Unit Title: Growing, Growing, Growing 5.1 and 5.2 & Common Core Units Investigations 1 Suggested Time: 6 Days

Enduring understanding (Big Idea): Write expressions involving repeated multiplication using exponents, simplify fractions and decimals raised to powers, apply properties of integer exponents to generate equivalent expressions; use cube root symbols to represent solutions

Essential Questions: How to use the patterns in powers to estimate the ones digit for unknown patterns? What do you do to multiply numbers with the same base? What do you do to raise a power to a power? What do you do to divide numbers with the same base? How do you find the cube root of a number?

Unit Plans

Common Core Standards Alignment

Connection to 2003 Standards

Investigation 5
Patterns with Exponents
Problems 5.1, 5.2
Math Reflections

Work with radicals and integer exponents8.EE.1- Know and apply the properties of integer exponents to generateequivalent numerical expressions. 8.EE.3- Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities,and to express how many times as much one is than the other.

8.EE.4-Perform operations with numbers expressed in scientific notation,including problems where both decimal and scientific notationare used. Use scientific notation and choose units of appropriatesize for measurements of very large or very small quantities

Define, evaluate, and compare functions 8.F.3- Interpret the equation y = mx + b as defining a linear function,whose graph is a straight line; give examples of functions thatare not linear

Goal 1.01

CC Investigation 1: Negative Exponents
Problems 1.1, 1.2

Work with radicals and integer exponents8.EE.1- Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE.2 -Use cube root symbols to represent solutions toequations of the form and x3 = p, where p is a positive rationalnumber. Evaluate cube rootsof small perfect cubes.

Goal 1.01

Prior Knowledge: Looking for graphical or symbolic models to describe a pattern in data; Reasoning relationships such as connections among attributes of geometric figures; representing relationships with words, tables, graphs and equations; exploring the significance of shapes of graphs and patterns in tables; attaching meaning to symbols in linear equations of the form y = mx + b; using exponents to express large and small quantities

Mathematical Practices Standards for Common Core 1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and critique the reasoning of others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for and make use of structure 8-Look for and express regularity in repeated reasoning

Essential Terms Developed in This Unit

Useful Terms Referenced in This Unit

Terms Developed in Previous Unit

Base
Cube Root
Exponent
Law
Growing, Growing, Growing

Now that the students have a solid understanding of linear relationships -- relationships based on repeated addition -- Growing, Growing, Growing expands that knowledge to include exponential relationships, which are relationships based on repeated multiplication. Students study various real-life scenarios in which exponential relationships exist, such as population growth, the growth of bacteria, the spread of an invasive plant species across a pond. They learn to move fluently among the four ways to represent these relationships, which are words, tables, graphs and equations.

Example of a linear function: y = 2x + 7

Example of an exponential function: y = 4^x + 7

For an in-depth explanation of unit goals, specific questions to ask your student and examples of core concepts from the unit, go to Growing, Growing, Growing.

Unit Technology Tips Goals of the Unit • Recognize situations in which one variable is an exponential function of another variable • Recognize the connections between exponential equations and growth patterns in tables and graphs of those equations • Construct equations to express exponential patterns that appear in data tables, graphs, and problem conditions • Understand and apply the rules for operating on numerical expressions with exponents • Solve problems about exponential growth and decay from a variety of different subject areas, including science and business • Compare exponential and linear relationships

Unit Title: Growing, Growing, Growing 5.1 and 5.2 & Common Core Units Investigations 1Suggested Time: 6 DaysEnduring understanding (Big Idea):Write expressions involving repeated multiplication using exponents, simplify fractions and decimals raised to powers, apply properties of integer exponents to generate equivalent expressions; use cube root symbols to represent solutionsEssential Questions:How to use the patterns in powers to estimate the ones digit for unknown patterns? What do you do to multiply numbers with the same base? What do you do to raise a power to a power? What do you do to divide numbers with the same base? How do you find the cube root of a number?Unit PlansCommon Core Standards AlignmentConnection to 2003 StandardsInvestigation 5Patterns with Exponents

Problems 5.1, 5.2

Math Reflections

Work with radicals and integer exponents8.EE.1- Know and apply the properties of integer exponents to generateequivalent numerical expressions.8.EE.3-Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities,and to express how many times as much one is than the other.8.EE.4-Perform operations with numbers expressed in scientific notation,including problems where both decimal and scientific notationare used. Use scientific notation and choose units of appropriatesize for measurements of very large or very small quantitiesDefine, evaluate, and compare functions8.F.3- Interpret the equationy=mx+bas defining a linear function,whose graph is a straight line; give examples of functions thatare not linearCC Investigation 1: Negative ExponentsProblems 1.1, 1.2

Work with radicals and integer exponents8.EE.1- Know and apply the properties of integer exponents to generate equivalent numerical expressions.8.EE.2 -Use cube root symbols to represent solutions toequations of the form and x3 = p, where p is a positive rationalnumber. Evaluate cube rootsof small perfect cubes.Prior Knowledge:Looking for graphical or symbolic models to describe a pattern in data; Reasoning relationships such as connections among attributes of geometric figures; representing relationships with words, tables, graphs and equations; exploring the significance of shapes of graphs and patterns in tables; attaching meaning to symbols in linear equations of the form y = mx + b; using exponents to express large and small quantitiesMathematical Practices Standards for Common Core1-Make sense of problems and persevere in solving them 2-Reason abstractly and quantitatively 3-Construct viable arguments and critique the reasoning of others 4-Model with mathematics 5-Use appropriate tools strategically 6-Attend to precision 7-Look for and make use of structure 8-Look for and express regularity in repeated reasoningEssential Terms Developed in This UnitUseful Terms Referenced in This UnitTerms Developed in Previous UnitCube Root

Exponent

Law

Growing, Growing, Growing

Exponential equations## Now that the students have a solid understanding of linear relationships -- relationships based on repeated addition --

Growing, Growing, Growingexpands that knowledge to include exponential relationships, which are relationships based on repeated multiplication. Students study various real-life scenarios in which exponential relationships exist, such as population growth, the growth of bacteria, the spread of an invasive plant species across a pond. They learn to move fluently among the four ways to represent these relationships, which are words, tables, graphs and equations.## Example of a linear function:

y= 2x+ 7## Example of an exponential function:

y= 4^x+ 7## For an in-depth explanation of unit goals, specific questions to ask your student and examples of core concepts from the unit, go to Growing, Growing, Growing.

Online resources for*Growing, Growing, Growing## Exponents

## Exponent Review

## Laws of Exponents—Power of a Product & Power of a Power

## Laws of Exponents—Power of a Quotient

## Laws of Exponents—The shortcuts

## Exponential Functions

## Interactive example of exponential growth

## Trout population tool

## Two real-life lessons using exponential growth

## A powerful example of exponential growth

Other online resources- General Homework Tips
- Homework examples from Growing, Growing, Growing

s of ExponentsEvaluate

Linear growth

Standard form

Rate

Ratio

Relationship

Power

Scientific notation

ResourcesLab-Sheet

Additional Practice/Skills Worksheets

CMP2 Website –online & technology resources

Formal Assessment

- Check-Ups
- Partner Quiz
- Unit Test

Assessment Options- Notebook check
- Multiple-Choice
- Question Bank
- ExamView CD-ROM

Parent Guide-Unit LettersSpanish Assessment Resources

PHSchool.com

TeacherExpress CD-ROM

LessonLab Online Courses

Unit Technology Tips

Goals of the Unit• Recognize situations in which one variable is anexponential function of another variable• Recognize the connections between exponentialequations and growth patterns in tables andgraphs of those equations• Construct equations to express exponentialpatterns that appear in data tables, graphs, andproblem conditions• Understand and apply the rules for operatingon numerical expressions with exponents• Solve problems about exponential growth anddecay from a variety of different subject areas,including science and business• Compare exponential and linear relationshipsHomework Help