Go Math! Yearly Plan. 1 st Grade. By Yanina Jimenez. From Houghton Mifflin Harcourt. Aligned with the Common Core

Transcription

1 Go Math! 1 st Grade From Houghton Mifflin Harcourt Yearly Plan Aligned with the Common Core AND ready to use for Unit and Daily Lesson Plans By Yanina Jimenez 1

2 Dear colleagues, This Yearly Plan for the new Math curriculum Go Math! for first grade is especially designed to help you keep track of your pace at the busy time of teaching Math. You will find it extremely helpful, not only because it contains a fair pace for the whole year by weeks, but because it is ready to be used at the time of planning for your unit or lesson plans since it has the Common Core performance standards by each unit. Last, but certainly not least, it integrates Faith in Learning. Enjoy and if you have any questions, don t hesitate to contact me at yjimenez@illinoisadventist.org May God bless you and give you a wonderful school year! mycutegraphics.com/graphics/school/school-kids/math-center.html Yanina Jimenez 2

3 In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes. 1. Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, puttogether, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., making tens ) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction. 2. Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes. 3. Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry. NUMBERS AND OPERATIONS Essential Question: What do numbers represent and how do they help us order and compare things in God s world? Big idea: Numbers represent an amount that helps us order and compare things in God s world. OPERATIONS AND ALGEBRAIC THINKING Essential Question: How can objects be represented to help us understand the variety of God s creation? Big idea: A single collection of objects can always be represented in more than one way to help us understand the variety of God s creation. Integration Faith and Learning MEASUREMENT Essential Question: How does measurement help us fulfill God s plan? Big idea: Measurement allows us to be accurate and orderly as God planned. GEOMETRY Essential Question: How do shapes and their parts help us appreciate God s creation? Big idea: Shapes and their parts help us appreciate the beauty and order in everything God has designed. DATA ANALYSIS, STATISTICS, & PROBABILITY Essential Question: How can we quantify our findings in a way that pleases God? Big idea: God has at various times commanded men to count, measure, and record their findings. 3

4 TIME FRAME CHAPTERS CHAPTER CONTENT COMMON CORE Week 1-2 Week 3 6 Chapter 1 Addition Concepts Chapter 2 Subtraction Concepts 1.1 Algebra: Use Pictures to Add To 1.2 Hands On: Model Adding To 1.3 Hands On: Model Putting Together 1.4 Problem Solving: Model Addition 1.5 Algebra: Add Zero 1.6 Hands On: Algebra Add in Any Order 1.7Hands On: Algebra Put Together Numbers to Addition to 10 Chapter 1 Review/Test 2.1Use Pictures to Show Taking From 2.2 Hands On: Model Taking From 2.3Hands On: Model Taking Apart 2.4 Problem Solving: Model Subtraction 2.5 Use Pictures and Subtraction to Compare 2.6 Hands On: Subtract to Compare 2.7 Subtract All or Zero 2.8 Hands On: Algebra Take Apart Numbers 2.9 Subtraction from 10 or Less Chapter 2 Review/Test 1.Oat.1 Understand, represent, compare, and apply addition and subtraction properties to word problems within 20; fluently add and subtract within 10 (1.OA.1,2,3,4,5,6); add up to three whole numbers within 20 1.OA.2 add two-digit and one-digit numbers with regrouping within 100 using models or drawings (1.NBT.4) 1.Oat.1 Understand, represent, compare, and apply addition and subtraction properties to word problems within 20; fluently add and subtract within 10 (1.OA.1,2,3,4,5,6); add up to three whole numbers within 20 (1.OA.2); add two-digit and one-digit numbers with regrouping within 100 using models or drawings (1.NBT.4) 4

5 Week 7-10 Week 11 to 13 Week Chapter 3 Addition Strategies Chapter 4 Subtraction Strategies Chapter 5 Addition and Subtraction Relationships 3.1 Algebra: Add in Any Order 3.2 Count On 3.3 Hands On: Add Doubles 3.4 Hands On: Use Doubles to Add 3.5 Hands On: Doubles Plus 1 and Doubles Minus Practice the Strategies 3.7 Hands On: Add 10 and More 3.8 Hands On: Make a 10 to Add 3.9 Use Make a Ten to Add 3.10 Hands On: Algebra: Add 3 Numbers 3.11 Algebra: Add 3 Numbers 3.12 Problem Solving: Use Addition Strategies Chapter 3 Review/Test 4.1 Count Back 4.2Hands On: Think Addition to Subtract 4.3 Use Think Addition to Subtract 4.4 Hands On: Make a 10 to Subtract 4.5 Break Apart to Subtract 4.6 Problem Solving: Use Subtraction Strategies Chapter 4 Review/Test 5.1 Problem Solving: Add or Subtract 5.2 Hands On: Record Related Facts 5.3 Identify Related Facts 5.4Use Addition to Check Subtraction 5.5Hands On: Algebra Missing Numbers 1.Oat.1 Understand, represent, compare, and apply addition and subtraction properties to word problems within 20; fluently add and subtract within 10 (1.OA.1,2,3,4,5,6); add up to three whole numbers within 20 1.OA.2 add two-digit and one-digit numbers with regrouping within 100 using models or drawings (1.NBT.4) 1.Oat.1 Understand, represent, compare, and apply addition and subtraction properties to word problems within 20; fluently add and subtract within OA.1,2,3,4,5,6; add up to three whole numbers within 20 (1.OA.2); add two-digit and one-digit numbers with regrouping within 100 using models or drawings (1.NBT.4) 1.Oat.2 Work with addition and subtraction equations including unknowns (1.OA.7,8) 1.Oat.1 Understand, represent, compare, and apply addition and subtraction properties to word problems within 20; fluently add and subtract within 10 (1.OA.1,2,3,4,5,6); add up to 5

6 5.6 Algebra: Use Related Facts 5.7 Choose an Operation 5.8 Hands On: Algebra Ways to Make Numbers to Algebra: Equal and Not Equal 5.10 Basic Facts to 20 Chapter 5 Review/Test three whole numbers within 20 1.OA.2 add two-digit and one-digit numbers with regrouping within 100 using models or drawings (1.NBT.4) Week Week 22 to 25 Chapter 6 Count and Model Numbers Chapter 7 Compare Numbers Chapter 8 Two-Digit Addition and Subtraction Term Break 6.1 Count by Ones to Count by Tens to Understand Ten and Ones 6.4Hands On: Make Ten and Ones 6.5 Hands On: Tens 6.6 Hands On: Tens and Ones to Hands On: Tens and Ones to Problem Solving: Show Numbers in Different Way 6.9 Model, Read, and Write Numbers from 100 to Model, Read, and Write Numbers from 110 to 120 Chapter 6 Review/Test 7.1Hands On: Algebra Greater Than 7.2 Hands On: Algebra Less Than 7.3 Hands On: Algebra Use Symbols to Compare 7.4 Problem Solving: Compare Numbers 7.5 Hands On: 10 Less, 10 More Chapter 7 Review/Test 8.1 Add and Subtract within 20 1.nO.1 Count, read, write, and understand numbers up to 120 (1.NBT.1) 1.nO.2 Count by twos, fives, and twenty-fives up to nO.3 Understand and compare two-digit numbers organized as groups of tens and ones (1.NBT.2,3) 1.Oat.1 Understand, represent, compare, and apply addition and subtraction properties to word problems within 20; fluently add and subtract within 10 (1.OA.1,2,3,4,5,6); add up to three whole numbers within OA.2 add two-digit and one-digit numbers with regrouping within 100 using models or drawings 1.NBT.4 6

7 Week 26 to 29 Chapter 9 Measurement 8.2 Hands On: Add Tens 8.3 Hands On: Subtract Tens 8.4 Use a Hundred Chart to Add 8.5 Hands On: Use Models to Add 8.6Hands On: Make Ten to Add 8.7 Hands On: Use Place Value to Add 8.8 Problem Solving: Addition Word Problems 8.9 Practice Addition and Subtraction Chapter 8 Review/Test 9.1 Hands On: Order Length 9.2 Indirect Measurement 9.3 Hands On: Use Nonstandard Units to Measure Length 9.4 Hands On: Make a Nonstandard Measuring Tool 9.5 Problem Solving: Measure and Compare 9.6 Time to the Hour 9.7 Time to the Half Hour 9.8 Hands On: Tell Time to the Hour and Half Hour 9.9 Practice Time to the Hour and Half Hour Chapter 9 Review/Test 10.1 Read Picture Graphs 10.2Hands On: Make Picture Graphs 10.3 Read Bar Graphs 10.4Hands On: Make Bar Graphs 10.5 Read Tally Charts 1.nO.4 Understand and mentally find ten more or ten less than a given two-digit number (1.NBT.5) 1.nO.5 Add and subtract multiples of ten within 100 using models or drawings (1.NBT.4,6) 1.m.1 Measure, order, compare, and express lengths of objects by counting non-standard units (1.MD.1,2) 1.m.2 Tell and write time in hours and half-hours using analog and digital clocks (1.MD.3) chapter 9.6, 9.7, 9.8, m.3 Identify pennies, nickels, dimes, quarters, half-dollars, and dollar bills 1.dsP.1 Organize, represent, compare, and interpret data with up to three categories (1.MD.4) 1.GeO.1 Describe, build, and draw shapes with defining attributes (1.G.1) 7

8 Week 30 to 35 Week 36 to 39* Chapter 10 Represent Data Chapter 11 Three- Dimensional Geometry Chapter 12 Two- Dimensional Geometry 10.6Hands On: Make Tally Charts 10.7 Problem Solving: Represent Data Chapter 10 Review/Test 11.1 Hands On: Three-Dimensional Shapes 11.2Combine Three-Dimensional Shapes 11.3 Make New Three-Dimensional Shapes 11.4Problem Solving: Take Apart Three-dimensional Shapes 11.5 Hands On: Two-Dimensional Shapes on Three-dimensional Shapes Chapter 11 Review/Test 12.1Sort Two-Dimensional Shapes 12.2Hands On: Describe Two- Dimensional Shapes 12.3 Hands On: Combine Two- Dimensional Shapes 12.4 Combine More Shapes 12.5Problem Solving: Make New Two- Dimensional Shapes 12.6 Find Shapes in Shapes 12.7Take Apart Two-Dimensional Shapes 12.8 Equal or Unequal Parts 12.9 Halves Fourths Chapter 12 Review/Test Enjoy your break! 1.GeO.2 Compose two- and three- dimensional shapes to form composite or new shapes (1.G.2) 1.GeO.3 Partition circles and rectangles into two and four equal parts; describe the whole and its parts using the words halves, fourths, quarters, half of, quarter of and third of (1.G.3) 1.GeO.1 Describe, build, and draw shapes with defining attributes (1.G.1) 1.GeO.2 Compose two- and three- dimensional shapes to form composite or new shapes (1.G.2) 1.GeO.3 Partition circles and rectangles into two and four equal parts; describe the whole and its parts using the words halves, fourths, quarters, half of, quarter of and third of (1.G.3) 8

9 *I planned only up to 39 weeks so you have room for days that teaching Math was a challenge due to performances, holidays, emergency school closing days, etc. 9

10 Go Math! 2 nd Grade From Houghton Mifflin Harcourt Yearly Plan Aligned with the Common Core AND ready to use for Unit and Daily Lesson Plans By Yanina Jimenez 1

11 Dear colleagues, This Yearly Plan for the new Math curriculum Go Math! for second grade is especially designed to help you keep track of your pace at the busy time of teaching Math. You will find it extremely helpful, not only because it contains a fair pace for the whole year by weeks, but because it is ready to be used at the time of planning for your unit or lesson plans since it has the Common Core performance standards by each unit. Last, but certainly not least, it integrates Faith in Learning. Enjoy and if you have any questions, don t hesitate to contact me at yjimenez@illinoisadventist.org May God bless you and give you a wonderful school year! mycutegraphics.com/graphics/school/school-kids/math-center.html Yanina Jimenez 2

12 In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. 1. Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones). 2. Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds. 3. Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a given length. 4. Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. NUMBERS AND OPERATIONS Essential Question: What do numbers represent and how do they help us order and compare things in God s world? Big idea: Numbers represent an amount that helps us order and compare things in God s world. OPERATIONS AND ALGEBRAIC THINKING Essential Question: How can objects be represented to help us understand the variety of God s creation? Big idea: A single collection of objects can always be represented in more than one way to help us understand the variety of God s creation. Integration Faith and Learning MEASUREMENT Essential Question: How does measurement help us fulfill God s plan? Big idea: Measurement allows us to be accurate and orderly as God planned. GEOMETRY Essential Question: How do shapes and their parts help us appreciate God s creation? Big idea: Shapes and their parts help us appreciate the beauty and order in everything God has designed. DATA ANALYSIS, STATISTICS, & PROBABILITY Essential Question: How can we quantify our findings in a way that pleases God? Big idea: God has at various times commanded men to count, measure, and record their findings. 3

13 TIME FRAME CHAPTERS CHAPTER CONTENT COMMON CORE Week 1-2 Week 3-6 Week 7-10 Chapter 1 Number Concepts Chapter 2 Numbers to 1,000 Chapter 3 Basic Facts and Relationships 1.1 Hands On: Even and Odd Numbers 1.2 Represent Even Numbers 1.3 Understand Place Value 1.4 Expanded Form 1.5 Different Ways to Write Numbers 1.6 Different Names for Numbers 1.7 Problem Solving: Tens and Ones 1.8 Counting Patterns within Counting Patterns within 1,000 Chapter 1 Review/Test Performance Assessment 2.1 Group Tens as Hundreds 2.2 Explore 3-Digit Numbers 2.3Hands On: Model 3-Digit Numbers 2.4 Hundreds, Tens, and Ones 2.5 Place Value to 1, Number Names 2.7 Different Forms of Numbers 2.8 Different Ways to Show Numbers 2.9Count On and Count Back by 10 and Algebra: Number Patterns 2.11 Problem Solving: Compare Numbers 2.12 Algebra: Compare Numbers Chapter 2 Review/Test Performance Assessment 3.1 Use Doubles Facts 3.2 Practice Addition Facts 3.3Make a Ten to Add 3.4 Add 3 Addends 2.nO.1 Read, write, and understand numbers up to 1000 using standard, number name, and expanded forms (2.NBT.3) 2.nO.2 Count by ones, fives, tens, and hundreds up to 1000 (2.NBT.2) 2.Oat.3 Determine if a group of objects within 20 represents an odd or even number (2.OA.3) 2.Oat.4 Write an equation to represent the total as a sum of equal addends with up to 5 groups of 5 objects (2.OA.3,4) 2.nO.3 Understand and compare three-digit numbers organized as groups of hundreds, tens, and ones; use place value to understand addition and subtraction (2.NBT.1,4,9) 2.Oat.1 Understand, represent, compare, and apply addition and subtraction properties within 100 to solve one- and two- step word problems (2.OA.1) (2.NBT.5); add up to four 2-digit 4

14 Week 11 to 13 Week Chapter 4 2-Digit Addition Chapter 5 2-Digit Subtraction 3.5 Relate Addition and Subtraction 3.6 Practice Subtraction Facts 3.7 Using Ten to Subtract 3.8 Use Drawings to Represent Problems 3.9 Use Equations to Represent Problems 3.10 Problem Solving: Equal Groups 3.11 Repeated Addition Chapter 3 Review/Test Performance Assessment 4.1Break Apart Ones to Add 4.2 Use Compensation 4.3 Break Apart Addends as Tens and Ones 4.4 Model Regrouping for Addition 4.5Model and Record 2-Digit Addition Digit Addition 4.7Practice 2-Digit Addition 4.8Rewrite 2-Digit Addition 4.9 Problem Solving: Addition 4.10 Write Equations to Represent Addition 4.11 Find Sums for 3 Addends 4.12 Find Sums for 4 Addends Chapter 4 Review/Test Performance Assessment 5.1 Break Apart Ones to Subtract 5.2Break Apart Numbers to Subtract 5.3 Model Regrouping for Subtraction 5.4Model and Record 2-Digit Subtraction Digit Subtraction 5.6Practice 2-Digit Subtraction numbers (2.NBT.6) 2.Oat.2 Memorize and fluently add and subtract within 20 (2.OA.2) 2.Oat.4 Write an equation to represent the total as a sum of equal addends with up to 5 groups of 5 objects (2.OA.3,4) 2.Oat.1 Understand, represent, compare, and apply addition and subtraction properties within 100 to solve one- and two- step word problems (2.OA.1) (2.NBT.5); add up to four 2-digit numbers (2.NBT.6) 2.Oat.1 Understand, represent, compare, and apply addition and subtraction properties within 100 to solve one- and two- step word problems (2.OA.1) (2.NBT.5); add up to four 2-digit numbers (2.NBT.6) 5

15 5.7Rewrite 2-Digit Subtraction 5.8 Add to Find Differences 5.9 Problem Solving: Subtraction 5.10 Write Equations to Represent Subtraction 5.11 Solve Multistep Problems Chapter 5 Review/Test Performance Assessment Week Week 22 to 25 Chapter 6 3-Digit Addition and Subtraction Chapter 7 Money and Time Term Break 6.1Draw to Represent 3-Digit Addition 6.2Break Apart 3-Digit Addends Digit Addition: Regroup Ones Digit Addition: Regroup Tens 6.5 Addition: Regroup Ones and Tens 6.6Problem Solving: 3-Digit Subtraction 6.73-Digit Subtraction: Regroup Tens Digit Subtraction: Regroup Hundreds 6.9 Subtraction: Regroup Hundreds and Tens 6.10 Regrouping with Zeros Chapter 6 Review/Test Performance Assessment 7.1Dimes, Nickels, and Pennies 7.2 Quarters 7.3 Count Collections 7.4 Hands On: Show Amounts in Two Ways 7.5 One Dollar 7.6 Amounts Greater than $1 7.7 Problem Solving: Money 7.8 Time to the Hour and Half Hour 7.9 Time to 5 Minutes 2.nO.4 Mentally add and subtract multiples of ten and multiples of a hundred within 1000 (2.NBT.8) 2.nO.5 Add and subtract within 1000 with regrouping using models or drawings (2.NBT.7) 2.m.6 Tell and write time to the nearest five minutes from analog and digital clocks using a.m. and p.m. (2.MD.7) 2.m.7 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and (2.MD.8) 6

16 Week 26 to 29 Chapter 8 Length in Customary Units 7.10 Practice Telling Time 7.11 A.M. and P.M. Chapter 7 Review/Test Performance Assessment 8.1 Hands On: Measure with Inch Models 8.2Hands On: Make and Use a Ruler 8.3 Estimate Lengths in Inches 8.4 Hands On: Measure with an Inch Ruler 8.5 Problem Solving: Add and Subtract in Inches 8.6 Hands On: Measure in Inches and Feet 8.7 Estimate Lengths in Feet 8.8 Choose a Tool 8.9 Display Measurement Data Chapter 8 Review/Test Performance Assessment 2.m.1 Measure and estimate lengths in standard units (e.g., inches, feet, centimeters, meters) using appropriate tools (e.g., rulers, yardsticks, meter sticks) (2.MD.1,3) 2.m.2 Measure, compare, and describe the length of an object using two units of measurement (e.g, inches and yards, centimeters and meters) (2.MD.2) 2.m.4 Use addition and subtraction equations within 100 to solve word problems involving lengths of the same unit (2.MD.5) 2.m.5 Represent whole numbers as equally spaced lengths from 0 on a number line; represent sums and differences within 100 on a number line (2.MD.6) 2.dsP.1 Generate measurement data by measuring lengths of several objects to the nearest whole unit; show the measurements by making a line plot (2.MD.9) Week 30 to 35 Chapter 9 Length in Metric Units Chapter 10 Data 9.1 Hands On: Measure with a Centimeter Model 9.2 Estimate Lengths in Centimeters 9.3 Hands On: Measure with a Centimeter Ruler 9.4 Problem Solving: Add and Subtract Lengths 9.5 Hands On: Centimeters and Meters 9.6 Estimate Lengths in Meters 2.m.3 Measure to compare the length of two objects using a standard length unit (2.MD.4) 2.dsP.2 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve simple addition, subtraction, and comparison problems using information in a bar graph (2.MD.10) 7

17 Week 36 to 39* Chapter 11 Geometry and Fraction Concepts 9.7 Hands On: Measure and Compare Lengths Chapter 9 Review/Test Performance Assessment 10.1 Collect Data 10.2 Read Picture Graphs 10.3 Make Picture Graphs 10.4 Read Bar Graphs 10.5Make Bar Graphs 10.6 Problem Solving: Display Data Chapter 10 Review/Test Performance Assessment 11.1 Three-Dimensional Shapes 11.2 Attributes of Three-Dimensional Shapes 11.3 Two-Dimensional Shapes 11.4Angles in Two-Dimensional Shapes 11.5Sort Two-Dimensional Shapes 11.6 Hands On: Partition Rectangles 11.7 Equal Parts 11.8 Show Equal Parts of a Whole 11.9 Describe Equal Parts Problem Solving: Equal Shares Chapter 11 Review/Test Performance Assessment Enjoy your break! 2.GeO.1 Recognize and draw two- and threedimensional shapes having specified attributes (2.G.1) 2.GeO.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares (2.G.2) 2.GeO.3 Partition circles and rectangles into two, three, and four equal parts; describe the whole and its parts using the words halves, thirds, half of, third of, etc.; understand that equal parts need not have the same shape (2.G.3) 8

18 *I planned only up to 39 weeks so you have room for days that teaching Math was a challenge due to performances, holidays, emergency school closing days, etc. 9

19 Go Math! 3 rd Grade From Houghton Mifflin Harcourt Yearly Plan Aligned with the Common Core AND ready to use for Unit and Daily Lesson Plans By Yanina Jimenez 1

20 Dear colleagues, This Yearly Plan for the new Math curriculum Go Math! for third grade is especially designed to help you keep track of your pace at the busy time of teaching Math. You will find it extremely helpful, not only because it contains a fair pace for the whole year by weeks, but because it is ready to be used at the time of planning for your unit or lesson plans since it has the Common Core performance standards by each unit. Last, but certainly not least, it integrates Faith in Learning. Enjoy and if you have any questions, don t hesitate to contact me at yjimenez@illinoisadventist.org May God bless you and give you a wonderful school year! mycutegraphics.com/graphics/school/school-kids/math-center.html Yanina Jimenez 2

21 In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes. 1. Students develop an understanding of the meanings of multiplication and division of whole numbers through activities and problems involving equal-sized groups, arrays, and area models; multiplication is finding an unknown product, and division is finding an unknown factor in these situations. For equal-sized group situations, division can require finding the unknown number of groups or the unknown group size. Students use properties of operations to calculate products of whole numbers, using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors. By comparing a variety of solution strategies, students learn the relationship between multiplication and division. 2. Students develop an understanding of fractions, beginning with unit fractions. Students view fractions in general as being built out of unit fractions, and they use fractions along with visual fraction models to represent parts of a whole. Students understand that the size of a fractional part is relative to the size of the whole. For example, 1/2 of the paint in a small bucket could be less paint than 1/3 of the paint in a larger bucket, but 1/3 of a ribbon is longer than 1/5 of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 5 equal parts. Students are able to use fractions to represent numbers equal to, less than, and greater than one. They solve problems that involve comparing fractions by using visual fraction models and strategies based on noticing equal numerators or denominators. 3. Students recognize area as an attribute of two-dimensional regions. They measure the area of a shape by finding the total number of same-size units of area required to cover the shape without gaps or overlaps, a square with sides of unit length being the standard unit for measuring area. Students understand that rectangular arrays can be decomposed into identical rows or into identical columns. By decomposing rectangles into rectangular arrays of squares, students connect area to multiplication, and justify using multiplication to determine the area of a rectangle. 4. Students describe, analyze, and compare properties of two-dimensional shapes. They compare and classify shapes by their sides and angles, and connect these with definitions of shapes. Students also relate their fraction work to geometry by expressing the area of part of a shape as a unit fraction of the whole. NUMBERS AND OPERATIONS Essential Question: What do numbers represent and how do they help us order and compare things in God s world? Big idea: Numbers represent an OPERATIONS & ALGEBRAIC THINKING Essential Question: How can objects be represented to help us understand the variety of God s creation? Big idea: A single collection of objects can always be represented in more Integration Faith and Learning MEASUREMENT Essential Question: How does measurement help us fulfill God s plan? Big idea: Measurement allows us to be accurate GEOMETRY Essential Question: How do shapes and their parts help us appreciate God s creation? Big idea: Shapes and their parts help us appreciate the beauty DATA ANALYSIS, STATISTICS, & PROBABILITY Essential Question: How can we quantify our findings in a way that pleases God? Big idea: God has at various times commanded men to count, 3

22 amount that helps us order and compare things in God s world. than one way to help us understand the variety of God s creation. and orderly as God planned. and order in everything God has designed. measure, and record their findings. TIME FRAME CHAPTERS CHAPTER CONTENT COMMON CORE Week 1-2 Week 3-6 Chapter 1 Addition and Subtraction Within 1,000 Chapter 2 Represent and Interpret Data 1.1 Algebra: Number Patterns 1.2 Round to the Nearest Ten or Hundred 1.3 Estimate Sums 1.4 Mental Math Strategies for Addition 1.5 Algebra: Use Properties to Add 1.6 Use the Break Apart Strategy to Add 1.7 Use Place Value to Add 1.8 Estimate Differences 1.9 Mental Math Strategies for Subtraction 1.10 Use Place Value to Subtract 1.11 Combine Place Values to Subtract 1.12 Problem Solving: Addition and Subtraction Chapter 1 Review/Test 2.1 Problem Solving: Organize Data 2.2 Use Picture Graphs 2.3Make Picture Graphs 2.4 Use Bar Graphs 2.5Make Bar Graphs 2.6 Solve Problems Using Data 2.7 Use and Make Line Plots Chapter 2 Review/Test 3.nO.1 Use place value understanding of up to five-digit whole numbers to round to the nearest 10, 100, and 1,000 (3.NBT.1) 3.nO.2 Add and subtract up to four digits with and without regrouping (3.NBT.2) 3.Oat.5 Solve two-step word problems using the four basic operations and estimate to check (3.OA.8) 3.Oat.6 Begin to understand and apply the standard order of operations (3.OA.8) 3.Oat.7 Identify arithmetic patterns using properties of operations (3.OA.9) 3.dsP.1 Draw and interpret scaled picture and bar graphs to represent a data set (3.MD.3) 3.dsP.2 Measure length using rulers marked with halves and fourths of an inch and the nearest whole centimeter; show data by making a line plot (3.MD.4) 4

23 Week 7-10 Week 11 to 13 Chapter 3 Understand Multiplication Chapter 4 Multiplication Facts and Strategies 3.1 Count Equal Groups 3.2 Algebra: Relate Addition and Multiplication 3.3 Skip Count on a Number Line 3.4 Problem Solving: Model Multiplication 3.5 Model with Arrays 3.6 Algebra: Commutative Property of Multiplication 3.7 Algebra: Multiply with 1 and 0 Chapter 3 Review/Test 4.1 Multiply with 2 and Multiply with 5 and Multiply with 3 and Algebra: Distributive Property 4.5 Multiply with Algebra: Associative Property of Multiplication 4.7 Algebra: Patterns on the Multiplication Table 4.8 Multiply with Multiply with 9 3.nO.4 Understand and create equivalent fractions with denominators 2,3,4,6,8 using fraction models (3.NF.3) 3.Oat.1 Understand the meaning and relationship of multiplication and division (3.OA.1,2,6) 3.Oat.2 Memorize and fluently multiply and divide using the multiplication facts through 10 (3.OA.3,7); mentally multiply by 10 and 100 (3.NBT.3) 3.Oat.3 Represent and determine the unknown whole number in an equation (3.OA.4) 3.Oat.4 Apply properties of operations (commutative, associative, distributive) to multiply and divide (3.OA.5) 3.Oat.5 Solve two-step word problems using the four basic operations and estimate to check (3.OA.8) 3.Oat.6 Begin to understand and apply the standard order of operations (3.OA.8) 3.nO.4 Understand and create equivalent fractions with denominators 2,3,4,6,8 using fraction models (3.NF.3) 3.Oat.1 Understand the meaning and relationship of multiplication and division (3.OA.1,2,6) 3.Oat.2 Memorize and fluently multiply and divide using the multiplication facts through 10 (3.OA.3,7); mentally multiply by 10 and 100 (3.NBT.3) 5

24 4.10 Problem Solving: Multiplication Chapter 4 Review/Test 3.Oat.3 Represent and determine the unknown whole number in an equation (3.OA.4) 3.Oat.4 Apply properties of operations (commutative, associative, distributive) to multiply and divide (3.OA.5) 3.Oat.5 Solve two-step word problems using the four basic operations and estimate to check (3.OA.8) 3.Oat.6 Begin to understand and apply the standard order of operations (3.OA.8) 3.Oat.7 Identify arithmetic patterns using properties of operations (3.OA.9) Week Chapter 5 Use Multiplication Facts 5.1 Algebra: Describe Patterns 5.2 Algebra: Find Unknown Factors 5.3 Problem Solving: Use the Distributive Property 5.4 Use Place Value to Multiply with Multiply with Multiples of 10 Chapter 5 Review/Test 3.Oat.3 Represent and determine the unknown whole number in an equation (3.OA.4) 3.Oat.4 Apply properties of operations (commutative, associative, distributive) to multiply and divide (3.OA.5) 3.Oat.7 Identify arithmetic patterns using properties of operations (3.OA.9) Week Chapter 6 Understand Division Term Break 6.1 Problem Solving: Model Division 6.2 Size of Equal Groups 6.3 Number of Equal Groups 6.4 Model with Bar Models 6.5 Algebra: Relate Subtraction and Division 3.Oat.1 Understand the meaning and relationship of multiplication and division (3.OA.1,2,6) 3.Oat.2 Memorize and fluently multiply and divide using the multiplication facts 6

25 6.6 Investigate: Model with Arrays 6.7 Algebra: Relate Multiplication and Division 6.8 Algebra: Write Related Facts 6.9 Algebra: Division Rules for 1 and 0 Chapter 6 Review/Test through 10 (3.OA.3,7); mentally multiply by 10 and 100 (3.NBT.3) 3.Oat.3 Represent and determine the unknown whole number in an equation (3.OA.4) 3.Oat.4 Apply properties of operations (commutative, associative, distributive) to multiply and divide (3.OA.5) Week 22 to 25 Chapter 7 Division Facts and Strategies Chapter 8 Understand Fractions 7.1 Divide by Divide by Divide by Divide by Divide by Divide by Divide by Divide by Divide by Problem Solving: Two-Step Problems 7.11 Investigate: Order of Operations Chapter 7 Review/Test 8.1 Equal Parts of a Whole 8.2 Equal Shares 8.3 Unit Fractions of a Whole 8.4 Fractions of a Whole 8.5 Fractions on a Number Line 8.6 Relate Fractions and Whole 3.nO.3 Understand, express, and order fractions between zero and one, simple mixed numbers, and whole numbers as fractions (3.NF.1,2) 3.nO.4 Understand and create equivalent fractions with denominators 2,3,4,6,8 using fraction models (3.NF.3) 3.Oat.1 Understand the meaning and relationship of multiplication and division (3.OA.1,2,6) 3.Oat.2 Memorize and fluently multiply and divide using the multiplication facts through 10 (3.OA.3,7); mentally multiply by 10 and 100 (3.NBT.3) 3.Oat.5 Solve two-step word problems using the four basic operations and estimate to check (3.OA.8) 3.Oat.6 Begin to understand and apply the 7

26 Week 26 to 29 Chapter 9 Compare Fractions Chapter 10 Time, Length, Liquid Volume, and Mass Numbers 8.7 Fractions of a Group 8.8 Find Part of a Group Using Unit Fractions 8.9 Problem Solving: Find the Whole Group Using Unit Fractions Chapter 8 Review/Test 9.1 Problem Solving: Compare Fractions 9.2 Compare Fractions with the Same Denominator 9.3 Compare Fractions with the Same Numerator 9.4 Compare Fractions 9.5 Compare and Order Fractions 9.6 Investigate: Model Equivalent Fractions 9.7 Equivalent Fractions Chapter 9 Review/Test 10.1 Time to the Minute 10.2 A.M. and P.M Measure Time Intervals 10.4 Use Time Intervals 10.5 Problem Solving: Time Intervals 10.6 Measure Length 10.7 Estimate and Measure Liquid Volume 10.8 Estimate and Measure Mass 10.9 Solve Problems About Liquid Volume and Mass standard order of operations (3.OA.8) 3.m.1 Solve problems involving measurement and estimation of intervals of time (nearest minute), liquid volume (liter), and masses of objects (gram, kilogram) (3.MD.1,2) 3.m.2 Read and understand a calendar using day, week, month, and year 3.m.3 Explain and measure temperature using Celsius and Fahrenheit scales 3.m.6 Construct various equivalent combinations of money; add and subtract money amounts 8

27 Week 30 to 35 Week 36 to 39* Chapter 11 Perimeter and Area Chapter 12 Two-Dimensional Shapes Chapter 10 Review/Test Chapter 11 Perimeter and Area 11.1 Investigate: Model Perimeter 11.2 Find Perimeter 11.3 Algebra: Find Unknown Side Lengths 11.4 Understand Area 11.5 Investigate: Measure Area 11.6 Use Area Models 11.7 Problem Solving: Area of Rectangles 11.8 Area of Combined Rectangles 11.9 Same Perimeter, Different Areas Same Area, Different Perimeters Chapter 11 Review/Test 12.1 Describe Plane Shapes 12.2 Describe Angles in Plane Shapes 12.3 Identify Polygons 12.4 Describe Sides of Polygons 12.5 Classify Quadrilaterals 12.6 Draw Quadrilaterals 12.7 Describe Triangles 12.8 Problem Solving: Classify Plane Shapes 12.9 Investigate: Relate Shapes, Fractions, and Area Chapter 12 Review/Test 3.m.4 Understand concepts of area and its measurement by counting unit squares (cm2 m2, in 2, ft. 2); apply multiplication and addition to area (3.MD.5,6,7) 3.m.5 Solve real-world and mathematical problems recognizing area and perimeter of plane figures; distinguish between linear and area measurements (3.MD.8) 3.GeO.1 Sort and classify shapes to compare and contrast attributes (3.G.1,2) 3.GeO.2 Partition shapes into equal areas and express as a fraction (3.G.2)

28 Enjoy your break! *I planned only up to 39 weeks so you have room for days that teaching Math was a challenge due to performances, holidays, emergency school closing days, etc. 9

29 10 Go Math! 4 th Grade From Houghton Mifflin Harcourt Yearly Plan Aligned with the Common Core AND ready to use for Unit and Daily Lesson Plans

30 By Yanina Jimenez Dear colleagues, This Yearly Plan for the new Math curriculum Go Math! for fourth grade is especially designed to help you keep track of your pace at the busy time of teaching Math. You will find it extremely helpful, not only because it contains a fair pace for the whole year by weeks, but because it is ready to be used at the time of planning for your unit or lesson plans since it has the Common Core performance standards by each unit. Last, but certainly not least, it integrates Faith in Learning. Enjoy and if you have any questions, don t hesitate to contact me at yjimenez@illinoisadventist.org May God bless you and give you a wonderful school year! 1 mycutegraphics.com/graphics/school/school-kids/math-center.html

31 Yanina Jimenez In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry Students generalize their understanding of place value to 1,000,000, understanding the relative sizes of numbers in each place. They apply their understanding of models for multiplication (equal-sized groups, arrays, area models), place value, and properties of operations, in particular the distributive property, as they develop, discuss, and use efficient, accurate, and generalizable methods to compute products of multi-digit whole numbers. Depending on the numbers and the context, they select and accurately apply appropriate methods to estimate or mentally calculate products. They develop fluency with efficient procedures for multiplying whole numbers; understand and explain why the procedures work based on place value and properties of operations; and use them to solve problems. Students apply their understanding of models for division, place value, properties of operations, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multi-digit dividends. They select and accurately apply appropriate methods to estimate and mentally calculate quotients, and interpret remainders based upon the context. 2. Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions. Students extend previous understandings about how fractions are built from unit fractions, composing fractions from unit fractions, decomposing fractions into unit fractions, and using the meaning of fractions and the meaning of multiplication to multiply a fraction by a whole number. 3. Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry. 4. Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry. Integration Faith and Learning NUMBERS AND OPERATIONS Essential: What do numbers represent and how do they help us order and compare things in God s world? OPERATIONS AND ALGEBRAIC THINKING Essential Question: How can objects be represented to help us understand the variety of God s creation? MEASUREMENT Essential Question: How does measurement help us fulfill God s plan? GEOMETRY Essential Question: How do shapes and their parts help us appreciate God s creation? DATA ANALYSIS, STATISTICS, & PROBABILITY Essential Question: How can we quantify our findings in a way that pleases God?

32 Big idea: Numbers represent an amount that helps us order and compare things in God s world. Big idea: A single collection of objects can always be represented in more than one way to help us understand the variety of God s creation. Big idea: Measurement allows us to be accurate and orderly as God planned. Big idea: Shapes and their parts help us appreciate the beauty and order in everything God has designed. TIME FRAME CHAPTERS CHAPTER CONTENT COMMON CORE Big idea: God has at various times commanded men to count, measure, and record their findings. Week 1-2 Chapter 1 Place Value, Addition, and Subtraction to One Million Week 3-6 Chapter 2 Multiply by 1- Digit Numbers 1.1 Model Place Value Relationships 1.2 Read and Write Numbers 1.3 Compare and Order Numbers 1.4 Round Numbers 1.5 Rename Numbers 1.6 Add Multi-Digit Numbers 1.7 Subtract Multi-Digit Numbers 1.8 Problem Solving: Comparison Problems with Addition and Subtraction Chapter 1 Review/Test 2.1 Meaning of Multiplication 2.2 Comparison Problems 2.3 Multiply Tens, Hundreds, and Thousands 2.4 Estimate Products 2.5 Investigate: Multiply Using the Distributive Property 2.6 Multiply Using Expanded Form 2.7 Multiply Using Partial Products 2.8 Multiply Using Mental Math 2.9 Problem Solving: Multistep Multiplication Problems 2.10Multiply 2-Digit Numbers with 4.nO.1 Use place value understanding of multidigit whole numbers to round to any place up to millions (4.NBT.1,3) 4.nO.2 Read, write, compare, and understand whole numbers using standard, number name, and expanded forms (4.NBT.2) 4.nO.3 Add and subtract multi-digit whole numbers; multiply up to 4 digits X 1 digit and 2 digits X 2 digits; divide using a one-digit divisor and up to a four-digit dividend with and without a remainder (4.NBT.4,5,6) 4.nO.3 Add and subtract multi-digit whole numbers; multiply up to 4 digits X 1 digit and 2 digits X 2 digits; divide using a one-digit divisor and up to a four-digit dividend with and without a remainder (4.NBT.4,5,6) 4.Oat.2 Solve multi-step word problems including remainder interpretation and estimate to check; create equations with a letter for the unknown (4.OA.1,2,3)

33 Week 7-10 Week 11 to 13 Chapter 3 Multiply 2-Digit Numbers Chapter 4 Divide by 1-Digit Numbers Regrouping 2.11Multiply 3-Digit and 4-Digit Numbers with Regrouping 2.12 Algebra: Solve Multistep Problems Using Equations Chapter 2 Review/Test 3.1 Multiply Tens 3.2 Estimate Products 3.3 Investigate: Area Models and Partial Products 3.4 Multiply Using Partial Products 3.5 Multiply with Regrouping 3.6 Choose a Multiplication Method 3.7Problem Solving: Multiply 2-Digit Numbers Chapter 3 Review/Test 4.1 Estimate Quotients Using Multiples 4.2 Investigate: Remainders 4.3 Interpret the Remainder 4.4 Divide Tens, Hundreds, and Thousands 4.5 Estimate Quotients Using Compatible Numbers 4.6 Investigate: Division and the Distributive Property 4.7 Divide Using Repeated Subtraction 4.8 Divide Using Partial Quotients 4.9 Investigate: Model Division with Regrouping 4.10 Place the First Digit 4.nO.3 Add and subtract multi-digit whole numbers; multiply up to 4 digits X 1 digit and 2 digits; divide using a one-digit divisor and up to a four-digit dividend with and without a remainder (4.NBT.4,5,6) 4.Oat.1 Memorize and fluently multiply using the multiplication facts through 12 4.nO.3 Add and subtract multi-digit whole numbers; multiply up to 4 digits X 1 digit and 2 digits; divide using a one-digit divisor and up to a four-digit dividend with and without a remainder (4.NBT.4,5,6) 4.Oat.2 Solve multi-step word problems including remainder interpretation and estimate to check; create equations with a letter for the unknown (4.OA.1,2,3)

34 Week Chapter 5 Factors, Multiples, and Patterns 4.11Divide by 1-Digit Numbers 4.12 Problem Solving: Multistep Division Problems Chapter 4 Review/Test 5.1 Model Factors 5.2 Find Factors 5.3 Problem Solving: Common Factors 5.4 Relate Factors and Multiples 5.5 Prime and Composite Numbers 5.6 Algebra: Number Patterns Chapter 5 Review/Test 4.Oat.3 Find all factor pairs for a whole number within 100; identify whole numbers as prime or composite (4.OA.4) 4.Oat.4 Understand the basic concepts of least common multiple (LCM) and greatest common factor (GCF) 4.Oat.5 Generate and analyze number and shape patterns (4.OA.5) Week Chapter 6 Fraction Equivalence and Comparison Chapter 7 Add and Subtract Fractions Term Break 6.1 Investigate: Equivalent Fractions 6.2 Generate Equivalent Fractions 6.3 Simplest Forms 6.4 Common Denominators 6.5 Problem Solving: Factors, Multiples, and Equivalent Fractions 6.6Compare Fractions Using Benchmarks 6.7 Compare Fractions 6.8 Compare and Order Fractions Chapter 6 Review/Test 7.1 Investigate: Join and Separate Fractions 7.2 Write Fractions as Sums 7.3 Add Fractions Using Models 7.4 Subtract Fractions Using Models 7.5 Add and Subtract Fractions 4.nO.4 Understand, express, and order fractions with different numerators and denominators; numerically express equivalent fractions (4.NF.1,2) 4.nO.5 Add and subtract fractions and mixed numbers with common denominators; multiply fractions by whole numbers (4.NF.3,4) 4.nO.6 Understand, compare, and use decimal notation for fractions with denominators of 10 or 100 (4.NF.5,6,7)

35 Week 22 to 25 Chapter 8 Multiply Fractions by Whole Numbers Chapter 9 Relate Fractions and Decimals 7.6 Rename Fractions and Mixed Numbers 7.7 Add and Subtract Mixed Numbers 7.8 Record Subtraction with Renaming 7.9 Algebra: Fractions and Properties of Addition 7.10 Problem Solving: Multistep Problems with Fractions Chapter 7 Review/Test 8.1 Investigate: Multiples of Unit Fractions 8.2 Investigate: Multiples of Fractions 8.3 Model Multiplication of a Fraction by a Whole Number 8.4 Multiply a Fraction by a Whole Number 8.5 Problem Solving: Comparison Problems with Multiplication Chapter 8 Review/Test 9.1 Relate Tenths and Decimals 9.2 Relate Hundredths and Decimals 9.3 Equivalent Fractions Decimals 9.4 Relate Fractions, Decimals, and Money 9.5 Problem Solving: Money 9.6 Add Fractional Parts of 10 and Compare Decimals Chapter 9 Review/Test 4.nO.5 Add and subtract fractions and mixed numbers with common denominators; multiply fractions by whole numbers (4.NF.3,4) 4.nO.6 Understand, compare, and use decimal notation for fractions with denominators of 10 or 100 (4.NF.5,6,7) 4.m.1 Solve problems involving measurement (time, volume, mass, money, simple fractions, decimals, distance) (4.MD.2) 4.m.2 Convert measurement from a larger unit to a smaller unit (km, m, cm; kg, g; lb., oz.; L, ml; hr., min, sec) (4.MD.1) 4.m.3 Apply area and perimeter formulas (4.MD.3) 4.m.4 Read a Fahrenheit and Celsius thermometer knowing the significance of 32 F, 212 F, 0 C, and 100 C 5.dsP.1 Use basic operations to solve problems using a line plot to display a data set of measurement in fractions of a unit (halves, fourths, and eighths) (5.MD.2) 5.dsP.2 Find the mean, median, mode, and range of a given set of data 10.1 Lines, Rays, and Angles 4.Oat.5 Generate and analyze number and