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LFS DIGITAL > Instructional Unit Topics > Math Unit Topics > Simplifying expressions  

Simplifying expressions

LFS-DIGITAL K-U-D 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.

Grade-Level Standards Addressed in the Unit

(List the critical grade-level 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.)

 

8.1.5-Perform computations with exponents, powers of 10, and scientific notation

8.1.8-Explain how the distributive property is used to multiply (e.g., partial products, mixed numbers)

8.1.9-Use 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 grade-level standards.)

Understand

(Conceptual:  key understandings that students will gain as a result of the instruction within the unit, found in the language of the grade-level 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 grade-level 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 8-52),

                 Algebra Rules (pages 1-11, 47-54)

  • Algebra I, Holt, Rinehart, & Winston, (2003), (pages 54-103, 141-146, 370-403)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

Discovery Education Resources


8.1.5-Perform 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: Exponents--Interest

Example 2: Scientific Notation--Blood Cells

Example 3: Scientific Notation for Very Low Numbers--DNA

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

Powers-of-10

 

8.1.8-Explain 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

8.1.9-Use 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 Integers--Going 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 07-08: Using a Number Line to Add Integers

Grades 07-08: Dividing Integers

Grades 07-08: Multiplying Integers

Grades 07-08: 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 07-08: 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 Orders--Roller Coaster Capacity

Example 2: More Orders--Revenue

Math Overview:

Grades 07-08: Order of Operations

Math Explanation:

Grades 07-08: Order of Operations: Insert Parentheses to Make an Equation True

Grades 07-08: Order of Operations: Understanding Order of Operations

Grades 07-08: Order of Operations: Evaluating Expressions Using Order of Operations

Grades 07-08: 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 Terms--Dolls

Example 3: Expanding, Combining, and Substituting--Skateboards

Section A: Mixing Numbers and Letters

Math Overview:

Grades 07-08: Combining Like Terms

Math Explanation:

Grades 07-08: Combining Like Terms: Simplifying Expressions with Two Variables and Evaluating

Grades 07-08: Combining Like Terms: Writing a Variable Expression to Find Perimeter and Evaluating

Grades 07-08: Combining Like Terms: Writing Variable Expression from a Diagram and Evaluating

Grades 07-08: Combining Like Terms: Describing Steps to Simplify a Variable Expression

Grades 07-08: Expressions and Variables: Simplifying a Variable Expression and Evaluating for a given Variable

Grades 07-08: 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

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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, non-commercial

Notes/activity suggestions:

Tags: grade8, math, distributive property, variables, expressions, associative property, commutative property, algebra

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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 post-assessment and practice worksheets.

Credit: HelpingWithMath.com
License: CC BY SA

Notes/activity suggestions:

Tags: grade8, math, factoring, distributive property, common factor, GCF

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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

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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

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Resource 6:  Balancing with Parentheses (distributive property), Comparing apples to x's (combining like terms)

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

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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

 

 



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Last modified at 7/21/2011 10:25 AM  by SEAFORD\jwwhite