Established Goal(s)/Content Standard(s):  8.EE.2 

Use square root and cube  root symbols to represent  solutions to equations of the  form x2 = p and x3 = p, where  p is a positive rational  

number. Evaluate square  roots of small perfect squares  and cube roots of small  

perfect cubes. Know that √2 is  irrational.

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.  For example, estimate the  population of the United States  as 3 times 108 and the  

population of the world as 7  times 109, and determine that  the world population is more  than 20 times larger

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.

Understanding (s)

Students will understand that:

• How to recognize perfect squares. • How to recognize perfect cubes. • That non-perfect squares and non perfect cubes are irrational  

numbers. 

• Squaring a number and taking the  square root (√ ) of a number are  inverse operations. 

• Cubing a number and taking the  cube root (√3) of a number are  

inverse operations. 

• When solving x2 = 36, there are two  solutions, ±6 since 6 x 6 = 36  

and -6 x -6 = 36.

EE3• Scientific notation is used to  

express very large or very small  

numbers. 

• When looking at a number in  

scientific notation, if the exponent  increases by one, the value  

increases 10 times. 

• When looking at a number in  

scientific notation, if the exponent  decreases by one, the value  

decreases 10 times.

EE4 • Scientific notation is used to  

express very large or very small  

numbers. 

• How to compare and interpret  scientific notation quantities in the  context of the situation with or  

without a scientific calculator. 

• When looking at a number in  

scientific notation, if the exponent  increases by one, the value  

increases 10 times. 

• When looking at a number in  

scientific notation, if the exponent  decreases by one, the value  

decreases 10 times. 

• How to read a number that is  written in scientific notation using  

technology. For example, 3.7E-2 is  3.7 x 10-2.

Essential Question(s):(found in Pearson book)

• How do you evaluate square roots and cube roots?
• How can you solve equations with squares and cubes?

Student objectives (outcomes): See Scaffolding Document

Students will be able to: What key knowledge and skills will students acquire as a result of this unit?

• Find square roots of numbers. 

• Find cube roots of numbers. 

• Estimate square roots and cube  roots to the nearest integer. 

• Order and compare real numbers. • Find the distance between two  points using the distance formula. 

• Find parts of a right triangle using  the Pythagorean Theorem.  

• Find the edge length of a cubical  object with a given volume.

EE3- • Compare and interpret scientific  notation quantities in the context of  the situation. 

• Evaluate expressions involving  addition, subtraction, multiplication,  or division and express the answer  in scientific notation.

EE4 • Perform operations with numbers  expressed in both decimal and  

scientific notation and express the  answer in scientific notation without  a scientific calculator. 

• Compare and order numbers  

expressed as decimals and  

scientific notation without a  

calculator. 

• Choose a meaningful unit of  

measure in the context of the  

situation with and without a  

scientific calculator. 

• Interpret scientific notation that has  been generated by a scientific  

calculator.

What do students need to know to meet the above standard?

To understand, students will need to know……

• • The radical sign is the symbol √ placed  before a number or quantity to indicate  the extraction of a root, which will be the  square root. The value of a higher root is  indicated by a raised digit in front of the  symbol, as in√3,√4, …√����, where n is  an integer. 
• • The square root of a number is one of its  two equal factors. If a2 = b, then a = ± √����. • A perfect square is a rational number  whose square root is a whole number.  For example, 36 is a perfect square  
• because its square root is 6. 
•  
• • The cube root of a number is one of three  equal factors of a number. If a3 = b, then  a =√���� 3. 
• • A perfect cube is a rational number  whose cube root is a whole number. For  example, 64 is a perfect cube because its  cube root is 4. 
• • A rational number is a number expressed  in the form a/b or –a/b for some fraction  a/b. The rational numbers include the  integers. 
• • An irrational number is a number that  cannot be expressed as the ratio a/b,  where a and b are integers and b ≠ 0. 

EE3-• Scientific notation is when you  express a number as the product of  two factors. The first factor must be  greater than or equal to one but less  than 10 and the second factor is a  power of 10. For example, ���� × 10���� , ����ℎ������������ 1 ≤ ���� < 10 and n is an integer 

• How to write a number in scientific  notation from standard form. 

• How to write a number in standard  form from scientific notation. 

• Exponential and standard forms of  powers of 10. For example, 0.1 is  10-1.

EE4 • Scientific notation is when you  express a number as the product of  two factors. The first factor must be  greater than or equal to one but less  than ten and the second factor is a  power of ten. For example, ���� × 

10���� , ����ℎ������������ 1 ≤ ���� < 10 and n is an  integer 

• How to write a number in scientific  notation from standard form. 

• How to write a number in standard  form from scientific notation. 

• Exponential and standard forms of  powers of 10. For example, 0.1 is  10-1. 

• How to convert a number from  standard form to scientific notation  with and without the use of  

technology

Performance Task(s):

Through what authentic performance task(s) will students demonstrate the desired understandings?

• Edulastic
• Envision MAth XL
• Lesson Quiz

Other Evidence:

Through what other evidence will students demonstrate achievement of the desired results?

• Bellringer
• Exit Ticket
• Homework

Learning Activities:

Day 1- Quotient of Powers and Product of Powers

Bellringer- Envision Midtopic Check point, Numbers 1-3

Intro-  1-6 Additional Vocab and Essential Question “How do properties of integer exponents help you write equivalent expressions?

Model: 1-6 reteach to build, #2,5,8 page 42. 

Guided Practice- #9 and 10 page 43  

Independent Practice- page 43,13a-b.,14,16 and 17

Homework- Quotient of Powers (1st page) and Mathland Worksheet (Product of Powers)

Day 2- Power of a Power and Power of Products

Bellringer: Midtopic Check point 4-6

Review: Homework

Drill: Product of Powers and Quotient of Powers

Introduce: Power of Power and Power of Products ( review Additional Vocab definitions)

Model/ Guided: 4,7,and 12 page 42-43 AND 3,6,11,13 c and d,15

Independent/ hw: 1-6  Additional Practice

Day 3- Negative Exponent and Zero Exponent Rule

1.  Bellringer: Topic 1 Mid Topic Assessment,1-3
2. Review homework
3. Drill: All exponent rules learned so far.
4. Intro: Video https://psn.virtualnerd.com/viewtutorial/Alg1_6_2_7 and https://psn.virtualnerd.com/viewtutorial/Alg1_6_2_8
5. Vocabulary: Additional Vocab 1-7

• Model: 1-7 Reteach to Build
• Guided Practice: pages48
• Independent/ Practice: Envision page 49-50 (13 minutes)

1. Homework: Lesson Quiz 1-7

• Exit Ticket: Topic 1 Mid Topic Assessment,4-6

Day 4- Independent Practice On ALL EXPONENT RULES

1. Bellringer: Midtopic Performance Task Part A-C
2. Review: Homework (5 minutes)
3. Drill and discuss:All exponent rules (One of each will be on board)

• Independent Practice:  1-6 and 1-7 Additional Practices Math XL

Day 5 - More Practice with Exponent Rules STATION/Groups

Bellringer: Enter Bells and Exits into ENVISION ( will try to get this done thursday so we can have time for stations)

Station 1: Sq. Roots and Cube Roots Puzzle

Station 2: Properties of Exponents Cut and Paste

Station 3: Properties of Exponents Solve and Color

Station 4: Prop. of Exponents Technology Station (Computer work)