Warm Up – copy these into your notes on a new notes page!!!

Warm Up – copy these into your notes on a new notes page!!!
Divisibility Rules: A quick way to know if numbers are divisible by another number. 2: A number is divisible by 2 if… 3: A number is divisible by 3 if… 4: A number is divisible by 4 if… 5: A number is divisible by 5 if… 6: A number is divisible by 6 if… 8: A number is divisible by 8 if… 9: A number is divisible by 9 if… 10: A number is divisible by 10 if…

A number is divisible by 2 if the last digit of the number is 0, 2, 4, 6, or 8.
Ex: 28, 536, 974

A number is divisible by 3 if the sum of the digits is divisible by 3.
Ex: 12 » = 3 96 » = 15 945 » = 18

A number is divisible by 4 if the last two digits create a number that is divisible by 4 or if the last two digits are 00. Ex: 348 » 48  4 = 12 328 » 28  4 = 7 500 (500  4 = 125)

A number is divisible by 5 if the last digit is a 0 or a 5.
Ex: 45, 120, 935

A number is divisible by 6 if the number is divisible by 2 (even) and 3 (sum of digits divisible by 3). Ex: 846 » = 18 522 » = 9 1, 356 » = 15

A number is divisible by 9 if the sum of the digits is divisible by 9.
Ex: 81 » = 9 945 » = 18 7,578 » = 27

A number is divisible by 10 if the last digit is a 0.
Ex: 80, 470, 990

List 3 numbers greater than 100 that are divisible by each number.
Homework: List 3 numbers greater than 100 that are divisible by each number. 2 3 4 5 6 9 10

What numbers less than or equal to 20 are divisible by 2?
Do you notice a pattern among these numbers?

P. O. D. 9/14/07 What numbers less than or equal to 50 are divisible by 4? Do you notice a pattern among these numbers?

P. O. D. 9/18/07 What is your favorite number between 10 and 100?
Write your number in your POD notebook. Explain why you chose that number. List three or four mathematical facts about your number. List three or four connections you can make between your number and the world.

Prime Time Definitions
Divisible: meaning that a number can divide evenly into another number Ex: 12 is divisible by 2 2. Product: the answer to a multiplication problem 3. Multiple: the product of a whole number and another whole number Ex: 4x3 is 12 so 12 is a multiple of 3 4. Least Common Multiple: The smallest number that is a multiple of two numbers. Ex: 12 is the LCM of 3 and 4.

5. Factor: one of two or more numbers that are multiplied to get a product Ex: 2 x 5 = 10 so 2 and 5 are factors of 10 6. Greatest Common Factor: the biggest factor that two or more numbers share in common 7. Prime Numbers: A number with only two factors: 1 and the number itself. Ex: the factors of 11 are 1 and 11. 8. Composite Numbers: A whole number with factors other than itself and 1. Ex: 4, 24, and 30 are composite numbers because they have many factors.

9. Square Number: The product of a number with itself. Ex: 3 x 3 = 9, 5 x 5 = 25, 6 x 6 = 36. 10. Exponent: The small raised number that tells you how many times to multiply a base (or factor) times itself. 11. Prime Factorization: The longest factor string for a number that is made up of all prime numbers.

The Product Game 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81 Factors:

Follow Up Questions – Product Game
Suppose one paper clip is on 5 – what products can you make by moving the other paper clip? List five multiples of 5 that are not on the game board. Suppose one paper clip is on 3 – what products can you make by moving the other paper clip? List five multiples of 3 that are not on the game board. 1.

Use product and factor in a sentence to describe
P. O. D. 9/18/07 If one of the paper clips is on 5, what products can you make by moving the other paper clip? Use product and factor in a sentence to describe 6 x 3 = 18. 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81 Factors:

P. O. D. 9/18/07 List 5 multiples of 5 that are not listed on the product game board. Use product and factor in a sentence to describe 9 x 6 = 54. 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81 Factors:

Put at least 3 numbers in each region.
Multiples of 3 Multiples of 4

POD Friday, September 21, 2007 Put at least 3 numbers in each region.

Place at least 5 numbers in each region of the diagram.

Multiples of 2 Multiples of 3 Multiples of 5

P. O. D. 8/31/06 What strategies have you found to help you win the Product Game? List at least 3. 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81 Factors: Factors:

Making your own Product Game
Decide on a factor list. Figure out all products. Figure out board size and layout. Do a rough draft of your game. Do a neat final copy. Final copy due tomorrow.

P. O. D. 9/5/06 What is my number? When you divide my number by 5, the remainder is 4. My number has two digits and both are even The sum of my digits is 10.

Multiples of 2 Multiples of 3 Multiples of 5

P. O. D. 9/24/07 What is a factor? What are the factors of 36?

The Factor Game 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

The best first move in the factor game is…
P. O. D. 8/31/06 The Factor Game The best first move in the factor game is… because…. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

P. O. D. 9/25/07 Your partner’s first move of the game is 28.
1. What factors do you get to circle? 2. What is your score? 3. What is their score? The Factor Game 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Solve the following problems: 4. (33 -14) + 25 x 2 – 5 = ______ ÷ 2 x =_____

Use factor and product in a sentence to describe 4 x 5 = 20
Use factor and product in a sentence to describe 4 x 5 = Use multiple and divisible by in a sentence to describe 7 x 7 = 49.

List the factor pairs for each number: 40. _______________________ 45
List the factor pairs for each number: 40 _______________________ 45 _______________________ 47 _______________________ Draw rectangles to represent the factor pairs of 32. Draw rectangles to represent the factor pairs of 17.

The Factor Game 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

What is the best first move on the 49 board?
P. O. D. 9/1/06 What is the best first move on the 49 board? The 49 Board Factor Game 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

P. O. D. 9/7/06 Using the words factor, multiple, product, and divisible by, write at least 4 facts about the number 48.

P. O. D. 9/6/06 List all of the multiples of 9 that are less than 100 in order from least to greatest. 9: List all of the multiples of 7 that are less than 100 in order from least to greatest. 7:

P. O. D. 10/1/07 What factors can be paired to make 12?
Ex: 2 x 3 can be paired to make 6 and 3 x 2 counts as a pair too for 6

The Smiths want to set up a tailgate area near the stadium
The Smiths want to set up a tailgate area near the stadium. They want to use 8 square yards of space. What size rectangles can the Smiths use to set up their tailgate? 1 X 8 4 X 2 2 x 4 8 X 1

The Johnsons want their tailgate to be better than the Smiths
The Johnsons want their tailgate to be better than the Smiths. Their tailgate will be 16 square yards of space. What size rectangles can the Johnsons use to set up their tailgate? 1 X 16 2 X 8 4 X 4 8 X 2 16 X 1

The Lewis family knows their tailgate is the best
The Lewis family knows their tailgate is the best. They have TVs set up, grills, and tons of food. Their tailgate will be 30 square yards of space. What size rectangles can the Lewis family use to set up their tailgate? 5 x 6 2 x 15 6 x x 2 10 x x 1 3 x x 30

Finding Patterns Among Factor Pairs
Investigation 3.2 Finding Patterns Among Factor Pairs Find all factor pair rectangles for your number. Cut each out neatly from the grid paper. Paste to the number sheet. Label with the dimensions. Ex: 8 x 4 4 x 8

32: 36: 35: 40: 45: List the factor pairs for these numbers:
Discussion Questions: What numbers between 1 and 30 are prime? Can you locate perfect squares just by looking at the factor rectangles? Which numbers have the most factors? Which pairs of primes differ by exactly 2? These are called _____________. Do larger numbers always have more factors than smaller numbers? 32: 36: 35: 40: 45:

Make a guess about whether each result below will be even or odd
Make a guess about whether each result below will be even or odd. After testing your ideas, explain a "reason" for this occurrence in words. A. The sum of two even numbers B. The sum of two odd numbers. C. The sum of an odd number and an even number. D. The product of two even numbers. E. The product of two even numbers. F. The product of an odd number and an even number.

List the factor pairs for 48.
P. O. D. 9/12/06 List the factor pairs for 48.

Investigation 3.2 Follow-Up Questions
What patterns do you see? Do you notice anything about even or odd numbers? Which numbers have the most rectangles? What kind of numbers are these? Which numbers have the fewest rectangles? What kind of numbers are these? Why do some numbers make squares? How do the dimensions of the rectangles relate to the number’s factors?

4. Least Common Multiple: The smallest number that is a multiple of two numbers. Ex: 12 is the LCM of 3 and 4. 5. Square Number: The product of a number with itself. Ex: 3 x 3 = 9, 5 x 5 = 25, 6 x 6 = 36. 6. Even Number: An even number has 2 as a factor. Ex: 2 is a factor of 6 and 358. 7. Odd Number: An odd number does not have 2 as a factor. Ex: 5 and 443 are not divisible by 2.

8. Prime Numbers: A number with only two factors: 1 and the number itself. Ex: the factors of 11 are 1 and 11. 9. Composite Numbers: A whole number with factors other than itself and 1. Ex: 4, 24, and 30 are composite numbers because they have many factors.

HOMEWORK: Draw all factor pair rectangles for 36. There will be a lot!

Draw all factor pair rectangles for 32.
P. O. D. 9/13/06 Draw all factor pair rectangles for 32.

What size rectangles can be made for 32?
32 x 1 What size rectangles can be made for 32? 16 x 2 2 x 16 8 x 4 4 x 8 1 x 32

An amusement park wants to build a bumper car track that takes up 12 square meters of floor space. Tiles for the floor come in square meter shapes. Rails to surround the floor are each one meter long. With a neighbor, discuss and sketch some possible rectangular designs for this floor plan. For each design, label how many total floor tiles and how many rail sections you will need.

A different amusement park wants to build a bumper car track that takes up 18 square meters of floor space. With a neighbor, move your tiles, sketching all possible rectangular designs for this floor plan as you find them. For each design, label how many total floor tiles and how many rail sections you will need. Are there more possibilities if you do not keep with the rectangular shape? Find and sketch two more possibilities, labeling number of floor tiles and rail sections.

Looking at your plans for 18 square meters of space…
Which of the rectangular designs do you think is the best shape for a bumper car area? Which of the nonrectangular designs would be the best for a bumper car area? Which of the rectangular designs requires the most rail sections? Which requires the least? Do they require the same amount of floor tiles? How would you persuade you’re a customer to buy your favorite design if you worked the design company?

HOMEWORK Sketch all rectangular options for a bumper car track with an area of 24 square meters. Draw at least two nonrectangular options that you think would be good designs. BONUS for a SPOT: Write a persuasive paragraph selling your favorite of these designs to an amusement park. Why should they pick your design?

List 3 numbers greater than 100 that are divisible by each number.
Homework: List 3 numbers greater than 100 that are divisible by each number. 2 3 4 5 6 9 10

P. O. D. 9/16/05 Put at least 3 numbers in each region.

List all of the factors of the number and then the first three multiples. 8 Factors _______________ Multiples _____________

List all of the factors of the number and then the first three multiples Factors _______________ Multiples _____________

Using your divisibility rules, circle each factor of the number
Using your divisibility rules, circle each factor of the number. X out any numbers that are not factors

Use factor and product in a sentence to describe 4 x 5 = 20
Use factor and product in a sentence to describe 4 x 5 = Use multiple and divisible by in a sentence to describe 7 x 7 = 49.

List the factor pairs for each number: 40. _______________________ 45
List the factor pairs for each number: 40 _______________________ 45 _______________________ 47 _______________________ Draw rectangles to represent the factor pairs of 32. Draw rectangles to represent the factor pairs of 17.

Factors of 48 Factors of 36 Warm Up Oct. 6, 2008
How could you explain the difference in a multiple of 10 and a factor of 10?

Greatest Common Factor
The GCF is simply the largest factor that two (or more) numbers share! For example, using the warm-up from today, what is the largest factor that 36 and 48 share (in the middle of the Venn Diagram)? There are a variety of ways to find GCF List the factors in a T-chart Make a Venn diagram

Factors of 28 Factors of 56 What is the GCF for these two numbers? _______

GCF Practice: Find the GCF for the following numbers – use either a Venn Diagram or a T-chart to list the factors. 24 and 30 15 and 60 30 and 50

Least Common Multiple Very much the same as GCF – you are trying to find the smallest multiple that two or more numbers share! You can use a list, a venn diagram. Example: Find the LCM of 5 and 7.

You and a friend are shopping for new shirts
You and a friend are shopping for new shirts. You find one you like that costs $5. Your friend finds one they like that costs $7. How many shirts would you each have to buy to spend the same amount of money?

You have 27 Reese’s Cups and 66 M & M’s
You have 27 Reese’s Cups and 66 M & M’s. Including yourself, what is the greatest number of friends you can enjoy your candy with so that everyone gets the same amount?

Miriam’s uncle donated 100 cans of juice and 20 packs of cheese crackers for the school picnic. Each student is to receive the same number of cans of juice and the same number of packs of crackers. What is the largest number of students that can come to the picnic and share the food equally? How many cans of juice and how many packs of crackers will each student receive?

Mrs. Armstrong and 23 of her students are planning to eat hot dogs at the upcoming DMS picnic. Hot dogs come in packages of 12 and buns come in packages of 8. What is the smallest number of packs of dogs and the smallest number of packs of buns Mrs. Armstrong can buy so that everyone INCLUDING HER can have the same number of hot dogs and there are no leftovers? How many dogs and buns does each person get?

Warm Up Oct. 8, 2008 List the first five multiples of 7.
List all the factors of 42 Find the GCF for 24 and 60 Find the LCM for 5 and 9

Name 5 ways you might use multiplication in the real world.
P. O. D. 9/23/05 Name 5 ways you might use multiplication in the real world.

Fun Problem – Warm Up Write down the number of the month in which you were born. Multiply that number by 4. Add 13. Multiply by 25. Subtract 200. Add the day of the month on which you were born. Multiply by 2. Subtract 40 Multiply by 50 Add the last two digits of the year in which you were born. Subtract 10,500. Does the number look familiar????

P. O. D. 9/26/05 Using more than 2 factors, what numbers can you multiply together to get 30?

What numbers can you multiply together to get 360
What numbers can you multiply together to get 360? Ex: 3 x 3 x 40 = 360 What is the longest string of factors you found?

What is the longest string of factors you found for 360 that doesn’t include 1?

Prime Factorization Notes
Step 1: Using your divisibility rules, think about what prime numbers will go into the number. Step 2: Continue dividing the number by prime numbers until all you have left is prime numbers. Step 3: Write your answer using exponents. **You cannot use the number one for this because one is NOT prime!!! **Remember the prime numbers 2, 3, 5, 7, 11, 13*

One method: Making a Factor Tree
Put the number at the top. Break the number down into a prime number times another factor and branch out. Circle all prime numbers as you go! Continue breaking it down until all you have left is prime numbers. Use exponents if you can to write the prime number factors. Ex. 100

Another Method: Using a Division Ladder
Put the number at the top. Draw an upside-down division sign underneath it and divide it by a prime number. Write the new number underneath. All prime numbers should be down the left side. Continue breaking it down until all you have left is a prime number at the bottom. The numbers on the outside of the ladders are the prime factorization Ex. 100

EXAMPLE of both methods on the same number:
Factor Tree Division Ladder

YOU TRY SOME PRIME FACTORIZATION:
Factor Tree Division Ladder

Warm UP Find the Prime Factorization of the Following using either the division ladder or a factor tree. Write your answer using exponents.

You can use a division ladder to help you find the GCF and the LCM!
The SLED METHOD You can use a division ladder to help you find the GCF and the LCM! Step 1: Put both numbers in a division ladder. Step 2: Find a factor that goes into both numbers. Continue the division ladder until you can’t break down the numbers anymore. Step 3: Multiply the numbers on the left to find the GCF of the two numbers. Step 4: Multiply all of the the numbers on the outside to find the LCM.

Warm Up Linus always waits in the pumpkin patch for the Great Pumpkin to arrive on Halloween. The great pumpkin came by early this year and hid toys for Linus. Can you find which pumpkin he hid toys in for Linus? He didn’t hide it in the fourth pumpkin from either end. He didn’t hide it in the pumpkin to the left of center. The pumpkin he hid them in had at least three pumpkins on either side. The pumpkin he hid it in was not next to or on the end of the vine.

Warm Up How far can a bat travel in 7 hours if it is flying at twenty-nine miles per hour? Jonathan gave away one hundred twenty six pieces of candy on Halloween. He gave six pieces to each child. How many children visited his house? Robert bought 4 big bags of candy and each bag had 58 pieces in it. On Halloween, 24 children came to Robert’s house and he gave them each 3 pieces of candy. How much does he have left?

Example of the SLED Method
Find the GCF and LCM for 120 and 80.

Greatest Common Factor (GCF): The greatest factor that two numbers share. Ex: The GCF for 36 and 24 is 12. Prime Factorization: The longest factor string for a number, composed entirely of prime numbers. Ex: the prime factorization of 12 is 2 x 2 x 3.

The Product Puzzle 30 x 14 8 7 210 2 4 3 105 5 84 56 21 40 20 28 6 10 32 60 15

Find the longest factor string possible for 360.
Homework Find the longest factor string possible for 360.

Find factor strings of numbers with a product of 840.
The Product Puzzle Find factor strings of numbers with a product of 840. Name two strings of 840 that are not on the puzzle. What is the longest string you found? Can you name a string with a product of 840 that is longer than any string you found in the puzzle? How do you know when you have found the longest factor string? How many different factor strings do you think there are for numbers?

P. O. D. 9/27/05 What is the longest factor string you can find for 480? Have your homework out on your desk.

Homework from last night
Find the longest factor string possible for 360.

Is there an organized way to find the longest factor string for 360

Can you shorten the factor string for 840?
2 x 2 x 2 x 3 x 5 x 7

3 x 2 x 3 x 2 x 5 x 2

2 x 2 x 5 x 5

17.Prime Factorization: The longest factor string for a number, composed entirely of prime numbers. Ex: the prime factorization of 12 is 2 x 2 x 3. 18.Exponent: The small raised number that tells how many times a factor is used. Ex: 53 means 5 x 5 x 5.

What’s so special about your number?
At the beginning of our Prime Time Unit, you chose a special number and wrote several things about it in your journal. Now it is time for you to show off your special number. Write a story, compose a poem, or find some other way to highlight your number. Your project will be used to determine how well you understand the concepts in this unit, so be sure to include all of the things you have learned while working through the investigations. You will present a poster of your special number, which details all of the information you have learned about it. You may use poster board or butcher paper. Please let me know if you need butcher paper.

Item Points Possible Points Received
The number must be displayed in number and word form on your poster. 10 Write a story, song, poem, or something that highlights the number. Write at least 5 math facts about your number. Write at least 5 mathematical problems in which the answer is your number. Write at least 5 connections between your number and the real world. Draw a factor tree or division ladder for your number. Use all vocabulary correctly. (odd/even number, composite/prime number, divisor, factor, multiple, product, prime factorization, exponent) Use correct spelling and grammar. 5 Name, date, and period on back. Neatness, appearance, creativity Class presentation Final Grade 100

This is a 100 point Test/Project grade!
You must go above and beyond in order to receive the full 100 points! Projects are due Monday, October 3, 2005

P. O. D. 9/29/05 Do a division ladder and factor tree for 63 and then for 6,300. Circle your final answer and write it in exponent form.

What’s so special about your number?
At the beginning of our Prime Time Unit, you chose a special number and wrote several things about it in your journal. Now it is time for you to show off your special number. Write a story, compose a poem, or find some other way to highlight your number. Your project will be used to determine how well you understand the concepts in this unit, so be sure to include all of the things you have learned while working through the investigations. You will present a poster of your special number, which details all of the information you have learned about it. You may use poster board or butcher paper. Please let me know if you need butcher paper.

Item Points Possible Points Received
The number must be displayed in number and word form on your poster. 10 Write a story, song, poem, or something that highlights the number. Write at least 5 math facts about your number. Write at least 5 mathematical problems in which the answer is your number. Write at least 5 connections between your number and the real world. Draw a factor tree or division ladder for your number. Use all vocabulary correctly. (odd/even number, composite/prime number, divisor, factor, multiple, product, prime factorization, exponent) Use correct spelling and grammar. 5 Name, date, and period on back. Neatness, appearance, creativity Class presentation Final Grade 100

This is a 100 point Test/Project grade!
You must go above and beyond in order to receive the full 100 points! Projects are due Monday, October 3, 2005

2 x 2 x 2 x 3 x 5 x 7

3 x 2 x 3 x 2 x 5 x 2

2 x 2 x 5 x 5

Do a division ladder and factor tree for ________
Do a division ladder and factor tree for ________. Circle your final answer and write it in exponent form.

P. O. D. 10/8/07 Find the GCF and LCM for 200 and 250 using the SLED method. What does 62 mean? What does it equal?

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