This week we’re learning about exponents, expanded form, and prime factorization!

This week we will begin discussing exponents. Exponents are the little tiny numbers that sit to the top right corner of the larger numbers. Those larger numbers are called the base number.

The base number is the number that is to be multiplied, the exponent tells you how many times it should be multiplied. In this example, you will multiply 8 by itself 2 times. So 8² would be written 8 x 8.

Check out another example below!

Whenever you have the exponents, you must multiply the base as many times as the exponent designates. DO NOT MULTIPLY THE BASE TIMES THE EXPONENT!!!!

Exponents can also be used to help write a number in expanded form. Instead of writing out 50,000; one can simply write 5 x 10⁴. To check this, you can perform the operations 5 x 10 x 10 x 10 x 10. You will find this is 50,000. Please see the example below for more expanded form using exponents.

Lastly, exponents can be used to write the prime factorization of a number. Please view the factor tree below:

In this tree, we are breaking down 96 to find its prime factors. We chose to first break 96 into 8 x 12. (You can always choose other factors of 96 to break it down, these are just the factors chosen for this particular example). Next, we break down 8 and twelve. We know that 4 x 2 = 8, so we will break 8 down into 4 and 2. We also know that 4 x 3 = 12, so we will break down 12 into 4 and 3. Two and three are red because they are prime numbers, therefore they cannot be broken down any more. The 4’s however, can be broken down into 2 x 2. The twos are then written in red as well. Therefore, our prime factors of 96 are 2 x 2 x 2 x 2 x 2 x 3. This prime factorization can also be written: 2⁵ x 3.

Monday: BLACK
Learning Target(s): I can identify the prime factors of a number.
Success Criteria:  I can express and find the value of numbers using an exponent and base.
Procedures:

·         Introduction of terms: exponent and base.

·         Work together to rewrite 3⁴ as a multiplication problem and to find the value of 3⁴.

·         Students also discuss in groups how 2⁶ and 6² are different.

·         Work in groups to complete #’s 3-15 in class.

o   Use discussion cards to discuss and explain answers.

o   Go over answers as a class.

·         STUDENTS WRITE: how to write 7⁴ as a multiplication problem prior to leaving class.

FLEX: Go over Lesson 16 answers in class. Then we will discuss Quiz #4 problems for Wednesday.

Students will also work in discussion groups to use the problem-solving checklist to solve a math problem together.

Assessment: Student discussion, student writing, and class discussion will help students and teacher to assess understanding of exponents.
Resources: Harcourt Math book, Flocabulary.com

Tuesday: GOLD
Learning Target(s): I can identify the prime factors of a number.
Success Criteria: I can express and find the value of numbers using an exponent and base.
                                   I can find the value of a number with an exponent of 1 or 0.
                                   I can write the expanded form of a number using exponents.
Procedures:  

·         DATA DUMP: Students write everything they remember from using exponents yesterday.

o   Discuss with the person next to you.

o   Did they have anything you didn’t have? Is there anything they wrote that you don’t understand?

·         Go over homework from last night, reviewing exponents and how to find the value of a number with an exponent.

·         Review rules for the power of zero as well as the first power of any number.

o   The zero power of any number, except 0, is 1.

o   The first power of any number equals that number.

o   Students write these rules in their notebooks.

·         Discuss having 10 as the base with an exponent. How can this be used to write expanded form? How might we write a number in standard form using this method?

·         Students practice independently on #’s 2-8. Then discuss answers with a partner.

o   Go over answers as a class.

FLEX: Students complete Quiz # 4.

Upon completion, students use knowledge of exponents and order of operations to solve for given expressions involving more than one operation.

 Assessment: Data Dump will assess student retention of Monday’s lesson. Student understanding of 10 based exponents, as well as zero and first power rules will be assessed through questioning, independent work, and student-led discussions.
Resources: Harcourt Math book, flocabulary.com, prezi.com

Wednesday: BLACK
Learning Target(s): I can identify the prime factors of a number.
Success Criteria: I can write the prime factorization of a number by using exponents.
                                   I can use a factor tree to identify the prime factors of a number.
Procedures:  

·         Go over Tuesday’s homework.

·         Review Prime and Composite.

·         Review identifying factors of a number.

·         Practice creating a tree using factors of numbers and breaking numbers down until they are prime. We will then discuss identifying the prime factors and writing them using our prior knowledge of exponents.

·         Students will work together in pairs to identify the prime factors of given numbers. They will also work together to write the prime factorization in exponential form.

o   They will complete #’s 1, 5-7, 11-13, and 14-18 on pg 303 together.

o   Discuss answers and strategies together as a class.

FLEX: Students complete Quiz # 4.

Upon completion, students use knowledge of exponents and order of operations to solve for given expressions involving more than one operation.

Assessment: Student assess understanding through discussion with peers.
Teacher assesses student understanding through observation of student discussions, questioning, and student work.
Resources: Harcourt Math book, prezi.com

Thursday: GOLD
Learning Target(s): I can identify the prime factors of a number.
Success Criteria: I can write the prime factorization of a number by using exponents.
                                   I can use a factor tree to identify the prime factors of a number.
Procedures:  

·         Go over Wednesday’s homework.

·         Continue to practice finding the prime factors of a number using a factor tree and writing prime factors. Students will split up according to comfort-level with factoring.

o   Group 1 will be introduced to using the factor tree to find things such as LCM and GCF.

o   Groups 2 and 3 will receive extra (leveled) practice using factor trees and exponents.

FLEX: Students will solve extended response questions using discussion cards in groups. We will also practice math facts (2 min)

Assessment: Student will assess own comfort level and understanding of factor trees and prime factors and indicate his/her level of understanding in groups.
Teacher will assess student understanding through student work as well as observations of group work.
Students who continue to struggle with exponents and prime factors will receive intervention next week during study halls, lunch recess, and/or with a tutor.
Resources: Teacher-made worksheets, khanacademy.com

Friday: NO SCHOOL STAFF IN-SERVICE