OREGON MATH STANDARDS (2021): [2.NBT]
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: 2.NBT.A.1
Cluster: 2.NBT.A - Understand place value.
STANDARD: 2.NBT.A.1
Standards Statement (2021):
Understand 100 as a bundle of ten tens and that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
1.NBT.B.2, 2.NBT.A.2 | 2.NBT.A.3, 2.NBT.A.4, 2.NBT.B.6, 2.NBT.B.7, 2.NBT.B.8, 3.NBT.A.1, 3.NBT.A.3, 4.NBT.A.1 | N/A | 2.NBT.A.1 2.NBT.A Crosswalk |
Standards Guidance:
Clarifications
- Students should be able to put together (compose) and break apart (decompose) three-digit numbers.
- Students should have multiple opportunities use concrete materials to develop an understanding of the place value structures, the relationship between numbers, and the value of quantities.
Teaching Strategies
- Students should be given the opportunity to discover base-ten units can be broken down and built back up in different ways. For example, understand the number 706 can be represented as:
- 7 hundreds, 0 tens, and 6 ones where a 0 is used as a placeholder.
- 70 tens and 6 ones.
- 706 ones.
- Students should be able to explain that a bundle of ten 10s is equal to 100.
Progressions
- This content lays the groundwork for understanding the structure of the base-ten system as based in repeated bundling in groups of 10 and understanding that the unit associated with each place is 10 of the unit associated with the place to its right. (Please reference page 8 in the Progression document).
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 2.NBT.A.2
Cluster: 2.NBT.A - Understand place value.
STANDARD: 2.NBT.A.2
Standards Statement (2021):
Count within 1000; skip-count by 5's, 10's, and 100's.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
N/A | 2.NBT.A.1 | 2.OA.C.3 | 2.NBT.A.2 2.NBT.A Crosswalk |
Standards Guidance:
Teaching Strategies
- Students need to be provided the opportunity to count and skip count both forward and backward starting from any number within 1000 to notice patterns within the number system.
- Students should explore patterns on a hundred-chart, starting from a given number 10-90.
- Students should be able to use coins to count, including nickels, dimes, quarters, and dollars. Half-dollars may also be used, if available.
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 2.NBT.A.3
Cluster: 2.NBT.A - Understand place value.
STANDARD: 2.NBT.A.3
Standards Statement (2021):
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.NBT.A.1 | 4.NBT.A.2 | N/A | 2.NBT.A.3 2.NBT.A Crosswalk |
Standards Guidance:
Boundaries
- Students should be able to represent a quantity from word form.
Teaching Strategies
- Representations should include concrete materials (i.e., base ten blocks, counters, etc.), base ten numerals, words, expanded form, and pictures.
Progressions
- Representations such as manipulative materials, math drawings, and layered three-digit place value cards afford connections between written three-digit numbers and hundreds, tens, and ones...
- Unlayering three-digit place value cards... reveals the expanded form of the number.
Examples
- The number 706 in base-ten numerals is represented as 7 hundreds, 0 tens, and 6 ones, in number names is represented as "seven hundred six" and in expanded form is represented as 700 + 6.
- The number two-hundred forty-one written in standard form is 241 and in expanded form is 200+40+1.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 2.NBT.A.4
Cluster: 2.NBT.A - Understand place value.
STANDARD: 2.NBT.A.4
Standards Statement (2021):
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
1.NBT.B.3, 2.NBT.A.1 | 4.NBT.A.2 | N/A | 2.NBT.A.4 2.NBT.A Crosswalk |
Standards Guidance:
Teaching Strategies
- Tools such as a hundred chart and visual number lines may be used to help students compare three digit numbers.
Progressions
- Comparing magnitude of three-digit numbers uses the understanding that 1 hundred (the smallest three-digit number) is greater than any amount of tens and ones represented by a two-digit number. For this reason, three-digit numbers are compared by first inspecting the hundreds place (e.g., 845 > 799; 849 < 855). Drawings help support these understandings. (Please reference page 8 in the Progression document).
Examples
- Students should be given the opportunity to provide explanations of their results based on their understanding of place value, for example:
- 2 hundreds + 3 ones > 5 tens + 9 ones
- 9 tens + 2 hundreds + 4 ones < 924
- 456 < 5 hundreds
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 2.NBT.B.5
Cluster: 2.NBT.B - Use place value understanding and properties of operations to add and subtract.
STANDARD: 2.NBT.B.5
Standards Statement (2021):
Fluently add & subtract within 100 using accurate, efficient, & flexible strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
1.NBT.C.4, 1.NBT.C.5, 1.NBT.C.6, 2.OA.B.2 | 3.NBT.A.2 | 2.OA.A.1 | 2.NBT.B.5 2.NBT.B Crosswalk |
Standards Guidance:
Terminology
- This standard uses the word fluently, which means accuracy, efficiency (using a reasonable amount of steps and time), and flexibility (using strategies such as the distributive property or partial sums).
- Fluently/Fluency – To achieve fluency, students should be able to choose flexibly among methods and strategies to solve mathematical problems accurately and efficiently.
Boundaries
- Students should be given multiple opportunities to solve contextual, mathematical problems as they work to build fluency.
- The sum of the number should be no greater than 100.
Progressions
- Students should be able to use numerical reasoning to solve contextual, mathematical problems involving all problem types.
Examples
- Students should move from count all toward strategies that are efficient, accurate, and flexible based on the math situation presented. For example:
- 56+38 = 50+30+6+8 = 80+14 = 94
- 56+38 = 54+2+38 = 54+40 = 94
- 56-38 can be thought of as 38+x = 56
- Student Achievement Partners:
2021 Oregon Math Guidance: 2.NBT.B.6
Cluster: 2.NBT.B - Use place value understanding and properties of operations to add and subtract.
STANDARD: 2.NBT.B.6
Standards Statement (2021):
Add up to four two-digit numbers using strategies based on place value and properties of operations and describe how two different strategies result in the same sum.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.NBT.A.1, 2.NBT.B.7 | 3.NBT.A.2 | N/A | 2.NBT.B.6 2.NBT.B Crosswalk |
Standards Guidance:
Clarifications
- Students should investigate repeating patterns to make predictions and build algebraic reasoning.
- Patterns may include exposure to even and odd.
- Students should be using any tools available such as a number line, hundred-chart, 99-chart, etc., to create and analyze the patterns.
- Patterns should be extended from 1st grade, where they explore intervals of 1s, 2s, 5s, and 10s, to also include intervals of 25s and 100s.
Boundaries
- Patterns involving addition and subtraction should include sums within 1,000 through models and representations.
- Problems presented may include money as a context.
Teaching Strategies
- Students should be given the opportunity to use a variety of strategies to identify, describe, and create numerical patterns.
- Students describe how two different strategies result in the same sum
Progressions
- Problems should be presented through contexts to provide students with the opportunity to make sense of the mathematics.
- This work affords opportunities for students to see that they may have to compose more than one ten, and as many as three new tens. (Please reference page 11 in the Progression document).
Examples
- Students should be given the opportunity to connect representations. For example:
- 42 + 31 + 12 + 83 may be decomposed into tens and ones to add 40 + 30 + 10 + 80 and then 2 + 1 + 2 + 3.
- 42+31= 73 and 12+83= 95 so 73+95= 168.
- Start with 3 and jump by 5s to create a pattern. Change the start number and create another pattern. What do you notice about the two patterns? How did they change?
- Illustrative Mathematics:
2021 Oregon Math Guidance: 2.NBT.B.7
Cluster: 2.NBT.B - Use place value understanding and properties of operations to add and subtract.
STANDARD: 2.NBT.B.7
Standards Statement (2021):
Add and subtract within 1000 using concrete or visual representations 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 why sometimes it is necessary to compose or decompose tens or hundreds.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.NBT.A.1 | 2.NBT.B.6, 2.NBT.B.8, 2.NBT.B.9, 3.NBT.A.2 | N/A | 2.NBT.B.7 2.NBT.B Crosswalk |
Standards Guidance:
Teaching Strategies
- Students should be encouraged to use place value language such as hundreds, tens and ones, when connecting their representation to their explanation.
- Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Progressions
- Drawings can support students in explaining [methods for addition within 1000] how addends can be decomposed into their base-ten units (e.g. hundreds, tens, and ones).
- The drawing below shows the base-ten units of 278 and 147. Like units are shown together, with boundaries drawn around the newly composed hundred and the newly composed ten. The newly composed units could also be indicated by crossing out grouped units and drawing the next highests unit (e.g. crossing out the group of ten ones and drawing a single ten).
- The putting together of quick drawings can illustrate adding adding like units as specified in 2.NBT.[B.]7: add ones to ones, tens to tens, and hundreds to hundreds. (Please reference pages 9 and 10 in the Progression document)
Examples:
- Students may use equations to represent their strategies based on place value such as: 324+515=(300+500)+(20+10)+(4+5)=839.
- Illustrative Mathematics:
2021 Oregon Math Guidance: 2.NBT.B.8
Cluster: 2.NBT.B - Use place value understanding and properties of operations to add and subtract.
STANDARD: 2.NBT.B.8
Standards Statement (2021):
Without having to count, mentally find 10 more or 10 less and 100 more or 100 less than a given three-digit number.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.NBT.A.1, 2.NBT.B.7 | 3.NBT.A.2 | N/A | 2.NBT.B.8 2.NBT.B Crosswalk |
Standards Guidance:
Boundaries
- Mental addition and subtraction is limited to adding or subtracting by 10 or 100 for numbers between 100-900.
Teaching Strategies
- Add and subtract within 1000 using properties of operations and/or the relationship between addition and subtraction, including mentally adding or subtracting 10 or 100 to a given number;
- Relate the strategies used to a written method.
- Tools such as a hundred chart and visual number lines may be used to help students discover the patterns of ten more and ten less.
Examples
- Illustrative Mathematics:
2021 Oregon Math Guidance: 2.NBT.B.9
Cluster: 2.NBT.B - Use place value understanding and properties of operations to add and subtract.
STANDARD: 2.NBT.B.9
Standards Statement (2021):
Explain why strategies to add and subtract work using properties of operations and the relationship between addition and subtraction.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.NBT.B.7 | 3.NBT.A.2 | 1.OA.B.3 | 2.NBT.B.9 2.NBT.B Crosswalk |
Standards Guidance:
Clarification
- Provide many activities that will help students develop a strong understanding of number relationships, addition and subtraction so they can develop, share and use efficient strategies for computation.
- Students gain computational fluency, using efficient and accurate methods for computing, as they come to understand the role and meaning of arithmetic operations in number systems.
Teaching Strategies
- Explanations may be supported by drawings or objects.
- Make anchor charts/posters for student-developed mental strategies for addition and subtraction within 20.
- Use names for the strategies that make sense to the students and include examples of the strategies (e.g. making ten, doubling, etc).
Examples
- A student uses number talk to say “I know that 9 plus 4 equals 13. So 13 minus 9 equals 4”.
- When presented the problem, 4 + 8 + 6, the student uses number talk to say “I know 6 + 4 = 10, so I can add 4 + 8 + 6 by adding 4 + 6 to make 10 and then add 8 to make 18.”