OREGON MATH STANDARDS (2021): [1.OA]
Overview
The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.
Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.
2021 Oregon Math Guidance: 1.OA.A.1
Cluster: 1.OA.A - Represent and solve problems involving addition and subtraction.
STANDARD: 1.OA.A.1
Standards Statement (2021):
Use addition and subtraction within 20 to solve and represent problems in authentic contexts involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
1.OA.D.8, K.OA.A.1, K.OA.A.2 | 1.OA.A.2, 2.OA.A.1 | 1.DR.B.2 | 1.OA.A.1 1.OA.A Crosswalk |
Standards Guidance:
Clarifications
- Students should be given opportunities to use mental reasoning to solve problems involving number strings within 20.
- Students should also solve problem situations with an unknown in all positions.
- Students recognize and represent taking from, taking apart, and comparing situations as either subtraction or addition with a missing addend.
Boundaries
- Students should not be encouraged to use key/clue words because they will not work with subsequent problem types.
- The unknown quantity should be represented in all positions.
Terminology
- Addition and Subtraction Situations by Grade Level are presented in Table 1 pictured here, which include:
- adding to,
- taking from,
- putting together, taking apart, and
- comparing, with unknowns in all positions.
- Please reference pages 9 and 14 in the Progression document for additional information.
Teaching Strategies
- Symbols can be used to represent unknown amounts in equations.
- Use the relationship between addition and subtraction within 20 (knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (6 + 7 is the same as 6 + 6 + 1 = 12 + 1 = 13).
- Students should be provided with learning experiences to develop strategies such as:
- Advanced Counting; Counting On, Making Ten, Decomposing a number leading to a ten
- Counting All: 5 + 2 = . The student counts five counters. The student adds two more. The student counts 1, 2, 3, 4, 5, 6, 7 to get the answer.
- Counting Back: 12 – 3 = . The student counts twelve counters. The student removes a counter and says 11, removes another counter and says 10, and removes a third counter and says 9. The student knows the answer is 9 since they counted back 3.
Examples
- Represent addition and subtraction word problems using objects, drawings, and equations. Write an addition or subtraction equation with a symbol for the unknown number in different position, such as:
- 13 + 5 = n, 13 - 5 = n, 13 + n= 18, 18 - n= 13.
- Recognize and represent adding to and putting together situations as addition.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 1.OA.A.2
Cluster: 1.OA.A - Represent and solve problems involving addition and subtraction.
STANDARD: 1.OA.A.2
Standards Statement (2021):
Solve problems that call for addition of three whole numbers whose sum is less than or equal to 20 using objects, drawings or equations.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
1.OA.A.1 | N/A | 1.DR.B.2 | 1.OA.A.2 1.OA.A Crosswalk |
Standards Guidance:
Clarifications
- Students should understand subtraction as an unknown-addend problem.
- Students are not expected to know nor use the term inverse.
Terminology
- The terms below are used to clarify expectations for the teaching professional. Students are not required to use this terminology when engaging with the learning objective.
- Addend – a number that is added to another number in an addition expression or equation. For example, in the expression 5 + 8, 5 and 8 are both addends.
- An inverse relationship shows the relationship between addition and subtraction where addition can be used to find the quantity of a set after some in the set are removed. For example, 3+2 = 5 is related to 5 - 3 = 2 because of the inverse relationship.
Boundaries
- Problems should be within 20.
Examples
- Solve word problems by using objects, drawings or equations to represent the quantities in the problem.
- Solve word problems with an equation where a symbol stands for the unknown. For example, 5 + 4 + 6 = ___.
- Understand that objects, drawings, and equations are interchangeable representations of a story problem.
- There are 14 birds in the tree. 8 of them flew away. How many birds are left in the tree?
- The student thinks of 14 – 8 = as 8 + = 14
- Jenny had 10 pencils and gave some to Eric. Jenny now has 8 pencils. How many pencils did she give to Eric?
- The student thinks of 10 - = 8 as + 8 = 10
- Illustrative Mathematics:
2021 Oregon Math Guidance: 1.OA.B.3
Cluster: 1.OA.B - Understand and apply properties of operations and the relationship between addition and subtraction.
STANDARD: 1.OA.B.3
Standards Statement (2021):
Apply properties of operations as strategies to add and subtract.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
K.OA.A.2 | 1.OA.C.6 | 2.NBT.B.9, 3.NBT.A.2 | 1.OA.B.3 1.OA.B Crosswalk |
Standards Guidance:
Clarifications
- Students should solve problem situations with an unknown in all positions.
- Understand that numbers can be added flexibly.
- Students do not necessarily have to justify their representations or solution using properties, but they can begin to learn to recognize these properties in action and discuss their use after solving. (Please reference page 15 in the Progression document)
Boundaries
- Students should not be encouraged to use key/clue words because they will not work with subsequent problem types.
- The unknown quantity should be represented in all positions.
- The terminology above is used to clarify expectations for the teaching professional. Students are not required to use this terminology when engaging with the learning objective.
Terminology
- Properties of operations used as strategies include:
- Commutative property of addition: For example, if 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.
- Associative property of addition: For example, add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
- Addend – any number that is added to another number in an addition expression or equation. For example, in the expression 7 + 3, 7 and 3 are addends.
Examples
- Illustrative Mathematics:
2021 Oregon Math Guidance: 1.OA.B.4
Cluster: 1.OA.B - Understand and apply properties of operations and the relationship between addition and subtraction.
STANDARD: 1.OA.B.4
Standards Statement (2021):
Understand subtraction as an unknown-addend problem.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
K.OA.A.2 | 1.OA.C.6 | 2.NBT.B.9, 3.NBT.A.2 | 1.OA.B.4 1.OA.B Crosswalk |
Standards Guidance:
Teaching Strategies
- Restate a subtraction problem as a missing addend problem using the relationship between addition and subtraction.
- Recognize the inverse relationship between subtraction and addition within 20 and use this inverse relationship to solve real-life problems.
Progressions
- Put Together/Take Apart problems with Addend Unknown afford students the opportunity to see subtraction as the opposite of addition in a different way than as reversing the action, namely as finding an unknown addend.
- The meaning of subtraction as an unknown-addend addition problem is one of the essential understandings students will need in middle school in order to extend arithmetic to negative rational numbers. (Please reference page 13 in the Progression document).
Examples
- Subtract 10 – 8 by finding the number that makes 10 when added to 8.
- Understand that subtraction is equivalent to an unknown-addend problem because both ask for the unknown part in a situation where the total and another part are known.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 1.OA.C.5
Cluster: 1.OA.C - Add and subtract within 20.
STANDARD: 1.OA.C.5
Standards Statement (2021):
Relate counting to addition and subtraction.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
K.NCC.B.4 | 1.OA.C.6 | N/A | 1.OA.C.5 1.OA.C Crosswalk |
Standards Guidance:
Clarifications
- Students should be able to relate counting to addition and subtraction by counting all, counting on, and counting back when making sense of contextual addition and subtraction problems within 20.
Teaching Strategies
- Students should understand how addition and subtraction relate by solving situations in context.
- Students should use strategies to count up, count back, etc., to model this relationship on tools such as ten frames, rekenreks, number lines (predetermined and open), etc.
- Relate counting on to addition. For example, recognize counting on two after 15 as solving 15+2.
- Relate counting back to subtraction. For example, recognize counting back two from 15 as solving 15-2.
- Relate counting between two numbers to finding their difference. For example, recognize counting two number between 15 and 17 as solving 17-15.
Progression
- Unlike counting down, counting on reinforces that subtraction is an unknown-addend problem. Learning to think of and solve subtractions as unknown addend problems makes subtraction as easy as addition (or even easier), and it emphasizes the relationship between addition and subtraction. (Please reference page 20 in the Progression document).
Examples
- When students count on 3 from 4, they should write this as 4+3=7.
- When students count on for subtraction, 3 from 7, they should connect this to 7−3=4. Students write "7−3= ?” and think “I count on 3+ ?=7.”
- Illustrative Mathematics:
2021 Oregon Math Guidance: 1.OA.C.6
Cluster: 1.OA.C - Add and subtract within 20.
STANDARD: 1.OA.C.6
Standards Statement (2021):
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 with accurate, efficient, and flexible strategies.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
K.OA.A.2, K.OA.A.3, K.OA.A.4, K.OA.A.5, 1.OA.C.5, 1.OA.B.4, 1.OA.B.3 | 2.OA.B.2 | 1.NBT.C.4 | 1.OA.C.6 1.OA.C Crosswalk |
Standards Guidance:
Terminology
- Fluently/Fluency – To achieve fluency, students should be able to choose flexibly among methods and strategies to solve mathematical problems accurately and efficiently.
- Accuracy includes attending to precision.
- Efficiency includes using well-understood strategy with ease.
- Flexibility involves using strategies such as making 5 or making 10.
Boundaries
- Fluency does not lend itself to timed tests or speed.
Progression
- Students might use the commutative property of addition to change ? + 6 = 15 to 6 + ? = 15, then count on or use methods to compose 4 (to make ten) plus 5 (ones in the 15) to find 9.
- Students might reverse the action in the situation represented by ? - 6 = 9 so that is becomes 9 + 6 = ?. Or they might use their knowledge that the total is the first number in a subtraction equation and the last number in an addition equation to rewrite the situation equation as a solution equation: ? - 6 = 9 becomes 9 + 6 = ? or 6 + 9 = ?. (Please reference page 16 in the Progression document).
Examples
- Use strategies such as counting on; making ten, for example 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14; decomposing a number leading to a ten for example, 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9;
- Use the relationship between addition and subtraction, for example, knowing that 8 + 4 = 12, one knows 12 – 8 = 4;
- Create equivalent but easier or known sums, for example, adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 1.OA.D.7
Cluster: 1.OA.D - Work with addition and subtraction equations.
STANDARD: 1.OA.D.7
Standards Statement (2021):
Use the meaning of the equal sign to determine whether equations involving addition and subtraction are true or false.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
N/A | 1.OA.D.8, 2.OA.C.3, 2.OA.C.4 | N/A | 1.OA.D.7 1.OA.D Crosswalk |
Standards Guidance:
Clarifications
- Students should explore and explain the relationship of the equal sign to quantities and orally justify if equations involving addition and subtraction are “true” (equal) or “false” (not equal).
Teaching Strategies
- Use the meaning of the equal sign (“is the same as”) to determine if two expressions involving a whole number and/or addition or subtraction expressions are equivalent.
Examples
- Determine if the equation is true or false, for example determining that 3-1 = 2+3 is false because the expressions do not have equal values.
- Which of the following equations are true and which are false? How do you know?
- 6 = 6 (True/Correct Statement)
- 7 = 8 – 1 (True/Correct Statement)
- 5 + 2 = 2 + 5 (True/Correct Statement)
- 4 + 1 = 5 + 2 (False/Incorrect Statement)
- Illustrative Mathematics:
2021 Oregon Math Guidance: 1.OA.D.8
Cluster: 1.OA.D - Work with addition and subtraction equations.
STANDARD: 1.OA.D.8
Standards Statement (2021):
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
1.OA.D.7 | 1.OA.A.1 | N/A | 1.OA.D.8 1.OA.D Crosswalk |
Standards Guidance:
Clarifications
- Determine the unknown whole number relating three whole numbers, with the unknown in any position.
Teaching Strategies
- Symbols can be used to represent unknown amounts in equations.
Progressions
- Students advancement of methods can be clearly seen in the context of situations with unknown addends. These are the situations that can be represented by an addition equation with one unknown addend, e.g., 9 + = 13. Students can start solving for some unknown addend problems by trial and error or by knowing the relevant decomposition of the total. But a more advanced counting on solution involves seeing the 9 as part of 13, and understanding that counting the 9 things can be “taken as done” if we begin the count from 9. (Please reference page 14 in the Progression document).
Examples
- Students should be given the opportunity to find missing part given a known part and total, such as:
- A missing addend in an addition equation, for example 3+_=5.
- A missing subtrahend in a subtraction equation, for example 5-_=2.
- A missing difference in a subtraction equation, for example 5-3=_
- Students should be given the opportunity to find missing totals given known parts, such as:
- A missing sum in an addition equation, for example 3+2=_.
- A missing minuend in a subtraction equation, for example _-2=3.
- Determine the unknown number that makes the equation true in each of the equations: 8 + ? = 10, 5 = – 3, 3 + 4 = ∆. These are some possible ways to record equations that indicate an unknown number.
- Illustrative Mathematics:
- Student Achievement Partners: