OREGON MATH STANDARDS (2021): [5.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: 5.NBT.A.1
Cluster: 5.NBT.A - Understand the place value system.
STANDARD: 5.NBT.A.1
Standards Statement (2021):
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NBT.A.1, 4.NBT.A.2, 4.NF.B.3 | 5.NBT.A.2, 5.NBT.A.3, 5.NBT.A.4, 5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7 | 4.NF.C.5, 4.NF.C.6, 4.NF.C.7 | 5.NBT.A.1 5.NBT.A Crosswalk |
Standards Guidance:
Clarifications
- Students should identify the value of a digit up 100 times greater or 11000 of the value of a digit.
- Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Examples
- Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
- For example, 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
- 700 is 10 times as much as 70, and 70 is 1/10 of 700.
- Mara has a digital scale. He placed one playing card on the scale and it read 1.3 grams. How much would you expect 10 playing cards to weigh?
- Chris took the cards off the scale and then placed 10 pennies on the scale and the scale read 24 grams. How much would you expect one penny to weigh.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NBT.A.2
Cluster: 5.NBT.A - Understand the place value system.
STANDARD: 5.NBT.A.2
Standards Statement (2021):
Use whole number exponents to denote powers of 10 and explain the patterns in placement of digits that occur when multiplying and/or dividing whole numbers and decimals by powers of 10.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.NBT.A.1 | 6.AEE.A.1, 8.AEE.A.3 | N/A | 5.NBT.A.2 5.NBT.A Crosswalk |
Standards Guidance:
Clarifications
- Students should explain what happens to the value of a digit as it shifts to the left or right and discover the decimal point remains between the ones and tenths place as the digits shift.
- Use whole-number exponents to denote powers of 10, up to 10^3.
Boundaries
- Work with exponents at this grade is limited to powers of 10.
Progressions
- New at Grade 5 is the use of whole number exponents to denote powers of 10. Students understand why multiplying by a power of 10 shifts the digits of a whole number or decimal that many places to the left.
- For example, multiplying by 104 is multiplying by 10 four times. Multiplying by 10 once shifts every digit of the multiplicand one place to the left in the product (the product is ten times as large) because in the base-ten system the value of each place is 10 times the value of the place to its right. So multiplying by 10 four times shifts every digit 4 places to the left. Patterns in the number of 0s in products of a whole number and a power of 10 can be explained in terms of place value. (Please reference page 18 in the Progression document).
Examples
- Observe and explain the patterns in the number of zeros of a product when multiplying a whole number by a power of 10, and the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
- Illustrative Mathematics:
2021 Oregon Math Guidance: 5.NBT.A.3
Cluster: 5.NBT.A - Understand the place value system.
STANDARD: 5.NBT.A.3
Standards Statement (2021):
Read, write, and compare decimals to thousandths.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NBT.A.2, 5.NBT.A.1, 4.NF.C.7 | 5.NBT.A.4 | 6.AEE.B.7 | 5.NBT.A.3 5.NBT.A Crosswalk |
Standards Guidance:
Clarification
- Read and write decimals to thousandths using standard form, expanded form, and word from.
- Compare two decimals to thousandths based on meanings of the digits in each place, and record the results of the comparisons using >,=, and <.
Boundaries
- Students should be provided opportunities to simultaneously compare decimals and fractions, including equivalent fractions and decimals, on both single and double number lines.
- Base-ten numerals should range between millions and thousandths.
- Students are not expected to write decimal numbers in word form.
- Exponents and decimal numbers should not be included in expanded form notation.
- The decimal fractions used in Grade 5 should be limited to those for which the equivalent fraction can be written as a fraction where the denominator is a power of ten.
Teaching Strategies
- Students should be presented with decimal number comparisons from contextual, mathematical situations.
- Students should have opportunities to determine and explain comparisons using a variety of tools such as concrete materials, drawings, number lines, other visual representations, and strategies.
Examples
- Use >, =, and < symbols to record comparisons of two decimals. For example:
- 347.392 =
- = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
- =three hundred forty-seven and three hundred ninety-two thousandths
- 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (110) + 9 × (1100) + 2 × (11000)
- Which is greater 0.13 or 0.031? Explain. Use a visual representation to illustrate your explanation.
- I think 0.13 is greater because it fills up more of the whole square than 0.031 does.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NBT.A.4
Cluster: 5.NBT.A - Understand the place value system.
STANDARD: 5.NBT.A.4
Standards Statement (2021):
Use place value understanding to round decimals to any place.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NBT.A.3, 5.NBT.A.1, 5.NBT.A.3 | N/A | 8.AEE.A.3 | 5.NBT.A.4 5.NBT.A Crosswalk |
Standards Guidance:
Boundaries
- Work with decimals at this grade is limited to decimals up to the thousandths.
Teaching Strategies
- Students should round decimal numbers to the hundredths place in contextual, mathematical problems using visual aids, such as a number line.
Examples
- Illustrative Mathematics:
2021 Oregon Math Guidance: 5.NBT.B.5
Cluster: 5.NBT.B - Perform operations with multi-digit whole numbers and with decimals to hundredths.
STANDARD: 5.NBT.B.5
Standards Statement (2021):
Fluently multiply 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) |
4.NBT.B.4, 4.NBT.B.5, 5.NBT.A.1 | 6.NS.B.3 | N/A | 5.NBT.B.5 5.NBT.B Crosswalk |
Standards Guidance:
Terminology
- The National Council of Teachers of Mathematics provides the following definition of procedural fluency:
- “Procedural fluency is the ability to apply procedures accurately, efficiently, and flexibly; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another.
Boundaries
- Students may use but are not limited to partial products (area model).
- Students may also use a standard algorithm by making connections from previous part-whole strategies.
- Students should choose a strategy that makes sense to them based on the context of the problem. The focus should always be on efficiency.
Teaching Strategies
- Students should be presented with contextual, real-life situations involving multiplication of multi-digit whole numbers.
- Students should fluently (flexibly, accurately, and efficiently) multiply to solve contextual, mathematical problems using efficient strategies that are based on knowledge of place value and properties of operations.
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NBT.B.6
Cluster: 5.NBT.B - Perform operations with multi-digit whole numbers and with decimals to hundredths.
STANDARD: 5.NBT.B.6
Standards Statement (2021):
Use a variety of representations and strategies to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NBT.B.4, 4.NBT.B.6, 5.NBT.A.1 | 6.NS.B.2, 6.NS.B.3 | N/A | 5.NBT.B.6 5.NBT.B Crosswalk |
Standards Guidance:
Clarification
- Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
- Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
Boundaries
- Students should divide multi-digit whole numbers up to 4- digit dividends and 2-digit divisors no greater than 25.
- Students may use but are not limited to partial quotients (area model).
- Students should choose a strategy that makes sense to them based on the context of the problem. The focus should always be on efficiency.
Teaching Strategies
- Students should be presented with contextual, real-life situations involving the division of multi-digit whole numbers.
- Students should fluently (flexibly, accurately, and efficiently) divide, to solve contextual, mathematical problems using an efficient algorithm and flexible strategies, based on knowledge of place value and properties of operations.
- Examples of different strategies and representations can be found within the Computational Strategies for Whole Numbers document found in the appendices.
Progressions
- Division in Grade 5 extends Grade 4 methods to two-digit divisors. Students continue to decompose the dividend into base-ten units and find the quotient place by place, starting from the highest place.
- Estimating the quotients is a new aspect of dividing by a two-digit number. Even if students round the dividend appropriately, the resulting estimate may need to be adjusted up or down. (Please reference page 18 in the Progression document).
Examples
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NBT.B.7
Cluster: 5.NBT.B - Perform operations with multi-digit whole numbers and with decimals to hundredths.
STANDARD: 5.NBT.B.7
Standards Statement (2021):
Use a variety of representations and strategies to add, subtract, multiply, and divide decimals to hundredths. Relate the strategy to a written method and explain the reasoning used.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NBT.B.4, 5.NBT.A.1, 5.NF.A.1 | 6.NS.B.3 | 5.NF.B.4, 5.GM.A.1, 5.GM.C.4 | 5.NBT.B.7 5.NBT.B Crosswalk |
Standards Guidance:
Clarification
- As part of this standard, students must be able to use concrete models, visual drawings and strategies based on place value, properties of operations, and the relationship between addition and subtraction.
Boundaries
- Fluency with operations with decimals is part of the 6th grade standards.
- Students should be given the choice of which strategy they can use.
Teaching Strategies
- Students should be presented with a variety of contextual, real-life situations involving addition and subtraction of decimal numbers to the hundredths place.
- Students should add and subtract decimal numbers to hundredths, using concrete models, drawings, strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Progressions
- Because of the uniformity of the structure of the base-ten system, students use the same place value understanding for adding and subtracting decimals that they used for adding and subtracting whole numbers. Like base-ten units must be added and subtracted, so students need to attend to aligning the corresponding places correctly (this also aligns the decimal points).
- General methods used for computing products of whole numbers extend to products of decimals. Because the expectations for decimals are limited to thousandths and expectations for factors are limited to hundredths at this grade level, students will multiply tenths with tenths and tenths with hundredths, but they need not multiply hundredths with hundredths.
- General methods used for computing quotients of whole numbers extend to decimals with the additional issue of placing the decimal point in the quotient. (Please reference page 19 in the Progression document)
Examples
- Illustrative Mathematics:
- Student Achievement Partners: