1st Grade ADDITION and SUBTRACTION Standards
*with some bonus standards for measurement, coins, and data analysis
1.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
A. Apply mathematics to problems arising in everyday life, society, and the workplace;
B. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
C. Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
D. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
E. Create and use representations to organize, record, and communicate mathematical ideas.
F. Analyze mathematical relationships to connect and communicate mathematical ideas;
G. Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication;
1.2 Number and operations. The student applies mathematical process standards to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:
A. Recognize instantly the quantity of structured arrangements.
1.3 Number and operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to:
A. Use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99;
B. Use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] – 3;
C. Compose 10 with two or more addends with and without concrete objects;
D. Apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10;
E. Explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences;
F. Generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20.
1.4 Number and operations. The student applies mathematical process standards to identify coins, their values, and the relationships among them in order to recognize the need for monetary transactions. The student is expected to:
A. Identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them;
B. Write a number with the cent symbol to describe the value of a coin; and
C. Use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes.
1.5 Algebraic reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:
B. Skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set;
C. Use relationships to determine the number that is 10 more and 10 less than a given number up to 120;
D. Represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences;
E. Understand that the equal sign represents a relationship where expressions on each side of the equal sign represent the same value(s);
F. Determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation; and
G. Apply properties of operations to add and subtract two or three numbers.
1.6 Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:
H. Identify examples and non-examples of halves and fourths.
1.7 Geometry and measurement. The student applies mathematical process standards to select and use units to describe length and time. The student is expected to:
A. Use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement;
B. Illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other;
C. Measure the same object/distance with units of two different lengths and describe how and why the measurements differ;
D. Describe a length to the nearest whole unit using a number and a unit.
1.8 Data analysis. The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to:
B. Use data to create picture and bar-type graphs; and
C. Draw conclusions and generate and answer questions using information from picture and bar-type graphs.
Operations & Algebraic Thinking:
Represent and solve problems involving addition and subtraction.
1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Understand and apply properties of operations and the relationship between addition and subtraction.
1.OA.B.3 Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
1.OA.B.4 Understand subtraction as an unknown addend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8.
Add and subtract within 20.
1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Work with addition and subtraction equations.
1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ 3, 6 + 6 = _.
Number & Operation in Base Ten:
Understand place value.
1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
1.NBT.B.2.A 10 can be thought of as a bundle of ten ones — called a "ten."
1.NBT.B.2.B The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
1.NBT.B.2.C The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
Use place value understanding and properties of operations to add and subtract.
1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
1.NBT.C.4 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
1.NBT.C.5 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), 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 and explain the reasoning used.
Measure lengths indirectly and by iterating length units.
1.MD.A.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.
1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Represent and interpret data.
1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
Reason with shapes and their attributes.
1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.