Common Core Unpacked Grade 1

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These are the unpacking documents to better help you understand the expectations for 1st grade students under the Common Core State Standards for Math. The example problems are great.

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Common Core Unpacked Grade 1

  1. 1. 1st Grade Mathematics ● Unpacked ContentFor the new Common Core State Standards that will be effective in all North Carolina schools in the 2012-13.This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continuallyupdating and improving these tools to better serve teachers. What is the purpose of this document? To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand and be able to do. What is in the document? Descriptions of what each standard means a student will know, understand and be able to do. The ―unpacking‖ of the standards done in this document is an effort to answer a simple question ―What does this standard mean that a student must know and be able to do?‖ and to ensure the description is helpful, specific and comprehensive for educators. How do I send Feedback? We intend the explanations and examples in this document to be helpful and specific. That said, we believe that as this document is used, teachers and educators will find ways in which the unpacking can be improved and made ever more useful. Please send feedback to us at feedback@dpi.state.nc.us and we will use your input to refine our unpacking of the standards. Thank You! Just want the standards alone? You can find the standards alone at http://corestandards.org/the-standards Mathematical Vocabulary is identified in bold print. These are words that students should know and be able to use in context. 1st Grade Mathematics ● Unpacked Content
  2. 2. Critical Areas and Changes in Grade 1Critical 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 non-standard linear measurement and measuring lengths as iterating length units 4. Reasoning about attributes of, and composing and decomposing geometric shapesNew to 1st Grade: Properties of Operations – Commutative and Associative (1.0A.3) Counting sequence to 120 (1.NBT.1) Comparison Symbols (<, >) (1.NBT.3) Defining and non-defining attributes of shapes (1.G.1) Half-circles, quarter-circles, cubes (1.G.2) Relationships among halves, fourths and quarters (1.G.3)Moved from 1st Grade: Estimation (1.01f) Groupings of 2’s, 5’s, and 10’s to count collections (1.02) Fair Shares (1.04) Specified types of data displays (4.01) Certain, impossible, more likely or less likely to occur (4.02) Sort by two attributes (5.01) Venn Diagrams (5.02) Extending patterns (5.03)Note:Topics may appear to be similar between the CCSS and the 2003 NCSCOS; however, the CCSS may be presentedat a higher cognitive demand.1st Grade Mathematics ● Unpacked Content
  3. 3. Critical Areas in Grade 1(1) Students develop strategies for adding and subtracting whole numbers based on their prior work with smallnumbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connectedto form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaningfor the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with theseoperations. Students understand connections between counting and addition and subtraction (e.g., adding two isthe same as counting on two). They use properties of addition to add whole numbers and to create and useincreasingly sophisticated strategies based on these properties (e.g., ―making tens‖) to solve addition andsubtraction problems within 20. By comparing a variety of solution strategies, children build their understandingof the relationship between addition and subtraction.(2) Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 andsubtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solveproblems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens andones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities thatbuild 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 underlyingconcepts such as iterating (the mental activity of building up the length of an object with equal-sized units) andthe transitivity principle for indirect measurement.(4) Students compose and decompose plane or solid figures (e.g., put two triangles together to make aquadrilateral) and build understanding of part-whole relationships as well as the properties of the original andcomposite 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 formeasurement and for initial understandings of properties such as congruence and symmetry.1st Grade Mathematics ● Unpacked Content page3
  4. 4. Standards for Mathematical Practice in Grade 1The Common Core State Standards for Mathematical Practice are practices expected to be integrated into every mathematics lesson for all studentsGrades K-12. Below are a few examples of how these Practices may be integrated into tasks that Grade 1 students complete.1 ) Make Sense Mathematically proficient students in Grade 1 examine problems (tasks), can make sense of the meaning of the task and findand Persevere an entry point or a way to start the task. Grade 1 students also develop a foundation for problem solving strategies and becomein Solving independently proficient on using those strategies to solve new tasks. In Grade 1, students’ work builds from Kindergarten andProblems. still heavily relies on concrete manipulatives and pictorial representations. The exception is when the CCSS uses to the word fluently, which denotes mental mathematics. Grade 1 students also are expected to persevere while solving tasks; that is, if students reach a point in which they are stuck, they can reexamine the task in a different way and continue to solve the task. Lastly, at the end of a task mathematically proficient students in Grade ask themselves the question, ―Does my answer make sense?‖2) Reason Mathematically proficient students in Grade 1 make sense of quantities and the relationships while solving tasks. This involvesabstractly and two processes- decontexualizing and contextualizing. In Grade 1, students represent situations by decontextualizing tasks intoquantitatively. numbers and symbols. For example, in the task, ―There are 60 children on the playground and some children go line up. If there are 20 children still playing, how many children lined up?‖ Grade 1 students are expected to translate that situation into the equation: 60 – 20 = ___ and then solve the task. Students also contextualize situations during the problem solving process. For example, while solving the task above, students refer to the context of the task to determine that they need to subtract 20 since the number of children on the playground is the total number except for the 20 that are still playing. The processes of reasoning also applies to Grade 1, as they look at ways to partition 2-dimensional geometric figures into halves, and fourths.3) Construct Mathematically proficient students in Grade 1 accurately use definitions and previously established answers to construct viableviable arguments about mathematics. For example, while solving the task, ―There are 15 books on the shelf. If you take some booksarguments and off the shelf and there are now 7 left, how many books did you take off the shelf?‖ students will use a variety of strategies tocritique the solve the task. After solving the class, Grade 1 students are expected to share problem solving strategies and discuss thereasoning of reasonableness of their classmates’ strategies.others.4) Model with Mathematically proficient students in Grade 1 model real-life mathematical situations with a number sentence or an equation,mathematics. and check to make sure that their equation accurately matches the problem context. Grade 1 students rely on concrete manipulatives and pictorial representations while solving tasks, but the expectation is that they will also write an equation to model problem situations. For example, while solving the task ―there are 11 bananas on the counter. If you eat 4 bananas, how many are left?‖ Grade 1 students are expected to write the equation 11-4 = 7. Likewise, Grade 1 students are expected to create an appropriate problem situation from an equation. For example, students are expected to create a story problem for the equation 13-7 = 6.1st Grade Mathematics ● Unpacked Content
  5. 5. 5) Use Mathematically proficient students in Grade 1 have access to and use tools appropriately. These tools may include counters,appropriate place value (base ten) blocks, hundreds number boards, number lines, and concrete geometric shapes (e.g., pattern blocks, 3-dtools solids). Students should also have experiences with educational technologies, such as calculators and virtual manipulatives thatstrategically. support conceptual understanding and higher-order thinking skills. During classroom instruction, students should have access to various mathematical tools as well as paper, and determine which tools are the most appropriate to use. For example, while solving 12 + 8 = __, students explain why place value blocks are more appropriate than counters.6) Attend to Mathematically proficient students in Grade 1 are precise in their communication, calculations, and measurements. In allprecision. mathematical tasks, students in Grade 1 describe their actions and strategies clearly, using grade-level appropriate vocabulary accurately as well as giving precise explanations and reasoning regarding their process of finding solutions. For example, while measuring objects iteratively (repetitively), students check to make sure that there are no gaps or overlaps. During tasks involving number sense, students check their work to ensure the accuracy and reasonableness of solutions.7) Look for and Mathematically proficient students in Grade 1 carefully look for patterns and structures in the number system and other areasmake use of of mathematics. While solving addition problems, students begin to recognize the commutative property, in that 7+4 = 11, andstructure. 4+7 = 11. While decomposing two-digit numbers, students realize that any two-digit number can be broken up into tens and ones, e.g. 35 = 30 + 5, 76 = 70+6. Further, Grade 1 students make use of structure when they work with subtraction as missing addend problems, such as 13- 7 = __ can be written as 7+ __ = 13 and can be thought of as how much more do I need to add to 7 to get to 13?8) Look for and Mathematically proficient students in Grade 1` begin to look for regularity in problem structures when solving mathematicalexpress tasks. For example, when adding up three one-digit numbers and using the make 10 strategy or doubles strategy, studentsregularity in engage in future tasks looking for opportunities to employ those same strategies. For example, when solving 8+7+2, a studentrepeated may say, ―I know that 8 and 2 equal 10 and then I add 7 to get to 17. It helps to see if I can make a 10 out of 2 numbers when Ireasoning. start.‖ Further, students use repeated reasoning while solving a task with multiple correct answers. For example, in the task ―There are 12 crayons in the box. Some are red and some are blue. How many of each could there be?‖ Grade 1 students are expected to realize that the 12 crayons could include 6 of each color (6+6 = 12), 7 of one color and 5 of another (7+5 = 12), etc. In essence, students are repeatedly finding numbers that will add up to 12.1st Grade Mathematics ● Unpacked Content page5
  6. 6. Operations and Algebraic Thinking 1.0ACommon Core ClusterRepresent and solve problems involving addition and subtraction.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, put-together, take-apart, andcompare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with theseoperations.Prior to first grade students should recognize that any given group of objects (up to 10) can be separated into sub groups in multiple ways and remainequivalent in amount to the original group (Ex: A set of 6 cubes can be separated into a set of 2 cubes and a set of 4 cubes and remain 6 total cubes).Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: adding to, taking from, putting together, taking apart, comparing,unknown, sum, less than, equal to, Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.OA.1 Use addition and subtraction 1.OA.1 builds on the work in Kindergarten by having students use a variety of mathematical representations (e.g.,within 20 to solve word problems objects, drawings, and equations) during their work. The unknown symbols should include boxes or pictures, andinvolving situations of adding to, not letters.taking from, putting together, takingapart, and comparing, with unknowns Teachers should be cognizant of the three types of problems (Glossary, Table 1). There are three types of additionin all positions, e.g., by using objects, and subtraction problems: Result Unknown, Change Unknown, and Start Unknown. Here are some Additiondrawings, and equations with a symbolfor the unknown number to represent Use informal language (and, minus/subtract, the same as) to describe joining situations (putting together) and separating situations (breaking apart).the problem.11 Use the addition symbol (+) to represent joining situations, the subtraction symbol (-) to represent separating See Glossary, Table 1 situations, and the equal sign (=) to represent a relationship regarding quantity between one side of the equation and the other. A helpful strategy is for students to recognize sets of objects in common patterned arrangements (0-6) to tell how many without counting (subitizing). 1st Grade Mathematics ● Unpacked Content
  7. 7. Examples below: Result Unknown: Change Unknown: Start Unknown: There are 9 students on the There are 9 students on the There are some students on the playground. Then 8 more playground. Some more playground. Then 8 more students students showed up. How students show up. There are came. There are now 17 students. many students are there now 17 students. How many How many students were on the now? (9+8 = __) students came? playground at the beginning? (9+ __ = 17) (__ + 8 = 17) Please see Glossary, Table 1 for additional examples. The level of difficulty for these problems can be differentiated by using smaller numbers (up to 10) or larger numbers (up to 20).1.OA.2 Solve word problems that call 1.OA.2 asks students to add (join) three numbers whose sum is less than or equal to 20, using a variety offor addition of three whole numbers mathematical representations.whose sum is less than or equal to 20, This objective does address multi-step word problems.e.g., by using objects, drawings, andequations with a symbol for the Example:unknown number to represent the There are cookies on the plate. There are 4 oatmeal raisin cookies, 5 chocolate chip cookies, and 6 gingerbreadproblem. cookies. How many cookies are there total? Student 1 Adding with a Ten Frame and Counters I put 4 counters on the Ten Frame for the oatmeal raisin cookies. Then I put 5 different color counters on the ten frame for the chocolate chip cookies. Then I put another 6 color counters out for the gingerbread cookies. Only one of the gingerbread cookies fit, so I had 5 leftover. One ten and five leftover makes 15 cookies. Student 2 Look for ways to make 10 I know that 4 and 6 equal 10, so the oatmeal raisin and gingerbread equals 10 cookies. Then I add the 5 chocolate chip cookies and get 15 total cookies. 1st Grade Mathematics ● Unpacked Content page7
  8. 8. Student 3 Number line I counted on the number line. First I counted 4, and then I counted 5 more and landed on 9. Then I counted 6 more and landed on 15. So there were 15 total cookies. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18Common Core ClusterUnderstand and apply properties of operations and the relationship between addition and subtraction.Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties ofaddition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., ―making tens‖) to solve additionand subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between additionand subtraction. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.OA.3 Apply properties of operations 1.OA.3 calls for students to apply properties of operations as strategies to add and subtract. Students do not needas strategies to add and subtract.2 to use formal terms for these properties. Students should use mathematical tools, such as cubes and counters, andExamples: If 8 + 3 = 11 is known, then representations such as the number line and a 100 chart to model these ideas.3 + 8 = 11 is also known.(Commutative property of addition.) Example:To add 2 + 6 + 4, the second two Student can build a tower of 8 green cubes and 3 yellow cubes and another tower of 3 yellow and 8 green cubes tonumbers can be added to make a ten, show that order does not change the result in the operation of addition. Students can also use cubes of 3 differentso 2 + 6 + 4 = 2 + 10 = 12. colors to ―prove‖ that (2 + 6) + 4 is equivalent to 2 + (6 + 4) and then to prove 2 + 6 + 4 = 2 + 10.(Associative property of addition.)2 Students need not use formal termsfor these properties. 1st Grade Mathematics ● Unpacked Content page8
  9. 9. Commutative property of addition: Associative property of addition: Order does not matter when you add When adding a string of numbers you can numbers. For example, if 8 + 2 = 10 add any two numbers first. For example, is known, then 2 + 8 = 10 is also when adding 2 + 6 + 4, the second two known. numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. Student 1 Using a number balance to investigate the commutative property. If I put a weight on 8 first and then 2, I think that it will balance if I put a weight on 2 first this time and then on 8.1.OA.4 Understand subtraction as an 1.OA.4 asks for students to use subtraction in the context of unknown addend problems.unknown-addend problem.For example, subtract 10 – 8 by Example:finding the number that makes 10 when 12 – 5 = __ could be expressed as 5 + __ = 12. Students should use cubes and counters, and representations suchadded to 8. Add and subtract within as the number line and the100 chart, to model and solve problems involving the inverse relationship between20. addition and subtraction. Student 1 I used a ten frame. I started with 5 counters. I knew that I had to have 12, which is one full ten frame and two leftovers. I needed 7 counters, so 12 - 5 = 7. 1st Grade Mathematics ● Unpacked Content page9
  10. 10. Student 2 I used a part-part-whole diagram. I put 5 counters on one side. I wrote 12 above the diagram. I put counters into the other side until there were 12 in all. I know I put 7 counters into the other side, so 12 – 5 = 7. 12 5 7 Student 3. Draw number line I started at 5 and counted up until I reached 12. I counted 7 numbers, so I know that 12 – 5 = 7. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1st Grade Mathematics ● Unpacked Content page10
  11. 11. Common Core ClusterAdd and subtract within 20.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: addition, subtraction, counting all, counting on, counting back, makingten. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.OA.5 Relate counting to addition 1.OA.5 asks for students to make a connection between counting and adding and subtraction. Students use variousand subtraction (e.g., by counting on 2 counting strategies, including counting all, counting on, and counting back with numbers up to 20. This standardto add 2). calls for students to move beyond counting all and become comfortable at counting on and counting back. The counting all strategy requires students to count an entire set. The counting and counting back strategies occur when students are able to hold the ―start number‖ in their head and count on from that number. Example: 5 + 2 = __ Student 1 Student 2 Counting All Counting On 5 + 2 = __. The student counts 5 + 2 = __. Student counts five counters. five counters. The student adds The student adds the first counter and says two more. The student counts 1, 6, then adds another counter and says 7. The 2, 3, 4, 5, 6, 7 to get the answer. student knows the answer is 7, since they counted on 2. Example: 12 – 3 = __ Student 1 Student 2 Counting All Counting Back 12 - 3 = __. The student counts 12 - 3 = __. The student counts twelve twelve counters. The student counters. The student removes a counter and removes 3 of them. The student says 11, removes another counter and says counts 1, 2, 3, 4, 5, 6, 7, 8, 9 to 10, and removes a third counter and says 9. get the answer. The student knows the answer is 9, since they counted back 3 1st Grade Mathematics ● Unpacked Content page11
  12. 12. 1.OA.6 Add and subtract within 20, 1.OA.6 mentions the word fluency when students are adding and subtracting numbers within 10. Fluency meansdemonstrating fluency for addition and accuracy (correct answer), efficiency (within 4-5 seconds), and flexibility (using strategies such as making 5 orsubtraction within 10. Use strategies making 10).such as counting on; making ten (e.g.,8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); The standard also calls for students to use a variety of strategies when adding and subtracting numbers within 20.decomposing a number leading to a ten Students should have ample experiences modeling these operations before working on fluency. Teacher could(e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); differentiate using smaller numbers.using the relationship between addition It is importance to move beyond the strategy of counting on, which is considered a less important skill than theand subtraction (e.g., knowing that 8 + ones here in 1.OA.6. Many times teachers think that counting on is all a child needs, when it is really not much4 = 12, one knows 12 – 8 = 4); and better skill than counting all and can becomes a hindrance when working with larger numbers.creating equivalent but easier orknown sums (e.g., adding 6 + 7 by Example: 8 + 7= __creating the known equivalent 6 + 6 + Student 1 Student 21 = 12 + 1 = 13). Making 10 and Decomposing a Creating an Easier Problem with Number Known Sums I know that 8 plus 2 is 10, so I I know 8 is 7 + 1. decomposed (broke) the 7 up into a 2 I also know that 7 and 7 equal 14 and and a 5. First I added 8 and 2 to get then I added 1 more to get 15. 10, and then added the 5 to get 15. 8 + 7 = (7 + 7) + 1 = 15 8 + 7 = (8 + 2) + 5 = 10 + 5 = 15 Example: 14 - 6 = __ Student 1 Student 2 Decomposing the Number You Relationship between Addition and Subtract Subtraction I know that 14 minus 4 is 10 so I 6 plus is 14, I know that 6 plus broke the 6 up into a 4 and a 2. 14 8 is 14, so that means that 14 minus 4 is 10. Then I take away 2 minus 6 is 8. more to get 8. 6 + 8 = 14 so 14 – 6 + 8 14 - 6 = (14 – 4) - 2 = 10 - 2 = 8 Algebraic ideas underlie what students are doing when they create equivalent expressions in order to solve a 1st Grade Mathematics ● Unpacked Content page12
  13. 13. problem or when they use addition combinations they know to solve more difficult problems. Students begin to consider the relationship between the parts. For example, students notice that the whole remains the same, as one part increases the other part decreases. 5 + 2 = 4 + 3Common Core Standard and ClusterWork with addition and subtraction equations.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: equations, equal, true, false. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.OA.7 Understand the meaning of the 1.OA.7 calls for students to work with the concept of equality by identifying whether equations are true or false.equal sign, and determine if equations Therefore, students need to understand that the equal sign does not mean ―answer comes next‖, but rather that theinvolving addition and subtraction are equal sign signifies a relationship between the left and right side of the equation.true or false. For example, which of The number sentence 4 + 5 = 9 can be read as, ―Four plus five is the same amount as nine.‖the following equations are true and In addition, Students should be exposed to various representations of equations, such as:which are false? 6 = 6, 7 = 8 – 1, 5 + 2 an operation on the left side of the equal sign and the answer on the right side (5 + 8 = 13)= 2 + 5, 4 + 1 = 5 + 2. an operation on the right side of the equal sign and the answer on the left side (13 = 5 + 8) numbers on both sides of the equal sign (6 = 6) operations on both sides of the equal sign (5 + 2 = 4 + 3). Students need many opportunities to model equations using cubes, counters, drawings, etc.1.OA.8 Determine the unknown whole 1.OA.8 extends the work that students do in 1.OA.4 by relating addition and subtraction as related operations fornumber in an addition or subtraction situations with an unknown. This standard builds upon the ―think addition‖ for subtraction problems as explainedequation relating three whole numbers. by Student 2 in 1.OA.6.For example, determine the unknownnumber that makes the equation true in Student 1each of the equations 8 + ? = 11, 5 = 5 = ___ - 3_ – 3, 6 + 6 = _. I know that 5 plus 3 is 8. So, 8 minus 3 is 5. 1st Grade Mathematics ● Unpacked Content page13
  14. 14. Number and Operations in Base Ten 1.NBTCommon Core ClusterExtend the counting sequence. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.NBT.1 Count to 120, starting at any 1.NBT.1 calls for students to rote count forward to 120 by Counting On from any number less than 120. Studentsnumber less than 120. In this range, should have ample experiences with the hundreds chart to see patterns between numbers, such as all of theread and write numerals and represent a numbers in a column on the hundreds chart have the same digit in the ones place, and all of the numbers in a rownumber of objects with a written have the same digit in the tens place.numeral. This standard also calls for students to read, write and represent a number of objects with a written numeral (number form or standard form). These representations can include cubes, place value (base 10) blocks, pictorial representations or other concrete materials. As students are developing accurate counting strategies they are also building an understanding of how the numbers in the counting sequence are related—each number is one more (or one less) than the number before (or after).Common Core ClusterUnderstand place value.Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare wholenumbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 interms 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, theyunderstand the order of the counting numbers and their relative magnitudes.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: tens, ones, bundle. Common Core Standard Unpacking 1st Grade Mathematics ● Unpacked Content page14
  15. 15. What does this standards mean a child will know and be able to do?1.NBT.2 Understand that the two 1.NBT.2a asks students to unitize a group of ten ones as a whole unit: a ten. This is the foundation of the placedigits of a two-digit number represent value system. So, rather than seeing a group of ten cubes as ten individual cubes, the student is now asked to seeamounts of tens and ones. Understand those ten cubes as a bundle- one bundle of ten.the following as special cases:a. 10 can be thought of as a bundle of ten ones — called a ―ten.‖b. The numbers from 11 to 19 are 1.NBT.2b asks students to extend their work from Kindergarten when they composed and decomposed numbers composed of a ten and one, two, from 11 to 19 into ten ones and some further ones. In Kindergarten, everything was thought of as individual units: three, four, five, six, seven, eight, ―ones‖. In First Grade, students are asked to unitize those ten individual ones as a whole unit: ―one ten‖. or nine ones. Students in first grade explore the idea that the teen numbers (11 to 19) can be expressed as one ten and some leftover ones. Ample experiences with ten frames will help develop this concept. Example: For the number 12, do you have enough to make a ten? Would you have any leftover? If so, how many leftovers would you have? Student 1 I filled a ten frame to make one ten and had two counters left over. I had enough to make a ten with some leftover. The number 12 has 1 ten and 2 ones. 1st Grade Mathematics ● Unpacked Content page15
  16. 16. Student 2 I counted out 12 place value cubes. I had enough to trade 10 cubes for a ten- rod (stick). I now have 1 ten-rod and 2 cubes left over. So the number 12 has 1 ten and 2 ones.c. The numbers 10, 20, 30, 40, 50, 1.NBT.2c builds on the work of 1.NBT.2b. Students should explore the idea that decade numbers (e.g. 10, 20, 30, 60, 70, 80, 90 refer to one, two, 40) are groups of tens with no left over ones. Students can represent this with cubes or place value (base 10) rods. three, four, five, six, seven, eight, (Most first grade students view the ten stick (numeration rod) as ONE. It is recommended to make a ten with unfix or nine tens (and 0 ones). cubes or other materials that students can group. Provide students with opportunities to count books, cubes, pennies, etc. Counting 30 or more objects supports grouping to keep track of the number of objects.) 1st Grade Mathematics ● Unpacked Content page16
  17. 17. 1.NBT.3 Compare two two-digit 1.NBT.3 builds on the work of 1.NBT.1 and 1.NBT.2 by having students compare two numbers by examining thenumbers based on meanings of the tens amount of tens and ones in each number. Students are introduced to the symbols greater than (>), less than (<) andand ones digits, recording the results of equal to (=). Students should have ample experiences communicating their comparisons using words, models andcomparisons with the symbols >, =, in context before using only symbols in this standard.and <. Example: 42 __ 45 Student 1 Student 2 42 has 4 tens and 2 ones. 45 has 4 42 is less than 45. I know this tens and 5 ones. They have the same because when I count up I say 42 number of tens, but 45 has more ones before I say 45. than 42. So 45 is greater than 42. So, 42 < 45. So, 42 < 45.Common Core ClusterUse place value understanding and properties of operations to add and subtract. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.NBT.4Add within 100, including 1.NBT.4 calls for students to use concrete models, drawings and place value strategies to add and subtract withinadding a two-digit number and a one- 100. Students should not be exposed to the standard algorithm of carrying or borrowing in first gradedigit number, and adding a two-digitnumber and a multiple of 10, usingconcrete models or drawings andstrategies based on place value,properties of operations, and/or therelationship between addition andsubtraction; relate the strategy to awritten method and explain thereasoning used. Understand that inadding two-digit numbers, one addstens and tens, ones and ones; andsometimes it is necessary to compose aten. 1st Grade Mathematics ● Unpacked Content page17
  18. 18. Student 1 I used a hundreds chart. I started at 37 and moved over 3 to land on 40. Then to add 20 I moved down 2 rows and landed on 60. So, there are 60 people on the playground. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Student 2 I used place value blocks and made a pile of 37 and a pile of 23. I joined the tens and got 50. I then joined the ones and got 10. I then combined those piles and got to 60. So, there are 60 people on the playground. Relate models to symbolic notation.1st Grade Mathematics ● Unpacked Content page18
  19. 19. Student 3 I broke 37 and 23 into tens and ones. I added the tens and got 50. I added the ones and got 10. I know that 50 and 10 more is 60. So, there are 60 people on the playground. Relate models to symbolic notation. Student 4 Using mental math, I started at 37 and counted on 3 to get to 40. Then I added 20 which is 2 tens, to land on 60. So, there are 60 people on the playground.Example:There are 37 people on the playground. 20 more people show up. How many people are now on the playground? Student 5 I used a number line. I started at 37. Then I broke up 23 into 20 and 3 in my head. Next, I added 3 ones to get to 40. I then jumped 10 to get to 50 and 10 more to get to 60. So, there are 60 people on the playground. 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 661.NBT.5 Given a two-digit number, 1.NBT.5 builds on students’ work with tens and ones by mentally adding ten more and ten less than any numbermentally find 10 more or 10 less than less than 100. Ample experiences with ten frames and the hundreds chart help students use the patterns found inthe number, without having to count; the tens place to solve such problems.explain the reasoning used. Example: 1st Grade Mathematics ● Unpacked Content page19
  20. 20. There are 74 birds in the park. 10 birds fly away. How many are left? Student 1 I used a 100s board. I started at 74. Then, because 10 birds flew away, I moved back one row. I landed on 64. So, there are 64 birds left in the park. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Student 2 I pictured 7 ten frames and 4 left over in my head. Since 10 birds flew away, I took one of the ten frames away. That left 6 ten frames and 4 left over. So, there are 64 birds left in the park.1st Grade Mathematics ● Unpacked Content page20
  21. 21. 1.NBT.6 Subtract multiples of 10 in 1.NBT.6 calls for students to use concrete models, drawings and place value strategies to subtract multiples of 10the range 10-90 from multiples of 10 from decade numbers (e.g., 30, 40, 50).in the range 10-90 (positive or zerodifferences), using concrete models or Example:drawings and strategies based on place There are 60 students in the gym. 30 students leave. How many students are still in the gym?value, properties of operations, and/or Student 1the relationship between addition and I used a hundreds chart and started at 60. I moved up 3 rows to land on 30.subtraction; relate the strategy to a There are 30 students left.written method and explain thereasoning used. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Student 2 I used place value blocks or unfix cubes to build towers of 10. I started with 6 towered of 10 and removed 3. I had 3 towers left. 3 towers have a value of 30. There are 30 students left. 1st Grade Mathematics ● Unpacked Content page21
  22. 22. Student 3 Students mentally apply their knowledge of addition to solve this subtraction problem. I know that 30 plus 30 is 60, so 60 minus 30 equals 30. There are 30 students left. Student 4 I used a number line. I started at 60 and moved back 3 jumps of 10 and landed on 30. There are 30 students left. 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66Measurement and Data 1.MDCommon Core ClusterMeasure lengths indirectly and by iterating length units.Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity ofbuilding up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.11 Students should apply the principle of transitivity of measurement to make indirect comparisons, but they need not use this technical term.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: order, lengths. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.MD.1 Order three objects by length; 1.MD.1 calls for students to indirectly measure objects by comparing the length of two objects by using a thirdcompare the lengths of two objects object as a measuring tool. This concept is referred to as transitivity.indirectly by using a third object. Example: 1st Grade Mathematics ● Unpacked Content page22
  23. 23. Which is longer: the height of the bookshelf or the height of a desk? Student 1 Student 2 I used a pencil to measure the I used a book to measure the height of the bookshelf and it bookshelf and it was 3 books was 6 pencils long. I used the long. I used the same book to same pencil to measure the measure the height of the desk and height of the desk and the desk it was a little less than 2 books was 4 pencils long. Therefore, long. Therefore, the bookshelf is the bookshelf is taller than the taller than the desk. desk.1.MD.2 Express the length of an object 1.MD.2 asks students to use multiple copies of one object to measure a larger object. This concept is referred to asas a whole number of length units, by iteration. Through numerous experiences and careful questioning by the teacher, students will recognize thelaying multiple copies of a shorter importance of making sure that there are not any gaps or overlaps in order to get an accurate measurement. Thisobject (the length unit) end to end; concept is a foundational building block for the concept of area in 3rd Grade.understand that the lengthmeasurement of an object is the Example:number of same-size length units that How long is the paper in terms of paper clips?span it with no gaps or overlaps. Limitto contexts where the object beingmeasured is spanned by a wholenumber of length units with no gaps oroverlaps.Common Core ClusterTell and write time.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: time, hours, half-hours. 1st Grade Mathematics ● Unpacked Content page23
  24. 24. Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.MD.3 Tell and write time in hours 1.MD.3 calls for students to read both analog and digital clocks and then orally tell and write the time. Timesand half-hours using analog and digital should be limited to the hour and the half-hour. Students need experiences exploring the idea that when the timeclocks. is at the half-hour the hour hand is between numbers and not on a number. Further, the hour is the number before where the hour hand is. For example, in the clock below, the time is 8:30. The hour hand is between the 8 and 9, but the hour is 8 since it is not yet on the 9.Common Core ClusterRepresent and interpret data.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: data, how many more, how many less Common Core Standard Unpacking What do these standards mean a child will know and be able to do?1.MD.4 Organize, represent, and 1.MD.4 calls for students to work with categorical data by organizing, representing and interpreting data.interpret data with up to three Students should have experiences posing a question with 3 possible responses and then work with the data thatcategories; ask and answer questions they collect.about the total number of data points,how many in each category, and how Example below:many more or less are in one category Students pose a question and the 3 possible responses.than in another. Which is your favorite flavor of ice cream? Chocolate, vanilla or strawberry? Students collect their data by using tallies or another way of keeping track. Students organize their data by totaling each category in a chart or table. 1st Grade Mathematics ● Unpacked Content page24
  25. 25. Picture and bar graphs are introduced in Second Grade. What is your favorite flavor of ice cream? Chocolate 12 Vanilla 5 Strawberry 6 Students interpret the data by comparing categories. Examples of comparisons: What does the data tell us? Does it answer our question? More people like chocolate than the other two flavors. Only 5 people liked vanilla. Six people liked Strawberry. 7 more people liked Chocolate than Vanilla. The number of people that liked Vanilla was 1 less than the number of people who liked Strawberry. The number of people who liked either Vanilla or Strawberry was 1 less than the number of people who liked chocolate. 23 people answered this question.1st Grade Mathematics ● Unpacked Content page25
  26. 26. Geometry 1.GCommon Core ClusterReason with shapes and their attributes.Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-wholerelationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives andorientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initialunderstandings of properties such as congruence and symmetry.Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. Theterms students should learn to use with increasing precision with this cluster are: shape, closed, side, attribute, two-dimensional shapes (rectangles,squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, cones, cylinders), equal shares, halves, fourths,quarters. Common Core Standards Unpacking What do these standards mean a child will know and be able to do?1.G.1 Distinguish between defining 1.G.1 calls for students to determine which attributes of shapes are defining compared to those that are non-attributes (e.g., triangles are closed and defining. Defining attributes are attributes that must always be present. Non-defining attributes are attributes thatthree-sided) versus non-defining do not always have to be present. The shapes can include triangles, squares, rectangles, and trapezoids.attributes (e.g., color, orientation,overall size) ; build and draw shapes to Asks students to determine which attributes of shapes are defining compared to those that are non-defining.possess defining attributes. Defining attributes are attributes that help to define a particular shape (#angles, # sides, length of sides, etc.). Non-defining attributes are attributes that do not define a particular shape (color, position, location, etc.). The shapes can include triangles, squares, rectangles, and trapezoids. 1.G.2 includes half-circles and quarter-circles. Example: All triangles must be closed figures and have 3 sides. These are defining attributes. Triangles can be different colors, sizes and be turned in different directions, so these are non-defining. 1st Grade Mathematics ● Unpacked Content page26
