Number Theory and Fractions Review

Number Theory Review

by Ms. Knowles

Objectives

You will be able to solve questions about prime factorization, sequences and order of operations.​

Poll

How are you feeling today?

• 4,6,9

• 2

• 3

• 1

• 5,7,8

Open Ended

What are the two methods used for Prime Factorization?

​Factor Tree

• ​Use your prime numbers to factorize a number.

• ​Always start off with the smallest prime number that can go into the digit you are factorizing.

Draw

Draw a factor tree to show the prime factors of 16.

​Ladder Method

• ​​Use your prime numbers to factorize a number.

• ​Always start off with the smallest prime number that can go into the digit you are factorizing.

Draw

Draw the ladder method to show the prime factors of 16.

Multiple Choice

Find the prime factorization of 32

• 2 x 2 x 2 x 4

• 2 x 2 x 2 x 2 x 2

Multiple Choice

Write 28 as a product of its prime factors.

• 2 x 2 x 7

• 4 x 7

Multiple Choice

Which is the prime factorization of 12? 

• 2 x 6
• 2 + 2 + 2 + 2 + 2 + 2 
• 2² x 3
• 1 x 2² x 3

Multiple Choice

Find the prime factorization for 80

• 4² ⋅ 5

• 2⁴ ⋅ 5

• 2 ⋅ 2 ⋅ 2

• 8 ⋅ 5 ⋅ 2

Multiple Choice

Which of the following are all prime numbers

• 2, 3, 6, 7, 9
• 2, 4, 8, 16
• 2, 3, 5, 7, 9
• 2, 3, 5, 7, 11

​Sequences

• ​Look at the numbers carefully, determine the pattern and find the next terms/numbers.

• ​Example: 7, 14, 21, ___, ___ What would be the next two terms?

Multiple Choice

Given the sequence 2, 8, 14, 20, 26, ... What is the common difference?

• 2

• 4

• 6

• 8

Multiple Choice

Describe the pattern in the sequence. Find the next three terms.

13, 15, 17, 19,...

• Add 2; 23, 25, 27

• Multiply by 2; 38, 76, 152

• Add -2; 17, 15, 13

• Add 2; 21, 23, 25

Multiple Choice

What do we call this sequence: 1,8,27, 64, 125...,

• Arithmetic Sequence

• Geometric Sequence

• Cube Number Sequence

• Triangular Sequence

Multiple Choice

What do we call this sequence: 1, 4, 9, 16, 25,...

• Harmonic Sequence

• Cube Number Sequence

• Square Number Sequence

• Triangular Sequence

Multiple Choice

Find the sequence 10, 20, 30, 40.........

• Multiply by 10
• Add 10  
• Multiply by 2

Multiple Choice

Find the sequence;  2, 4, 6, 8,...........

• add 2
• multiply by 2

Multiple Choice

Find the sequence; 2, 4, 8, 16, 32...............

• add 4
• multiply by 2
• add 2

Multiple Choice

What are the next three terms in the sequence 2, 9, 16, 23, 30, . . . ?

• 37, 43, 50

• 37, 44, 51

• 37, 43, 50

• 37, 44, 50

Fill in the Blanks

The next three terms in the sequence 49, 44, 39, 34, 29, … are

Multiple Select

Choose the next two terms of the sequence 1, 4, 9, 16, 25, …

• 30

• 36

• 40

• 49

Open Ended

What is the importance of order of operations?

​Order of Operations

• Order of Operations is a rule that explains which procedure should be done first.

• ​All multiplication and division operations are carried out first, from left to right, in the order they occur.

• ​All addition and subtraction operations are carried out, from left to right, in the order they occur.

Draw

$$7\times2-10\div5$$  

Multiple Choice

Pick the correct order for Order of Operations

• Parentheses, Multiplication, Division, Addition, Exponents, Subtraction

• Exponents, Multiplication, Division, Addition, Parentheses, Subtraction

• Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Multiple Choice

Which operation would you do first in the following equation?

10 - 4 ÷ 1 x 5

• Subtraction

• Division

• Multiplication

• Addition

Open Ended

Is there any topic from today's review that you would like me to reteach?

Multiple Choice

12 - 4 x 2 = 

• 16
• 4
• 8
• 18

Multiple Choice

Solve.
25 - 14 + 3 =

• 14
• 8
• 11
• 10

Multiple Choice

7 x (7 - 4) ÷ 3 =

• 8

• 6

• 7

• 5

Multiple Choice

18 + (6 – 2) × 2 =

• 26
• 29
• 44
• 40