Topic: 1  Understanding Addition and Subtraction


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1 8 days / September Topic: 1  Understanding Addition and Subtraction Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. /Enduring What are some ways to think about addition and subtraction? Parts of a whole is one interpretation of addition. Addition number sentences can be used to show parts of a whole. Joining parts to make a whole is one interpretation of addition. Addition number sentences can be used to show joining parts of a whole. Separating parts from a hole and comparison are two interpretations of subtraction. Subtraction number sentences can be used to show separating parts from a hole or comparison subtraction situations. Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. 1.1 Writing addition number sentences 1.2 Stories about joining 1.3 Writing subtraction number sentences 1.4 Stories about separating 1.5 Stories about comparing 1.6 Connecting addition & subtraction 1.7 Use objects for solving problems
2 9 days / September / October Topic: 2  Addition Strategies Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Add and subtract within OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two onedigit numbers. /Enduring What are strategies for finding addition facts? Doubles facts can be associated with memorable realworld situations. Basic addition facts that are near doubles can be found using a related doubles fact. Addition facts involving 9 can be changed to an equivalent fact with 10. Addition facts involving 8 can be changed to an equivalent fact with 10. Two numbers can be added in any order. Three or more whole numbers can be grouped and added in any order. 2.1 Adding 0, 1, Adding doubles 2.3 Adding near doubles 2.4 Adding in any order 2.5 Adding 3 numbers 2.6 Making 10 to add 2.7 Draw a picture and write a # sentence
3 8 days / October Topic: 3  Subtraction Strategies Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Add and subtract within OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two onedigit numbers. /Enduring What are strategies for finding subtraction facts? Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. Some subtraction facts can be found by subtracting from the minuend (the larger number) an amount to get to 10 and then subtracting the amount that remains. 3.1 Subtracting 0, 1,2 3.2 Thinking addition to subtraction doubles 3.3 Thinking addition to 10 subtract 3.4 Thinking addition to 18 to subtract 3.5 Making 10 to subtract 3.6 Two question problems
4 6 days /October Topic: 4  Working with Equal Groups Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 2.NBT.4. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. /Enduring What is the relationship between arrays and repeated addition? Repeated addition involves joining equal groups. An array involves joining equal groups and is one way to think about repeated addition. 4.1 Repeated addition 4.2 Building arrays 4.3 Practicing repeated addition 4.4 Draw a picture and write a number sentence
5 9 days / November Understand place value. 2.NBT.1. Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 2.NBT.2. Count within 1000; skipcount by 5s, 10s, and 100s. 2.NBT.3. Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 2.NBT.4. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and <. Use place value understanding and properties of operations to add and subtract. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Work with equal groups of objects to gain foundations for multiplication. 2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Topic: 5  Place Value to 100 /Enduring How can numbers to 100 be shown and compared? In a twodigit number, the tens digit tells how many groups of ten and the ones digit tells the number of ones. The numbers are written by joining two number words that describe the number of tens and the number of ones. Numbers through 20 are each represented by a unique number word. Our place value number system makes it easy to name the number that is 10 more or 10 less than any other given number by simply adjusting the digit in the tens place. Numbers can be used to tell how many. Place value can be used to compare and order numbers. The position of words before and after can be sued to explain number relationships. Some numbers can be divided into two equal parts and some cannot. 5.1 Models for tens and ones 5.2 Reading & writing numbers 5.3 Using symbols to compare # s 5.4 Counting to Ten more or ten less 5.6 Even and odd numbers 5.7 Use fata from a chart
6 8 days / December Topic: 6  Mental Addition Understand place value. 2.NBT.2. Count within 1000; skipcount by 5s, 10s, and 100s. Use place value understanding and properties of operations to add and subtract. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. /Enduring How can sums be found mentally? Adding tens is like adding ones. When adding a number less than ten to a twodigit number using the traditional algorithm, it may be necessary to rename 10 ones as 1 ten. Twodigit numbers can be broken apart using tens and ones and added in different ways. Patterns on a hundred chart can be used to add numbers and to develop mental math strategies and number sense. Adding groups of tens is similar to adding numbers less than Adding tens 6.2 Adding ones 6.3 Adding tend and ones 6.4 Adding on a hundred chart 6.5 Adding multiples of Look for a pattern
7 7 days / January Topic: 7  Mental Subtraction Use place value understanding and properties of operations to add and subtract. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.8. Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a given number /Enduring How can differences be found mentally? Subtracting tens is like subtracting ones. To find parts of 100, add on ones to make a ten and count on by tens to reach 100. Patterns in a hundred chart can be used to subtract numbers and to develop mental math strategies and number sense. Subtracting groups of tens is similar to subtracting numbers less than Subtracting tens 7.2 Finding parts of Subtracting on a hundreds chart 7.4 Subtracting multiples of Missing or extra information
8 11 days / January Topic: 8  Adding TwoDigit Numbers Use place value understanding and properties of operations to add and subtract. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6. Add up to four twodigit numbers using strategies based on place value and properties of operations. Relate addition and subtraction to length. 2.MD.6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent wholenumber sums and differences within 100 on a number line diagram. /Enduring What is a standard procedure for adding two digit numbers? 10 ones can be regrouped for 1 ten. The standard addition algorithm for twodigit and onedigit numbers breaks the calculations into simpler calculations using place value, starting with the ones and then the tens. Answers to the simpler calculations are used to give the final sum. The standard algorithm for adding twodigit and twodigit numbers is just an extension of the algorithm for adding twodigit and onedigit numbers. The ones are added first and then the tens. All sums and differences can be found using models (cubes). Some calculations are done easily using mental math or paper and pencil. More complex calculations can be done using a calculator. Sums can be represented as lengths on a number line diagram of addition. Three and four twodigit numbers can be grouped and added in any order. 8.1 Regrouping 10 ones for 1 ten 8.2 Models to add 2 and 1 digit numbers 8.3 Adding 2 and 1 digit numbers 8.4 Models to add 2 digit numbers 8.5 Adding 2 digit numbers 8.6 Adding on a number line 8.7 Adding more than two numbers 8.8 Ways to add 8.9 Draw a picture and write a # sentence
9 11 days / January / February Topic: 9  Subtracting TwoDigit Numbers Use place value understanding and properties of operations to add and subtract. 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Relate addition and subtraction to length. 2.MD.6. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., and represent wholenumber sums and differences within 100 on a number line diagram. /Enduring What is a standard procedure for subtracting two digit numbers? One ten can be regrouped for 10 ones. The standard subtraction algorithm breaks the calculation into simpler calculations starting with the ones and then the tens. The standard algorithm for subtracting twodigit and twodigit numbers is just an extension of the algorithm for subtracting twodigit and onedigit numbers. All sums and differences can be found using models (cubes). Some calculations are done easily using mental math or paper and pencil. More complex calculations can be done using a calculator. Differences can be represented as lengths in a number line diagram of subtraction. The inverse relationship between addition and subtraction can be used to check subtraction. 9.1 Regrouping 1 ten for 10 ones 9.2 Models to subtract 2 and 1 digit numbers 9.3 Subtracting 2 and 1 digit numbers 9.4 Models to subtract 2 digit numbers 9.5 Subtracting 2 digit numbers 9.6 Subtracting on a number line 9.7 Using addition to check subtraction 9.8 Ways to subtract 9.9Two question problems
10 11 days / February / March Topic: 10  Place Value to 1,000 Understand place value. 2.NBT.1. Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 1a. 100 can be thought of as a bundle of ten tens called a hundred. 1b.The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.2. Count within 1000; skipcount by 5s, 10s, and 100s. 2.NBT.3. Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 2.NBT.4. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 2.NBT.8. Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a given number /Enduring What number patterns are helpful in reading and writing numbers to 1,000? Numbers can be used to tell how many. Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. Adding or subtracting hundreds or tens is similar to adding or subtracting singledigit numbers. Counting and placevalue can be seen on a hundreds chart. Number lines can help with skip counting. Place value can be used to compare and order numbers. Ordering three or more numbers is similar to comparing two numbers because each number must be compared to each of the other numbers Building 1, Counting 100 s, 10 s an 1 s 10.3 Reading & writing numbers to 1, Changing numbers by 100 s & 10 s 10.5 Patterns with # s on hundred s chart 10.6 Skip counting 5, 10, 100 to 1, Comparing numbers 10.8 Ordering numbers 10.9 Look for a pattern
11 11 days / March Topic: 11  ThreeDigit Addition and Subtraction Use place value understanding and properties of operations to add and subtract. 2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Number to represent the problem. /Enduring What are the ways to add & subtract three digit numbers? There are a variety of ways to add three digit numbers. There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers or the expression so the calculation is easy to do mentally. The standard addition algorithm for threedigit numbers breaks the calculation into simpler calculations using place value starting with the ones, then the tens, and then the hundreds. There is a variety of ways to subtract threedigit numbers. The standard subtraction algorithm for threedigit numbers breaks the calculation into simpler calculations using place value starting with the ones, then the tens, and then the hundreds Exploring adding 3 digit numbers 11.2 Mental math 11.3 Models for adding with 3 digit numbers 11.4 Adding 3 digit numbers 11.5 Exploring subtracting 3 digit numbers 11.6 Mental Math: Ways to find missing parts 11.7 Models for subtracting with 3 digit # s 11.8 Subtracting 3 digit numbers 11.9 Use logical reasoning
12 10 days / March / April Reason with shapes and their attributes. 2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2. Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Topic: 12  Geometry /Enduring How can shapes and solids be described, and compared, and used to make other shapes? Threedimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces or flat surfaces, edges, and vertices. Many everyday objects closely approximate standard geometric solids. A shape can be identified by the number of its sides, vertices, angles. Some shapes can be combined to make new shapes. Same shapes can be decomposed into other shapes. Rectangles can be partitioned into equal squares. A region can be divided into equalsized parts in different ways. Equalsized parts of a region have the same area but not necessarily the same shape Flat surfaces, vertices, and edges 12.2 Relating plane figures to solid figures 12.3 Polygons & angles 12.4 Making new shapes 12.5 Cutting shapes apart 12.6 Dividing rectangles into equal shares 12.7 Wholes and equal parts 12.8 Use reasoning to solve problems
13 7 days / April Work with time and money. 2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Topic: 13  Counting Money /Enduring What strategies can be used to count money? Specific coins or bills each have a unique value. The size of a coin does not indicate its value. Money amounts can usually be counted in different ways. When counting money, it is usually easier to start with the coin or bill with the greatest value. The amount of money can often be represented using different combinations of coins and bills Coins 13.2 Counting collections of coins 13.3 Ways to show the same amount 13.4 One dollar 13.5 Make an organized list
14 6 days / April Topic: 14  Money Work with time and money 2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. /Enduring How can sums and differences be estimated? The process for adding money, written using cent notations, is the same as adding whole numbers. The process for subtracting money, written using cent notation, is the same as subtracting whole numbers. Rounding can be used to estimate sums and differences as can place value and number relationships Adding money 14.2 Subtracting money 14.3 Estimating sums & differences 14.4 Try, check & revise
15 11 days / April / May Topic: 15  Measuring Length Measure and estimate lengths in standard units. 2.MD.1. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3. Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. 2.MD.5. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. /Enduring How can you measure the length of an object using nonstandard units? How can you use addition and subtraction to solve measurement problems? The length of some objects is measureable. The length of any object can be sued as a measurement unit for length, but a standard unit, such as an inch or centimeter, is always the same length. The length of any object can be used as a measurement unit for length, but a standard unit is always the same length. Measurement is a process of comparing a unit to the object being measured. The length of any object can be used as a measurement unit for length. Measurements in the same unit like inches can be added or subtracted in the same way as adding and subtracting whole numbers. The measurement unit needs to be written with the sum or difference. The length of two objects can be compared by subtracting to find the difference. Materials: EnVision Math 15.1 Exploring length 15.2 Inches 15.3 Centimeters 15.4 Inches, feet and yards 15.5 Centimeters & meters 15.6 Measuring length 15.7 Adding & subtracting in measurement 15.8 Comparing lengths 15.9 Use objects to solve problems
16 8 days / May Relate addition and subtraction to length. 2.MD.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Represent and interpret data. 2.MD.9. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units. 2.MD.10. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Topic: 16  Time, Graphs, and Data /Enduring How can clocks, bar graphs, and pictographs be used to show data and answer questions? Time can be given to the nearest five minutes. Time can be expressed using different units that are related to each other. A.M. and P.M. are used to designate certain time periods. Time can be expressed before or after the hour. Data can be organized in different ways. The lengths of objects can be organized in different ways. A line plot can be used as a visual representation of the relative lengths of objects. Each type of graph is most appropriate for certain kinds of data. Pictographs and bar graphs make it easy to compare data Telling time to five minutes 16.2 Telling time before & after the hour 16.3 Organizing data 16.4 Graphing lengths 16.5 Pictographs 16.6 Use a graph
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