Word (.docx)
Acrobat (.pdf)
Examples
Evaluate the expression
, where a=-1 and b=15.
Clarifications
Clarification 1: Within this benchmark, the expectation is to perform all operations with integers.Clarification 2: Refer to Properties of Operations, Equality and Inequality (Appendix D).
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Base
- Coefficient
- Exponent
- Expression
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 5, students translated written real-world and mathematical descriptions into numerical expressions, evaluated multi-step numerical expressions used order of operations involving combinations of the four arithmetic operations and parentheses with whole numbers, decimals and fractions. They also determined and explained whether an equation involving any of the four operations is true or false. In grade 6, students will use substitution to evaluate algebraic expressions, including exponents and integer coefficients. The values being substituted will also be integers. This benchmark extends to grade 7 where students will evaluate more complex numerical expressions with rational coefficients, apply laws of exponents and generate equivalent linear expressions.- Substitution is the process in which a symbol or variable is replaced by a given value. In prior grades students have found missing terms in equations and then substituted the value back in to check it they are correct.
- For example, students may have seen something such as 2+? =10 and decided that 8 is the value that should replace the ?.
- This prior experience can be used to connect prior student understanding with new learning. In grade 6, instead of seeing a symbol like a question mark or a box for a missing value, we use letters called variables.
- An algebraic expression is built from integer constants, variables and operations whereas an equation is the statement of two equivalent expressions. This benchmark is specifically addressing substitution.
- Depending on the given expression, students may see opportunities to start generating equivalent expressions before substituting the value of the variable(s). This is a way students can demonstrate flexible thinking and the understanding of patterns and structure in mathematical concepts (MTR.5.1).
Common Misconceptions or Errors
- Students may incorrectly generate equivalent expressions using the order of operations.
- If more than one variable is present in a given expression, students may incorrectly substitute one value in for all given variables or apply the wrong value to each of the variables. To address this misconception, students can use colors (pens, pencils, markers) to keep track of which variable and location correspond to each given value.
- If students try to generate an equivalent expression before substituting integer values, they may try to combine unlike terms (constants with variables or unlike variable terms).
Strategies to Support Tiered Instruction
- Instruction includes building a foundation for the meaning of substitution by introducing algebraic expressions in a single variable with an exponent of 1 and representing the expression with algebra tiles. Then the variable tile can be replaced with the appropriate number of unit tiles to represent the provided value and the expression can be evaluated. The algebraic expression should be represented simultaneously to draw connections between the concrete and abstract representations. Use this foundation to build towards using algebraic strategies to evaluate expressions that cannot be represented with algebra tiles.
- For example, when evaluating 3 + 5 when = −4, students can represent this as shown below.
- For example, when evaluating 3 + 5 when = −4, students can represent this as shown below.
- Teacher provides opportunities for students to use different colored pencils to represent different variables and use the coordinating color to replace the variable with its assigned value before utilizing the order of operations to evaluate.
- For example, if evaluating the expression −52 + , where = −3 and =−12, the teacher can color coordinate as shown below.
−52 + ; = −3 and = −12
−5(−3)2 + (−12)
−5(9) + (−12)
−45 + (−12)
−57
- For example, if evaluating the expression −52 + , where = −3 and =−12, the teacher can color coordinate as shown below.
- Teacher models how students can use colors (pens, pencils, markers) to keep track of which variable and location correspond to each given value.
Instructional Tasks
Instructional Task 1 (MTR.5.1)To compute the perimeter of a rectangle you add the length, l, and width, w, and double this sum.
- Part A. Write an expression for the perimeter of a rectangle.
- Part B. Use the expression to find the perimeter of a rectangle with length of 15 feet and width of 8 feet.
Instructional Task 2 (MTR.6.1)
To determine the distance traveled by a car you multiply the speed the car traveled by the amount of time the car was traveling at that speed. The scenario can be represented as st, where s is speed, and t is time. What is the distance traveled by a car that travels at an average speed of 75 miles per hour for 20 minutes?
Instructional Items
Instructional Item 1If x = 3, find 3x + 8.
Instructional Item 2
If p = 8, find 1 p − 3.
Evaluate the expression −5 a2 + c, where a=−3 and c= −12.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Tutorials
Virtual Manipulative
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
Original Student Tutorials Mathematics - Grades 6-8
Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.
Evaluate numerical expressions with fractions using the order of operations and properties of operations in this interactive tutorial.
Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial.
Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.
Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.
This is part 2 of a series on evaluating expressions with whole numbers.
Computer Science Original Student Tutorials
Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.
Student Resources
Original Student Tutorials
Evaluate numerical expressions with fractions using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Evaluate numerical expressions with decimals using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.
This is part 2 of a series on evaluating expressions with whole numbers.
Type: Original Student Tutorial
Evaluate numerical expressions with integers using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.
Type: Original Student Tutorial
Evaluate numerical expressions with whole numbers using the order of operations and properties of operations in this interactive tutorial.
Type: Original Student Tutorial
Tutorials
Learn how to evaluate an expression with variables using a technique called substitution.
Type: Tutorial
This video demonstrates evaluating expressions with two variables.
Type: Tutorial
Explore how the value of an algebraic expression changes as the value of its variable changes.
Type: Tutorial
In this example, we have a formula for converting a Celsius temperature to Fahrenheit.
Type: Tutorial
Students will evaluate expressions using the order of operations.
Type: Tutorial
Work through a challenging order of operations example with only positive numbers.
Type: Tutorial
Work through a challenging order of operations example with only positive numbers.
Type: Tutorial
This video will show how to evaluate expressions with exponents using the order of operations.
Type: Tutorial
In this example we have a formula for converting Celsius temperature to Fahrenheit. Let's substitute the variable with a value (Celsius temp) to get the degrees in Fahrenheit. Great problem to practice with us!
Type: Tutorial
Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.
Type: Tutorial
Virtual Manipulative
In this activity, students practice solving algebraic expressions using order of operations. The applet records their score so the student can track their progress. This activity allows students to practice applying the order of operations when solving problems. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
