2.OA.1. Use addition and subtraction within 100 to solve one- and two- step 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 Students will understand how to solve one- step word problems using addition and subtraction within Students will understand how to solve two- step word problems using addition and subtraction within 100. (This could include two addition functions, two subtraction functions or both an addition and subtraction function in the same word problem.) Students will understand how to solve word problems with unknowns in all positions using these adding to taking from putting together/taking apart comparing (Refer to Glossary, Table 1 and Standard 1.OA.6 for a list of mental strategies.) Students can solve one- and two- step word problems with the unknown in all positions using objects, drawings, number lines or hundreds charts. Students can write equations for one- and two- step word problems for each problem type. Students can model each one- and two- step word problem type using objects, drawings, number lines Students can represent an unknown number with a symbol using drawings and equations. 2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of, know from memory all sums of two one- digit numbers. Students will understand how to use whole- part relationships of numbers to efficiently compose and decompose one- digit numbers. Students will understand the relationship between addition and subtraction. Students will understand that fluency includes accuracy, efficiency, appropriateness, and flexibility. Some of the mental strategies students use may include: Counting on: 8 + 4 = (8 9, 10,11,12) Counting back: 12-4 = (12 11, 10, 9, 8) Making tens: 5 + 7 = (5 = 2 + 3 so 3 + 7 = 10 therefore 10 + 2 = 12) Doubles: 6 + 6 = Doubles plus/minus one: 6 + 7 = (6 + 6 + 1 or 7 + 7 1) Decomposing a number leading to a ten: 15 7 =, so 15 5 = 10, therefore 10 2 = 8) Working knowledge of fact families/related facts: 3 + 9 = 12 so 12-9 = (See Standard 1.OA.6 for a list of mental strategies.) Students may use objects, pictures, words, and numbers to show and explain their thinking process at beginning. By the time they reach fluency they should be using mental strategies and their reflect that. 1
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 twos; write an equation to express an even number as a Students will understand that an even number can be separated into two equal groups without any Students will understand that an odd number cannot be separated into two equal groups without Students will understand that the number in the ones place shows whether a number is odd or even. Students will understand that a group of tens will always be even. Students will understand that an equation with two equal addends will have an even sum. Students can identify an odd number by pairing objects and having one left over. Students can identify an even number by pairing objects and having none left over. Students can solve problems with two equal addends. Students can count by twos. Students can draw pictures or arrange counters to show even and odd numbers. Students can search for and highlight patterns on a hundreds chart. Students can write equations showing double facts (e.g., 2 + 2 = 4; 5 + 5 = 10). 2.OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Students will understand what a rectangular array is. Students will understand how to arrange any set of objects into a rectangular array. Students will understand how the rectangular array represents repeated addition. Students will understand how to write an addition equation representing the array as a sum of equal Students can determine the total number of objects in each row or column for arrays with up to five rows and up to five columns. Students can use addition to find the total number of objects in a rectangular array. Students can write an addition equation to express the total of objects or representations in a rectangular array as a sum of equal addends (adding either columns or rows). Students can build a rectangular array with objects. Students can build a rectangular array on a geoboard. Students can draw a rectangular array using grid paper or a pictorial representation. 2.NBT.1. Understand that the three digits of a three- digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special 100 can be thought of as a bundle of ten tens called a hundred. 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). Students will understand that one represents a single unit of measurement in counting. 2
Students will understand that ten ones can be bundled together to make one set of ten; a ten can also be represented as 10 single units. Students will understand that ten sets of ten can be bundled together to make a hundred; a hundred can also be represented as 100 single units. Students will understand that when numbers are bundled into sets of hundreds, there are zero tens Students can identify the value of a given digit in a three- digit number (e.g., find the value of the 7 in 706; where 7 = 700). Students can model a given number using base ten blocks, straws, beans, etc (e.g., of most efficient form of base 10 where 706 can be thought of as 7 hundreds and 6 ones). 2.NBT.2. Count within 1000; skip- count by 5s, 10s, and 100s. Students will understand that numbers increase through counting patterns. Students will understand that counting patterns can start from any number of that pattern s multiple. Students will understand that counting by fives is just half of counting by 10s. Students will understand that when counting by tens within a hundred, only the digit in the tens place Students will understand that when counting by hundreds within a thousand, only the digit in the hundreds place increases. Students will understand that skip- counting is the same as repeated addition. In addition to standard skip- counting patterns starting at zero (such as 10, 20, 30, etc.) students need to be able to add 5, 10, or 100 to ANY starting number within the counting pattern and extend the counting pattern (e.g., 425 count on by fives: 430, 435, 440, etc.). Students will be able to demonstrate multiple skip- counting patterns from the same starting point (example: start at 200 skip count by 5s, 10s, and 100s). Representational: Students can model skip- counting with objects. Students can use a hundreds chart to skip- count by fives, tens, or hundreds and highlight each pattern (by coloring or using objects). Students can use number line to skip- count. Students can model the relationship between skip- counting and monetary units (nickel, dime, dollar). 2.NBT.3. Read and write numbers to 1000 using base- ten numerals, number names, and expanded Students will understand that there are multiple ways to express a given number (base ten, number name, expanded form). Students will understand what expanded form is. Students will understand how to compose and decompose numbers between standard and expanded Students can express the same number in multiple ways: 671 3
Six hundred seventy- one 6 hundreds, 7 tens, and 1 one 600 + 70 + 1 (six hundred plus seventy plus one) In addition to the procedural process, students can show the number 671 pictorially with base 10 2.NBT.4. Compare two three- digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Students will understand that when comparing two numbers, one is looking at the whole number, not just individual digits. Students will understand that when comparing two numbers, if the number of hundreds is the same then one should look at and compare the number of tens. Students will understand that two three- digit numbers that have equal value are represented by the = Students can use the vocabulary words (greater than, less than, equal to) to compare two three- digit numbers in terms of value. Students can use the vocabulary words and >, <, = symbols together to compare two three- digit numbers in terms of value. Students can use only symbols to compare two three- digit numbers in terms of value. Students can model greater than, less than and equal to using sets of money. Students can model each number with base ten blocks (straws, beans, or place value drawings, etc.), attending to precision in the placement of hundreds with hundreds, tens with tens, and ones with 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. Students will understand a variety of computation strategies for addition and subtraction. Students will understand related addition and subtraction facts and how to use addition to solve for subtraction (and vice versa). Students will understand the commutative property, associative property of addition, and identity Students will understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and that sometimes it is necessary to compose or decompose tens or hundreds. Students can solve single- and double- digit addition and subtraction problems in both vertical and horizontal form using a variety of strategies. Students can use more than one strategy to solve a given equation: Adding by place value 58 + 34 (50 + 30 = 80 8 + 4 = 12 80 + 12 = 92) Properties of operation commutative property: 7 + 8 = 15 8 + 7 = 15; associative property: (3 + 8) + 1 = 12 3 + (8 + 1) = 12; identity property of zero: 9 + 0 = 9 Compensation (48 + 22 22 2 = 20 48 + 2 = 50 50 + 20 = 70) Incremental (58 + 34 58 + 10 68 + 10 78 + 10 88 + 4 = 92) 4
Students can demonstrate the relationship between addition and subtraction. Example: fact family (25 + 12 = 37 12 + 25 = 37 37 12 = 25 37 25 = 12) Students can represent addition and subtraction strategies in oral and written form. Students can model addition and subtraction problems and their relationship using manipulatives such as base ten blocks, straws, beans, or place value drawings. Students can use the number line to model addition and subtraction situations. 2.NBT.6: Add up to four two- digit numbers using strategies based on place value and properties of Students will recognize that adding with more than two addends follows the same process as adding with two addends. Students will understand the commutative property (e.g., 23 + 15 = 15 + 23) and associative property (e.g., [13 + 2] + 57 = 13 + [2 + 57]) of addition. Students will understand that regrouping may be necessary when adding up to four two- digit Students can solve double- digit addition problems in both vertical and horizontal form. Students can use more than one strategy to solve a given equation. Students can draw a model of a problem with more than two addends. Students can represent sums and differences in oral and written form. Students can demonstrate with manipulatives or writing how to group the order of addends while solving the problem. Students can model addition of two- digit numbers up to four addends with base ten blocks. 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 three- digit 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. Students will understand computation strategies relating to place value (hundreds and hundreds, tens and tens, ones and ones). Students will understand how to compose and decompose large numbers in addition and subtraction. Students will understand the principle of decomposing a number with relation to subtraction (commonly known as regrouping). Students will understand that ten ones can be composed into a ten in the ten s place. Similarly, ten tens can be composed into a hundred in the hundreds place (this is commonly known as regrouping). Students will understand how to strategically use compensation to make friendly numbers. Students will understand how to use incremental adding (i.e., breaking one number into tens and Students can solve addition and subtraction problems (up to 1,000) in both vertical and horizontal Students can use more than one strategy to solve a given equation. Students can demonstrate the relationship between addition and subtraction. 5
Students can represent sums and differences in oral and written form. Students can model addition and subtraction problems and their relationships using manipulatives. 2.NBT.8. Mentally add 10 or 100 to a given number 100 900, and mentally subtract 10 or 100 from a given number 100 900. Students will understand that adding 10 or 100 to any number only changes the digit in the 10s or Students can add or subtract 10 or 100 mentally. Students can draw a picture of the number in base ten format (or use base ten blocks), and demonstrate the change being made (i.e., cross out a set of 10 or 100, or draw another set of 10 or After children have a solid understanding of how to relate the drawing to adding/subtracting 10 or 100, they can demonstrate proficiency in being able to mentally add or subtract 10 or 100 from a 2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations.1 Students will understand place value and the value of each digit, as well as the whole number Students will understand the properties of operations. Students can solve the same problem in more than one way, as well as: Clearly explain their thinking and justify their reasoning. Connect a given addition problem to a related subtraction problem. Connect a given subtraction problem to a related addition problem. Connect models to written numbers in relation to addition and subtraction problems. Connect properties of operations to addition and subtraction strategies. Representational: Students can represent the connections between strategies and identify similarities and differences of various strategies. Students can use numbers, pictures, or words to explain addition and subtraction strategies. 2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Students will identify and understand the difference between the standard tools for linear Students will understand that longer units of measure take fewer repetitions to measure objects. Students will understand that shorter units of measure take more repetitions to measure objects. Students will understand that they will typically use tools closest to the size of the measured object for efficiency (e.g., use a ruler to measure a book, not a meter stick). Students will identify and understand the beginning point of the appropriate measuring tool. Students can investigate and use customary and metric tools of linear measurement. Students can learn tool names and linear measurement vocabulary. 6
Students can measure a variety of objects using the appropriate tools. Students can measure accurately (leave no gaps, allow no overlays, and start at 0 on a measurement Students can identify and record the appropriate length and unit (5 inches, 2 yards, or 9 cm). 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. Students will identify and understand the difference between the standard tools for linear Students will understand that longer units of measure take fewer repetitions to measure objects. Students will understand that shorter units of measure take more repetitions to measure objects. Students will understand the difference between the size of units (e.g., centimeters/inches, meters/yards, inches/feet, feet/yards). Students can measure the same object with two different measurement tools and compare the difference in units used. Students can record the measurements using the correct units, and record their observations with a focus on the comparison and unit difference (centimeters vs. inches, inches vs. feet, etc.). 2.MD.3. Estimate lengths using units of inches, feet, centimeters, and meters. Students will understand the length of inches, feet, centimeters, and meters. Students will understand the value of using a point of reference when estimating length (e.g., the top joint of your thumb is approximately an inch). Students will understand how to check the reasonableness of an estimate and adjust as needed. Students can estimate a length, then justify the reasonableness of the estimation and the unit of measurement used. Students can estimate a length, measure only a small section, then adjust the estimation as needed. Students can record the estimation of an object s length and specify the purpose for the unit of Students can show justification for use of chosen unit of measurement. 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. Students will understand that differences in length can be measured. Students will understand how to express the difference in length between two objects in terms of standard length units. Students can compare objects visually, side by side, and measure the difference. Students can express that difference in terms of a standard length unit. Students can record length and unit of measure of actual objects. 7
Students can record lengths of objects in scientific units 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. Students will understand how to add and subtract lengths. Students will understand how to interpret a word problem involving lengths. Students will understand how to set up equations, including a measurement unit, and solve for the unknown number. Students can measure different lengths (objects or activities such as jumping distances). Students can record measurements. Students can compute different length equations with the unknown in different positions. Use a variety of lengths within 100 (sum of 100 or less; e.g., 45 + 36). Students can solve word problems involving lengths of various objects. Students can use pictures, words, and or numbers to solve measurement equations. Record the 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 whole- number sums and differences within 100 on a number line diagram Students will understand that 0 represents the beginning point of the number line. Students will understand that numbers can label an equal space marked on a number line. Students will understand that numbers from 0 to 100 can be placed on the number line. Students will understand that addition and subtraction problems can be solved using a number line that does not begin at zero. Students can consider the numbers in the addition or subtraction problem to determine the range of numbers needed for the number line. Students can create a number line using the numbers that correspond to an addition or subtraction problem, and solve the problem using the number line to perform the operation. Students can draw a number line with equally spaced points to illustrate thinking used in finding sums and differences of given problems. 2.MD.7. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. Students will understand that the numbers on an analog clock are divided into intervals of five Students will understand that a day is 24 hours long and is divided into two 12- hour segments, one being called a.m. and the other p.m. Students can look at a clock, count by fives to the position of the minutes hand, note the position of the hour hand, and figure out the time to the nearest five minutes. 8
Students can use analog and digital clocks. Students can write the time using correct format (e.g., 5:40 p.m.) to the nearest five minutes. Students can use both digital and analog clocks. Students can include a.m. and p.m. 2.MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you Students will recognize the different coins and their names. Students will understand the values of each of the coins and bills. Students will understand that coins represent a part of a dollar. Students will understand that only one money symbol should be used ($ for dollars, for cents only). (Since students haven t been exposed to decimals, use problems with either only dollars or only Students can introduce each of the coins individually, stating its name and value. Students can introduce money symbols ($ for dollars, for cents only). Students can practice counting money, starting with the larger values and adding on the smaller ones. Students can write monetary amounts using the correct notations (e.g., 57 or $1). Students can represent money by writing amounts (e.g., 25 + 30 =55 ). Students can accurately calculate total amount of money given pictures of coins and bills 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 whole- number units. Students will understand that a line plot is a visual representation of data. Students will understand and interpret data on a line plot. Students will understand data and how to transfer it to a line plot. Students can take measurements and collect data. Students can make a line plot. Include a horizontal scale, title, labels, and straight columns of data Students can transfer measurement data to the line plot. Students can read information from the completed line plot. Students can make comparisons from the data. Students can represent data in a visual line plot. 2.MD.10. Draw a picture graph and a bar graph (with single- unit scale) to represent a data set with up to four categories. Solve simple put- together, take- apart, and compare problems1 using information presented in a bar graph. Students will understand what a picture graph is and what the pictures represent. Students will understand what a bar graph is and what the data represents. 9
Students will understand how to organize data in picture and bar graphs. Students will understand the parts of a graph and how to label them. Students will understand how to read and interpret bar and picture graphs. Students will understand that data can be used to solve problems. Students can read and understand data. Students can organize data into up to four categories. Students can draw a graph representing these categories. Students can label the parts of a graph. Students can analyze and solve put- together, take- apart, and comparison problems using a graph. Using procedural steps, students can create a picture graph and bar graph to represent data. Students can solve simple problems using these graphs. Students can make comparisons within data sets. 2.G.1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Students will understand that two- dimensional and three- dimensional shapes have angles. Students will understand that three- dimensional shapes have faces. Students will understand the difference between two- dimensional shapes and three- dimensional Students will recognize the attributes of a triangle, quadrilateral, pentagon, hexagon, and cube. Students will recognize that all four- sided shapes are quadrilaterals. Students can identify and describe a two- dimensional shape. Students can identify and describe a three- dimensional shape. Students can identify the number of angles on a triangle, quadrilateral, pentagon, and hexagon. Students can identify the number of equal faces on a cube. Students can draw a two- dimensional shape when given a specific number of angles. Students can draw a three- dimensional shape when given a specific number of equal faces. Students can build/find shapes when given specific attributes. Students can write about the differences between a two- dimensional shape and a three- dimensional 2.G.2. Partition a rectangle into rows and columns of same- size squares and count to find the total number of them. Students will understand that a row is horizontal. Students will understand that a column is vertical. Students will understand the meaning of partition. Students can identify and describe a row. Students can identify and describe a column. Students can determine the number of same- size squares in a rectangle. 10
Students can draw and partition a rectangle into rows and columns of same- size squares. 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. Students will understand the meaning of partition. Students will understand that circles and rectangles can be divided into two, three, and four equal Students will recognize halves, thirds, and fourths of a shape. Students will understand that two halves equal one whole, three thirds equal one whole, and four fourths equal one whole. Students will recognize that equal shares of identical wholes do not necessarily have the same shape. Students can identify two, three, and four equal shares of a whole. Students can identify equal shares by using the vocabulary halves, half of, thirds, third of, fourths, and Students can identify that equal shares within identical circles/rectangles may not have the same Students can describe a circle/rectangle as having two halves, three thirds, or four fourths. Draw a circle/rectangle showing two, three, or four equal shares. Partition two identical circles/rectangles in different ways to show that equal shares do not need to have the same shape. 11