NAME DATE. b) Then do the same for Jett s pennies (6 sets of 9 pennies with 4 leftover pennies).
|
|
- Stewart Cory Mosley
- 5 years ago
- Views:
Transcription
1 NAME DATE 1.2.2/1.2.3 NOTES 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 pennies. Each student thinks he has the most pennies. a) Work on your own to draw a diagram and write an expression with numbers and symbols. Both your diagram and expression should represent the way Cody could have arranged his pennies (3 sets of 16 with 9 leftover pennies). Is there a different way you could have represented this same number of pennies with a diagram and numerical expression? b) Then do the same for Jett s pennies (6 sets of 9 pennies with 4 leftover pennies). c) Compare your results with your team. d) Copy the different numerical expressions for each student from your team to your paper. How many different ways did your team find to represent the number of pennies with diagrams and numerical expressions? e) With your team, decide which arrangements best represent the groups of pennies held by Cody and Jett. a. Which student has more pennies? How did you figure this out? b. Jett decided to rearrange all of his pennies into groups of 10, even though one group will not be complete. How many groups can he make? How can he represent his new grouping with a number expression?
2 1-54. Allen and Dwayne would like help comparing two piles of pennies. The pennies are arranged and represented in the diagrams at right. a) Which pile has more pennies? How do you know? b) With your team, write expressions that represent each pile. Then write a comparison of these expressions showing if one is greater than the other or if they are the same Doreen and Delilah were comparing pennies from two teams. They wrote the comparison statement 6(16) + 3 > 4(9) + 4(9) + 2. What arrangements could this represent? Can you find more than one possibility? Work with your team to draw diagrams of the arrangements of pennies that Doreen and Delilah could have been comparing The figure below is reprinted from problem Using different colors within the pattern may help your team find various patterns. a) Working with a partner, write as many numerical expressions as you can to describe the number and organization of dots in this figure. How many different ways can you see the pattern? b) Now compare your numerical expressions with those from the rest of your team. Are some easier to match to the diagram than others? As a team, choose two numerical expressions that represent the dots in the figure in very different ways. Be sure that everyone has these two expressions written on their own papers. c) Find the value of both expressions. How do they compare?
3 In Lesson 1.2.1, you worked with your team to find different ways of showing different numbers of pennies. One arrangement that can be used to represent any whole number is a rectangular array. An example is shown at right. The horizontal lines of pennies are called rows, while the vertical lines of pennies are called columns. In this lesson, you will use rectangular arrays to investigate some properties of numbers. As you work on the problems in this lesson, use the following questions to help focus your team s discussion. Can all numbers be represented the same way? What can we learn about a number from its representations? HOW MANY PENNIES? Part One Jenny, Ann, and Gigi have different numbers of pennies. Each girl has between 10 and 40 pennies. Work with your team to figure out all the possible numbers of pennies that each girl could have. Use the clues given below. Be ready to explain your thinking to the class. (Be sure to draw the arrays on your paper to use later.) a. Jenny can arrange all of her pennies into a rectangular array that looks like a square. Looking like a square means it has the same number of rows as columns. b. Whenever Gigi arranges her pennies into a rectangular array with more than one row or column, she has a remainder (some leftover pennies). c. Ann can arrange all of her pennies into five different rectangular arrays.
4 1-63. What can you learn about a number from its rectangular arrays? Consider this question as you complete parts (a) and (b) below. a. A number that can be arranged into more than one rectangular array, such as Ann s in part (b) of problem 1-62, is called a composite number. List all composite numbers less than 15. b. Consider the number 17, which could be Gigi s number. Seventeen pennies can be arranged into only one rectangular array: 1 penny by 17 pennies. Any number, like 17, that can form only one rectangular array is called a prime number. Work with your team to find all prime numbers less than Jenny, Ann, and Gigi were thinking about odd and even numbers. (When even numbers are divided by two, there is no remainder. When odd numbers are divided by two, there is a remainder of one.) Jenny said, Odd numbers cannot be formed into a rectangle with two rows. Does that mean they are prime? Consider Jenny s question with your team. Are all odd numbers prime? If so, explain how you know. If not, find a counterexample. A counterexample is an example that can be used to show a statement is false (in this case, finding a number that is odd but not prime).
5 NAME DATE 1.2.2/1.2.3 HOMEWORK Rules Review: (Remember to check examples in the Rules Section of your binder for help!) Write in words and expanded form, what each numerical expression represents and then solve. 1.) 4 x (7 + 3) 2.) 3 (9 + 6) Words: Expanded: Solution: Words: Expanded: Solution: Which is greater: three sets of (5 2) or two sets of (2 + 3)? Draw diagrams to support your conclusion The diagrams at right represent piles of pennies. Which pile has more pennies? Explain your reasoning. a. Write two different numerical expressions to represent the number of pennies in each pile. b. Write a number comparison statement (using >, <, or = ) to show if the number of pennies in one pile is greater than the other or if they are the same.
6 1-61. Aria and 19 of her friends plan to go to a baseball game. They all want to sit together. Aria wants to order the seats in the shape of a rectangle, but she cannot decide on the best arrangement. She starts by considering one row of 20 seats. Draw a diagram showing Aria s idea for a seat arrangement. Then draw all of the other possible rectangular arrangements for 20 seats. Label each arrangement with its number of rows and the number of seats in each row. Are all arrangements practical? Explain Harry had a pile of 48 pennies. He organized them into a rectangular array with exactly four rows with 12 pennies in each row. Draw diagrams to represent at least two other rectangular arrays he could use. Do you think there are more? Explain your thinking For each number of pennies below, arrange them first into a complete rectangular array and then into a different rectangular array that has a remainder of one (so there is one extra penny). Write an expression for each arrangement. a. 10 pennies b. 15 pennies c. 25 pennies How many pennies are represented by each expression below? a. 3 + (4 5) b. (4 3) + 7 c. (2 3) (4 2)
7 Comparisons Mathematical symbols are used to compare quantities. The most commonly used symbols are the two inequality signs (< and >) and the equal sign (=). You can see how these symbols are used below. greater than: > 7 > 5 less than: < 3 < 5 equal to: = = 3 greater than or equal to: 4 4 less than or equal to: 8 9 Natural, Whole, and Prime Numbers The numbers {1, 2, 3, 4, 5, 6, } are called natural numbers or counting numbers. A natural number is even if it is divisible by two with no remainder. Otherwise the natural number is odd. The whole numbers include the natural numbers and zero. If one natural number divides another without remainder, the first one is called a factor of the second. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. If a number has exactly two factors (1 and itself), it is called a prime number. If a number has more than two factors, it is called a composite number. The number 1 has only one factor, so it is neither prime nor composite. The prime numbers less than 40 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37.
