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Mathematics 6
Q2 Week 6
Prepared by:
Helen D. Canono
Disiplina Village ES
SDO-Valenzuela
DAY 1
Today's Lesson
Objectives:
MAGNETS
Magnets have the power of attracting objects made of steel, iron, and other metals. The discoveries of the magnet and the many things that have been made out of it have brought about many discoveries and useful things.
The magnet makes possible the compass that was used and still being used by travelers- pilots, sailors, boy scouts, soldiers, engineers, and others. The magnet which makes use of electricity has made all types of electric and industrial motors.
Describe the pattern:
Figure 1
Figure 2
Figure 3
Look at the pictures below.
Read the following sentences.
1) General Emilio Aguinaldo is the First President of the Philippine Republic.
2) The Philippines is in Southeast Asia.
3) Most Filipinos celebrate Christmas in the 10th month of the year.
Problem Opener
Rhoda has to sew a tablecloth 9 dm by 9 dm for their square-shaped table in the living room. How big is the area of the tablecloth?
Answering questions about the problem
1.How will you find the area of the table cloth?
2. What number sentence will be used to solve the problem?
3. Are the two quantities equal?
Equation:
(9 x 9 = 81)
How many times did you multiple 9 to get 81? The product 9 x 9 can be written as power of 9 where 9 is the base and 2 is the exponent.
The exponent tells how many times the base is used as a factor to form a product.
The base is the factor which is to be multiplied by itself the number of times indicated in the exponent to obtain the product.
In the problem, how big is the tablecloth to be sewed by Rhoda?
Valuing:
a) Who has to sew a tablecloth?
b) Where will she put the tablecloth?
c) If you were Rhoda, will you also sew a tablecloth? Why?
Let's Try
The side of a small cutout square is 7cm. What is its area?
Write an expression about the problem.
What is the equation?
Rewrite each of the following using exponents. Determine the numerical value.
1. second power of 7
2. fourth power of 5
3. 2 x 2 x 2 x 2 x 2 x 2
4. 8 x 8 x 8
5. 15 x 15
What is an exponent?
What is a base?
Nuggets of Thought
ASSESSMENT
Write the base, exponent, value, equation, and the meaning of the following expressions.
| Base | Exponent | Meaning | Value | Equation |
| 5 | 3 | 5 x 5 x 5 | 125 | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
ASSIGNMENT
Rewrite the following using exponents.
1. fourth power of 6 ___.
2. eight power of 5 ___.
3. ninth power of 10 ___.
4. second power of 9 ___.
5. third power of 7 ____.
DAY 2
Today's Lesson
Objectives:
MAGNETS
Magnets have the power of attracting objects made of steel, iron, and other metals. The discoveries of the magnet and the many things that have been made out of it have brought about many discoveries and useful things.
The magnet makes possible the compass that was used and still being used by travelers- pilots, sailors, boy scouts, soldiers, engineers, and others. The magnet which makes use of electricity has made all types of electric and industrial motors.
What is a base?
What is an exponent?
What are the different dreaded diseases?
In a particular clinical research, a special type of cancer cells affecting the skin was discovered to exist as a pair in the beginning and was found out to double every 24 hours. The table shows the listing of the number of cancer cells present for the first 10 days.
DAY Number | Number of Cancer Cells |
1 | 2 |
2 | (2) (2) = 4 |
3 | (4) (2) = 8 |
4 | (8) (2) = 16 |
5 | (16) (2) = 32 |
6 | (32) (2) = 64 |
7 | (64) (2) =128 |
8 | (128) (2) = 256 |
9 | (256) (2) = 512 |
10 | (512) (2) = 1024 |
TABLE 1
What do you notice about the cancer cells from day 1 to day 10?
How is this obtained?
Remember:
The exponent tells the number of times the base is used as a factor.
The base is the number used as a factor.
If we try to rewrite this product in terms of the number of cancer cells present on the first day, we will have the following table:
In 1637, Rene Descartes, a French mathematician, introduced a system of writing numbers indicating repeated multiplication.
Write the number using an exponent then answer.
1) 7 x 7 x 7 =
2) 8 x 8 x 8 x 8 x 8 =
3) 6 x 6 x 6 x 6=
4) two to the seventh power
5) six with the exponent nine
Based on tables 1, 2, and 3, how many cancer cells have grown on the fifteenth day?
What is an exponent?
What is a base?
Nuggets of Thought
ASSESSMENT
A. Complete the following sentences:
1) In 53, _____ is the base and ______ is the exponent.
2) 62 is the exponential form of 6 x _____.
3) 144 is the ___ power of 12.
4) 22 means 2 multiplied by _.
5) 74 means _____ is multiplied by itself four times.
ASSIGNMENT
Fill in the blanks.
1) 9 = 3 x 3 = 3_
2)16 = _____ x _____ = _____2
3)8 = 2 x 2 x 2 = 2‑
4)102 = 10 x 10 = _____
5)103 = _____ x _____ x ______ = _____
DAY 3
Today's Lesson
Objectives:
MAGNETS
Magnets have the power of attracting objects made of steel, iron, and other metals. The discoveries of the magnet and the many things that have been made out of it have brought about many discoveries and useful things.
The magnet makes possible the compass that was used and still being used by travelers- pilots, sailors, boy scouts, soldiers, engineers, and others. The magnet which makes use of electricity has made all types of electric and industrial motors.
What is the answer to the following expressions?
a.3×4+1 = b.62+3 =
c. (6+3) + 2 = e. (15 + 3) × 2 =
d. (16 ÷ 4) × 3 =
*Do you have siblings?
*How do your siblings help you in your assignments?
What are the given data?
What operations must be done first? second? next? last? Why?
The numerical expressions above can be solved using GEMDAS rule.
In GEMDAS rule, the letters stand for:
G-Grouping symbols
E-Exponents
M- Multiplication
D-Division
A-Addition
S-Subtraction
To know more about GEMDAS rule, here the steps to be followed:
1. Simplify the operation/s inside the grouping symbols.
2. Evaluate exponential expressions.
3. Do multiplication and division starting from left to right whichever of the two comes first.
4. Lastly, do addition and subtraction starting from left to right whichever of the two comes first.
Evaluate and answer the following expressions.
a) 12-3 + 18 ÷ 6 x 3
b) 7 x 9 – 3 + 8
c) 18-12 ÷ 6 + 7
d) 9 x 9 ÷ 3 – 9 + 6
e) 16 ÷ 4 x 5 – 7 + 8
What rule would you follow in order to perform the order of operation?
Nuggets of Thought
ASSESSMENT
Evaluate the following expressions by following the rules:
1.(9 – 2) + (3 × 21)
2. (18 + 14) ÷ (6 + 2)
3. (36 ÷ 22 + 4 × (4 – 2)
4. (36 – 6) + [(3 × 42) + 7]
5. (72+ 15) × 4 – (625 ÷125)
ASSIGNMENT
Evaluate the following expressions by following the rules:
1. 63 ÷ 7 + 5 + 2 – 6 + 3
2. 6 + (2 × 7 + 5)
3. 3 × (4 + 82) – 8
4. 37 + 3 × 2 ÷ 6
5. 14 ÷ 2 – 3 + 2 × 2
DAY 4
Today's Lesson
Objectives:
MAGNETS
Magnets have the power of attracting objects made of steel, iron, and other metals. The discoveries of the magnet and the many things that have been made out of it have brought about many discoveries and useful things.
The magnet makes possible the compass that was used and still being used by travelers- pilots, sailors, boy scouts, soldiers, engineers, and others. The magnet which makes use of electricity has made all types of electric and industrial motors.
Evaluate the expression if:
1) D=3
D x 9 – D ÷ D + 7
2) T= 4
96 ÷ T x 6 – T + 9
*What are the occupations of your parents?
*Do you help your parents in earning a living?
Jethro was helping his mother in their store when a delivery man delivered 20 dozens of eggs at 42 a dozen. If the delivery man gave him 160, how much was his money? Was he right in asking for a change of 260, if his money was 1,000? Why?
Problem Opener
Who helped mother in the store?
Who delivered dozens of eggs?
How many dozens of eggs were delivered to them ?
If you were Jethro:
Will you help your family earn a living? Why?
Will you keep the change given by the delivery man? Why?
What are the given data?
What are the operations to be used?
Evaluate the expression:
160 + (20 x P42)
160 + P840
1,000 money of Jethro
Use of Test Items
Tita was absent for a week because she was sick. When she went to school, she had to take a test. Few of the items given are shown below.
a) 2 x 3 + 4
b) 7 x 9 – 3
c) 18 – 12 ÷ 2
d) 35 – 6 x 3
e) 3 x 2 + 4
f) 48 ÷ 12 + 8
What facts are given?
What operations are in each problem? Which operations come first? Which operation will you do first?
Group Activity: Evaluate the expression.
a) 8 + 4 ÷2
b) 5 x 8 ÷ 4
c) 65 – 91 ÷ 7
d) 72 ÷ 3 x 8
e) 67 + 33 ÷ 25
Write an expression about the problems. Then evaluate the expression.
1)In a certain eatery, there are 5 glass racks having 24 glasses and 8 left over. The answer says there are 130 glasses in all. Is it right? Why?
How do we evaluate an expression with two different operations without exponents and parenthesis/grouping symbols?
Nuggets of Thought
ASSESSMENT
Evaluate the following expressions.
1) 4 x 3 + 8
2) 84 ÷ 3 x 4
3) 76 – 8 + 5
4) 53 + 7 – 20
5) 3 x 5 ÷ 25
ASSIGNMENT
Evaluate the following.
1. 7 x 8 + 130
2. 195 ÷ 3 x 5
3. 3 + 83 – 73
4. 76 – 8 x 9
5. 90 x 5 ÷ 75
DAY 5
Today's Lesson
exponents and parenthesis/grouping symbols
Objectives:
MAGNETS
Magnets have the power of attracting objects made of steel, iron, and other metals. The discoveries of the magnet and the many things that have been made out of it have brought about many discoveries and useful things.
The magnet makes possible the compass that was used and still being used by travelers- pilots, sailors, boy scouts, soldiers, engineers, and others. The magnet which makes use of electricity has made all types of electric and industrial motors.
Evaluate the following expressions.
1. 4 x 5 + 115
2. 24 ÷ 6 x 14
3. 54 + 47 – 65
4. 80- 4 x 12 + 37
5. 24 x 8 ÷ 12
*What do you observe when somebody in your home is sick? *Does he take medicine? Is it liquid or tablets? How are tablets kept?
In a certain drugstore, the pharmacist, daughter of the owner helps her mother account the medicines for fever. She finds specialized square holders of tablets. She has recorded 4 groups of 10 layers of 10 tablets on each side of the holders and 6 sets of 10 tablets. Is she right in reporting that there are 40 060 tablets? Why?
Problem Opener
a) What is the profession of the daughter of the drugstore owner?
b) What does the pharmacist do?
c) What does she find?
d) If you were the pharmacist, will you also have a systematic arrangement of your medicines? Why?
a) What will you find in the problem?
b) What are the data given?
c) What are the operations to be used?
Is she right in reporting that they have 40 060 tablets? Why? Evaluate the expression as in:
(4 x 103) + (6 x 10)
(4 x 1000) + (6 x 10)
4000 + 60
4060
EXERCISE # 1
Emma helps her mother arrange the items in their store.Her mother has specialized square tray for quail eggs. She finds 4 groups of 5 rows with 5 quail eggs placed in trays and 3 groups with 10 quail eggs. She informs her mother that they have 1 030 quail eggs. Is she right? Why?
Answer the following questions:
Who helps her mother in the store?
What does Emma do to help her mother?
If you were Emma, will you also arrange the items for sale in the store of your mother? Why?
*What facts are given?
*What are the processes to be used?
Is Emma, right? Why?
Evaluate the numerical expression.
(4 x 52) + (3 x 10)
(4 x 25) + (3 x 10)
100 + 30
130
EXERCISE #2
Bing asks her son to do his homework and looks at his notebook.She finds the following:
Evaluate the expressions:
1) 6 + (2 x 7 + 52)
2) 3 x (4 x 82) – 8
3) 5 x [24÷ 2 x (10 – 8)2 ÷ 10]
4) (15 – 6) + (4 – 1) x 23
5) 3 x [3 + 2 x (10 – 32)]
How do we evaluate an expression with more than two operations with exponents and parenthesis/grouping symbols?
Nuggets of Thought
ASSESSMENT
1.Evaluate the following expressions:
a) (9 – 2) + (32 x 21)
b) (18 + 14) ÷ (6 + 2)
c) 36 ÷ 22 + 4 x (4 – 2)
d) (36 – 6) + [(3 x 42) + 7]
e) (72 + 15) x 4 – (625 ÷ 125)
ASSIGNMENT
Evaluate the following expressions:
1. (34 – 4) x (75 ÷ 52)
2. (35 – 3) x 32 + 9
3. (38 – 7) + 6 ÷ (2 x 3)