Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards Introduction The North Dakota Common Core State Standards (NDCCSS) define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. These NDCCSS emphasize conceptual understanding and procedural knowledge, which is different from the skill based focus of the previous ND standards. Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. NDCCSS should be read as allowing for the widest possible range of students to participate fully from the outset, along with appropriate accommodations to ensure maximum participation of students with special education needs. No set of grade-specific standards can fully reflect the great variety in abilities, needs, learning rates, and achievement levels of students in any given classroom. However, the Standards do provide clear signposts along the way to the goal of college and career readiness for all students. NDCCSS require students to master skills and concepts found within the specified grade. In order for mastery to be obtained, teachers must be aware that skills and concepts will need to be introduced prior to the grade in which the Standard is listed. Consider this example: 2.MD.8- Students must solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 2 pennies, how many cents do you have? Students will need to be able to identify dollar bills and coins prior to mastery of the standard. Therefore, these skills need to be introduced in Kindergarten and First grade even though they are not found as standards in those grades. It has been noted many life skills are not included as specific NDCCSS; these would include concepts such as reading a calendar, patterning, identifying the value of coins and paper money, and counting of like coins. It is necessary to include these life skills during daily routine so that students will develop a complete understanding of mathematical concepts and gain prior knowledge for mastery of standards. Draft- NDCT October 2011 1 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) Notes Activities CCSS Domain: Operations and Algebraic Thinking CCSS Cluster: Represent and solve problems involving addition and subtraction. 2.1.12 2.OA.1 Strong correlation. Select an operation to Use addition and solve problems involving subtraction within 100 to addition and subtraction solve one- and two-step of whole numbers. word problems involving situations of adding to, 2.1.13 taking from, putting Add and subtract twotogether, taking apart, digit whole numbers and comparing, with between 0 and 100 unknowns in all positions, without regrouping. e.g., by using drawings and equations with a 2.5.3 symbol for the unknown Solve addition and number to represent the subtraction equations problem. with unknown numbers, e.g., 2 + i = 5 2.5.4 Use symbols (i.e., +, -, =, <, >) to write simple number sentences. 2.5.5 Use words, objects, and number sentences to represent addition and subtraction problems. Draft- NDCT October 2011 2 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) Notes 2.1.2 Count backward from 100. Counting backward can be used as a strategy for subtraction. 2.1.9 Round numbers to 10. Moved to third grade. 2.1.10 Use grade appropriate terms when communicating about addition and subtraction, i.e.: addend, sum, difference. Mathematical practices – see CCSS pages 6-9. 2.5.1 Extend and create number patterns. Moved to fourth grade. 2.5.2 State the rule that describes a given repeating and growing pattern. Moved to fourth grade. Draft- NDCT October 2011 Activities 3 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard CCSS Cluster: Add and subtract within 20. 2.1.15 Add and subtract twodigit whole numbers between 0 and 100 without regrouping. 2.1.16 Recall addition facts and subtraction facts (0-18). ND Common Core State Standard (CCSS) 2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Notes Activities Strong correlation. 2.1.17 Estimate whole number sums and differences. CCSS Cluster: Work with equal groups of objects to gain foundations for multiplication. 2.1.6 2.OA.3 Strong correlation. Demonstrate, identify, Determine whether a and explain the difference group of objects (up to between odd and even 20) has an odd or even numbers using concrete number of members, e.g., objects or drawings. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Draft- NDCT October 2011 4 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard 2.1.14 Model multiplication using equal sets of objects. CCSS Domain: Number and Operations in Base Ten CCSS Cluster: Understand place value. 2.1.5 Connect number words and numerals to the quantities they represent up to 100. 2.1.7 Identify place value concepts through the hundreds place. Draft- NDCT October 2011 ND Common Core State Standard (CCSS) Notes 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. Includes writing an equation. Specifies rectangular arrays. 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 cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. 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). Deeper understanding of place value. Activities 5 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard 2.1.1 Count and order numbers up to 1,000. ND Common Core State Standard (CCSS) Notes 2.NBT.2 Count within 1000; skipcount by 5s, 10s, and 100s. Strong correlation. Includes counting by 100s. 2.1.4 Identify and write numerals to 1,000. 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Includes writing number names and expanded form. 2.1.8 Use symbols (i.e., >, <, =) to compare whole numbers to 1,000. 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. Deeper understanding of place value. Activities 2.1.3 Count by 2's, 5's, and 10's. 2.5.4 Use symbols (i.e., +, -, =, <, >) to write simple number sentences. Draft- NDCT October 2011 6 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) Notes Activities CCSS Cluster: Use place value understanding and properties of operations to add and subtract. 2.1.13 2.NBT.5 Strong correlation. Demonstrate the inverse Fluently add and subtract relationship between within 100 using addition and subtraction, strategies based on place i.e., 3+4 = 7, 7-4 = 3. value, properties of operations, and/or the 2.1.15 relationship between Add and subtract twoaddition and subtraction. digit whole numbers between 0 and 100 without regrouping. 2.1.7 Identify place value concepts through the hundreds place. 2.1.7 Identify place value concepts through the hundreds place. 2.1.15 Add and subtract twodigit whole numbers between 0 and 100 without regrouping. Draft- NDCT October 2011 2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations. Emphasizes use of strategies. Includes adding four numbers. Includes regrouping. 7 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard 2.1.15 Add and subtract twodigit whole numbers between 0 and 100 without regrouping. Draft- NDCT October 2011 ND Common Core State Standard (CCSS) Notes 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. New second grade expectation. 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. Includes numbers to 900 (instead of 100). Emphasizes mental math. Activities 8 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) 2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. CCSS Domain: Measurement and Data CCSS Cluster: 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. 2.4.11 Select the appropriate units for measuring time, length, weight, and temperature. 2.4.10 Identify the approximate size of basic units, e.g., width of finger is about one centimeter, large soda bottle is two liters, a paper clip weighs one gram. Draft- NDCT October 2011 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. Notes Activities New second grade expectation. New second grade expectation. Deeper understanding of the uses of measurement and measurement tools. 9 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS Draft- NDCT October 2011 ND Standard ND Common Core State Standard (CCSS) Notes 2.4.7 Estimate and measure length to the nearest inch, half-inch, foot, or centimeter. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. Broader. Includes meters. 2.4.9 Compare and order given lengths, capacities, weights, or temperatures that are expressed in the same unit of measure. 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. Focuses on length. Includes difference when comparing lengths. Activities 10 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) CCSS Cluster: Relate addition and subtraction to length. 2.5.3 2.MD.5 Solve addition and Use addition and subtraction equations subtraction within 100 to with unknown numbers, solve word problems e.g., 2 + i = 5 involving lengths that are given in the same units, 2.1.12 e.g., by using drawings Select an operation to (such as drawings of solve problems involving rulers) and equations with addition and subtraction a symbol for the unknown of whole numbers. number to represent the problem. 2.1.15 Add and subtract twodigit whole numbers between 0 and 100 without regrouping. Notes Activities Strong correlation. 2.5.5 Use words, objects, and number sentences to represent addition and subtraction problems. 2.4.9 Compare and order given lengths, capacities, weights, or temperatures that are expressed in the same unit of measure. Draft- NDCT October 2011 11 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) 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. Notes New second grade expectation. 2.4.5 Estimate and measure weight to the nearest pound or kilogram. Moved to third grade. 2.4.6 Estimate and measure capacity to the nearest cup or liter. Moved to third grade. 2.4.8 Estimate and verify a quantity, e.g.: marbles in a jar. Not addressed. Draft- NDCT October 2011 Activities 12 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard CCSS Cluster: Work with time and money. 2.4.1 Tell time to the nearest quarter hour and 5 minute interval using digital and analog clocks. 2.4.12 Use the symbols for the dollar and cent. 2.4.4 Count mixed coins to $1.00. ND Common Core State Standard (CCSS) Notes 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Includes writing time and 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 have? Counting money is in the context of a word problem. 2.4.2 Distinguish between weekdays and weekend days. Daily routines – see introduction to this document. 2.4.3 Recall the months of the year in order. Daily routines – see introduction to this document. Draft- NDCT October 2011 Activities 13 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard CCSS Cluster: Represent and interpret data. 2.3.2 Demonstrate that data can be represented in a variety of ways. 2.4.7 Estimate and measure length to the nearest inch, half-inch, foot, or centimeter. 2.3.2 Demonstrate that data can be represented in a variety of ways 2.3.3 Formulate and answer simple questions from data represented by graphs ND Common Core State Standard (CCSS) 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. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Notes Activities Application of measurement, data collection, representation and analysis. Strong correlation. 2.3.1 Sort and classify objects according to their attributes and organize data about the objects, e.g.: Venn diagrams, graphs, tables Draft- NDCT October 2011 14 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) Notes 2.3.4. Record results of activities involving chance (e.g.: coin flips, dice rolls) and make reasonable predictions based upon data. Moved to seventh grade. 2.3.5 Describe the likelihood of an event, e.g.: cloudy, it may rain. Not addressed. CCSS Domain: Geometry CCSS Cluster: 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. Draft- NDCT October 2011 Activities New second grade expectation. 15 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard 2.1.14 Model multiplication using equal sets of objects. 2.1.11 Represent and explain fractions (i.e., one half, one third, one fourth, one sixth and one eighth) as part of a whole and part of a set. 2.1.11 Represent and explain fractions (i.e., one half, one third, one fourth, one sixth and one eighth) as part of a whole and part of a set. 2.2.1 Recognize geometric shapes and structures in their environment. Draft- NDCT October 2011 ND Common Core State Standard (CCSS) Notes 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Relates to the area model of multiplication and fractions. 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. Strong correlation. Activities Moved to kindergarten. 16 Grade 2 Mathematics Transition Document: North Dakota State Standards to the Common Core State Standards ND Standards Not Addressed at this Grade Level in ND CCSS ND Standard ND Common Core State Standard (CCSS) Notes 2.2.2 Identify, describe and sort three –dimensional objects, i.e.: pyramid, cube, rectangular prism, cone, cylinder and sphere. Moved to kindergarten. 2.2.3 Predict and demonstrate the results of putting together and taking apart shapes. Moved to kindergarten and first grade. 2.2.4 Identify symmetrical shapes and draw their line of symmetry. Moved to fourth grade. Activities 2.2.5 Identify congruent figures from a selection of similar figures. Draft- NDCT October 2011 17
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