6.EE.2 - About the Math, Learning Targets, and Increasing Rigor

Grade 5AGL Expressions and Equations

6.EE.2

About the Math

Full Standard

Write, read, and evaluate expressions in which letters stand for numbers.

  1. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
  2. Identify 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. For example, 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.
  3. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. 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). For example, use the formulas V = s3  and SA = 6 s2  to find the volume and surface area of a cube with sides of length s = 1/2.

 

Learning Targets (I can)

  • Write expressions with unknowns.
  • Identify mathematical terms and use them to write or interpret expressions.
  • Evaluate expressions with unknowns using the order of operations.
  • Recognize and use expressions as common real-world formulas (i.e. volume of a cube, V = s3).

 

About the Math 

  • Write expressions with unknowns.
  • Identify mathematical terms and use them to write or interpret expressions.

Students write expressions from verbal descriptions using letters and numbers, understanding order is important in writing subtraction and division problems. Students understand that the expression “5 times any number, n” could be represented with 5n and that a number and letter written together means to multiply. All rational numbers may be used in writing expressions when operations are not expected. Students use appropriate mathematical language to write verbal expressions from algebraic expressions. It is important for students to read algebraic expressions in a manner that reinforces that the variable represents a number.

Students can describe expressions such as 3 (2 + 6) as the product of two factors: 3 and (2 + 6). The quantity (2 + 6) is viewed as one factor consisting of two terms.

Terms are the parts of a sum. When the term is an explicit number, it is called a constant. When the term is a product of a number and a variable, the number is called the coefficient of the variable.

Students should identify the parts of an algebraic expression including variables, coefficients, constants, and the names of operations (sum, difference, product, and quotient). Variables are letters that represent numbers. There are various possibilities for the number they can represent.

  • Evaluate expressions with unknowns using the order of operations.

 Expressions can be evaluated by using a given value for the unknown in an expression. Students should be able to articulate how a give expression can have different values based on the value being substituted for the unknown.

  • Recognize and use expressions as common real-world formulas (i.e. volume of a cube, V = s3).

Formulas are examples of real-world expressions and equations. When introducing this standard (and/or learning target), we can connect to known formulas such as the area of a rectangle. It is acceptable to introduce other common formulas at this point. There are opportunities throughout the year to connect to and reinforce this standard/learning target (e.g. the volume of various quadrilaterals). 

 Essential vocabulary for this standard includes: numerical expressions, algebraic expressions, evaluate, sum, term, product, factor, quantity, quotient, like terms, equivalent expressions, and variables. 

 

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Write expressions with unknowns.
  • Identify mathematical terms and use them to write or interpret expressions.
  • Evaluate expressions with unknowns using the order of operations.
  • Recognize and use expressions as common real-world formulas (i.e. volume of a cube, V = s3).

 

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 5 Grade 7
  • Write simple expressions (5.OA.2)
  • Graph two patterns/rules on coordinate plane (5.OA.3)
  • Apply properties of operations to linear expressions (7.EE.1)

 

 

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

  • Write an algebraic expression for this situation: 9 more trees than the t trees planted in each of the two rows.
  • What is the value of the expression 0.25x + 0.5y3 - z when x = 8, y = 2, and z = 5. Explain how you know you are correct.
  • For 4 weeks a group of students decide to ride their bikes to school everyday except on the days it rains. It rained 1 day each week. Let d represent the distance each student rode to school in miles per day. Write an expression that represents how far a student travels by bike in the 4 weeks. 4(4d) or 16d
  • The formula C = 5/9(F - 32) is used to convert temperatures in degrees Fahrenheit to temperatures in degrees Celsius. What is the temperature in degrees Celsius when the temperature is 68 degrees Fahrenheit?

 

SLIDE-BASED TASKS 

 These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 5 • Expressions

Read, Write, and Evaluate Expressions (no exponents):

 

 

Additional Tasks 

These links provide instructional ideas connected to this standard. 

A30Y5W

 

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them. 

Print Resources
Book Thumbnail Book Title Grade Pages
Teaching Student-Centered Mathematics 6-8

Tilt or Balance, Activity 12.3, Page 228
Number Tricks, Activity 12.9, Page 235
Teaching Student-Centered Mathematics 5-8

275 (Story Translations, Activity 9.7)
277 (What's True for All Numbers, Activity 9.9)
277 (Special Quantities, Activity 9.10)
279 (Names for Numbers, Activity 9.11)
280 (Adjust the Balance, Activity 9.13)

Hands-On Standards

 

 5-6 106 (Order of Operations)

Nimble with Numbers

 5-6

14

17-19

22-23

Nimble with Numbers

6-7

129 (Phrases to Symbols)

132-135 (Creating Equations)

140-142 (Solve and Travel)

Groundworks: Reasoning with Numbers

 5 57-59

 

 

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

 

 

 

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

 These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

 

 

 

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Assessment

Learning Targets

rubric

  • Write expressions with unknowns.
  • Identify mathematical terms and use them to write or interpret expressions.
  • Evaluate expressions with unknowns using the order of operations.
  • Recognize and use expressions as common real-world formulas (i.e. volume of a cube, V = s3).

 

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading. 

 

 

 

 

 

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