OREGON MATH STANDARDS (2021): [5.NF]
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.NF.A.1
Cluster: 5.NF.A - Use equivalent fractions as a strategy to add and subtract fractions.
STANDARD: 5.NF.A.1
Standards Statement (2021):
Add and subtract fractions with unlike denominators, including common fractions larger than one and mixed numbers.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NF.A.1, 4.NF.B.3 | 5.NF.A.2, 5.NBT.B.7, 7.NS.A.1 | 6.AEE.B.6 | 5.NF.A.1 5.NF.A Crosswalk |
Standards Guidance:
Terminology
- A common fraction is a fraction in which numerator and denominator are both integers, as opposed to fractions. Fractions such as 4/3, or 14/5 should be thought of as common fractions greater than one, which could also be written using mixed numbers as 1-1/3 and 2-4/5 respectively.
- Use of the term "improper fraction" should be avoided.
Boundaries
- Work with fractions at grade 5 should focus on fractions with denominators 2-10, 12, 16, 20, 25, 50, 100 and 1000.
Progressions
- In Grade 4, students have some experience calculating sums of fractions with different denominators...where one denominator is a divisor of the other, so that only one fraction has to be changed.
- Grade 5 students extend this reasoning to situations where it is necessary to re-express both fractions in terms of a new denominator. For example, in calculating 2/3 + 5/4 they reason that if each third in 2/3 is subdivided into fourths, and if each fourth in 5/4 is subdivided into thirds, then each fraction will be a sum of unit fractions with denominator 3 x 4 = 4 x 3 = 12:
- 2/3 + 5/4 = 2x4 / 3x4 + 5x3 / 4x3 = 8/12 + 15/12 = 23/12.
- Please reference page 11 in the Progression document
Examples
- Include replacing given fractions with equivalent fractions to produce an equivalent sum or difference.
- 2/3 + 5/4 = 8/12 + 15/12 = 23/12 or 1 11/12.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NF.A.2
Cluster: 5.NF.A - Use equivalent fractions as a strategy to add and subtract fractions.
STANDARD: 5.NF.A.2
Standards Statement (2021):
Solve problems in authentic contexts involving addition and subtraction of fractions with unlike denominators, including common fractions larger than one and mixed numbers.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NF.A.2, 4.NF.C.5, 5.NF.A.1 | 6.NS.B.2, 6.NS.B.3 | 5.DR.B.2, 5.GM.A.2 | 5.NF.A.2 5.NF.A Crosswalk |
Standards Guidance:
Clarifications
- Use visual fraction models or equations to represent the problem.
- Use benchmark fractions and number sense of fractions to estimate and assess the reasonableness of answers.
- Students should use benchmark fractions and number sense of fractions to estimate and assess the reasonableness of answers as an introduction to addition and subtraction.
Boundaries
- Work with fractions at grade 5 should focus on fractions with denominators 2-10, 12, 16, 25, 100 and 1000.
Teaching Strategies
- Students should use numerical reasoning to add and subtract fractions and mixed numbers with unlike denominators in contextual, mathematical problems by finding a common denominator and equivalent fractions to produce like denominators using a variety of tools and strategies.
Progressions
- Students make sense of fractional quantities when solving word problems, estimating answers mentally to see if they make sense. For example in the problem:
- Ludmilla and Lazarus each have a lemon. They need a cup of lemon juice to make hummus for a party. Ludmilla squeezes 1/2 a cup from hers and Lazarus squeezes 2/5 of a cup from his. How much lemon juice do they have? Is it enough?
- Students estimate that there is almost but not quite one cup of lemon juice, because 2/5 < 1/2. They calculate 1/2 + 2/5 = 9/10, and see this as 1/10 less than 1, which is probably a small enough shortfall that it will not ruin a recipe. (Please reference page 11 in the Progression document).
Examples
- Tom is baking a cake. He added 12 teaspoon of vanilla extract to the cake mix. He tasted the batter and determined he needed more, so he added another 34 teaspoon of vanilla extract. How much total vanilla extract did he add to the cake mix?
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NF.B.3
Cluster: 5.NF.B - Apply and extend previous understandings of multiplication and division.
STANDARD: 5.NF.B.3
Standards Statement (2021):
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve problems in authentic contexts involving division of whole numbers that result in answers that are common fractions or mixed numbers.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NF.B.3, 4.NF.B.4 | 6.RP.A.1, 6.RP.A.2, 6.RP.A.3 | 3.OA.A.2, 3.OA.B.6, 4.OA.A.1, 4.OA.A.2, 4.GM.B.5, 6.AEE.B.6 | 5.NF.B.3 5.NF.B Crosswalk |
Standards Guidance:
Boundaries
- As part of this standard, students should have opportunities to use visual models or equations to represent and solve problems.
Progressions
- In Grade 5, [students] connect fractions with division, understanding that
- 5 div 3 = 5/3,
- or, more generally, a/b = a div b for whole numbers a and b, with b not equal to zero.
(Please reference page 17 in the Progression document). Examples
- If 5 cookies are shared equally among 3 people each person receives of a cookie.
- If you divide 5 objects equally among 3 shares, each of the 5 objects should contribute 1/3 of itself to each share.
- Thus, each share consists of 5 pieces, each of which is 1/3 of an object, and so each share is of an object
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NF.B.4
Cluster: 5.NF.B - Apply and extend previous understandings of multiplication and division.
STANDARD: 5.NF.B.4
Standards Statement (2021):
Apply and extend previous understanding and strategies of multiplication to multiply a fraction or whole number by a fraction. Multiply fractional side lengths to find areas of rectangles, and represent fractional products as rectangular areas.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.OA.A.1, 3.GM.C.7, 4.OA.A.1, 4.NF.B.4 | 6.RP.A.1, 6.RP.A.2, 6.RP.A.3 | 5.NBT.B.7, 6.NS.B.2, 6.AEE.B.6, 6.GM.A.1, 7.NS.A.2 | 5.NF.B.4 5.NF.B Crosswalk |
Standards Guidance:
Boundaries
- Students should explain the meaning of a fraction 𝑎/𝑏 as a multiple of 1/𝑏.
- Students should be exposed to fractions less than 1, equal to 1, and greater than 1.
Teaching Strategies
- Interpret the product of the fraction a/b and a whole number (q) as
- partitioning the whole number into b parts and counting a parts
- Repeating the fraction a/b q number of times.
- Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths
- Students should be presented with a variety of real-life, mathematical problems involving multiplication of a fraction and a whole number.
- Students should use their understanding of equivalency to flexibly reason with equivalent fractions based on the context of the problem. Simplifying fractions is not an expectation of this grade level.
Progressions
- Students should use a variety of models to conecptualize multiplicaiton of fractions, including use of a number line, fraction strip, and area models. Please reference page 17 in the Progression document for additional information.
Examples
- Understand that ⅔ x 4 can be seen as partitioning 4 into 3 equal parts as well as counting 2 of the 3 (4/3 x 2) parts or as iterating ⅔ four times [(2 x 4)/3]. In general, a/b x q = q/b x a = (a x q)/b.
- Use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15.
- Each cupcake takes 1/4 cup of frosting. If Betty wants to make 20 cupcakes for a party, how much frosting will she need?
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NF.B.5
Cluster: 5.NF.B - Apply and extend previous understandings of multiplication and division.
STANDARD: 5.NF.B.5
Standards Statement (2021):
Apply and extend previous understandings of multiplication and division to represent and calculate multiplication and division of fractions. Interpret multiplication as scaling (resizing) by comparing the size of products of two factors.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.NF.A.1, 4.NF.C.5 | 6.RP.A.1 | 3.OA.A.1, 3.OA.A.2, 4.OA.A.1, 4.OA.A.2, 4.GM.B.5 | 5.NF.B.5 5.NF.B Crosswalk |
Standards Guidance:
Boundaries
- As part of this standard, students must be able to
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- Explain that multiplying a given number by a fraction greater than 1 results in a product greater than the given number.
- Explain that multiplying a given number by a fraction equivalent to 1 (such as 4/4) results in the same product as multiplying by 1.
- Explain that multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
Teaching Strategies
- Students should be presented with a variety of real-life, mathematical situations involving multiplication as scaling (resizing) that include fractions and whole numbers.
Progressions
- In preparation for Grade 6 work in ratios and proportional relationships, students learn to see products such as 5 x 3 or 1/2 x 3 as expressions that can be interpreted in terms of a quantity, 3, and a scaling factor, 5 or 1/2. Thus, in addition to knowing that 5 x 3 = 15, they can also say that 5 x 3 is 5 times as big as 3, without evaluating the product. Likewise, the see 1/2 x 3 as half the size of 3.
- Grade 5 work with multiplying by unit fractions, and interpreting fractions in terms of division, enables students to see that multiplying a quantity by a number smaller than 1 produces a smaller quantity, as when the budget of a large state university is multiplied by 1/2, for example. (Please reference page 19 in the Progression document).
Examples
- Mrs. Cole needs to make lunch for 12 children at a day care. Each child gets 1/2 of a sandwich. How many whole sandwiches does Mrs. Cole need to make?
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NF.B.6
Cluster: 5.NF.B - Apply and extend previous understandings of multiplication and division.
STANDARD: 5.NF.B.6
Standards Statement (2021):
Solve problems in authentic contexts involving multiplication of common fractions and mixed numbers.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.OA.A.2 | 6.RP.A.1, 6.NS.A.1 | 3.OA.A.1, 3.OA.A.2, 4.OA.A.1, 4.GM.B.5, 5.DR.B.2 | 5.NF.B.6 5.NF.B Crosswalk |
Standards Guidance:
Teaching Strategies
- Students should be given opportunities to use both visual fraction models and equations to represent and solve problems.
- Students should be given opportunities to use both visual fraction models and equations to represent and solve problems.
Progressions
- Solve applied problems involving multiplication of fractions and mixed numbers by using visual fraction models and/or equations to represent the problem.
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 5.NF.B.7
Cluster: 5.NF.B - Apply and extend previous understandings of multiplication and division.
STANDARD: 5.NF.B.7
Standards Statement (2021):
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions, including solving problems in authentic contexts.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
3.NF.A.1, 4.NF.B.4 | 6.RP.A.2, 6.NS.A.1 | 3.OA.B.6, 5.DR.B.2, 6.DR.A.1 | 5.NF.B.7 5.NF.B Crosswalk |
Standards Guidance:
Boundaries
- Division of a fraction by a fraction is not a requirement at this grade. However, students who are able to multiply fractions can develop strategies to divide a fraction by a fraction by reasoning about the relationship between multiplication and division.
Teaching Strategies
- Students should be given opportunities to use both visual fraction models and equations to represent and solve problems.
- Students should begin with modeling for deeper understanding.
- Students should be presented with a variety of contextual, real-life problems involving division of a whole number by a unit fraction and division of a unit fraction by a whole number.
Examples
- Create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient.
- Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
- Create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient.
- Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
- How much chocolate will each person get if 3 people share ½ lb of chocolate equally?
- How many ⅓-cup servings are in 2 cups of raisins?
- Knowing the number of groups/shares and finding how many/much in each group/share Four students sitting at a table were given 1/3 of a pan of brownies to share. How much of a pan will each student get if they share the pan of brownies equally? The diagram shows the 1/3 pan divided into 4 equal shares with each share equaling 1/12 of the pan.
- Illustrative Mathematics:
- Student Achievement Partners: