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MATHEMATICS

NAME :________________________________ GRADE : 4-5_____

Mr.Iman just bought a set of piano and he is lack of space. He plans to about to stack

ten drums to make some space. Give him some ideas how he should stack the drums?

You can cut and paste the drums on the space provided. How many combination you

can create? What strategies you can use?

1

GROUP WORK:

1. You will get containers and bean bags with 24 candies each.

2. You will do rotation to divide the candies into equally without any left over (instruction given on each table).

Table 1 : divide into 2 containers.




3. Record it in recording sheet.

Example

Number of candies :6

Number of Containers : 2

Each containers contains 3 candies

Arrays :

Factors :

ILLUSTRATION

Table 1 :

Number of candies :_______

Number of Containers : _______

Each containers contains _______ candies

Arrays :

Factors :

ILLUSTRATION

Table 2 :




Arrays :

Factors :

ILLUSTRATION

2

Table 3 :




Arrays :

Factors :

ILLUSTRATION

Table 4 :




Arrays :

Factors :

ILLUSTRATION

You get another 6 candies for each group, divide the candies into several groups without any left over.

You can use arrays as your illustration.

1. How many group you can made?

2. What strategy(s) you use?

3

Record it in recording sheet.

Combination 1 :




Factors :

ILLUSTRATION/ ARRAYS

Combination 2 :




Factors :


Combination 3 :



Each containers contains _______ can

Dies

Factors :


Combination 4 :




Factors :


4

Combination 5 :




Factors :


Combination 6 :




Factors :


Combination 7 :




Factors :


Combination 8 :




Factors :


Challenge : How many groups you can create if you have 24 chocolate candies and 30 mints candies and you want to

chare it equally?

5

FACTOR

What are factors? Factors are numbers you can multiply together to get another number:

Example: 2 and 3 are factors of 6, because 2 × 3 = 6.

A number can have MANY factors!

Example: What are the factors of 20?

4 and 5 are factors of 20, because 4 × 5 = 20.

Also 2 × 10 = 20 so 2 and 10 are also factors of 20.

And 1 × 20 = 20 so 1 and 20 are factors of 20 as well.

So 1, 2, 4, 5, 10 and 20 are all factors of 20

Methods to find factors are:

1. Fish-bone

2. T-chart

201

2

4

20

10

5

3. Listing

20 = 1, 2, 4, 5, 10, 20

So, factors of 20 are 1, 2, 4, 5, 10, and 20

6

Write all of the factors of each number (Tier 1), Math Connect Page 372

a.8 b. 11 c.6

d.8 e. 11 f.6

Identify all possible arrays arrangement from these set!

g.

h.

i.

j.

7

Write all of the factors of each number (Tier 2)

a.28 b. 81 c.60

d.36 e. 100 f.49

Identify all possible arrays arrangement from these set!

g.

i.

8

COMMON FACTORS AND GREATEST COMMON FACTORS

FIND THE COMMON FACTORS OF EACH SET OF NUMBER! (Math Connect Page 375 : Tier 1)

8 and 12

Factors of 8 =______________________

Factors of 12 =______________________

Common factors =______________________

GCF of 8 and 12 =______________________

8 and 16

Factors of 8 =______________________

Factors of 16 =______________________

Common factors =______________________

GCF of 8 and 16 =______________________

9 and 15

Factors of 9 =______________________

Factors of 15 =______________________

Common factors =______________________

GCF of 9 and 15 =______________________

10 and 15

Factors of 10 =______________________

Factors of 15 =______________________

Common factors =______________________

GCF of 10 and 15 =______________________

14 and 21

Factors of 14 =______________________

Factors of 21 =______________________

Common factors =______________________

GCF of 14 and 21 =______________________

10 and 25

Factors of 10 =______________________

Factors of 25 =______________________

Common factors =______________________

GCF of 10 and 25 =______________________

9

Problem solving

1. Travis is creating sewing kits for local high school students who are heading off to college. He has 4 needles

and 14 spools of thread, which he wants to divide evenly, with no materials left over. What is the greatest

number of sewing kits Travis can make?

2. Nancy is campaigning for class president and plans to distribute some campaign materials: 20 flyers and 15

buttons. She wants each classroom to receive an identical set of campaign materials, without having any

materials left over. What is the greatest number of classrooms Nancy can distribute materials to?

3. Kimberly has collected 18 T-shirts and 9 buttons from her favorite band. She wants to combine them into

identical sets to sell, with no pieces left over. What is the greatest number of sets Kimberly can make?

4. Kenji has 10 cans of regular soda and 20 cans of diet soda. He wants to create some identical refreshment

tables that will operate during the football game. He also doesn't want to have any sodas left over. What is

the greatest number of refreshment tables that Kenji can stock?

5. A choir teacher is dividing 12 sopranos and 9 altos into singing groups. He wants each group to have the

same combination of sopranos and altos, with no singers left over. What is the greatest number of groups

he can make?

10

COMMON FACTORS AND GREATEST COMMON FACTORS

FIND THE COMMON FACTORS OF EACH SET OF NUMBER! (Math Connect Page 375 : Tier 2)

13 and 15

Factors of 13 =______________________

Factors of 15 =______________________

Common factors =______________________

GCF of 13 and 15 =______________________

40 and 16

Factors of 40 =______________________

Factors of 16 =______________________

Common factors =______________________

GCF of 40 and 16 =______________________

60 and 15

Factors of 60 =______________________

Factors of 15 =______________________

Common factors =______________________

GCF of 60 and 15 =______________________

50 and 48

Factors of 50 =______________________

Factors of 48 =______________________

Common factors =______________________

GCF of 50 and 48 =______________________

24, 21 and 32

Factors of 24 =______________________

Factors of 21 =______________________

Factors of 32 =______________________

Common factors =______________________

GCF of 24, 21 and 32 =______________________

10 , 30 and 50

Factors of 10 =______________________

Factors of 30 =______________________

Factors of 50 =______________________

Common factors =______________________

GCF of 10 , 30 and 50 =______________________

11

Problem solving.

1. Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her

friends at school. She wants to divide the cookies into identical containers so that each container has the

same number of each kind of cookie. If she wants each container to have the greatest number of cookies

possible, how many plastic containers does she need?

2. The table below shows the number of students in the school choir.School Choir

The choir teacher plans to arrange the students in equal rows. Only girls or boys will be in each row. What

is the greatest number of students that could be in each row?

3. Dale is stocking bathrooms at the hotel where he works. He has 12 rolls of toilet paper and 16 soaps. If he

wants all bathrooms to be stocked identically, with the same combination of supplies in each one and

nothing left over, what is the greatest number of bathrooms Dale can stock?

4. An event has 46 adults and 23 children. The event planner wants to make each table identical, with the

same combination of adults and children and no people left over. What is the greatest number of tables

the planner can set up?

5. Dustin is creating lollipop bouquets using 45 cherry lollipops and 27 orange lollipops. He wants each

bouquet to be identical, with no lollipops left over. What is the greatest number of lollipop bouquets

Dustin can create?

12

Students

Number

Girls 48Boys 64

Enrichment : Find the GCF of each set of numbers.

13

Prime and Composite NumberFactor Games : Sieve of Erasthothenes

14

INSTRUCT ION :1. Underline1.2. Circle 2, Cross out every multiple of 2.3. Circle the next open number, 3. Now cross out every multiple of 3.4. Circle the next open number, 5. Now cross out every multiple of 5.5. Circle the next open number, 7. Now cross out every multiple of 7.6. Continue this process until all numbers in the table have been circled or crossed out.7. The number left on the chart is prime number.

The number left on the chart is prime number, while the rest is called composite number.Now List down all prime number left in a chart:The numbers are: ____________________________________________

Now find the factor of at least 3 prime number using fish-bone, t-chart or listing method. How many factor you can find? What are the similarities among those numbers? What is prime number?______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Choose at least 3 any composite (crossed out number) and find its factor using fish-bone, t-chart or listing method. How many factor you can find? What are the similarities among those numbers? What is composite number?______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Fill out using T-chart or Venn diagram about Prime Number and Composite Number!

PRIME COMPOSITE

15

Reflection:How about the underlined number (number 1), is it prime number or composite? Why?Use model to represent each number whether it is prime of composite! (Tier 1)

Example :

4

Factors of 4 are 1, 2, and 4

10Factors of 10 are_____________________

8Factors of 8 are_____________________

6Factors of 6 are_____________________

Factors of 2 are_____________________16

12

Label each number as prime or composite!

1. The tables shows how many Calories you can burn in 10 minutes for certain activities.

Activity Number of CaloriesBasketball 64Running 41Dancing 35Hiking 47Roller Skating 57Swimming 71

Which activity is the number of calories a prime number?

2. Are all even numbers composite? Use drawing or illustration in your explanation

3. Are all odd numbers prime? Use drawing or illustration to support your explanation

17

Use model to represent each number whether it is prime of composite! (Tier 2)

Example :

4

Factors of 4 are 1, 2, and 4

20Factors of 20 are_____________________

15Factors of 15 are_____________________

16Factors of 16 are_____________________

18

21Factors of 21 are_____________________

Complete the table below and define whether it is prime number or composite number!

1. Is there connection between the number of rectangular arrangement (arrays) that are possible when modeling a number and the number of factors the number has? Explain your reason!

19

40

2 20

2 10

2 5

PRIME FACTORIZATION

How to do Prime Factorization? Follow this steps!

So, prime factorization of 40 are 2 x 2 x 2 x 5

OR

23 x 5

Fact about Prime number

Composite number is formed by multiplying prime number with another prime number.

There is only one (unique) set of prime number for every composite number.

If you break down composite number using prime factorization, you will end up with the same prime number.

20

Choose at least 5 numbers, use a factor tree to find the prime factorization. (Put answer in exponential form)

1) 20 2) 54 3) 72

4) 100 5) 70 6) 24

7) 77 8) 120 9) 3,000

21

10) 450 11) 81 12) 36

13) 18 14) 200 15) 144

22

Collaborative Work

Follow instruction of each table to proof the facts of prime numbers!

Table 1 Fact : Composite number is formed by multiplying prime number with another prime number.

Proof :

Table 2 Fact : There is only one (unique) set of prime number for every composite number.

Proof :

23

Table 3 Fact : If you break down composite number using prime factorization, you will end up with the same prime

number.

Proof :

24

Instruction table 1

1. Choose more than two prime numbers randomly, you can use more than two times for each number.

2. Multiply the number you have choose.3. Record the result, is it prime number of composite number?

Instruction table 2

1. Choose more than two composite numbers randomly.2. Write down the prime factorization for each composite number.3. Compare, if the prime number set ever the same for two different composite number?

Instruction table 3

1. Choose one large composite numbers randomly.2. Make the prime factorization tree with different factor for starter.

Example :

3. Compare the result? Is the prime number set same or different?

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