Subject: Mathematics

Grade: 6

Unit Title: Number

Focus Question 1: What should I know about numbers in the Hindu-Arabic number systems?
Duration: 4 weeks
Time: 5 x 60 mins.
Attainment Target:
● Use computation, estimation and calculators appropriately to solve real world problems
including problems with fractions and decimals.

Benchmarks: Demonstrate an understanding of the use of numbers; number properties and types
of numbers; prime factors and fractional numbers.

Skills:
 List prime factors
 Write products of primes
 Write products of primes using exponents
 Compute with fractions
 Work in groups

Vocabularies: ratio, percentage, equivalent, fraction, decimals, problem solving

Materials: Mathematics workbook, worksheets, projector, laptop, bottle caps, crayons

CEP Intervention: Positive group cohesion and interaction

Content

Definition of a Factor
Factors are numbers that can be multiplied together to get another number. This
also means that the division of a number with all the factors will result in 0
remainders. In simple words, we can say that a factor of a particular number is an
exact divisor of that number.

Procedures/Activities

Day 1

Objectives- Students will be able to

1. Differentiate between multiples and factors.

2. List all the prime factors of a given number.

Engage

What are factors and multiples? Can you give some examples?

Explore

Multiples and Factors

 Show video lesson What Are Factors & Multiples?, pausing at 1:48.
 Have students work in small groups to generate lists of multiples. Give each
group a different number to use to draw block towers like the one shown in
the video to help them.
 Groups share their lists of multiples with the class.

Or

Let students watch this video https://youtu.be/0IZyGB1qQmM then discuss

with the class.

Each group will make a list of factors and then multiple, time students for
each activity. Groups will share their list with the class

 Let’s look at this question and try solving using counters

Let’s do this activity in your group then present it to the class

Explain

What is your understanding of the word multiple and factor? Give examples to clarify your
answers.

What are common factors? Gives examples. Teacher will clarify where it is needed,

Elaborate

Students will work in groups to answer the question below. The teacher will show students
the number chart from 1-100
 I'm thinking of a number less than 100.

1. It is a multiple of 6.

2. 5 is a factor of this number.

 3. It is also a multiple of 20.

The Mystery Number is 60

Lower Level Students- Tier 3

Students will use bottle caps to help them in getting the answer

Multiples of whole numbers

Grade 5 Multiples Worksheet

Example: The first five multiples of 2 are 2, 4, 6, 8, and 10.

List the first 5 multiples for each number.

1.
8

2.
10

3.
14

4.
5

5.
2

Answer

List the first 5 multiples for each number.

 1.
8 8, 16, 24, 32, 40

2.
10 10, 20, 30, 40, 50

3.
14 14, 28, 42, 56, 70

4.
5 5, 10, 15, 20, 25

5.
2 2, 4, 6, 8, 10
Evaluation

Tier 1

List the first 5 multiples for each number.

6.
18

7.
7

8.
17

9.
16
10.
4
Tier 1& 2

1. The following are factors of 6 except:

a. 12,6,1
b. 6,3,2
c. 1,2,3
2. The following are multiples of 4 except:
a. 4,12,16
b. 2,4,8
 c. 8,24,12
3. List ALL the factors of 24:
______ , ________ , ________ , ________ , ________ , ________ , ________ , __

4. List at least 8 multiples of 6:

______ , ________ , ________ , ________ , ________ , ________ , ________ , __

5. Find the factors of (limit to 5 factors only)

a. 12
b. 36
c. 42
d. 150
6. What are the common factors of 12 and 24?
Factors of 12:
Factors of 24:
Commons factors of 12 and 14:
7. What number is a factor of all multiples of 7?
a. 5
b. 14
c. 7

Answer Key:
1. a
2. b
3. 1,2,3,4,6,8,12,24
4. 6,12,18,24,30,36,42,48
5. a. 12 – 1,2,3,4,6
b. 36 – 1,2,3,4,9,12
c. 42 – 1,2,3,6,7,14,21
 d. 150 – 1,2,3,5,6,25,125,150
6. Factors of 12: 1,2,3,4,6,12
Factors of 24: 1,2,3,4,6,8,12
Common Factors: 1,2,3,4,6,12
7. c

Homework

Worksheet: Factors and Multiples

In this worksheet, we will practice identifying relations between factors and multiples and
determining if a number is a factor or a multiple of another.

Q1:

If 3, 6, and 12 are of 36, then 36 is a of them.

 A multiples, multiple
 B factors, factor
 C factors, multiple
 D multiples, factor
Q2:

We know that 3×6=18.Pick the true statement.

 A 3 is a multiple of 18.
 B 18 is a factor of 6.
 C 18 is a factor of 3.
 D 6 is a multiple of 18.
 E 3 is a factor of 18.

Q3:

In this table, we write a number on the left, its factors in the middle, and some of its multiples
on the right.

Some of the numbers are missing.

Number (𝑥) Factors of (𝑥) Some Multiples of (𝑥)

? 1,? 14,35,…
 8 1,2,?,8 16,40,…

The first number in the table only has 2 factors. What is the number?

A factor of 8 is missing from the table. What is this factor?

Teacher Evaluation:

3Areas Excellent Good Satisfactory Unsatisfactory

Effectiveness of strategy
Student participation
Effectiveness of instructional
material
Objectives met
% that grasped the content
taught
% that did not grasp the content
taught
Students # in class # present # absent/late

Plan of Action: Reteach Reinforce Concept Advance to Next

Topic

Comments:

Day 2

Content

Factors happen to be numbers that multiply to create another number.

For instance, take 3 * 2 = 6. Here 3 and 2 are factors of 6.
Prime Number-A number that has only two factors, i.e. 1 and the number itself, is
known as Prime Number.

What are Prime Factors?

The factors of a number that are prime numbers are called prime factors of that
number. As we know, 2 and 4 are the factors of 4, where 2 is considered the prime
factor of 4.
2 is the only even prime number. And only two consecutive natural numbers which
are prime are 2 and 3.

How to Find Prime Factors of a Number?

There are two important methods of finding prime factors of a given number. They
are:

 Prime Factors by Division Method

 Prime Factors using Factor Tree

Expressing a number as a product of its prime factors

A product of primes has only prime numbers in it multiplication. For example, 20 expressed
as a product of its prime factors is 2 x 2 x 5 = 20

Now if a number is broken down into factors which are prime numbers then the number is
said to have been expressed as a product of its prime factors.

Note that every composite number can be written as a product of its prime factors

When a number is given as a product of its prime factors, it is said to be factorized

completely. A prime factor tree is a special diagram where you find the factors of a number
until you can’t factorise any more. The result is all the prime factors of the number. For
example, the prime factor tree of 48 is shown below.
Example 1

A factor tree for the number 48 will always give “2“, “2“, “2“,”2“, and “3” as the prime
factors.
The number 48 can be written as a product of its prime factors by multiplying these five
numbers together.
Writing 48 as a product of its prime factors gives 2 × 2 × 2 ×2 ×3
To write the prime factor in exponential form, count how many of each prime number there
is. The number will become your exponent. 48 = 24×3

Example 2
Using a factor tree, write the following numbers as a product of their prime factors.

a) 8 b) 30 c) 42
Solution

a) 8=2×2×2 b) 30=2×3×5 c) 42= 2×3×7

prime factors
=23 index
form

Factorization.
Prime factors can also be understood in terms of the factor tree. Imagine the number
as the top of a tree and proceed by creating branches that represent different
factors of it.
For example, take 90. It would be 2 * 45. Now take 45 that would be 5 * 9. Again 9
would be 3 * 3. Hence 90 is 2 * 3 * 3 * 5. So 90 end up being on the top, while 2, 3, 3
and 5 are the different branches of 45. And the branches end there since the
numbers cannot be broken down further.

Topic- Prime Factors

Objective- Students will be able to

1. List all the prime factors of a given number.

Procedures/ Activities

Engage

 Prepare for the topic by asking them to write the definitions for 'factors' and
'prime numbers.' If necessary, review the concept of prime numbers with the
lesson What Are Prime Numbers? - Definition & Examples.
 Share the answer and preview vocabulary.
 Tell students they will be learning how to find the prime factors of a number,
called 'prime factorization.' Write this term on the board and have students
label their math notebooks as well.

Explore

Teachers will demonstrate how to find the prime factors of numbers using the factor tree.
Students will participate in the activity after watching the video below-
https://youtu.be/_SxuKsqBEC4 or https://youtu.be/LDwttuNNzi8

For example, the prime factor tree of 48 is shown below.

Example 1

Note: A factor tree grows by continually splitting numbers into their factors until only prime
numbers remain.

Using a factor tree, write the following numbers as a product of their

prime factors.

a) 8 b) 30 c) 42

Explain

 Ask:
o What are the rules for a number to be prime?
o Are all numbers prime? Why or why not?
o Why can't we break prime numbers?
o Teacher will clarify any misunderstanding

Elaborate

Students will now work as groups to complete the work. The teacher will choose how many
problems/items they will give students in the class.

Use the factor tree to find the prime factor of the following numbers

1. 18

2. 30
3. 81

 Students will do the first 5 numbers

Evaluation
Students will do the following worksheet

Tier 1& 2

Tier 3

List out all the possible factors for each number.

1) 24

2) 35
3) 9

4) 42

Teacher Evaluation:

3Areas Excellent Good Satisfactory Unsatisfactory

Effectiveness of strategy
Student participation
Effectiveness of instructional
material
Objectives met
% that grasped the content
taught
% that did not grasp the content
taught
Students # in class # present # absent/late

Plan of Action: Reteach Reinforce Concept Advance to Next

Topic

Comments:

Day 3

Topic- Composite Number

Content

Definition of Composite Numbers

In math, composite numbers can be defined as numbers that
have more than two factors. Numbers that are not prime are
composite numbers because they are divisible by more than two
numbers.

Examples:

1. Factors of 4 = 1, 2, 4 i.e.
Since 4 has more than two factors. So, 4 is a composite number.
 2. Factors of 6 = 1, 2, 3, 6
Since 6 also has more than two factors. So, 6 is also a composite
number.

Fun Facts

 The numbers 0 and 1 are neither prime nor composite

numbers.
 All even numbers except 2 are composite numbers.
 4 is the smallest composite number.
 Each composite number can be written as a product of
two or more primes..
 Composite numbers are divisible by other composite
numbers.
 All composite numbers are always divisible by 1 and
the number itself.

Expressing Composite Numbers as Product of

Prime Numbers
It is sometimes necessary to express a composite number as a product of
prime numbers. As an example, the number 24 may be expressed as:

2x2x2x3

While smaller numbers may often be determined by inspection, a method

for determining the product of prime numbers for larger numbers is
presented.

1. Using the original number continuously divide by the smallest prime

number possible (e.g., 2, 3, 5, 7) until the number can no longer be
reduced
 2. Collect the respective prime numbers, in addition to remaining prime
number and express them as a product

Example:

Express the composite number 960 as a product of prime numbers.

Solution:

Resulting in 960 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

Objective- Students will be able to

1. Write a composite number as a product of (a) Primes (b) Primes in exponential form.

Procedures/ Activities

Engage

Recap from the previous lesson- What are prime numbers? Give examples What is a composite
number?

Students will watch a video about prime and composite numbers. https://youtu.be/hW8-X1hQw90

Class discussion about the video.

Explore

 Students will find the composite numbers with the help of the teacher

Question

 Express the prime factorization of a number in exponential

form.
Solution
 Step: Take a random number as an example and factorize it
 Let us take a number 720.
 Factorize the given number, 720=2×2×2×2×3×3×5.
 The factors of the number are 4 twos, 2 threes and 1 five.
 Thus the exponential form can be written
as, 720=24×32×51.
 Therefore, the exponential form of the prime factorization of
the assumed number is 720=24×32×5. ( 2 to the 4th, 3 to the
2nd x 5 to the 1st )
 Group challenge in finding the exponential form of the
numbers below
Teacher will give students the numbers they will be working
with.
Which one of the following is not a composite number?

15
21
25

Elaborate
Students will work in pairs to do the following then present their answers to the class.
Evaluation

Students will do the following activities

Tier 1 & 2

Fill in the missing numbers

Tier 3

Tell whether each number is prime or composite

1. 45___________ 2. 57___________

3. 36 ______________ 4. 30____________

Teacher Evaluation:

3Areas Excellent Good Satisfactory Unsatisfactory

Effectiveness of strategy
Student participation
 Effectiveness of instructional
material
Objectives met
% that grasped the content
taught
% that did not grasp the content
taught
Students # in class # present # absent/late

Plan of Action: Reteach Reinforce Concept Advance to Next

Topic

Comments:

Day 4

Topic-Highest Common Factor

Content

HCF of two numbers is the highest common number, which is available in both the
numbers. Before we proceed ahead to find the HCF, let us discuss what HCF is. HCF
or highest common factor is the factor of any two or more numbers, which are
common among them. Sometimes, it is also called the greatest common factor (GCF)
or greatest common divisor (GCD).
For example, the HCF of 2 and 4 is 2, because 2 is the number which is common to
both 2 and 4. For such small numbers, finding HCF is an easy method. But for larger
numbers, we need to use different techniques such as prime factorisation and long
division method, to find the HCF.
Question 1: What is the HCF of 24 and 36?
Solution: By prime factorisation, we can write the two numbers;
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
Hence, after factoring the numbers 24 and 36, we can see, the factors 2x2x3 are
common.
Therefore, the HCF (24, 36) = 2x2x3 = 12

How to Find HCF (Highest Common Factor)?

There are three methods to find the Highest Common Factor of two or more numbers. The
three methods to find the HCF of the integers is as follows,
1. Prime Factorization Method (Factor Tree Method)
2. Division Method
3. Factorization Method
2. HCF by Division Method:
You have understood by now the strategy of finding the common highest factor using Prime
Factorization. Now, learn here to find HCF using Division Method. The division method is
nothing but divides the given number, simultaneously, to get the common factors between
them. Follow the steps mentioned below of division method,
Step 1: In the division method, first, treat the smaller number as the divisor and the bigger
number as the dividend.
Step 2: Divide the given number until you get the remainder as 0.
Step 3: We are going to get the common prime factors because the factors within the left-
hand side divide all the numbers exactly. The product of those common prime factors is that
the HCF of the given numbers.
Example: Find the HCF of the 10 and 15?
Solution: Given the values 10 and 15,
Using the division method,

Objective- Students will be able to

1. Identify the Highest Common Factor (H.C.F.) of two numbers.

Procedures/Activities

Engage

What are factors? When something is common what does that mean? Can you find something that
is common in your class?

Explore

What are highest common factors? Give examples. Students will watch the video below follow by a
class discussion. https://youtu.be/lzXv84rO9JI

 Let's look at the example below

Question 1: What is the HCF of 24 and 36?

Solution: By prime factorisation, we can write the two numbers;
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3
Hence, after factoring the numbers 24 and 36, we can see, the factors 2x2x3 are
common.
Therefore, the HCF (24, 36) = 2x2x3 = 12
Question 2: What is the HCF of 35 and 55?
Solution: By prime factorisaton we can write the two numbers as:
35 = 5 x 7
55 = 5 x 11
Hence, we can see the highest common factor for 35 and 55 here is 5.
Therefore, HCF (35, 55) = 5

Example: Find the HCF of 2 and 4

Solution:
Factors of 2 are 2 x 1
Factors of 4 are 2 x 2
Thus the Highest Common Factors of 2 and 4 are 2.
Group competition in finding the HCF of the numbers below

What is the HCF of 48 and 56 using the Prime Factorization Method?

Elaborate

Students will work in their groups to

 Find the HCF of the following numbers

15 and 12

14 and 21

(18 and 24

Explain

What are Highest Common Factors? Demonstrate how you can find the HCF of given
numbers. Teachers will clarify where needed.

Elaborate

Students will work in pairs to do the following

Evaluate

Do the following activity

Teacher Evaluation:

3Areas Excellent Good Satisfactory Unsatisfactory

Effectiveness of strategy
Student participation
Effectiveness of instructional
material
 Objectives met
% that grasped the content
taught
% that did not grasp the content
taught
Students # in class # present # absent/late

Plan of Action: Reteach Reinforce Concept Advance to Next

Topic

Comments:

Day 5

Objectives- Students will be able to

1. Identify the Highest Common Factor (H.C.F.) of two numbers.

2. Write a composite number as a product of (a) Primes (b) Primes in exponential form.

Procedures/Activities

Engage

The teacher will recap composite numbers and Highest common factors and clear up any
misunderstanding.

Explore

Students will explore 2 questions related to objectives

Elaborate

Students will work some problems on the board.

Evaluate

A class test will be given based on what was taught.

Teacher Evaluation:
3Areas Excellent Good Satisfactory Unsatisfactory
Effectiveness of strategy
Student participation
Effectiveness of instructional
material
Objectives met
% that grasped the content
taught
% that did not grasp the content
taught
Students # in class # present # absent/late

Plan of Action: Reteach Reinforce Concept Advance to Next

Topic

Comments: