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Operations and Algebraic Thinking Represent and solve problems. NC.1.OA.1 Represent and solve addition and subtraction word problems, within 20, with unknowns, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem, when solving: • Add to/Take from-Change Unknown • Put together/Take Apart-Addend Unknown • Compare-Difference Unknown Clarification Checking for Understanding In this standard, students extend their work from NC.K.OA.1 to solve addition and subtraction problems within 20. In addition to continuing work with the problem types introduced in Kindergarten, standard NC.1.OA.1 calls for first graders to work additional problem types, including: • add to/take from – change unknown • put together/take apart – addend unknown • compare – difference unknown Result Unknown Change Unknown Add To Two birds sat in a tree. Three more birds fly to the tree. How many birds are in the tree now? 2 + 3 = ? Two birds sat in a tree. Some more birds flew there. Then there were five birds in the tree. How many birds flew over to the first two? 2 + ? = 5 Take From Five birds were in a tree. Two birds flew away. How many birds are in the tree now? 5 – 2 = ? Five birds were in a tree. Some flew away. Then there were three birds in the tree. How many birds flew away? 5 - ? = 3 Total Unknown Addend Unknown Both Addends Unknown Put Together/ Take Apart Three red birds and two blue birds are in a tree. How many birds are in the tree? 3 + 2 = ? Five birds are in a tree. Three are red and the rest are blue. How many birds are blue? 3 + ? 5 5 – 3 = ? Five birds are in a tree. They could either be blue birds or red birds. How many birds could be red and how many could be blue? 5 = 0 + 5 5 = 5 + 0 5 = 1 + 4 5 = 4 + 1 5 = 2 + 3 5 = 3 + 2 As students develop strategies for solving a variety of problem situations, they build meaning for the operations of addition and subtraction. Nine bunnies were sitting on the grass. Some more bunnies hopped there. Now, there are 13 bunnies on the grass. How many bunnies hopped over there? Possible response: Counting On: Niiinnneee…. holding a finger for each next number counted 10, 11, 12, 13. Holding up her four fingers, 4! 4 bunnies hopped over there.” 13 apples are on the table. 6 of them are red and the rest are green. How many apples are green? Possible response: Doubles +/- 1 or 2: I know that 6 and 6 is 12. So, 6 and 7 is K 13. There are 7 green apples. K 1 1 K 1 K North Carolina Department of Public Instruction 1 5 st Grade Unpacking Document Rev. June 2018 Represent and solve problems. NC.1.OA.1 Represent and solve addition and subtraction word problems, within 20, with unknowns, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem, when solving: • Add to/Take from-Change Unknown • Put together/Take Apart-Addend Unknown • Compare-Difference Unknown Clarification Checking for Understanding Change unknown and addend unknown problems allow students to begin to see subtraction as the opposite of addition. Developing the understanding of subtraction as an unknown addend addition problem is an essential goal for later mathematics. As students work with change unknown and addend unknown problems, they will record situation equations (equations in which the operation and order of numbers matches the situation of the problem). Eventually, students notice that a problem may be solved with other solution equations (equations that lead to the answer, but do not match the situation of the story). In a Compare situation, two amounts are compared to find “How many more” or “How many less/fewer”. Students build on their understanding of equal to, more than, and less than for two groups of objects or two numbers. Strategies for determining which the difference in quantities include matching and counting. As First Graders work with a variety of problem types, they extend the sophistication of addition and subtraction methods used in Kindergarten (counting). Now, students use methods of counting on, making ten, and doubles +/- 1 or +/- 2 to solve problems. Students also use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths). In order for students to read and use equations to represent their thinking, they need extensive experiences with addition and subtraction situations in order to connect the experiences with symbols (+, -, =) and equations (5=3+2). In Kindergarten, students demonstrated the understanding of how objects can be joined (addition) and separated (subtraction) by representing addition and subtraction situations using objects, pictures and words. In First Grade, students extend this understanding of addition and subtraction situations to use the addition symbol (+) to represent joining situations, the subtraction symbol (-) to represent separating situations, and the equal sign (=) to represent a relationship regarding quantity between one side of the equation and the other. When solving comparison problems, students may write various equations to represent comparisons. Return to Standards North Carolina Department of Public Instruction 1 6 st Grade Unpacking Document Rev. June 2018 Number and Operations in Base Ten Extend and recognize patterns in the counting sequence NC.1.NBT.1 Count to 150, starting at any number less than 150. Clarification Checking for Understanding This standard calls for students to rote count from a given number without having to go back and start at one. Students should develop accurate counting strategies that build on the 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). This skill builds from counting work in Kindergarten, and serves as a prerequisite skill for counting on to add. The focus of this standard is rote counting only, and does not require recognition of numerals or writing numerals. Sample Student Interview: Teacher: Begin at 88 and count up to 102 Student: 88, 89…umm…90, 91, 92, 93, 94, 95, 96, 97, 98, 99…umm…100, 101 Teacher: I noticed you paused to think at 89. How did you figure out the next number? Student: After each number that ends in 9, comes a number that ends in 0. So, I remembered the next number is 90. Return to Standards Understand place value. NC.1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. • Unitize by making a ten from a collection of ten ones. • Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. • Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens, with 0 ones. Clarification Checking for Understanding The focus of this standard is to build place value understanding through tens. First Grade students extend their work from Kindergarten when they composed and decomposed numbers from 11 to 19 into ten ones and some further ones. In Kindergarten, everything was thought of as individual units, “ones”. In First Grade, students are asked to unitize those ten individual ones as a whole unit: “one ten”. Students are introduced to the idea that a bundle of ten ones is called “a ten”. This is known as unitizing. Students in first grade explore the idea that the teen numbers (11 to 19) can be expressed as one ten and some leftover ones. When students unitize a group of ten ones as a whole unit (“a ten”), they are able to count groups as though they were individual objects. For example, 4 trains of ten cubes each have a value of 10 and would be counted as 40 ones or as 4 tens. This can often be challenging for young children to consider a group of something as “one” when all previous experiences have been counting single objects. This is the foundation of the place value system and requires time and rich experiences with concrete manipulatives to develop. In addition, when learning about forming groups of 10, students learn that a numeral can stand for many different amounts, depending on its position or Here is a pile of 12 cubes. Do you have enough to make a ten? Would you have any leftover? If so, how many leftovers would you have? Student A: I filled a ten frame to make a ten and had two counters left over. The number 12 has 1 ten and 2 ones. Student B: I counted out 12 cubes. I had enough to make 10. I now have 1 ten and 2 cubes left over. The number 12 has 1 ten and 2 ones. Are the number 19 and 91 the same or different? (19 91) Teacher: Are these numbers the same or different? Students: Different! Teacher: Why do you think so? North Carolina Department of Public Instruction 1 7 st Grade Unpacking Document Rev. June 2018 Understand place value. NC.1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. • Unitize by making a ten from a collection of ten ones. • Model the numbers from 11 to 19 as composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. • Demonstrate that the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens, with 0 ones. Clarification Checking for Understanding place in a number. This is an important realization as young children begin to work through reversals of digits, particularly in the teen numbers. Students apply their understanding of groups of ten to decade numbers (e.g. 10, 20, 30, 40). As they work with groupable objects, students understand that 10, 20, 30…80, 90 are comprised of a certain amount of groups of tens with none left-over. A deep understanding of place value is developed over time as students have ample experiences with a variety of groupable materials (i.e., materials that can be grouped, snapped, or connected to make a ten). Pre-grouped materials (i.e., materials like base ten blocks and bean sticks, which must be traded to make a ten) are not introduced until a student has a firm understanding of composing and decomposing ten. Additionally, students should have access to proportional manipulatives, meaning the size of “ten” is ten times bigger than one single manipulative. Coins could cause a misconception with regards to developing an understanding of place value. Student A: Even though they both have a one and a nine, I know the 1 in 19 represents one group of ten. The 1 in 91 represents 1 one. Student B: I know the 9 in 91 represents nine groups of tens. The 9 in 19 represents 9 ones. Return to Standards Understand place value. NC.1.NBT.3 Compare two two-digit numbers based on the value of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Clarification Checking for Understanding In this standard, students use their understanding of groups and order of digits to compare two numbers by examining the amount of tens and ones in each number. After numerous experiences verbally comparing two sets of objects using comparison vocabulary (e.g., 42 is more than 31. 23 is less than 52, 61 is the same amount as 61.), first grade students connect the vocabulary to the symbols: greater than (>), less than (<), equal to (=). Compare these two numbers. 42 __ 45 Possible responses: Student A 42 has 4 tens and 2 ones. 45 has 4 tens and 5 ones. They have the same number of tens, but 45 has more ones than 42. So, 42 is less than 45. 42 < 45 Student B 42 is less than 45. I know this because when I count up I say 42 before I say 45. 42 < 45 91 19 North Carolina Department of Public Instruction 1 8 st Grade Unpacking Document Rev. June 2018 Measurement and Data Strand Represent and interpret data NC.1.MD.4 Organize, represent, and interpret data with up to three categories. • Ask and answer questions about the total number of data points. • Ask and answer questions about how many in each category. • Ask and answer questions about how many more or less are in one category than in another. Clarification Checking for Understanding In this standard, students collect and use categorical data (e.g., eye color, shoe size, age) to answer a question. The data collected are organized in a chart or table. Once the data are collected, students interpret the data to answer a question. Students are also expected to describe the data noting particular aspects such as the total number of answers, which category had the most/least responses, and interesting differences/similarities between the categories. New to Grade 1, students are expected to answer questions about how many more and how many less are in one category than in another. These should all be one-step problems limited to numbers within 20. The question, “What is your favorite flavor of ice cream?” is posed. The categories chocolate, vanilla and strawberry are determined as anticipated responses and written down on the recording sheet. When asking each classmate about their favorite flavor, the student’s name is written in the appropriate category. Once the data are collected, the student counts up the amounts for each category and records the amount. The student then analyzes the data by carefully looking at the data and writes 3 sentences about what they notice about the data. Possible response: Return to Standards