OREGON MATH STANDARDS (2021): [4.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: 4.NBT.A.1
Cluster: 4.NBT.A - Generalize place value understanding for multi-digit whole numbers.
STANDARD: 4.NBT.A.1
Standards Statement (2021):
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
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, 4.NBT.A.3, 4.NBT.B.4, 4.NBT.B.5, 4.NBT.B.6, 5.NBT.A.1 | N/A | 4.NBT.A.1 4.NBT.A Crosswalk |
Standards Guidance:
Clarifications
- Students should be able to use numerical reasoning to represent and explain using concrete materials, the relationship among the numbers 1, 10, 100, and 1,000. Students should be able to extend the pattern to the hundred-thousands place.
- Students should be able to recognize the relationship of same digits located in different places in a whole number.
Boundaries
- Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Progressions
- In the base-ten system, the value of each place is 10 times the value of the place to the immediate right. Because of this, multiplying by 10 yields a product in which each digit of the multiplicand is shifted one place to the left.
- Each of the 3 [groups of] tens becomes a hundred and moves to the left. In the product, the three in the tens place of 30 is shifted one place to the left to represent three hundreds. In 300 divided by 10 the 3 is shifted one place to the right in the quotient to represent three tens. (Please reference page 13 in the Progression document).
Examples
- Recognize that 700 ÷ 70 = 10 by applying concepts of place value and division
- The population of Atlanta is about 500,000 people and the population of Valdosta is about 50,000 people. How many times greater is the population of Atlanta than Valdosta?
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 4.NBT.A.2
Cluster: 4.NBT.A - Generalize place value understanding for multi-digit whole numbers.
STANDARD: 4.NBT.A.2
Standards Statement (2021):
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Use understandings of place value within these forms to compare two multi-digit numbers using >, =, and < symbols.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
2.NBT.A.3, 2.NBT.A.4, 4.NBT.A.1 | 4.NBT.A.3, 5.NBT.A.1, 5.NBT.A.3 | N/A | 4.NBT.A.2 4.NBT.A Crosswalk |
Standards Guidance:
Boundaries
- Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
- Students are not expected to write numbers in word form.
Teaching Strategies
- Make connections across representations of multi-digit whole numbers using base ten numerals, number names, and expanded form.
- Develop rules for comparing the multi-digit numbers.
Progressions
- To read numerals between 1,000 and 1,000,000, students need to understand the role of commas. Each sequence of three digits made by commas is read as hundreds, tens, and ones, followed by the name of the appropriate base-thousand unit (thousand, million, billion, trillion, etc.). Thus, 457,000 is read "four hundred fifty seven thousand." (Please reference page 13 in the Progression document).
Examples
- The number two hundred seventy-five thousand eight hundred two written in standard form is 275,802 and in expanded form is 200,000+70,000+5,000+800+2 or (2×100,000)+(7×10,000)+(5×1,000)+(8×100)+(2×1).
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 4.NBT.A.3
Cluster: 4.NBT.A - Generalize place value understanding for multi-digit whole numbers.
STANDARD: 4.NBT.A.3
Standards Statement (2021):
Use place value understanding to round multi-digit whole numbers to any place.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.NBT.A.1, 4.NBT.A.1, 4.NBT.A.2 | 5.NBT.A.4 | 4.OA.A.3 | 4.NBT.A.3 4.NBT.A Crosswalk |
Standards Guidance:
Boundaries
- Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
- Grade 4 students should explore rounding within contextual situations.
Teaching Strategies
- Students rounding to 348 to the nearest hundred may mistakenly round initially to 350 and then 400 by applying rules such as if the digit is 0-4 then round down and 5-9 and round up. Models can help them see that 348 is closer to 300 than 400.
- Students should locate numbers on a number line to determine the nearest multiple of 1,000s, 10,000s or 100,000s.
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 4.NBT.B.4
Cluster: 4.NBT.B - Use place value understanding and properties of operations to perform multi-digit arithmetic.
STANDARD: 4.NBT.B.4
Standards Statement (2021):
Fluently add and subtract multi-digit whole numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.NF.A.1, 3.NBT.A.2, 4.NBT.A.1 | 5.NBT.B.5, 5.NBT.B.7 | N/A | 4.NBT.B.4 4.NBT.B Crosswalk |
Standards Guidance:
Clarifications
- Students should fluently (flexibly, accurately, and efficiently) add and subtract multi-digit whole numbers, to solve contextual, mathematical problems using efficient and flexible procedures, based on knowledge of place value and properties of operations.
- Students should use efficient algorithms that make sense for the given numbers and draw upon their understanding of multi-digit whole numbers, the properties of operations, and place value.
Terminology
- Efficiency in mathematics is the ability to produce answers relatively easily with a minimal number of steps. An efficient strategy is one that the student can carry out easily, keeping track of sub-problems and making use of intermediate results to solve the problem. Efficiency does not mean students should be timed.
- Flexibility is the ability to think about a problem in more than one way and to adapt or adjust thinking, if necessary.
- Accuracy is the ability to produce mathematically precise answers.
- Appropriateness is the ability to select and apply a strategy that is appropriate for solving a given problem efficiently.
Boundaries
- Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.
- Students should be given the choice of which procedure they can use.
- Students should add and subtract multi-digit whole numbers within 100,000, to solve math problems using generalizable procedures, based on place value and properties of operations.
Progressions
- Because students in Grade 2 and Grade 3 have been using at least one method that readily generalizes to 1,000,000, this extension does not have to take a long time. Thus, students will have time for the major NBT focus for this grade: multiplication and division. (Please reference page 14 in the Progression document)
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 4.NBT.B.5
Cluster: 4.NBT.B - Use place value understanding and properties of operations to perform multi-digit arithmetic.
STANDARD: 4.NBT.B.5
Standards Statement (2021):
Use representations and strategies to multiply a whole number of up to four digits by a one-digit number, and a two-digit number by a two-digit number using strategies based on place value and the properties of operations.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.NBT.A.2, 3.NBT.A.3, 4.NBT.A.1 | 4.NBT.B.6, 5.NBT.B.5 | 3.OA.C.7, 3.OA.B.5 | 4.NBT.B.5 4.NBT.B Crosswalk |
Standards Guidance:
Boundaries
- Students should be familiar with multiple strategies but should be able to select and use the strategy with which they most closely connect and understand, with the ultimate goal of supporting students to use more efficient strategies.
- Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
- A range of efficient algorithms may be used.
Teaching Strategies
- Illustrate and explain calculations using rectangular arrays, area models, and/or equations, along with strategies based on place value and properties of operations.
- Students should be able to solve contextual, mathematical problems involving the multiplication of a number with up to four digits by a 1-digit whole number.
- Students should be able to illustrate and explain their calculations using equations, rectangular arrays, and/or area models for all numbers included in the learning objective.
Progressions
- In fourth grade, students compute products of one-digit numbers and multi-digit numbers (up to four digits) and products of two two-digit numbers. They divide multi-digit numbers (up to four digits) by one-digit numbers.
- As with addition and subtraction, students should use methods they understand and can explain. Visual representations such as area and array diagrams that students draw and connect to equations and other written numerical work are useful for this purpose. (Please reference pages 14 & 15 in the Progression document).
Examples
- Connect numeric and visual models such as those created by representing 285 with base 10 pieces and repeating three times. Use this area model with dimensions of 285 and 3 to find partial products.
- There are 7 boxes of chocolates. Each box contains 16 chocolates. How many chocolates are there all together?
- The school bought thirty-nine cases of popcorn for the school carnival. Each case contained 15 bags of popcorn. How many bags of popcorn is that all together?
2021 Oregon Math Guidance: 4.NBT.B.6
Cluster: 4.NBT.B - Use place value understanding and properties of operations to perform multi-digit arithmetic.
STANDARD: 4.NBT.B.6
Standards Statement (2021):
Use representations and strategies to find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.NBT.A.2, 4.NBT.A.1, 4.NBT.B.5 | 5.NBT.B.6 | 3.OA.B.5, 3.OA.B.6, 3.OA.C.7, 4.OA.A.3, 3.GM.C.7 | 4.NBT.B.6 4.NBT.B Crosswalk |
Standards Guidance:
Clarifications
- Students should be able to solve contextual, mathematical problems involving division of whole numbers.
- Students should be familiar with multiple strategies but should be able to select and use the strategy with which they most closely connect and understand, with the ultimate goal of supporting students to use more efficient strategies.
Content Boundaries
- Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.
- Long division is not an expectation at this grade level.
Teaching Strategies
- Students should be able to illustrate and explain their calculations using equations, rectangular arrays, and/or area models.
Progressions
- General methods for computing quotients of multi-digit numbers and one-digit numbers rely on the same understandings as for multiplication, but cast in terms of division. One component is quotients of multiples of 10, 100, or 1000 and one-digit numbers. For example, 42 ÷ 6 is related to 420 ÷ 6 and 4200 ÷ 6. Students can draw on their work with multiplication and they can also reason that 4200 ÷ 6 means partitioning 42 hundreds into 6 equal groups, so there are 7 hundreds in each group. (Please reference pages 16 & 17 in the Progression document).
Examples
- Apply knowledge of decomposing whole numbers into divisible parts. Such as, connect numeric and visual models such as those created by representing 136 with base 10 pieces and dividing into groups of 4 to determine either the size of the group or the number of groups.
- Antonio won a jar of 373 jellybeans in a school contest. He wants to share them. He and his 7 friends will share them. How many jellybeans will each of the friends get?
- Possible solution: 373 ÷ 8 = (368 ÷ 8) + (5 ÷ 8) = 46 with 5 jellybeans left over.
- Illustrative Mathematics:
- Student Achievement Partners: