

LFSDIGITAL KUD for Unit: Simplifying Expressions
Key Learning
(What is the big understanding for this unit? What will you ultimately want students to understand as a result of the instruction? This is a “big picture” understanding, based both on the most critical standards and the thematic focus of the unit.)

Numerical and algebraic expressions can be simplified using integer and exponent rules, scientific notation, and the distributive property.

Unit Essential Question
(What broad question will students be able to answer as a result of the instruction? This question should reflect the most critical standards on which the instruction is based. This question is the inverse of the Key Learning; the Key Learning would provide an “ideal” response to this question.)

What mathematical rules and properties can be used to simplify numerical and algebraic expressions?

Unit Description
(Briefly summarize the focus and content of the unit.) 
Students will learn to simplify a variety of numerical expressions using integer and exponent rules, order of operations, and scientific notation. Students will perform computations with large and small numbers expressed in scientific notation. Students will represent multiplication of whole and mixed numbers using the Distributive Property. Students will extend many of these concepts to combining like terms in algebraic expressions. The Distributive Property will again be used to multiply variable expressions prior to combining like terms. To extend or differentiate, linear equations requiring the use of the Distributive Property may be explored. 
GradeLevel Standards Addressed in the Unit
(List the critical gradelevel standards on which the instruction will be based. Since many of the standards are recursive, reinforced throughout the year’s instruction, list only those that will be the focus of the instruction and assessments for this unit.)

8.1.5Perform computations with exponents, powers of 10, and scientific notation
8.1.8Explain how the distributive property is used to multiply (e.g., partial products, mixed numbers)
8.1.9Use meaningful relationships between addition, subtraction, multiplication, and division of integers to justify the rules of operations
8.2.10 Apply the order of operations
8.2.13 – Combine two algebraic expressions to form a new expression
CC.8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(5) = 3^(3) = 1/(3^3) = 1/27.
CC.8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 
Know
(Factual: nouns or noun phrases related to key concepts; terminology, academic vocabulary, formulas, etc., often found or implied in the language of the gradelevel standards.) 
Understand
(Conceptual: key understandings that students will gain as a result of the instruction within the unit, found in the language of the gradelevel standards, and generally written in complete sentences. These understandings will contribute to the overall key learning of the unit.) 
Do
(Procedural, Extending Thinking: written as verb phrases, often found or implied in the language of the gradelevel standards. These statements provide discreet targets for demonstrating learning. Often the assessments for the learning will be selected
from this column.) 
· Simplify
· Order of operations
· Numerical expression
· Algebraic or variable expression
· Base
· Exponents
· Integers
· Scientific notation
· Mantissa
· Distributive property
· Like terms
· Linear equation 
· Order of operations requires numerical expressions to be simplified sequentially by grouping symbols, exponents, multiplication/division in order, and addition/subtraction in order left to right.
· When multiplying like bases, the base is rewritten, and the exponents are added.
· When dividing like bases, the base is rewritten, and the exponents are subtracted.
· Large numbers can be written in scientific notation by writing the product of the mantissa and ten raised to a positive exponent.
· Small numbers can be written in scientific notation by writing the product of the mantissa and ten raised to a negative exponent.
· Calculations can be performed on scientific notation by applying the exponent rules.
· The distributive property can be used to eliminate grouping symbols so that like terms can be combined.
· Whole number multiplication, combining like terms, and mixed number multiplication can be modeled using the distributive property.

· Use order of operations when simplifying numerical and algebraic expressions.
· Simplify multiplication and division problems involving like bases using exponent rules.
· Express large and small numbers in scientific notation.
· Translate scientific notation to an equivalent number in standard form.
· Perform calculations with numbers written in scientific notation.
· Interpret scientific notation as stated on different calculator displays.
· Apply the distributive property to solve multiplication problems involving whole and mixed numbers.
· Apply the distributive property to multiply algebraic expressions.
· Justify combining like algebraic terms using the order of operations and the distributive property.
· *Select and use the appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. (3,4,6)

Print Resources

 Mathematics in Context, Level 3, Holt, Rinehart, & Winston (2006), Revisiting Numbers (pages 852),
Algebra Rules (pages 111, 4754)
 Algebra I, Holt, Rinehart, & Winston, (2003), (pages 54103, 141146, 370403)

Discovery Education Resources
8.1.5Perform computations with exponents, powers of 10, and scientific notation
Video:
Exponents
Section A: What Is an Integer Exponent?
Section B: Rules of Exponents
Scientific Notation
An Introduction to Exponents
Practice Problems
Multiplying Numbers with Exponents
The Power of Zero
Exponents & Expanded Notation
Introduction (Scientific Notation)
Example 1: ExponentsInterest
Example 2: Scientific NotationBlood Cells
Example 3: Scientific Notation for Very Low NumbersDNA
Same Base: The First Law of Exponents (Product of Powers Property)
Multiplying Exponents
Same Base: The Second Law of Exponents (Quotient of Powers Property)
The Third Law of Exponents: Power of a Power Property
Different Bases: Using the First Law of Exponents
Definition of Zero Exponent
Dividing Exponents
Instructional Images:
Scientific notation; prefixes
Scientific notation; algebra
Powersof10
8.1.8Explain how the distributive property is used to multiply (e.g., partial products, mixed numbers)
Video:
The Distributive Properties of Multiplication over Addition
Distributive Property: Multiplying a Monomial and Binomial
Distributive Property: Multiplying Binomials
Working with Partial Products
8.1.9Use meaningful relationships between addition, subtraction, multiplication, and division of integers to justify the rules of operations
Video:
Integer: What Is It?
Modeling Addition With Zero Pairs: Part 1
Modeling Addition With Zero Pairs: Part 2
Modeling Subtraction With Zero Pairs: Part 1
Modeling Subtraction With Zero Pairs: Part 2
Addition and Subtraction of Integers: Algorithms
Example 2: Negative IntegersGoing Down
Adding Integers Using the Counter Model
Adding Integers: Computation
Multiplying Integers Using the Number Line
Multiplying Integers Using the Counter Method
Multiplying Integers: Computation
Integer Division: Using the Number Line, Counter Method, and Computation
Math Overview:
Grades 0708: Using a Number Line to Add Integers
Grades 0708: Dividing Integers
Grades 0708: Multiplying Integers
Grades 0708: Subtracting Integers
Math Explanation:
Grade 05: Add Integers: Explaining Whether a Sum will be Positive or Negative
Grade 05: Add Integers: Deciding if a Sum is Negative, Positive, or Zero without Adding
Grades 0708: Subtracting Integers: Understanding How to Subtract Integers with Different Signs
8.2.10 Apply the order of operations
Video:
Order of Operations
The Standard Order of Operations
Simplifying to Find the Answer: Three Practice Expressions
Order of Operations with Fractions & Radicals
Adding Parentheses to Equations
Introduction (Order of Operations)
Example 1: Simple OrdersRoller Coaster Capacity
Example 2: More OrdersRevenue
Math Overview:
Grades 0708: Order of Operations
Math Explanation:
Grades 0708: Order of Operations: Insert Parentheses to Make an Equation True
Grades 0708: Order of Operations: Understanding Order of Operations
Grades 0708: Order of Operations: Evaluating Expressions Using Order of Operations
Grades 0708: Order of Operations: Using Order of Operations and a Calculator to Evaluate Expressions
8.2.13 – Combine two algebraic expressions to form a new expression
Video:
Simplifying Equations and Understanding Expressions
Identifying Equivalent Expressions
De Nile: Creating Patterns and Solving Problems
Introduction (Algebraic Expressions)
Example 2: Expanding Expressions and Combining Like TermsDolls
Example 3: Expanding, Combining, and SubstitutingSkateboards
Section A: Mixing Numbers and Letters
Math Overview:
Grades 0708: Combining Like Terms
Math Explanation:
Grades 0708: Combining Like Terms: Simplifying Expressions with Two Variables and Evaluating
Grades 0708: Combining Like Terms: Writing a Variable Expression to Find Perimeter and Evaluating
Grades 0708: Combining Like Terms: Writing Variable Expression from a Diagram and Evaluating
Grades 0708: Combining Like Terms: Describing Steps to Simplify a Variable Expression
Grades 0708: Expressions and Variables: Simplifying a Variable Expression and Evaluating for a given Variable
Grades 0708: Combining Like Terms: Simplifying and Combining Like Terms
Open Resources
* See also Grade 7, Math, Exponents and Grade 8, Math, Growth
Resource 1: Factoring and the Distributive Property ebook and accompanying Factoring Using the Distributive Property video
Media type: ebook, video Description: An introductory video and ebook that includes descriptions and problems for factoring using the distributive property and finding the greatest common factors (GCF). Level: Intemediate
Credit: K12 Handhelds License: CC BY
Notes/activity suggestions:
Tags: grade8, math, factoring, distributive property, common factor, GCF, ebook 
Resource 2: Elementary Algebra  Variables, Expressions, Equations; Associative, Commutative, and Distributive Properties; Basic Expressions; Using the Distributive Property
Media type: online course Description: These modules in the Elementary Algebra course include audio, sample problems, and explanations for the topics listed. Level: Intermediate, Advanced
Credit: Monterey Institute for Technology and Education
License: custom, noncommercial
Notes/activity suggestions:
Tags: grade8, math, distributive property, variables, expressions, associative property, commutative property, algebra 
Resource 3: Equations and Expressions
Media type: text Description: A series of explanation pages and worksheets that begins with the basics of multiplication as comparison and grouping of expressions with parentheses and then goes on to cover order of operations, writing simple expressions, and evaluting expressions. Includes pre and postassessment and practice worksheets. Credit: HelpingWithMath.com License: CC BY SA
Notes/activity suggestions:
Tags: grade8, math, factoring, distributive property, common factor, GCF

Resource 4: Order of Operations Part 1, Order of Operations Part 2
Media type: video Description: Two short videos on the order of operations using PEMDAS Level: Intermediate
Credit: Duane Habecker, Next Vista License: CC BY SA
Notes/activity suggestions:
Tags: grade8, order of operations, PEMDAS 
Resource 5: FlexMath > Prime > Equations and Algebra Topics
Media type: interactive Description: Interactive drill practice of math skills. Wrong answers are penalized, and a 90% score is needed to pass. Topics include basic and advanced order of operations, basic exponential expressions, and more advanced topics. Level: Intermediate, Advanced
Credit: CK12 License: CC BY NC ND
Notes/activity suggestions:
Tags: grade8, math, order of operations, exponents, algebra 
Media type: text Description: Lesson plans that cover the distributive property and combining like terms through real world examples. Powerpoint presentation includes explanations and examples. Level: Advanced
Credit: mathercize Luke Lang License: CC BY
Notes/activity suggestions:
Tags: grade8, math, distributive property, combining like terms, algebra

Resource 7: Prealgebra  Variables, Expressions and Equations (includes combining like terms, the distributive property, and solving equations)
Media type: video, text Description: Algebra2Go units include class notes in English and Spanish, video lectures in multiple formats, and accompanying worksheets. These resources were produced for a community college audience, but are secondary level math concepts. They are presented with a great deal of scaffolding and support that will be helpful to at risk students. Level: Intermediate
Credit: Algebra2Go, Larry Perez License: CC BY SA
Notes/activity suggestions: Tags: grade8, math, distributive property, combining like terms, algebra
Thinkfinity Resources
Last modified at 7/21/2011 10:25 AM by SEAFORD\jwwhite