8 Math Expressions Pg. 5 Vocabulary: More/Sum Add Times/Product Multiply than switch Less/Difference Subtract Split/Quotient Divide Write the expressions of the following sentences: Example: (a) The sum of fourteen and twelve (b) Twenty less than forty-two 20 - switch (c) Twice the sum of seven and twelve. 2 x ( ) Practice: 1) The difference between fifteen and thirteen 2) Three times the sum of three and eleven 3) The quotient of twenty-four and three 4) Five more than the product of four and eight Write the statement to match the expression. Example: (a) 3 x 12 The product of three and twelve (b) 2 ( 5 3) Two times the difference of five and three (c) 15/3 1 One less than the quotient of fifteen and three 5) 4/2 6) 2 (3 + 4) 7) 18 6 (USE THAN)
Learning 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 informationStudy Guide: 5.3 Prime/Composite and Even/Odd
Standard: 5.1- The student will a) identify and describe the characteristics of prime and composite numbers; and b) identify and describe the characteristics of even and odd numbers. What you need to know
More informationSection 1: Whole Numbers
Grade 6 Play! Mathematics Answer Book 67 Section : Whole Numbers Question Value and Place Value of 7-digit Numbers TERM 2. Study: a) million 000 000 A million has 6 zeros. b) million 00 00 therefore million
More informationMultiplying Three Factors and Missing Factors
LESSON 18 Multiplying Three Factors and Missing Factors Power Up facts count aloud Power Up C Count up and down by 5s between 1 and 51. Count up and down by 200s between 0 and 2000. mental math a. Number
More informationSituations Involving Multiplication and Division with Products to 50
Mathematical Ideas Composing, decomposing, addition, and subtraction of numbers are foundations of multiplication and division. The following are examples of situations that involve multiplication and/or
More informationAlgebraic Expressions and Equations: Applications I: Translating Words to Mathematical Symbols *
OpenSta-CNX module: m35046 1 Algebraic Epressions and Equations: Applications I: Translating Words to Mathematical Symbols * Wade Ellis Denny Burzynski This work is produced by OpenSta-CNX and licensed
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 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 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 informationMeaningful Ways to Develop Math Facts
NCTM 206 San Francisco, California Meaningful Ways to Develop Math Facts -5 Sandra Niemiera Elizabeth Cape mathtrailblazer@uic.edu 2 4 5 6 7 Game Analysis Tool of Game Math Involved in the Game This game
More informationAnswer Key Lesson 5: Break-Apart Products
Student Guide Questions 1 5 (SG pp. 86 87) 1. A. The number of rows in the full rectangle. B. The number of columns in the full rectangle. C. 6 is the number of rows in the shaded rectangle, 5 is the number
More informationSituations Involving Multiplication and Division with Products to 100
Mathematical Ideas Composing, decomposing, addition, and subtraction of numbers are foundations of multiplication and division. The following are examples of situations that involve multiplication and/or
More information0:00:07.150,0:00: :00:08.880,0:00: this is common core state standards support video in mathematics
0:00:07.150,0:00:08.880 0:00:08.880,0:00:12.679 this is common core state standards support video in mathematics 0:00:12.679,0:00:15.990 the standard is three O A point nine 0:00:15.990,0:00:20.289 this
More informationHinojosa Kinder Math Vocabulary Words. Topic 1. number. zero. one
Topic 1 Word Picture number 2 zero 0 one 1 two 2 three 3 four 4 five 5 count 1 2 3 whole part none 0 picture objects order 0 1 2 3 4 represent triangle describe blue 3 sides 3 corners Topic 2 Word Picture
More informationPlace Value. Get in Place. WRITE how many tens and ones you see. Then WRITE the number they make. 5 3 = 53
Place Value Get in Place WRITE how many tens and ones you see. Then WRITE the number they make. 1. 2. 5 3 53 3. 4. 5. 6. 7. 8. 2 Place Value Get in Place 10 1 1 WRITE how many tens and ones you see. Then
More informationMANIPULATIVE MATHEMATICS FOR STUDENTS
MANIPULATIVE MATHEMATICS FOR STUDENTS Manipulative Mathematics Using Manipulatives to Promote Understanding of Elementary Algebra Concepts Lynn Marecek MaryAnne Anthony-Smith This file is copyright 07,
More informationShapes. Practice. Family Note. Unit. show 3-sided, 4-sided, 5-sided, and 6-sided shapes. Ask an adult for permission first. Add.
Home Link 8-1 Shapes In this lesson children examined different shapes, such as triangles, quadrilaterals, pentagons, and hexagons. They also discussed these shapes attributes or characteristics such as
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 informationPlace Value The value of a digit changes depending on its place in a number.
Place Value The value of a digit changes depending on its place in a number., hundred ten thousands hundreds tens ones thousands thousands In the two examples below, the digit 7 has different values. Math
More informationMATH MILESTONE # A1 NUMBERS & PLACE VALUES
Page 1 of 22 MATH MILESTONE # A1 NUMBERS & PLACE VALUES Researched and written by Vinay Agarwala (Revised 4/9/15) Milestone A1: Instructions The purpose of this document is to learn the Numbering System.
More informationFactors, Multiples, and Patterns
Factors, Multiples, and Patterns Check your understanding of important skills. Name Skip-Count Skip-count to find the unknown numbers. 1. Skip count by 3s. 2. Skip count by 5s. _, _, _, _ 3 5 _, _, _,
More informationSection 2.1 Factors and Multiples
Section 2.1 Factors and Multiples When you want to prepare a salad, you select certain ingredients (lettuce, tomatoes, broccoli, celery, olives, etc.) to give the salad a specific taste. You can think
More informationNS3 Part 1: BLM List. Workbook 3 - Number Sense, Part 1 1 BLACKLINE MASTERS
NS3 Part 1: BLM List Adding or Trading Game 2 Addition Rummy Blank Cards 3 Addition Rummy Preparation 4 Addition Table (Ordered) 5 Arrays in the Times Tables 6 Counting by 5s 7 Crossword Without Clues
More informationIs muddled about the correspondence between multiplication and division facts, recording, for example: 3 5 = 15, so 5 15 = 3
Is muddled about the correspondence between multiplication and division facts, recording, for example: 3 5 = 15, so 5 15 = 3 Opportunity for: recognising relationships Resources Board with space for four
More informationAn ordered collection of counters in rows or columns, showing multiplication facts.
Addend A number which is added to another number. Addition When a set of numbers are added together. E.g. 5 + 3 or 6 + 2 + 4 The answer is called the sum or the total and is shown by the equals sign (=)
More informationTable of Contents HUNDRED BOARD BOOK. Introduction...iv Connections to Common Core Standards...v
HUNDRED BOARD BOOK Table of Contents Introduction...iv Connections to Common Core Standards...v 1. Marching Forward 1 to 100... 2 2. Marching Backward 100 to 1... 4 3. Find the Three Lakes... 6 4. Don
More informationWorking with Teens! CA Kindergarten Number Sense 1.2: Count, recognize, represent, name, and order a number of objects (up to 30).
Standard: CA Kindergarten Number Sense 1.2: Count, recognize, represent, name, and order a number of objects (up to 30). CaCCSS Kindergarten Number and Operations in Base Ten 1: Compose and decompose numbers
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 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 informationNUMBER, NUMBER SYSTEMS, AND NUMBER RELATIONSHIPS. Kindergarten:
Kindergarten: NUMBER, NUMBER SYSTEMS, AND NUMBER RELATIONSHIPS Count by 1 s and 10 s to 100. Count on from a given number (other than 1) within the known sequence to 100. Count up to 20 objects with 1-1
More informationHuman Rights begins with the end. His Body. His Penis. His Foreskin. Say No to Circumcision. His Whole Body will Thank you. 100%
1. All pages are Legal Size with printer margins set at.33 CM for all sides 2. Use a "Brand Name" Dry Erase Marker for writing on laminate pages. 3. The Duck Brand Clear Contact Paper from Walmart is the
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 informationEstimation and Number Theory
2 CHAPTER Estimation and Number Theory Worksheet 1 Estimation Find each sum or difference. Then use rounding to check that your answer is reasonable. Round each number to the nearest 100. 475 1 382 5?
More informationModel Factors. Use tiles to find all the factors of the product. Record the. arrays and write the factors shown. Name
Lesson 5.1 Reteach Model Factors Use tiles to find all the factors of 25. Record the arrays and write the factors shown. Step 1 Record the array and list the factors. Think: Every whole number greater
More informationA Covering System with Minimum Modulus 42
Brigham Young University BYU ScholarsArchive All Theses and Dissertations 2014-12-01 A Covering System with Minimum Modulus 42 Tyler Owens Brigham Young University - Provo Follow this and additional works
More informationWhole Numbers WHOLE NUMBERS PASSPORT.