  27. 27. Student 1 Which figure is a triangle? How do you know that this it is a triangle? It has 3 sides. It’s also closed.1.G.2 Compose two-dimensional shapes 1.G.2 calls for students to compose (build) a two-dimensional or three-dimensional shape from two shapes. This(rectangles, squares, trapezoids, standard includes shape puzzles in which students use objects (e.g., pattern blocks) to fill a larger region. Studentstriangles, half-circles, and quarter- do not need to use the formal names such as ―right rectangular prism.‖circles) or three-dimensional shapes(cubes, right rectangular prisms, right Example:circular cones, and right circular Show the different shapes that you can make by joining a triangle with a square.cylinders) to create a composite shape,and compose new shapes from thecomposite shape.11 Students do not need to learn formalnames such as ―right rectangularprism.‖ Show the different shapes you can make by joining a trapezoid with a half- circle. 1st Grade Mathematics ● Unpacked Content page27
  28. 28. Show the different shapes you could make with a cube and a rectangular prism.1.G.3 Partition circles and rectangles 1.G.3 is the first time students begin partitioning regions into equal shares using a context such as cookies, pies,into two and four equal shares, describe pizza, etc... This is a foundational building block of fractions, which will be extended in future grades. Studentsthe shares using the words halves, should have ample experiences using the words, halves, fourths, and quarters, and the phrases half of, fourth of,fourths, and quarters, and use the and quarter of. Students should also work with the idea of the whole, which is composed of two halves, or fourphrases half of, fourth of, and quarter fourths or four quarters.of. Describe the whole as two of, or fourof the shares. Understand for these Example: How can you and a friend share equally (partition) this piece of paper so that you both have the same amount ofexamples that decomposing into more paper to paint a picture?equal shares creates smaller shares. 1st Grade Mathematics ● Unpacked Content page28
  29. 29. Student 1 Student 2 I would split the paper right down I would split it from corner to corner the middle. That gives us 2 halves. (diagonally). She gets half of the paper I have half of the paper and my and I get half of the paper. See, if we cut friend has the other half of the paper. here (along the line), the parts are the same size. Example: Teacher: There is pizza for dinner. Teacher: If we cut the same pizza into four What do you notice about the slices on slices (fourths), do you think the slices the pizza? would be the same size, larger, or smaller as the slices on this pizza? Student: There are two slices on the Student: When you cut the pizza into pizza. Each slice is the same size. fourths. The slices are smaller than the Those are big slices! other pizza. More slices mean that the slices get smaller and smaller. I want a slice from that first pizza!1st Grade Mathematics ● Unpacked Content page29
  30. 30. Table 1 Common addition and subtraction situations1 Result Unknown Change Unknown Start Unknown Two bunnies sat on Two bunnies were Some bunnies were sitting on the grass. Three more sitting on the grass. the grass. Three more bunnies bunnies hopped Some more bunnies hopped there. Then there there. How many hopped there. Then were five bunnies. How many Add to bunnies are on the there were five bunnies. bunnies were on the grass grass now? How many bunnies before? 2+3=? hopped over to the first ?+3=5 two? 2+?=5 Five apples were on Five apples were on the Some apples were on the the table. I ate two table. I ate some apples. table. I ate two apples. Then apples. How many Then there were three there were three apples. How Take from apples are on the apples. How many many apples were on the table now? apples did I eat? table before? ? – 2 = 3 5–2=? 5–?=3 Total Unknown Addend Unknown Both Addends Unknown2 Three red apples and Five apples are on the Grandma has five flowers. two green apples are table. Three are red and How many can she put in her Put on the table. How the rest are green. How red vase and how many in her Together/ many apples are on many apples are green? blue vase?Take Apart3 the table? 3 + ? = 5, 5 – 3 = ? 5 = 0 + 5, 5 = 5 + 0 3+2=? 5 = 1 + 4, 5 = 4 + 1 5 = 2 + 3, 5 = 3 + 21st Grade Mathematics ● Unpacked Content
  31. 31. Difference Unknown Bigger Unknown Smaller Unknown (“How many more?” (Version with “more”): (Version with “more”): version): Julie has three more Julie has three more apples Lucy has two apples. apples than Lucy. Lucy than Lucy. Julie has five Julie has five apples. has two apples. How apples. How many apples does How many more many apples does Julie Lucy have? apples does Julie have have? than Lucy? (Version with “fewer”): (Version with “fewer”): Lucy has 3 fewer apples than Compare4 (“How many fewer?” Lucy has 3 fewer apples Julie. Julie has five apples. version): than Julie. Lucy has two How many apples does Lucy Lucy has two apples. apples. How many have? Julie has five apples. apples does Julie have? 5 – 3 = ?, ? + 3 = 5 How many fewer 2 + 3 = ?, 3 + 2 = ? apples does Lucy have than Julie? 2 + ? = 5, 5 – 2 = ?2 These take apart situations can be used to show all the decompositions of a given number. The associated equations,which have the total on the left of the equal sign, help children understand that the = sign does not always meanmakes or results in but always does mean is the same number as.3 Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown isa productive extension of this basic situation, especially for small numbers less than or equal to 10.4 For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version usingmore for the bigger unknown and using less for the smaller unknown). The other versions are more difficult.1 Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).1st Grade Mathematics ● Unpacked Content page31

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