Answer keys to the assessment tasks 61 Answer keys to the challenge questions 63 Achievement Profile 64
|
|
- Meredith Patrick
- 5 years ago
- Views:
Transcription
1 Contents page Introduction 4 1. Odd and even numbers 5 Assessment task Counting techniques: Consecutive numbers 9 3. Counting techniques: How many digits? 11 Assessment task Number chains The Pigeonhole Principle The Pigeonhole Principle 2 19 Assessment task Divisibility Revision questions Challenge questions Problem solving without a calculator Problem solving without a calculator Prime and composite numbers Problem solving without a calculator Problem solving: Working backwards Logical questions: Balancing scales Super operations 41 Assessment task 4 43 Answer keys Odd and even numbers Counting techniques: Consecutive numbers Counting techniques: How many digits? Number chains The Pigeonhole Principle The Pigeonhole Principle Divisibility Revision questions Problem solving without a calculator Problem solving without a calculator Prime and composite numbers Problem solving without a calculator Problem solving: Working backwards Logical questions: Balancing scales Super operations 60 Answer keys to the assessment tasks 61 Answer keys to the challenge questions 63 Achievement Profile 64 3
2 Introduction The content of this book builds on the mathematics topics covered in Teaching and Assessing Working Mathematically Book 1. Teaching and Assessing Working Mathematically Book 2 consists of 16 interrelated topics presented in 31 teaching sessions. Complete solutions and answers are provided on all questions. The book presents challenging, but achievable curriculum that links workingmathematically processes and familiar Level 3 mathematics content. Most of the questions are suitable for mathematically able and talented mid-primary or upperprimary students. The questions aim at prompting students to use a range of problem-solving strategies, such as exploring possibilities, using diagrams, working backwards, constructing counter examples, and systematic counting, in familiar contexts. Most of the sessions include representative examples with the solution method shown. It is recommended that all representative examples are discussed and explained in detail at the beginning of the session. The book includes four assessment tasks and seven challenge questions. Complete solutions and appropriate marking keys are provided. The Achievement Profile gives an overview of the individual student achievement of the skills assessed cross the 16 mathematics topics. The following general structure for the teaching sessions is recommended: direct instruction: up to minutes. This part of the lesson should be focused on: revision of appropriate skills and understandings related to the given topic, followed by an introduction of the new mathematics concepts or problem-solving techniques by using additional examples; individual work: up to minutes. Students work on solving questions similar to the one already discussed. The teacher helps individual students on a one-to-one basis; whole-class discussion: up to minutes. At the centre of the discussion are the types of solution strategies used and verbal justifications of the way the answer was obtained. The teacher should prompt students to compare and comment on different solution strategies and pose questions similar to the ones already solved. 4
3 1. Odd and even numbers Mathematics language: counting numbers, even numbers, odd numbers, two-digit numbers, three-digit numbers, consecutive odd numbers, consecutive even numbers. Example: Write the next three numbers in the patterns below: Counting numbers: 1, 2, 3, 4, 5,...,...,...,... Three-digit numbers: 100, 101, 102, 103,...,...,...,... Four-digit numbers: 1 000, 1 001, 1 002,...,...,...,... Even numbers: 0, 2, 4, 6,...,...,...,... Odd numbers: 1, 3, 5, 7, 9,...,...,...,... Consecutive odd numbers: 11, 13, 15, 17,...,...,...,... Consecutive even numbers: 22, 24, 26, 28,...,...,...,... Exercise 1a 1. Write the first 10 even numbers. Find the difference between the largest and the smallest. 2. Write a number twice as large as the tenth odd number. 3. In your own words explain what is an even number. What is the smallest even number? Write the largest one-digit odd number as a sum of different odd numbers. 5. Write next to each other all one-digit numbers greater than 3. Delete all even digits. The sum of the remaining odd digits is: Write the smallest two-digit number with the sum of its digits equal to 2: Write the smallest three-digit number with the sum of its digits equal to 2: Write the greatest three-digit number that has different digits:... 5
4 9. By using all of the digits 4, 3, 2 and 1 write: a) the greatest possible four-digit even number:... b) the smallest possible four-digit odd number:... c) two numbers with the greatest possible sum:.. d) two two-digit numbers with the largest possible difference:.. e) two two-digit numbers with the smallest possible difference: By using all of the digits 0, 1, 2 and 3 write: a) the smallest possible four-digit number:... b) the greatest possible four-digit odd number:... c) the smallest possible four-digit even number:... d) two numbers with the smallest possible sum: e) two two-digit numbers with the smallest possible difference: By using all the digits of 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 write: a) the smallest possible ten-digit even number that ends on 8: b) the greatest possible ten-digit odd number that ends on 9: c) three odd numbers with the greatest possible sum: d) two five-digit numbers with the smallest possible difference:.. e) two five-digit odd numbers with the greatest possible sum:.. 6
5 Exercise 1b Example: The sum of two consecutive even numbers is 22. What is the smaller of the two numbers? Solution: If we halve 22, then 22 = The two even numbers closest to 11 are 10 and 12, and = 22. The smaller of these two numbers is The sum of two consecutive even numbers is 222. The smaller number is: A) 108 B) 110 C) 111 D) 112 E) The sum of two consecutive odd numbers is 220. The smaller number is: A) 109 B) 110 C) 111 D) 113 E) The sum of three consecutive odd numbers is 33. The smallest of the three numbers is: A) 7 B) 9 C) 10 D) 11 E) The sum of three consecutive even numbers is 48. The smallest of the three numbers is: A) 12 B) 14 C) 16 D) 18 E) Maria said: The result of is an even number. Maria is correct. Explain why. 17. How many different even numbers can be obtained from the number 51 * 2, when the * is replaced with a digit? A) 2 B) 4 C) 5 D) 6 E) How many different even numbers can be obtained from the number 52 *, when the * is replaced with a suitable digit? A) 2 B) 4 C) 5 D) 9 E) Find three consecutive numbers such that the sum of the first and the third is Helen deleted three of the digits in the number She obtained an even number between 20 and 30. The sum of the deleted digits is: A) 6 B) 10 C) 11 D) 14 E) None of these 21. How many two-digit numbers have different digits? A) 180 B) 99 C) 90 D) 81 E) None of these 22. Find the sum of in as many ways as you can. 7
6 Assessment task 1 Odd and even numbers, consecutive numbers 1. The sum of two odd consecutive numbers is 36. The sum of the digits of the smaller number is: A) 7 B) 8 C) 9 D) 17 E) 18 Show your working:.. 2. How many different even numbers can be obtained from the number 7 31 *, when the * is replaced with a suitable digit? A) 0 B) 4 C) 5 D) 9 E) Find three consecutive numbers such that the sum of the first and the third is 56. Show your working: 4. By using all of the digits 0, 3, 5 and 9 write: a) the smallest possible four-digit number:... b) the greatest possible four-digit odd number:... c) two two-digit numbers with the smallest possible difference:... 8
Developing Conceptual Understanding of Number. Set D: Number Theory
Developing Conceptual Understanding of Number Set D: Number Theory Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Vocabulary digit hundred s place whole numbers even Notes Number Theory 1 odd multiple
More informationOA4-16 Rounding on a Grid Pages 86 87
OA4-16 Rounding on a Grid Pages 86 87 STANDARDS 4.NBT.A.3 Goals Students will round whole numbers to the nearest ten, hundred, thousand, ten thousand, or hundred thousand. PRIOR KNOWLEDGE REQUIRED Knowing
More informationClass 8: Factors and Multiples (Lecture Notes)
Class 8: Factors and Multiples (Lecture Notes) If a number a divides another number b exactly, then we say that a is a factor of b and b is a multiple of a. Factor: A factor of a number is an exact divisor
More informationMath Shape and Space: Perimeter
F A C U L T Y O F E D U C A T I O N Department of Curriculum and Pedagogy Math Shape and Space: Perimeter Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement
More informationPRIME FACTORISATION Lesson 2: Prime Dice
PRIME FACTORISATION Lesson 2: Prime Dice Australian Curriculum: Mathematics Year 7 ACMNA149: Investigate index notation and represent whole numbers as products of powers of prime numbers. Applying knowledge
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 informationMultiples and Divisibility
Multiples and Divisibility A multiple of a number is a product of that number and an integer. Divisibility: A number b is said to be divisible by another number a if b is a multiple of a. 45 is divisible
More informationStation Activities. for Mathematics Grade 6
Station Activities for Mathematics Grade 6 WALCH EDUCATION The classroom teacher may reproduce materials in this book for classroom use only. The reproduction of any part for an entire school or school
More informationTarget Board Planet Maths Teacher Resources 1st Class
Target Board 1 The teacher points to each number/digit and the children identify it. How many numbers are on the first line, second line? How many numbers are in column 1, 2, 3, 4? Add all the numbers
More informationA C E. Answers Investigation 1. Applications. b. No; 6 18 = b. n = 12 c. n = 12 d. n = 20 e. n = 3
Answers Applications 1. a. Divide 24 by 12 to see if you get a whole number. Since 12 2 = 24 or 24 12 = 2, 12 is a factor b. Divide 291 by 7 to see if the answer is a whole number. Since 291 7 = 41.571429,
More information100 IDEAS FOR USING A HUNDRED SQUARE
100 IDEAS FOR USING A HUNDRED SQUARE These ideas are in no particular order and can be adapted to any age range or ability. The objectives are for children to learn to recognise numbers, understand numbers
More informationUNITED KINGDOM MATHEMATICS TRUST SHUTTLE ROUND. There are 4 rounds to this Shuttle Round. Each round contains a set of four questions.
UNITED KINGDOM MATHEMATICS TRUST SHUTTLE ROUND There are 4 rounds to this Shuttle Round. Each round contains a set of four questions. Each round lasts 8 minutes. Three marks are awarded for every answer
More informationThe Willows Primary School Mental Mathematics Policy
The Willows Primary School Mental Mathematics Policy The Willows Primary Mental Maths Policy Teaching methodology and organisation Teaching time All pupils will receive between 10 and 15 minutes of mental
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 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 informationMultiple : The product of a given whole number and another whole number. For example, some multiples of 3 are 3, 6, 9, and 12.
1.1 Factor (divisor): One of two or more whole numbers that are multiplied to get a product. For example, 1, 2, 3, 4, 6, and 12 are factors of 12 1 x 12 = 12 2 x 6 = 12 3 x 4 = 12 Factors are also called
More informationUNC Charlotte 2008 Algebra March 3, 2008
March 3, 2008 1. The sum of all divisors of 2008 is (A) 8 (B) 1771 (C) 1772 (D) 3765 (E) 3780 2. From the list of all natural numbers 2, 3,... 999, delete nine sublists as follows. First, delete all even
More informationSample pages. Multiples, factors and divisibility. Recall 2. Student Book
52 Recall 2 Prepare for this chapter by attempting the following questions. If you have difficulty with a question, go to Pearson Places and download the Recall from Pearson Reader. Copy and complete these
More informationPRIME FACTORISATION Lesson 1: Factor Strings
PRIME FACTORISATION Lesson 1: Factor Strings Australian Curriculum: Mathematics Year 7 ACMNA149: Investigate index notation and represent whole numbers as products of powers of prime numbers. Applying
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 informationFacilitator Guide. Unit 2
Facilitator Guide Unit 2 UNIT 02 Facilitator Guide ACTIVITIES NOTE: At many points in the activities for Mathematics Illuminated, workshop participants will be asked to explain, either verbally or in
More informationEstimating with Square Roots
ACTIVITY 3.2 Estimating with Square Roots The square root of most numbers is not an integer. You can estimate the square root of a number that is not a perfect square. Begin by determining the two perfect
More informationNS2-45 Skip Counting Pages 1-8
NS2-45 Skip Counting Pages 1-8 Goals Students will skip count by 2s, 5s, or 10s from 0 to 100, and back from 100 to 0. Students will skip count by 5s starting at multiples of 5, and by 2s or 10s starting
More informationTeacher s Notes. Problem of the Month: Courtney s Collection
Teacher s Notes Problem of the Month: Courtney s Collection Overview: In the Problem of the Month, Courtney s Collection, students use number theory, number operations, organized lists and counting methods
More informationComparing Numbers on a Place Value Chart
Comparing Numbers on a Place Value Chart Students will: Objective Identify the place value of specific digits in a number Represent numbers on a place vale chart Utilize place value charts to compare numbers
More information1.4 Practice A. List the factor pairs of the number
Name Date 1.4 Practice A Use divisibility rules to determine whether the number is divisible by, 3, 5, 6, 9, and 10. Use calculator to check your answers. 1. 100. 1515 3. 1071 4. A baseball camp is held
More informationCalifornia 1 st Grade Standards / Excel Math Correlation by Lesson Number
California 1 st Grade Standards / Excel Math Correlation by Lesson Lesson () L1 Using the numerals 0 to 9 Sense: L2 Selecting the correct numeral for a Sense: 2 given set of pictures Grouping and counting
More informationFibonacci Numbers ANSWERS Lesson 1 of 10, work individually or in pairs
Lesson 1 of 10, work individually or in pairs In 1202, the mathematician Leonardo Pisano Fibonacci (pronounced fi-buh-nah-chee) published a book with the famous Fibonacci sequence in it. (A sequence is
More informationNumeracy Warm Up. Introduction
Numeracy Warm Up Introduction Numeracy Warm Up is a set of numeracy exercises that can be used for starters, main lessons and plenaries. It is aimed at Numeracy lessons covering National Curriculum Levels
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 informationDIFFERENT SEQUENCES. Learning Outcomes and Assessment Standards T 2 T 3
Lesson 21 DIFFERENT SEQUENCES Learning Outcomes and Assessment Standards Learning Outcome 1: Number and number relationships Assessment Standard Investigate number patterns including but not limited to
More informationAnswer key to select Section 1.2 textbook exercises (If you believe I made a mistake, then please let me know ASAP) x x 50.
Math 60 Textbook : Elementary Algebra : Beginning Algebra, 12 th edition, by Lial Remember : Many homework exercises are used to teach you a concept we did not cover in class. It is important for you to
More informationChoose the correct answer. For 1 3, choose the number for the shaded box in the puzzle.
Choose the correct answer. Page 1 For 1 3, choose the number for the shaded box in the puzzle. For 4 5, use the number line. Choose the output for the empty box. 59 109 98 119 1 2 0 4 2 2 107 146 136 157
More informationMath 7 Notes Unit 02 Part A: Rational Numbers. Real Numbers
As we begin this unit it s a good idea to have an overview. When we look at the subsets of the real numbers it helps us organize the groups of numbers students have been exposed to and those that are soon
More informationQuantitative Aptitude Preparation Numbers. Prepared by: MS. RUPAL PATEL Assistant Professor CMPICA, CHARUSAT
Quantitative Aptitude Preparation Numbers Prepared by: MS. RUPAL PATEL Assistant Professor CMPICA, CHARUSAT Numbers Numbers In Hindu Arabic system, we have total 10 digits. Namely, 0, 1, 2, 3, 4, 5, 6,
More informationParent and child guide to mathematics. Booklet 2. Mathematics is being able to count to twenty without taking your shoes off!
Parent and child guide to mathematics. Booklet 2 Mathematics is being able to count to twenty without taking your shoes off! How do I work it out? There are three different ways that can be used to support.
More informationrepeated multiplication of a number, for example, 3 5. square roots and cube roots of numbers
NUMBER 456789012 Numbers form many interesting patterns. You already know about odd and even numbers. Pascal s triangle is a number pattern that looks like a triangle and contains number patterns. Fibonacci
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 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 informationIntroduction. It gives you some handy activities that you can do with your child to consolidate key ideas.
(Upper School) Introduction This booklet aims to show you how we teach the 4 main operations (addition, subtraction, multiplication and division) at St. Helen s College. It gives you some handy activities
More informationNumber: Number and Place Value with Reasoning
count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Number: Number and Place Value with Reasoning +COUNTING Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count
More informationUsing Structure I: Multiplication Puzzles
PS6-5 Using Structure I: Multiplication Puzzles Teach this lesson after: 6.2 Measurement Goals: Students will mentally compute the ones digit of a product of multi-digit numbers. Students will solve multi-digit
More informationLesson Plan for Teachers
Grade level recommendation: 8 th grade Lesson Plan for Teachers Learning goals: Problem solving Reasoning Basic algebra Exponents Recursive equations Explicit equations NCTM standards correlation: http://www.nctm.org/standards/
More informationGrade 6 Math Circles. Divisibility
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 6 Math Circles November 12/13, 2013 Divisibility A factor is a whole number that divides exactly into another number without a remainder.
More informationNumber: Number and Place Value with Reasoning
count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Number: Number and Place Value with Reasoning +COUNTING Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count
More informationThe Parkland Federation. February 2016
The Parkland Federation February 206 EYFS/KS Calculations: Recording Addition (page of ). Aggregation/combining 2. Augmentation/counting on 3. Counting Contexts: + + + + Pupils physically combining groups
More informationFactors and Multiples
Factors and Multiples 2. The first thing that you must do when figuring the least common multiple is to a. Multiply the two numbers together b. Divide the largest number by the smallest one c. Divide the
More informationLearning Log Title: CHAPTER 1: INTRODUCTION AND REPRESENTATION. Date: Lesson: Chapter 1: Introduction and Representation
CHAPTER 1: INTRODUCTION AND REPRESENTATION Date: Lesson: Learning Log Title: Toolkit 2013 CPM Educational Program. All rights reserved. 1 Date: Lesson: Learning Log Title: Toolkit 2013 CPM Educational
More informationMarch 5, What is the area (in square units) of the region in the first quadrant defined by 18 x + y 20?
March 5, 007 1. We randomly select 4 prime numbers without replacement from the first 10 prime numbers. What is the probability that the sum of the four selected numbers is odd? (A) 0.1 (B) 0.30 (C) 0.36
More informationA Seat at the Table OVERVIEW THE BIG IDEA
A Seat at the Table OVERVIEW OBJECTIVE Children will investigate the perimeter of polygons and of composite shapes in order to solve problems. They will also determine the perimeter of those shapes. WHAT
More information6 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers
Pellissippi State Middle School Mathematics Competition 6 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers Directions: For each multiple-choice problem
More informationRational Number Project
Rational Number Project Initial Fraction Ideas Lesson 4: Overview Students use paper folding to model and name unit and non-unit fractions. Students compare the paper-folding model to fraction circles.
More informationMath 60. : Elementary Algebra : Beginning Algebra, 12 th edition, by Lial
Math 60 Textbook : Elementary Algebra : Beginning Algebra, 12 th edition, by Lial Remember : Many homework exercises are used to teach you a concept we did not cover in class. It is important for you to
More informationFull Transcript for An Introduction to the Montessori Math Curriculum
Full Transcript for An Introduction to the Montessori Math Curriculum A young girl's small hands grasping beautiful objects sensing the world around her. Shapes dimensions relationships amounts all represented
More informationTeacher Sourcebook. Sample Unit. Authors Rosemary Reuille Irons M Sc Brian Tickle BA James Burnett M Ed
Teacher Sourcebook Sample Unit Authors Rosemary Reuille Irons M Sc Brian Tickle BA James Burnett M Ed Series Consultants Judith Anderson Ph D Jan Glazier MA Bruce Llewellyn B Sc Counting On Basic Facts
More informationLESSON 2: THE INCLUSION-EXCLUSION PRINCIPLE
LESSON 2: THE INCLUSION-EXCLUSION PRINCIPLE The inclusion-exclusion principle (also known as the sieve principle) is an extended version of the rule of the sum. It states that, for two (finite) sets, A
More informationIMOK Maclaurin Paper 2014
IMOK Maclaurin Paper 2014 1. What is the largest three-digit prime number whose digits, and are different prime numbers? We know that, and must be three of,, and. Let denote the largest of the three digits,
More informationAddition and Subtraction
Addition and Subtraction If any of your students don t know their addition and subtraction facts, teach them to add and subtract using their fi ngers by the methods taught below. You should also reinforce
More informationLesson 9: An Application of Linear Equations
Classwork Exercises 1 2 1. Write the equation for the fifteenth step. 2. How many people would see the photo after fifteen steps? Use a calculator if needed. Date: 4/5/14 S.28 Exercises 3 11 3. Marvin
More informationRational Number Project
Rational Number Project Initial Fraction Ideas Lesson : Overview Students use fraction circles to order fractions by comparing them to one-half. Materials Fraction Circles for students and teacher Student
More informationGeorgia Department of Education Common Core Georgia Performance Standards Framework Fifth Grade Mathematics Unit 2
PRACTICE TASK: Adapted from Investigations in Number, Data, and Space: How Many Tens? How Many Ones? Addition, Subtraction, and the Number System. STANDARDS FOR MATHEMATICAL CONTENT MCC5.NBT.7 Add, subtract,
More informationPROBLEMS & INVESTIGATIONS. Introducing Add to 15 & 15-Tac-Toe
Unit One Connecting Mathematical Topics Session 10 PROBLEMS & INVESTIGATIONS Introducing Add to 15 & 15-Tac-Toe Overview To begin, students find many different ways to add combinations of numbers from
More informationChapter 4 Number Theory
Chapter 4 Number Theory Throughout the study of numbers, students Á should identify classes of numbers and examine their properties. For example, integers that are divisible by 2 are called even numbers
More informationUNC Charlotte 2002 Comprehensive. March 4, 2002
UNC Charlotte March 4, 2002 1 It takes 852 digits to number the pages of a book consecutively How many pages are there in the book? A) 184 B) 235 C) 320 D) 368 E) 425 2 Solve the equation 8 1 6 + x 1 3
More informationMathematics Enhancement Programme TEACHING SUPPORT: Year 3
Mathematics Enhancement Programme TEACHING UPPORT: Year 3 1. Question and olution Write the operations without brackets if possible so that the result is the same. Do the calculations as a check. The first
More informationHow to Use the Gadget and Worksheets. Overview Week 3
How to Use the Gadget and Worksheets W3 Number Lines Overview Week 3 Overview: To explore number to 10 using a number line. Number Line Features: Number lines show the sequence of numbers and where they
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 informationAdding Fractions with Different Denominators. Subtracting Fractions with Different Denominators
Adding Fractions with Different Denominators How to Add Fractions with different denominators: Find the Least Common Denominator (LCD) of the fractions Rename the fractions to have the LCD Add the numerators
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 informationLesson 0.1 The Same yet Smaller
Lesson 0.1 The Same yet Smaller 1. Write an expression and find the total shaded area in each square. In each case, assume that the area of the largest square is 1. a. b. c. d. 2. Write an expression and
More informationUpdated October 2017
Updated October 2017 Roman numerals to 100 Round to the nearest 10 Round to the nearest 100 Count in 1,000s 1,000s, 100s, 10s and 1s Partitioning Number line to 10,000 1,000 more or less Compare numbers
More informationHealth in Action Project
Pillar: Active Living Division: III Grade Level: 7 Core Curriculum Connections: Math Health in Action Project I. Rationale: Students engage in an active game of "Divisibility Rock n Rule" to practice understanding
More informationFoundations of Multiplication and Division
Grade 2 Module 6 Foundations of Multiplication and Division OVERVIEW Grade 2 Module 6 lays the conceptual foundation for multiplication and division in Grade 3 and for the idea that numbers other than
More informationGRADE 4. M : Solve division problems without remainders. M : Recall basic addition, subtraction, and multiplication facts.
GRADE 4 Students will: Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as
More informationWestern Australian Junior Mathematics Olympiad 2007
Western Australian Junior Mathematics Olympiad 2007 Individual Questions 100 minutes General instructions: Each solution in this part is a positive integer less than 100. No working is needed for Questions
More informationSample pages. 3:06 HCF and LCM by prime factors
number AND INDICES 7 2 = 49 6 8 = 48 Contents 10 2 = 100 9 11 = 99 12 2 = 144 11 1 = 14 8 2 = 64 7 9 = 6 11 2 = 121 10 12 = 120 :01 Index notation Challenge :01 Now that s a google :02 Expanded notation
More informationFraction Game on Number Lines
SLIDESHOW Full Details and Transcript Fraction Game on Number Lines Tollgate Elementary School, Colorado February 2011 Topic Practice Highlights DEVELOPING EFFECTIVE FRACTIONS INSTRUCTION FOR K-8 FRACTIONS
More informationExploring Concepts with Cubes. A resource book
Exploring Concepts with Cubes A resource book ACTIVITY 1 Gauss s method Gauss s method is a fast and efficient way of determining the sum of an arithmetic series. Let s illustrate the method using the
More information7 Mathematics Curriculum
New York State Common Core 7 Mathematics Curriculum GRADE Table of Contents 1 Percent and Proportional Relationships GRADE 7 MODULE 4... 3 Topic A: Finding the Whole (7.RP.A.1, 7.RP.A.2c, 7.RP.A.3)...
More informationGame Variations: Ultimate Tic Tac Toe
Game Variations: Ultimate Tic Tac Toe Middle School In this lesson, students will experience the engineering process when creating modifications to a familiar game. Next Generation Science Standards MS-ETS1-1
More information3.1 Factors and Multiples of Whole Numbers
Math 1201 Date: 3.1 Factors and Multiples of Whole Numbers Prime Number: a whole number greater than 1, whose only two whole-number factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7,
More informationNumber Sense and Decimal Unit Notes
Number Sense and Decimal Unit Notes Table of Contents: Topic Page Place Value 2 Rounding Numbers 2 Face Value, Place Value, Total Value 3 Standard and Expanded Form 3 Factors 4 Prime and Composite Numbers
More informationPARTICIPANT Guide. Unit 2
PARTICIPANT Guide Unit 2 UNIT 02 participant Guide ACTIVITIES NOTE: At many points in the activities for Mathematics Illuminated, workshop participants will be asked to explain, either verbally or in
More information7 th Grade Exam Scoring Format: 3 points per correct response -1 each wrong response 0 for blank answers
Pellissippi State Middle School Mathematics Competition 7 th Grade Exam Scoring Format: points per correct response - each wrong response 0 for blank answers Directions: For each multiple-choice problem
More informationThe factors of a number are the numbers that divide exactly into it, with no remainder.
Divisibility in the set of integers: The multiples of a number are obtained multiplying the number by each integer. Usually, the set of multiples of a number a is written ȧ. Multiples of 2: 2={..., 6,
More informationCOUNTING TECHNIQUES. Prepared by Engr. JP Timola Reference: Discrete Math by Kenneth H. Rosen
COUNTING TECHNIQUES Prepared by Engr. JP Timola Reference: Discrete Math by Kenneth H. Rosen COMBINATORICS the study of arrangements of objects, is an important part of discrete mathematics. Counting Introduction
More informationThe Pigeonhole Principle
The Pigeonhole Principle Some Questions Does there have to be two trees on Earth with the same number of leaves? How large of a set of distinct integers between 1 and 200 is needed to assure that two numbers
More informationMATH GAMES THAT SUPPORT SINGAPORE MATH GRADES
Box Cars and One-Eyed Jacks MATH GAMES THAT SUPPORT SINGAPORE MATH GRADES 3-5 JOHN FELLING SMART TRAINING SCOTTSDALE, AZ July 9, 2015 john@boxcarsandoneeyedjacks.com phone 1-866-342-3386 / 1-780-440-6284
More informationIntroduction to Fractions
DELTA MATH SCIENCE PARTNERSHIP INITIATIVE M 3 Summer Institutes (Math, Middle School, MS Common Core) Introduction to Fractions Hook Problem: How can you share 4 pizzas among 6 people? Final Answer: Goals:
More informationWhole Numbers. Lesson 1.1 Numbers to 10,000,000
1 CHAPTER Whole Numbers Lesson 1.1 Numbers to 10,000,000 Fill in the table headings. Write Tens, Hundreds, Ten Thousands, or Hundred Thousands. Then write the number in word form and in standard form.
More informationFocus on Mathematics
Focus on Mathematics Year 4 Pre-Learning Tasks Number Pre-learning tasks are used at the start of each new topic in Maths. The children are grouped after the pre-learning task is marked to ensure the work
More informationPut these numbers in order from smallest to largest.
1 Put these numbers in order from smallest to largest. a. 4 9 7 6 b. 11 7 9 1 4 c. 8 0 7 4 1 6 Read the Warm-Up activity page to your students. SAY: Put these numbers in order from smallest to largest.
More informationCount in multiples of 6, 7, and Find 1000 more or less than a given number.
Roman numerals to 100 Round to the nearest 10 Round to the nearest 100 Count in 1,000s 1,000s, 100s, 10s and 1s Partitioning Number line to 10,000 1,000 more or less Compare numbers Order numbers Round
More informationSummer Solutions Common Core Mathematics 4. Common Core. Mathematics. Help Pages
4 Common Core Mathematics 63 Vocabulary Acute angle an angle measuring less than 90 Area the amount of space within a polygon; area is always measured in square units (feet 2, meters 2, ) Congruent figures
More informationN Strand. The World of Numbers
N Strand The World of Numbers WORLD OF NUMBERS INTRODUCTION Numbers are among the most important things that mathematics (at all levels) is about. Mathematicians are interested in numbers just as astronomers
More informationLaunchpad Maths. Arithmetic II
Launchpad Maths. Arithmetic II LAW OF DISTRIBUTION The Law of Distribution exploits the symmetries 1 of addition and multiplication to tell of how those operations behave when working together. Consider
More informationQ.1 Is 225 a perfect square? If so, find the number whose square is 225.
Chapter 6 Q.1 Is 225 a perfect square? If so, find the number whose square is 225. Q2.Show that 63504 is a perfect square. Also, find the number whose square is 63504. Q3.Show that 17640 is not a perfect
More informationFantastic Fractions. Integrated Unit of Study. Martha A. Ban. Fantastic Fractions
Fantastic Fractions An Integrated Unit of Study by Martha A. Ban Atlantic Union Conference Teacher Bulletin www.teacherbulletin.org Page 1 of 46 Major Concepts Basic Fractions Fourths, Eights, and Tenths
More informationReleased November /5. Small Steps Guidance and Examples. Block 4: Length & Perimeter
Released November 2017 4/5 Small Steps Guidance and Examples Block 4: Length & Perimeter Year 4/5 Autumn Term Teaching Guidance Overview Small Steps Year 4 Year 5 Kilometres Perimeter on a grid Perimeter
More informationPair counting. Maths focus: Counting on in ones, tens or hundreds from any number. What you need: Instructions
Cambridge University Press 978-1-107-69401-9 Cambridge Primary Mathematics Stage 3 Cherri Moseley and Janet Rees Excerpt More information Place value games Largest and smallest Maths focus: To understand
More information