WHOLE NUMBERS PASSPORT www.mathletics.co.uk It is important to be able to identify the different types of whole numbers and recognise their properties so that we can apply the correct strategies needed
More informationAnswer Key Lesson 6: Workshop: Factors, Multiples, and Primes
3 Answer Key Lesson 6: Student Activity Book Number and Multiplication Concepts Questions 1 27 (SAB pp. 61 7) 1. 21 and 99 are both multiples of 3; Possible response: I can make a rectangle that is 3 by
More informationOne Way Find factors.
Name Factors and Multiples Essential Question How are factors and multiples related? Unlock the Problem Toy animals are sold in sets of 3, 5, 10, and 12. Mason wants to make a display with 3 animals in
More informationIn this chapter, I give you a review of basic math, and I do mean basic. I bet you know a lot
Chapter 1 We ve Got Your Numbers In This Chapter Understanding how place value turns digits into numbers Rounding numbers to the nearest ten, hundred, or thousand Calculating with the Big Four operations
More informationWhat You ll Learn. Why It s Important. Students in a grade 7 class were raising money for charity. Some students had a bowl-a-thon.
Students in a grade 7 class were raising money for charity. Some students had a bowl-a-thon. This table shows the money that one student raised for different bowling times. Time (h) Money Raised ($) 1
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 informationEstimation. Number Theory
Name: Date: Chapter Practice 1 534 1 287 Estimation and Number Theory Estimation Find each sum or difference. Then use rounding to check that your answers are reasonable. Round each number to the nearest
More informationShillerMath Book 1 Test Answers
LESSON 1-56 REVIEW TEST #1-1 Now we will have a test to see what you have learned. This will help me understand what I need to do to make our math work more fun. You may take as much time and use whatever
More informationUNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet
Name Period Date UNIT 2: RATIONAL NUMBER CONCEPTS WEEK 5: Student Packet 5.1 Fractions: Parts and Wholes Identify the whole and its parts. Find and compare areas of different shapes. Identify congruent
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 informationTriangles, Rectangles, Squares, and Circles
Triangles, Rectangles, Squares, and Circles Triangle sides Rectangle 4 sides Lesson 21 21 Square length a rectangle with 4 equal sides width Measures of a circle: Radius = 1 diameter Diameter = 2 radius
More informationGrab Bag Math ➊ ➋ ➌ ➍ ➎ ➏ ON THEIR OWN. Can you figure out all the ways to build one-layer rectangular boxes with Snap Cubes?
Grab Bag Math ON THEIR OWN Can you figure out all the ways to build one-layer rectangular boxes with Snap Cubes? ➊ ➋ ➌ ➍ ➎ ➏ Work with a partner. Pick a grab bag from the box. Using the Snap Cubes in the
More informationA C E. Answers Investigation 4. Applications. Dimensions of 39 Square Unit Rectangles and Partitions. Small Medium Large
Answers Applications 1. An even number minus an even number will be even. Students may use examples, tiles, the idea of groups of two, or the inverse relationship between addition and subtraction. Using
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 informationExtra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million b) 6 billion c)
Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. 3 a) 3.6 million b) 6 billion c) 1 million 4 2 1 d) 2 billion e) 4.25 million f) 1.4 billion 10 2. Use
More informationExtra Practice 1. Name Date. Lesson 1: Numbers in the Media. 1. Rewrite each number in standard form. a) 3.6 million
Master 4.27 Extra Practice 1 Lesson 1: Numbers in the Media 1. Rewrite each number in standard form. a) 3.6 million 3 b) 6 billion 4 c) 1 million 2 1 d) 2 billion 10 e) 4.25 million f) 1.4 billion 2. Use
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 informationMeet #5 March Intermediate Mathematics League of Eastern Massachusetts
Meet #5 March 2008 Intermediate Mathematics League of Eastern Massachusetts Meet #5 March 2008 Category 1 Mystery 1. In the diagram to the right, each nonoverlapping section of the large rectangle is
More informationGPLMS Revision Programme GRADE 6 Booklet
GPLMS Revision Programme GRADE 6 Booklet Learner s name: School name: Day 1. 1. a) Study: 6 units 6 tens 6 hundreds 6 thousands 6 ten-thousands 6 hundredthousands HTh T Th Th H T U 6 6 0 6 0 0 6 0 0 0
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 informationGPLMS Revision Programme GRADE 4 Booklet
GPLMS Revision Programme GRADE 4 Booklet Learner s name: School name: Day 1. 1. Read carefully: a) The place or position of a digit in a number gives the value of that digit. b) In the number 4237, 4,
More informationObjective: Use square tiles to compose a rectangle, and relate to the array model. (9 minutes) (60 minutes)
Lesson 11 2 6 Lesson 11 Objective: Use square tiles to compose a rectangle, and relate to the array model. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief
More informationFifth Grade Spiraling Review Week 1 of Second Six Weeks
Week 1 of Second Six Weeks Advanced Preparation: See attachment: Spiraling Review Cards Note: Record all work in your math journal. Day 1 The world s largest glacier, located in the Swiss Alps, has more
More informationG RADE 1 MATHEMATICS. Blackline Masters
G RADE 1 MATHEMATICS Blackline Masters BLM K 4.1 Assessment Checklist Student s Name Comments BLM 1.N.1&3.1 Number Cards BLM 1.N.1&3.1 Number Cards (continued) BLM 1.N.1&3.1 Number Cards (continued) BLM
More informationN1-1 Whole Numbers. Pre-requisites: None Estimated Time: 2 hours. Summary Learn Solve Revise Answers. Summary
N1-1 Whole Numbers whole numbers to trillions the terms: whole number, counting number, multiple, factor, even, odd, composite, prime, >, < Pre-requisites: None Estimated Time: 2 hours Summary Learn Solve
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 informationRosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples
Rosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples Section 1.7 Proof Methods and Strategy Page references correspond to locations of Extra Examples icons in the textbook. p.87,
More informationSummer Solutions Problem Solving Level 4. Level 4. Problem Solving. Help Pages
Level Problem Solving 6 General Terms acute angle an angle measuring less than 90 addend a number being added angle formed by two rays that share a common endpoint area the size of a surface; always expressed
More informationUNIT 1: INTEGERS WEEK 2: Student Packet
Name Period Date UNIT 1: INTEGERS WEEK 2: Student Packet 2.1 Integers: Introduction Represent integers on a number line. Explore integer addition and subtraction using a number line model. Write equations
More informationYGB #2: Aren t You a Square?
YGB #2: Aren t You a Square? Problem Statement How can one mathematically determine the total number of squares on a chessboard? Counting them is certainly subject to error, so is it possible to know if
More informationReading and Understanding Whole Numbers
Reading and Understanding Whole Numbers Student Book Series D Mathletics Instant Workbooks Copyright Contents Series D Reading and Understanding Whole Numbers Topic Looking at whole numbers reading and
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 informationMath Pacing Guide. 2 nd Grade
Unit 1: Extending Base 10 Understanding 5, 10 5 weeks Instructional Days August 8 September 9, 2016 Understand place value. MGSE2.NBT.1 Understand that the three digits of a three-digit number represent
More informationHundred Thousands. Practice to review I can read and write numbers through 999,999! Practice to remember HW 1.2A. Chapter 1 Place Value.
Hundred Thousands Practice to review I can read and write numbers through 999,999! I can write the number in the place value chart in more than one way. Standard Form: HW 1.2A Short Word Form: Word Form:
More informationMastering Math Facts Multiplication and Division Grades 3 5 by Jillayne Prince Wallaker
Mastering Math Facts Multiplication and Division Grades 3 5 by Jillayne Prince Wallaker Carson Dellosa Publishing Company, Inc. Greensboro, North Carolina Credits Editor: Susan Morris Layout Design: Van
More informationNUMERATION AND NUMBER PROPERTIES
Section 1 NUMERATION AND NUMBER PROPERTIES Objective 1 Order three or more whole numbers up to ten thousands. Discussion To be able to compare three or more whole numbers in the thousands or ten thousands
More informationApplications. 30 Prime Time
Applications For Exercises 1 6, give the dimensions of each rectangle that can be made from the given number of tiles. Then use the dimensions of the rectangles to list all the factor pairs for each number.
More informationMath 081 Exam 1 Preparation V01 Ch 1-2 Winter 2010 Winter 2010 Dressler NO CALCULATOR/NO NOTES/NO BOOK/55 MINUTES. Name
Math 081 Exam 1 Preparation V01 Ch 1-2 Winter 2010 Winter 2010 Dressler NO CALCULATOR/NO NOTES/NO BOOK/55 MINUTES Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers
More informationVariables and expressions Block 1 Student Activity Sheet
Block 1 Student Activity Sheet 1. Record your understandings of key vocabulary for this topic. Vocabulary term My understanding of what the term means Examples that show the meaning of the term. a. Variable
More information30 6 = 5; because = 0 Subtract five times No remainder = 5 R3; because = 3 Subtract five times Remainder
Section 1: Basic Division MATH LEVEL 1 LESSON PLAN 5 DIVISION 2017 Copyright Vinay Agarwala, Revised: 10/24/17 1. DIVISION is the number of times a number can be taken out of another as if through repeated
More informationA Plan for Problem Solving (pages 6 9)
A A Plan for Problem Solving (pages 6 9) You can use a four-step plan to solve a problem. Explore Plan Solve Examine Read the problem carefully. Ask yourself questions like, What facts do I know? See how
More informationMATH LEVEL 2 LESSON PLAN 3 FACTORING Copyright Vinay Agarwala, Checked: 1/19/18
MATH LEVEL 2 LESSON PLAN 3 FACTORING 2018 Copyright Vinay Agarwala, Checked: 1/19/18 Section 1: Exact Division & Factors 1. In exact division there is no remainder. Both Divisor and quotient are factors
More informationGrade 6 Module 2 Lessons 1-19
Eureka Math Homework Helper 2015 201 Grade Module 2 Lessons 1-19 Eureka Math, A Story of R a t i o s Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced,
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 informationIntroduction to Counting and Probability
Randolph High School Math League 2013-2014 Page 1 If chance will have me king, why, chance may crown me. Shakespeare, Macbeth, Act I, Scene 3 1 Introduction Introduction to Counting and Probability Counting
More informationThese tests contain questions ranging from Level 2 to Level 3. Children should have five seconds to answer questions 1 3 in each test,
These tests contain questions ranging from Level to Level. Children should have five seconds to answer questions in each test, ten seconds to answer questions and fifteen seconds to answer questions -.
More informationShillerMath Book 4 Test Answers
ShillerMath Book 4 Test Answers LESSON 4-44 REVIEW TEST #4-1 ANSWERS HOW KIDS LEARN MATH Grading instructions: compare the answers here to the student s answers. For each correct answer, add the appropriate
More informationActivity: Even + Even + Odd =?
Activity: Even + Even + Odd =? USE THEORETICAL PROBABILITIES AND EXPERIMENTAL RESULTS TO MAKE PREDICTION & DECISIONS FIND THE PROBABILITIES OF DEPENDENT AND INDEPENDENT EVENTS VALIDATE CONCLUSIONS USING
More informationUnderstanding relationships between numbers can save you time when making
Divisibility Rules! Investigating Divisibility Rules Learning Goals In this lesson, you will: Formulate divisibility rules based on patterns seen in factors. Use factors to help you develop divisibility
More informationProblems from Russian Math Olympiads
Problems from Russian Math Olympiads LA Math Circle (Advanced) October, 205. Peter exchanges stickers with his friends. For every sticker he gives someone, he gets 5 stickers back. Suppose he starts the
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 informationNumber. Place value. Vocabulary. Raphael has eight digit cards. He uses the cards to make two four-digit numbers. He uses each card only once.
Cambridge Unive 978-1-107-61859-6 Cambridge Primary Mathematics Stage 6 Emma Low Excerpt More information Number Place value Vocabulary Raphael has eight digit cards. 1 2 3 4 5 6 7 8 million: equal to
More informationGrade Tennessee Middle/Junior High School Mathematics Competition 1 of 8
Grade 7 2011 Tennessee Middle/Junior High School Mathematics Competition 1 of 8 1. The day you were born, your grandmother put $500 in a savings account that earns 10% compounded annually. (On your first
More informationHigh-Impact Games and Meaningful Mathematical Dialog Grades 3-5
NCTM 2017 San Antonio, Texas High-Impact Games and Meaningful Mathematical Dialog Grades 3-5 Elizabeth Cape Jennifer Leimberer Sandra Niemiera mathtrailblazers@uic.edu Teaching Integrated Math and Science
More informationTranscriber(s): Baldev, Prashant Verifier(s): DeLeon, Christina Date Transcribed: Spring 2008 Page: 1 of 5
Page: 1 of 5 Speaker Transcription So, how about for eight? So you re saying, so how would you do for eight? For eight? [pointing to the paper] So your saying, your taking.. So why did you pick thirty-four?
More informationInstructional Tools Math Pack: Money n2y Unique Learning System
5 5 1 1 5 1 1 1 1 1 1 1 1 1 1 1 5 5 1 1 15 5 5 5 15 20 5 5 5 5 5 20 25 5 5 5 5 5 25 25 5 25 30 30 25 5 35 35 25 5 40 40 25 5 45 45 25 5 50 50 25 25 60 60 25 25 70 75 25 25 25 25 25 75 80 25 25 25 25 25
More informationBuilding Concepts: Visualizing Quadratic Expressions
Building Concepts: Visualizing Quadratic Epressions Lesson Overview In this TI-Nspire lesson, students manipulate geometric figures to eplore equivalent epressions that can be epressed in the form b c
More informationChapter 5 Review/Test
Name Chapter 5 Review/Test Personal Math Trainer Online Assessment and Intervention 1. List all the factors of the number. 14: 2. Select the numbers that have a factor of 5. Mark all that apply. A 15 D
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 informationLong vowels sound the same as the alphabet name. Aa Ee Ii Oo Uu. Learning English with Laughter Ltd. All Rights Reserved.
Aa Long vowels Long vowels sound the same as the alphabet name. Aa Ee Ii Oo Uu Aa Short vowels alien apple Ee Ee eel elephant Learning English with Laughter Ltd. All Rights Reserved. http://www.efl-esl.com
More informationconstant EXAMPLE #4:
Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value
More informationFirst Name: Last Name: Select the one best answer for each question. DO NOT use a calculator in completing this packet.
5 Entering 5 th Grade Summer Math Packet First Name: Last Name: 5 th Grade Teacher: I have checked the work completed: Parent Signature Select the one best answer for each question. DO NOT use a calculator
More informationAnswer Key. Easy Peasy All-In-One-Homeschool
Answer Key Easy Peasy All-In-One-Homeschool 4 5 6 Telling Time Adding 2-Digits Fractions Subtracting 2-Digits Adding and Subtracting Money A. Draw the hands on each clock face to show the time. 12:20 6:05
More information2nd Grade Math Curriculum Map
Standards Quarter 1 2.OA.2. Fluently add and subtract within 20 using mental strategies.* By end of Grade 2, know from memory all sums of two one-digit numbers. 2.OA.3. Determine whether a group of objects
More information1 Summer Math Booklet
Summer Math Booklet 1 2 How Many Combinations? Sarah has 68. What different combinations of dimes and pennies could she have to equal 68? Try to find all the possible combinations. Write an equation for
More information