chapter 2 Quiz Geometry. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: Chapter 2 Quiz Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is the value of x? Identify the missing justifications.,, and.
More informationG E N E R A L A P T I T U D E
G E N E R A L A P T I T U D E Aptitude for GATE The GATE syllabus for General Aptitude is as follows: Verbal Ability: English grammar, sentence completion, verbal analogies, word groups, instructions,
More informationNumber Relationships. Chapter GOAL
Chapter 1 Number Relationships GOAL You will be able to model perfect squares and square roots use a variety of strategies to recognize perfect squares use a variety of strategies to estimate and calculate
More informationModular arithmetic Math 2320
Modular arithmetic Math 220 Fix an integer m 2, called the modulus. For any other integer a, we can use the division algorithm to write a = qm + r. The reduction of a modulo m is the remainder r resulting
More informationGrade 6 Math Circles March 7/8, Magic and Latin Squares
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles March 7/8, 2017 Magic and Latin Squares Today we will be solving math and logic puzzles!
More informationChapter 01 Test. 1 Write an algebraic expression for the phrase the sum of g and 3. A 3g B 3g + 3 C g 3 D g Write a word phrase for.
hapter 01 Test Name: ate: 1 Write an algebraic expression for the phrase the sum of g and 3. 3g 3g + 3 g 3 g + 3 2 Write a word phrase for. negative 5 minus 4 plus a number n negative 5 minus 4 times a
More informationThe Unreasonably Beautiful World of Numbers
The Unreasonably Beautiful World of Numbers Sunil K. Chebolu Illinois State University Presentation for Math Club, March 3rd, 2010 1/28 Sunil Chebolu The Unreasonably Beautiful World of Numbers Why are
More information6th Grade. Factors and Multiple.
1 6th Grade Factors and Multiple 2015 10 20 www.njctl.org 2 Factors and Multiples Click on the topic to go to that section Even and Odd Numbers Divisibility Rules for 3 & 9 Greatest Common Factor Least
More informationUpdated December Year. Small Steps Guidance and Examples. Block 4: Multiplication & Division
Updated December 2017 Year 5 Small Steps Guidance and Examples Block 4: Multiplication & Division Year 5 Autumn Term Teaching Guidance Multiples Notes and Guidance Building on their times tables knowledge,
More informationUNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet
Name Period Date UNIT 6: CONJECTURE AND JUSTIFICATION WEEK 24: Student Packet 24.1 The Pythagorean Theorem Explore the Pythagorean theorem numerically, algebraically, and geometrically. Understand a proof
More informationGrade 3 Unit 4 Assessment Applying Multiplication and Division
Name: Date: Directions: Read and solve each problem. 1. What is 42 divided into 7 equal groups? A 5 B 7 C 8 D 6 2. Joseph has 36 baseball cards in his album. If he has 6 cards on each page, how many pages
More informationSynergy Round. Warming Up. Where in the World? Scrabble With Numbers. Earning a Gold Star
Synergy Round Warming Up Where in the World? You re standing at a point on earth. After walking a mile north, then a mile west, then a mile south, you re back where you started. Where are you? [4 points]
More informationCorrelation of USA Daily Math Grade 2 to Common Core State Standards for Mathematics
2.OA 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems with unknowns in all positions. 2.OA.2 Fluently add and subtract within 20 using mental strategies. 2.OA.3 Determine
More information6th FGCU Invitationdl Math Competition
6th FGCU nvitationdl Math Competition Geometry ndividual Test Option (E) for all questions is "None of the above." 1. MC = 12, NC = 6, ABCD is a square. 'h What is the shaded area? Ans ~ (A) 8 (C) 25 2.
More informationMrs. Ambre s Math Notebook
Mrs. Ambre s Math Notebook Almost everything you need to know for 7 th grade math Plus a little about 6 th grade math And a little about 8 th grade math 1 Table of Contents by Outcome Outcome Topic Page
More informationComprehensive. Do not open this test booklet until you have been advised to do so by the test proctor.
Indiana State Mathematics Contest 205 Comprehensive Do not open this test booklet until you have been advised to do so by the test proctor. This test was prepared by faculty at Ball State University Next
More information5.1, 5.2, 5.3 Properites of Exponents last revised 12/28/2010
48 5.1, 5.2, 5.3 Properites of Exponents last revised 12/28/2010 Properites of Exponents 1. *Simplify each of the following: a. b. 2. c. d. 3. e. 4. f. g. 5. h. i. j. Negative exponents are NOT considered
More informationGAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide
GAP CLOSING Powers and Roots Intermediate / Senior Facilitator Guide Powers and Roots Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5 Solutions...5
More informationCH 20 NUMBER WORD PROBLEMS
187 CH 20 NUMBER WORD PROBLEMS Terminology To double a number means to multiply it by 2. When n is doubled, it becomes 2n. The double of 12 is 2(12) = 24. To square a number means to multiply it by itself.
More informationCK-12 Geometry Inductive Reasoning
CK-12 Geometry Inductive Reasoning Learning Objectives Recognize visual and number patterns. Extend and generalize patterns. Write a counterexample. Review Queue a. Look at the patterns of numbers below.
More informationOdd one out. Odd one out
SAMPLE Odd one out Odd one out NUMBER AND PLACE VALUE Spot the difference Spot the difference The same different NUMBER AND PLACE VALUE Is it sixteen? Is it sixteen? Is it sixteen? Is it sixteen? Is it
More informationSolutions to the European Kangaroo Pink Paper
Solutions to the European Kangaroo Pink Paper 1. The calculation can be approximated as follows: 17 0.3 20.16 999 17 3 2 1000 2. A y plotting the points, it is easy to check that E is a square. Since any
More informationNAME DATE. b) Then do the same for Jett s pennies (6 sets of 9 pennies with 4 leftover pennies).
NAME DATE 1.2.2/1.2.3 NOTES 1-51. Cody and Jett each have a handful of pennies. Cody has arranged his pennies into 3 sets of 16, and has 9 leftover pennies. Jett has 6 sets of 9 pennies, and 4 leftover
More informationAnthony Chan. September, Georgia Adult Education Conference
Anthony Chan September, 2018 1 2018 Georgia Adult Education Conference Attendees will be able to: Make difficult math concepts simple and help their students discover math principles on their own. This
More informationThe CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Fryer Contest. Thursday, April 18, 2013
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 2013 Fryer Contest Thursday, April 18, 2013 (in North America and South America) Friday, April 19, 2013 (outside of North America
More informationConstructions of Coverings of the Integers: Exploring an Erdős Problem
Constructions of Coverings of the Integers: Exploring an Erdős Problem Kelly Bickel, Michael Firrisa, Juan Ortiz, and Kristen Pueschel August 20, 2008 Abstract In this paper, we study necessary conditions
More informationLecture 1, CS 2050, Intro Discrete Math for Computer Science
Lecture 1, 08--11 CS 050, Intro Discrete Math for Computer Science S n = 1++ 3+... +n =? Note: Recall that for the above sum we can also use the notation S n = n i. We will use a direct argument, in this
More informationWhole Numbers. Whole Numbers. Curriculum Ready.
Curriculum Ready www.mathletics.com It is important to be able to identify the different types of whole numbers and recognize their properties so that we can apply the correct strategies needed when completing
More informationUNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST
UNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST First Round For all Colorado Students Grades 7-12 October 31, 2009 You have 90 minutes no calculators allowed The average of n numbers is their sum divided
More informationMAT 1160 Mathematics, A Human Endeavor
MAT 1160 Mathematics, A Human Endeavor Syllabus: office hours, grading Schedule (note exam dates) Academic Integrity Guidelines Homework & Quizzes Course Web Site : www.eiu.edu/ mathcs/mat1160/ 2005 09,
More informationRIPPLES. 14 Patterns/Functions Grades 7-8 ETA.hand2mind. Getting Ready. The Activity On Their Own (Part 1) What You ll Need.
RIPPLES Pattern recognition Growth patterns Arithmetic sequences Writing algebraic expressions Getting Ready What You ll Need Pattern Blocks, set per pair Colored pencils or markers Activity master, page
More informationChapter Possibilities: goes to bank, gets money from parent, gets paid; buys lunch, goes shopping, pays a bill,
1.1.1: Chapter 1 1-3. Shapes (a), (c), (d), and (e) are rectangles. 1-4. a: 40 b: 6 c: 7 d: 59 1-5. a: y = x + 3 b: y =!x 2 c: y = x 2 + 3 d: y = 3x! 1 1-6. a: 22a + 28 b:!23x! 17 c: x 2 + 5x d: x 2 +
More informationGrades 7 & 8, Math Circles 27/28 February, 1 March, Mathematical Magic
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Card Tricks Grades 7 & 8, Math Circles 27/28 February, 1 March, 2018 Mathematical Magic Have you ever
More information16. DOK 1, I will succeed." In this conditional statement, the underlined portion is
Geometry Semester 1 REVIEW 1. DOK 1 The point that divides a line segment into two congruent segments. 2. DOK 1 lines have the same slope. 3. DOK 1 If you have two parallel lines and a transversal, then
More informationMAGIC SQUARES KATIE HAYMAKER
MAGIC SQUARES KATIE HAYMAKER Supplies: Paper and pen(cil) 1. Initial setup Today s topic is magic squares. We ll start with two examples. The unique magic square of order one is 1. An example of a magic
More informationLooking for Pythagoras An Investigation of the Pythagorean Theorem
Looking for Pythagoras An Investigation of the Pythagorean Theorem I2t2 2006 Stephen Walczyk Grade 8 7-Day Unit Plan Tools Used: Overhead Projector Overhead markers TI-83 Graphing Calculator (& class set)
More informationThere are 5 people upstairs on the bus, there are 4 people downstairs. How many altogether? Write a number sentence to show this.
National Curriculum Fluency Reasoning Problem Solving Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs. There are 5 people upstairs on the
More informationMATH 13150: Freshman Seminar Unit 15
MATH 1310: Freshman Seminar Unit 1 1. Powers in mod m arithmetic In this chapter, we ll learn an analogous result to Fermat s theorem. Fermat s theorem told us that if p is prime and p does not divide
More informationE G 2 3. MATH 1012 Section 8.1 Basic Geometric Terms Bland
MATH 1012 Section 8.1 Basic Geometric Terms Bland Point A point is a location in space. It has no length or width. A point is represented by a dot and is named by writing a capital letter next to the dot.
More informationPythagorean Theorem Unit
Pythagorean Theorem Unit TEKS covered: ~ Square roots and modeling square roots, 8.1(C); 7.1(C) ~ Real number system, 8.1(A), 8.1(C); 7.1(A) ~ Pythagorean Theorem and Pythagorean Theorem Applications,
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework Analytic Geometry Unit 1
Lunch Lines Mathematical Goals Prove vertical angles are congruent. Understand when a transversal is drawn through parallel lines, special angles relationships occur. Prove when a transversal crosses parallel
More informationIn this section, you will learn the basic trigonometric identities and how to use them to prove other identities.
4.6 Trigonometric Identities Solutions to equations that arise from real-world problems sometimes include trigonometric terms. One example is a trajectory problem. If a volleyball player serves a ball
More informationTHE COMMON CORE STATE STANDARDS FOR MATHEMATICS:
THE COMMON CORE STATE STANDARDS FOR MATHEMATICS: ASSESSMENT Depth of Knowledge (DOK) CCSS PD Grades K 5 Day 3 1 Complexity Difficulty 2 Rating Depth of Knowledge (DOK) Depth of Knowledge measures the degree
More informationThe Pythagorean Theorem and Right Triangles
The Pythagorean Theorem and Right Triangles Student Probe Triangle ABC is a right triangle, with right angle C. If the length of and the length of, find the length of. Answer: the length of, since and
More informationRoberto Clemente Middle School
Roberto Clemente Middle School Summer Math Packet for Students Entering Algebra I Name: 1. On the grid provided, draw a right triangle with whole number side lengths and a hypotenuse of 10 units. The
More informationReleased October Year. Small Steps Guidance and Examples. Block 4: Multiplication & Division
Released October 2017 Year 5 Small Steps Guidance and Examples Block 4: Multiplication & Division Multiply and divide numbers mentally drawing upon known facts. Multiples Factors Common factors Prime numbers
More informationGrade 6 Math Circles. Math Jeopardy
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 6 Math Circles November 28/29, 2017 Math Jeopardy Centre for Education in Mathematics and Computing This lessons covers all of the material
More information(A) Circle (B) Polygon (C) Line segment (D) None of them (A) (B) (C) (D) (A) Understanding Quadrilaterals <1M>
Understanding Quadrilaterals 1.A simple closed curve made up of only line segments is called a (A) Circle (B) Polygon (C) Line segment (D) None of them 2.In the following figure, which of the polygon
More informationVISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University
VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University Visual Algebra for College Students Copyright 010 All rights reserved Laurie J. Burton Western Oregon University Many of the
More information( for 2 lessons) Key vocabulary: triangle, square, root, hypotenuse, leg, angle, side, length, equation
LESSON: Pythagoras Theorem ( for 2 lessons) Level: Pre-intermediate, intermediate Learning objectives: to understand the relationship between the sides of right angled-triangle to solve problems using
More informationUnit 1 Foundations of Geometry: Vocabulary, Reasoning and Tools
Number of Days: 34 9/5/17-10/20/17 Unit Goals Stage 1 Unit Description: Using building blocks from Algebra 1, students will use a variety of tools and techniques to construct, understand, and prove geometric
More information1. Answer: 250. To reach 90% in the least number of problems involves Jim getting everything
. Answer: 50. To reach 90% in the least number of problems involves Jim getting everything 0 + x 9 correct. Let x be the number of questions he needs to do. Then = and cross 50 + x 0 multiplying and solving
More informationHow can I name the angle? What is the relationship? How do I know?
In Chapter 1, you compared shapes by looking at similarities between their parts. For example, two shapes might have sides of the same length or equal angles. In this chapter you will examine relationships
More informationGeometry. a) Rhombus b) Square c) Trapezium d) Rectangle
Geometry A polygon is a many sided closed shape. Four sided polygons are called quadrilaterals. Sum of angles in a quadrilateral equals 360. Parallelogram is a quadrilateral where opposite sides are parallel.
More informationCS1802 Week 6: Sets Operations, Product Sum Rule Pigeon Hole Principle (Ch )
CS1802 Discrete Structures Recitation Fall 2017 October 9-12, 2017 CS1802 Week 6: Sets Operations, Product Sum Rule Pigeon Hole Principle (Ch 8.5-9.3) Sets i. Set Notation: Draw an arrow from the box on
More informationThe Pythagorean Theorem
! The Pythagorean Theorem Recall that a right triangle is a triangle with a right, or 90, angle. The longest side of a right triangle is the side opposite the right angle. We call this side the hypotenuse
More information1. Answer: 250. To reach 90% in the least number of problems involves Jim getting everything
8 th grade solutions:. Answer: 50. To reach 90% in the least number of problems involves Jim getting everything 0 + x 9 correct. Let x be the number of questions he needs to do. Then = and cross 50 + x
More information(A) Circle (B) Polygon (C) Line segment (D) None of them
Understanding Quadrilaterals 1.The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60 degree. Find the angles of the parallelogram.
More informationChapter 1 Math Set: a collection of objects. For example, the set of whole numbers is W = {0, 1, 2, 3, }
Chapter 1 Math 3201 1 Chapter 1: Set Theory: Organizing information into sets and subsets Graphically illustrating the relationships between sets and subsets using Venn diagrams Solving problems by using
More informationGAP CLOSING. Powers and Roots. Intermediate / Senior Student Book GAP CLOSING. Powers and Roots. Intermediate / Senior Student Book
GAP CLOSING Powers and Roots GAP CLOSING Powers and Roots Intermediate / Senior Student Book Intermediate / Senior Student Book Powers and Roots Diagnostic...3 Perfect Squares and Square Roots...6 Powers...
More information