OREGON MATH STANDARDS (2021): [6.AEE]
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: 6.AEE.A.1
Cluster: 6.AEE.A - Apply and extend previous understandings of arithmetic to algebraic expressions.
STANDARD: 6.AEE.A.1
Standards Statement (2021):
Write and evaluate numerical expressions involving whole-number bases and exponents.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
4.OA.B.4, 5.OA.A.1 | 6.AEE.A.2, 7.AEE.B.3, 8.AEE.A.1 | 5.NBT.A.2 | 6.EE.A.1 6.AEE.A Crosswalk |
Standards Guidance:
Teaching Strategies
- Extend previous understanding by using brackets and parentheses and order of operations and exponents.
- Students should interpret real-life, mathematical situations to write and evaluate numerical expressions.
Progressions
- In Grade 6 [students] start to incorporate whole number exponents into numerical expressions, for example when they describe a square with side length 50 feet as having an area of 50 ft2 (square feet). (Please reference page 4 in the Progression document)
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.AEE.A.2
Cluster: 6.AEE.A - Apply and extend previous understandings of arithmetic to algebraic expressions.
STANDARD: 6.AEE.A.2
Standards Statement (2021):
Write, read, and evaluate expressions in which letters stand for numbers. Apply knowledge of common mathematical terms to move between the verbal and mathematical forms of an expression including expressions that arise from authentic contexts.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.OA.A.2, 5.OA.B.3, 6.AEE.A.1 | 6.AEE.A.3, 6.AEE.B.4, 6.AEE.B.5, 8.AEE.A.2, HS.AEE.A.1 |
| 6.EE.A.2 6.AEE.A Crosswalk |
Standards Guidance:
Clarifications
- Students should write expressions that record operations with numbers and with letters standing for numbers.
- Students should evaluate algebraic expressions for a given value of a variable, using the order of operations.
Boundaries
- Evaluate expressions at specific values of their variables. Numeric values should align with grade level expecations of positive rational numbers.
- Includes identificaiton of the parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
- Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
Teaching Strategies
- Include expressions that arise from formulas used in authentic problems.
- Students should understand letters called variables represent unknown numbers and the same rules apply in operations with numbers also apply in operations with variables.
Progressions
- Abstracting the pattern they write 10 - p for a book costing p dollars, thus summarizing a calculation that can be carried out repeatedly with different numbers. Such work also helps students interpret expressions. For example, if there are 3 and with letters standing for numbers. loose apples and 2 bags of A apples each, students relate quantities in the situation to the terms in the expression 3 + 2A. (Please reference page 4 in the Progression document)
Example
- Express the calculation subtract y from 5 as 5 – y.
- Describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.AEE.A.3
Cluster: 6.AEE.A - Apply and extend previous understandings of arithmetic to algebraic expressions.
STANDARD: 6.AEE.A.3
Standards Statement (2021):
Apply the properties of operations to generate equivalent expressions and to determine when two expressions are equivalent.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.OA.A.2, 6.AEE.A.2 | 7.AEE.A.1 | 6.NS.B.4 | 6.EE.A.3, 6.EE.A.4 6.AEE.A Crosswalk |
Standards Guidance:
Clarification
- Identify when two expressions are equivalent such as when the two expressions name the same number regardless of which value is substituted into them.
Boundaries
- This standard includes distributive property and combining like terms.
Progressions
- A firm grasp on variables as numbers helps students extend their work with the properties of operations from arithmetic to algebra. For example, students who are accustomed to mentally calculating 5 x 37 as 5 x (30 + 7) = 150 + 35 can now see that 5(3a + 7) = 15a + 35 for all numbers a. (Please reference page 5 in the Progression document).
Examples
- Apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x.
- Apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y)
- Apply properties of operation to the expression y + y + y to produce the equivalent expression 3y and know they are equivalent because they name the same number regardless of which number y stands for.
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.AEE.B.4
Cluster: 6.AEE.B - Reason about and solve one-variable equations and inequalities.
STANDARD: 6.AEE.B.4
Standards Statement (2021):
Understand solving an equation or inequality as a process of answering which values from a specified set, if any, make the equation or inequality true. Use substitution to determine which number(s) in a given set make an equation or inequality true.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.AEE.A.2 | 8.AEE.A.2, 8.AEE.C.8, HS.AEE.C.8, HS.AEE.D.9 | N/A | 6.EE.B.5 6.AEE.B Crosswalk |
Standards Guidance:
Teaching Strategies
- Students should be able to use algebraic reasoning to solve an equation as a process of answering a contextual question and explain their reasoning.
- When solving an equation or inequality as a process of answering a question, students should be able to explain why specific values from a specified set, if any, make the equation or inequality true.
- Students should use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Progressions
- Solving is a process of reasoning to find the numbers which make an equation true, which can include checking if a given number is a solution. Although the process of reasoning will eventually lead to standard methods for solving equations, students should study examples where looking for structure pays off, such as in 4x + 3x = 3x + 20, where they can see that 4x must be 20 to make the two sides equal. (Please reference page 6 in the Progression document)
Examples
- Use an inequality of the form x > c or x < c .
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.AEE.B.5
Cluster: 6.AEE.B - Reason about and solve one-variable equations and inequalities.
STANDARD: 6.AEE.B.5
Standards Statement (2021):
Use variables to represent numbers and write expressions when solving problems in authentic contexts.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.AEE.A.2 | 7.AEE.B.4 | N/A | 6.EE.B.6 6.AEE.B Crosswalk |
Standards Guidance:
Clarifications
- Understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Progressions
- As with all their work with variables, it is important for students to state precisely the meaning of variables they use when setting up equations (MP6). This includes specifying whether the variable refers to a specific number, or to all numbers in some range. For example, in the equation 0.44n = 11 the variable n refers to a specific number (the number of stamps you can buy for $11); however, if the expression 0.44n is presented as a general formula for calculating the price in dollars of n stamps, then n refers to all numbers in some domain. That domain might be specified by inequalities, such as n > 0. (Please reference page 7 in the Progression document).
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.AEE.B.6
Cluster: 6.AEE.B - Reason about and solve one-variable equations and inequalities.
STANDARD: 6.AEE.B.6
Standards Statement (2021):
Write and solve equations of the form x + p = q and px = q in problems that arise from authentic contexts for cases in which p, q and x are all nonnegative rational numbers.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.AEE.C.8 | 7.AEE.B.4 | 6.NS.A.1, 5.NF.A.1, 5.NF.B.3, 5.NF.B.4, 5.NF.B.5, 5.NF.B.6 | 6.EE.B.7 6.AEE.B Crosswalk |
Standards Guidance:
Teaching Strategies
- p, x, and q include non-whole numbers. Students should be able to solve equations of this form using strategies such as related equations, fact families, inverse operations, and visual models.
- Students should have opportunities to use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and multiplication and division when solving one-step equations.
- Students should be able to solve equations presented in contextual, mathematical problems involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation.
- Students should be able to interpret a solution in the original context and assess the reasonableness of results.
Progressions
- For example, how many 44-cent stamps can you buy with $11? Students are accustomed to solving such problems by division; now they see the parallel with representing the problem algebraically as 0.44n = 11, from which they use the same reasoning as in the numerical solution to conclude that n = 11 <div> 0.44. (Please reference page 7 in the Progression document).
Examples
- Illustrative Mathematics:
- Student Achievement Partners:
2021 Oregon Math Guidance: 6.AEE.B.7
Cluster: 6.AEE.B - Reason about and solve one-variable equations and inequalities.
STANDARD: 6.AEE.B.7
Standards Statement (2021):
Write inequalities of the form x > c and x < c to represent constraints or conditions to solve problems in authentic contexts. Describe and graph on a number line solutions of inequalities of the form x > c and x < c.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
6.NS.C.7, 6.NS.C.6 | 7.AEE.B.4 | 5.NBT.A.3 | 6.EE.B.8 6.AEE.B Crosswalk |
Standards Guidance:
Clarification
- Recognize that inequalities of the form 𝑥>𝑐 or 𝑥<𝑐 have infinitely many solutions.
- Represent solutions of such inequalities on number line diagrams.
Teaching Strategies
- Students should represent contextual, mathematical situations using inequalities involving variables.
- Students should be able to create contextual, mathematical situations corresponding to specific inequalities.
- This objective includes the use of the symbols, < , > , = , ≤ , ≥.
Examples
- Illustrative Mathematics:
2021 Oregon Math Guidance: 6.AEE.C.8
Cluster: 6.AEE.C - Represent and analyze quantitative relationships between dependent and independent variables.
STANDARD: 6.AEE.C.8
Standards Statement (2021):
Use variables to represent and analyze two quantities to solve problems in authentic contexts. Including those that change in relationship to one another; write an equation to express one quantity in terms of the other quantity.
Connections:
Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |
5.OA.B.3 | 6.AEE.B.6, 7.AEE.B.4 | 6.RP.A.3 | 6.EE.C.9 6.AEE.C Crosswalk |
Standards Guidance:
Boundaries
- Students should be able to represent equations involving positive variables and rational numbers.
- Students should have opportunities to solve contextual, mathematical problems.
Teaching Strategies
- Students should have an opportunity to solve problem situations with variables in all positions.
- Students should be able to explain that a variable can represent an unknown number, or depending on the purpose at hand, any number in a specified set.
Progressions
- As [students] work with such equations [they] begin to develop a dynamic understanding of variables, an appreciation that they can stand for any number from some domain.
- This use of variables arises when students study expressions such as 0.60n, [presented as a general formula for calculating the price in dollars of n stamps that cost $0.60],
- or equations in two variables such as d = 5 + 5t describing [the] relationship between distance in miles, d, and time in hours, t, for a person starting 5 miles from home and walking away at 5 miles per hour. Students can use tabular and graphical representations to develop an appreciation of varying quantities. (Please reference page 7 in the Progression document).
Examples
- Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example:
- In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
- Illustrative Mathematics:
- Student Achievement Partners: