LENGTH AND PYTHAGORAS RULE

Subject :

Mathematics

Topic :

LENGTH AND PYTHAGORAS RULE

Class :

Basic 6 / Primary 6

 

Term :

 

Second Term

Week :

 

Week 7

Instructional Materials :

• Pictures
• Wall Posters
• Related Online Videos
• Role Playing

 

Reference Materials

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum

Previous Knowledge :

The pupils have previous knowledge of money in their previous classes

 

 

Behavioural Objectives :  At the end of the lesson, the pupils should be able to

1. Define and understand the concept of length and how it is measured using standard units of measurement such as meters, centimeters, and millimeters.
2. Learn how to use a ruler or measuring tape to accurately measure the length of an object or distance between two points.
3. Understand how to apply the Pythagorean theorem to solve problems involving right triangles, including finding the lengths of the sides and the size of the angles.
4. Know how to use the Pythagorean theorem to determine the distance between two points in a plane, such as on a map or in a coordinate system.
5. Develop the ability to apply the Pythagorean theorem to real-world situations, such as finding the length of a ladder needed to reach a certain height or calculating the distance between two cities on a map.
6. Understand the relationship between the Pythagorean theorem and the three special right triangles (3-4-5, 5-12-13, and 8-15-17).
7. Develop problem-solving skills by applying the Pythagorean theorem to a variety of different types of problems.

 

Content :

Length is a measure of the distance between two points. It is a fundamental physical quantity that is used to describe the size or dimensions of objects, as well as the distance between objects or locations.

Length can be measured using a variety of standard units of measurement, such as meters, centimeters, and millimeters. These units are part of the International System of Units (SI), which is a standardized system of units used throughout the world.

Meters (m) are the base unit of length in the SI system. They are used to measure large distances, such as the length of a room or the height of a building.

Centimeters (cm) are a smaller unit of length that is equal to 1/100 of a meter. They are often used to measure the length of objects that are not very large, such as a pencil or a book.

Millimeters (mm) are an even smaller unit of length that is equal to 1/1000 of a meter. They are often used to measure very small objects or distances, such as the thickness of a sheet of paper or the diameter of a pin.

Here is a table of common units of linear measure for length:

Unit	Symbol	Length
Millimeter	mm	0.001 meter
Centimeter	cm	0.01 meter
Inch	in	0.0254 meter
Foot	ft	0.3048 meter
Yard	yd	0.9144 meter
Meter	m	1 meter
Kilometer	km	1000 meters
Mile	mi	1609.344 meters

Note that these units are arranged in order of increasing length, with millimeters being the smallest unit and miles being the largest.

It is important to use standard units of measurement when measuring length, as this ensures that measurements are consistent and comparable. For example, using inches to measure the length of an object and then using centimeters to measure the width could lead to confusion and inaccurate results.

To measure the length of an object or distance between two points, you can use a ruler or a measuring tape. A ruler is a flat, straight instrument with markings on it that indicate the length in inches or centimeters. A measuring tape is a flexible strip of material with markings on it that can be used to measure longer distances or around curved objects.

When measuring the length of an object, it is important to ensure that the end of the ruler or measuring tape is placed at one end of the object and that it is straightened out along the length of the object. The measurement should be taken at the longest point of the object, and it should be read at the end of the object where the ruler or measuring tape stops.

Here is a table showing how 10 millimeters make 1 centimeter, 10 centimeters make 1 decimeter, and 10 decimeters make 1 meter:

Millimeters	Centimeters	Decimeters	Meters
10 mm	1 cm	0.1 dm	0.01 m
20 mm	2 cm	0.2 dm	0.02 m
30 mm	3 cm	0.3 dm	0.03 m
40 mm	4 cm	0.4 dm	0.04 m
50 mm	5 cm	0.5 dm	0.05 m
60 mm	6 cm	0.6 dm	0.06 m
70 mm	7 cm	0.7 dm	0.07 m
80 mm	8 cm	0.8 dm	0.08 m
90 mm	9 cm	0.9 dm	0.09 m
100 mm	10 cm	1 dm	0.1 m

This table illustrates that 10 millimeters is equal to 1 centimeter, 10 centimeters is equal to 1 decimeter, and 10 decimeters is equal to 1 meter. To convert a measurement in millimeters to centimeters, you can divide the number of millimeters by 10. To convert a measurement in centimeters to decimeters, you can divide the number of centimeters by 10. To convert a measurement in decimeters to meters, you can divide the number of decimeters by 10.

For example, to convert 50 millimeters to centimeters, you would divide 50 by 10, which is equal to 5 centimeters. To convert 5 centimeters to decimeters, you would divide 5 by 10, which is equal to 0.5 decimeters. To convert 0.5 decimeters to meters, you would divide 0.5 by 10, which is equal to 0.05 meters.

Evaluation

1. What is the base unit of length in the International System of Units (SI)? a. Meter b. Centimeter c. Millimeter d. Inch
2. How many centimeters are in 1 meter? a. 10 b. 100 c. 1000 d. 10000
3. Which of the following is a tool used to measure the length of an object or distance between two points? a. Caliper b. Scale c. Ruler d. All of the above
4. When measuring the length of an object, where should the end of the ruler or measuring tape be placed? a. At the middle of the object b. At the widest point of the object c. At the shortest point of the object d. At one end of the object
5. What should you do when taking a measurement with a ruler or measuring tape? a. Bend the ruler or measuring tape to fit the shape of the object b. Hold the ruler or measuring tape at an angle c. Place the end of the ruler or measuring tape at one end of the object and straighten it out along the length of the object d. Take the measurement at the middle of the object
6. What is the smallest unit of length in the SI system? a. Meter b. Centimeter c. Millimeter d. Micrometer
7. How many millimeters are in 1 meter? a. 10 b. 100 c. 1000 d. 10000
8. Which of the following is NOT a unit of length in the SI system? a. Meter b. Centimeter c. Millimeter d. Pound
9. How many inches are in 1 meter? a. 10 b. 100 c. 39.37 d. 1000
10. When measuring the length of an object, which of the following is NOT a factor to consider? a. The shape of the object b. The position of the object c. The size of the object d. The weight of the object

 

To use a ruler or measuring tape to accurately measure the length of an object or distance between two points, follow these steps:

 

Place the end of the ruler or measuring tape at one end of the object or at one of the points between which you are measuring the distance.

Make sure the ruler or measuring tape is straight and aligned with the length of the object or the distance between the points.

Read the measurement at the other end of the object or at the other point.

Record the measurement in the appropriate units of length, such as meters, centimeters, or millimeters.

It is important to ensure that the end of the ruler or measuring tape is placed at the correct end of the object or at the correct point, and that the ruler or measuring tape is straightened out along the length of the object or distance being measured. This will help to ensure that the measurement is accurate.

When measuring the length of an object, it is important to take the measurement at the longest point of the object. If the object has a curved or irregular shape, you may need to use a flexible measuring tape or a flexible ruler to get an accurate measurement.

 

The Pythagoras Theory

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed as the equation a^2 + b^2 = c^2, where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

To use the Pythagorean theorem to solve problems involving right triangles, you need to first identify which side of the triangle you are trying to find. Then, use the theorem to set up an equation using the known values of the other sides. Finally, solve the equation to find the value of the unknown side.

For example, suppose you are given the lengths of the two legs of a right triangle and you want to find the length of the hypotenuse. You can set up the equation using the Pythagorean theorem as follows:

a^2 + b^2 = c^2

where a and b are the lengths of the legs and c is the length of the hypotenuse.

Suppose the lengths of the legs are 5 and 12. Then, the equation becomes:

5^2 + 12^2 = c^2

Solving this equation gives us:

25 + 144 = c^2 169 = c^2 13 = c

Evaluation

1. What is the Pythagorean theorem? a. The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. b. The product of the legs of a right triangle is equal to the hypotenuse. c. The sum of the legs of a right triangle is equal to the hypotenuse. d. The difference between the legs of a right triangle is equal to the hypotenuse.
2. In a right triangle, which side is opposite the right angle? a. The hypotenuse b. One of the legs c. The altitude d. The median
3. What is the equation for the Pythagorean theorem? a. a + b = c b. a – b = c c. a * b = c d. a^2 + b^2 = c^2
4. If the length of one leg of a right triangle is 5 and the length of the hypotenuse is 13, what is the length of the other leg? a. 12 b. 25 c. 144 d. 169
5. If the length of one leg of a right triangle is 3 and the length of the hypotenuse is 5, what is the length of the other leg? a. 4 b. 6 c. 8 d. 10
6. If the length of one leg of a right triangle is 4 and the length of the other leg is 5, what is the length of the hypotenuse? a. 3 b. 6 c. 8 d. 9
7. If the length of one leg of a right triangle is 6 and the length of the other leg is 8, what is the length of the hypotenuse? a. 10 b. 14 c. 16 d. 18
8. If the length of one leg of a right triangle is 2 and the length of the hypotenuse is 2.8, what is the length of the other leg? a. 1.2 b. 1.4 c. 2.4 d. 2.8
9. If the length of one leg of a right triangle is 3 and the length of the hypotenuse is 5, what is the size of the angle opposite the leg with length 3? a. 30 degrees b. 45 degrees c. 60 degrees d. 75 degrees
10. If the length of one leg of a right triangle is 4 and the length of the other leg is 5, what is the size of the right angle in the triangle? a. 30 degrees b. 45 degrees c. 60 degrees d. 75 degrees

The right angle triangle 

In the context of the Pythagorean theorem, the hypotenuse is the side of a right triangle that is opposite the right angle. It is typically the longest side of the triangle.

The two other sides of the triangle are called the legs or the sides of the right triangle. One of the legs is called the opposite side, and the other leg is called the adjacent side.

The opposite side is the leg of the right triangle that is opposite the angle in question. For example, if you are trying to find the size of the angle opposite the hypotenuse, the opposite side is the hypotenuse.

The adjacent side is the leg of the right triangle that is adjacent to the angle in question. For example, if you are trying to find the size of the angle opposite the hypotenuse, the adjacent side is the leg that is not the hypotenuse.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed as the equation a^2 + b^2 = c^2, where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

The Pythagorean theorem can be used to find the length of the hypotenuse if you know the lengths of the legs, or to find the lengths of the legs if you know the length of the hypotenuse. It can also be used to find the size of the angles in a right triangle using trigonometry.

Evaluation

1. In a right triangle, which side is opposite the right angle? a. The hypotenuse b. One of the legs c. The altitude d. The median
2. If the length of the hypotenuse of a right triangle is 5 and the length of one of the legs is 3, which of the following is the length of the other leg? a. 2 b. 4 c. 6 d. 8
3. If the length of one leg of a right triangle is 4 and the length of the hypotenuse is 5, what is the size of the angle opposite the leg with length 4? a. 30 degrees b. 45 degrees c. 60 degrees d. 75 degrees
4. If the length of one leg of a right triangle is 6 and the length of the hypotenuse is 8, what is the length of the other leg? a. 2 b. 3 c. 4 d. 5
5. If the length of one leg of a right triangle is 3 and the length of the hypotenuse is 5, what is the size of the angle opposite the hypotenuse? a. 30 degrees b. 45 degrees c. 60 degrees d. 75 degrees
6. If the length of one leg of a right triangle is 4 and the length of the other leg is 5, what is the size of the right angle in the triangle? a. 30 degrees b. 45 degrees c. 60 degrees d. 75 degrees
7. If the length of one leg of a right triangle is 3 and the length of the hypotenuse is 5, what is the length of the other leg? a. 4 b. 6 c. 8 d. 10

 

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed as the equation a^2 + b^2 = c^2, where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

The three special right triangles are 3-4-5, 5-12-13, and 8-15-17. These triangles are called special right triangles because the ratios of their sides are particularly simple and easy to remember.

In a 3-4-5 right triangle, the length of one leg is 3 and the length of the other leg is 4, while the length of the hypotenuse is 5. The Pythagorean theorem states that in this case, 3^2 + 4^2 = 5^2, which is true.

In a 5-12-13 right triangle, the length of one leg is 5 and the length of the other leg is 12, while the length of the hypotenuse is 13. The Pythagorean theorem states that in this case, 5^2 + 12^2 = 13^2, which is also true.

In an 8-15-17 right triangle, the length of one leg is 8 and the length of the other leg is 15, while the length of the hypotenuse is 17. The Pythagorean theorem states that in this case, 8^2 + 15^2 = 17

 

A Pythagorean triplet is a set of three positive integers a, b, and c that satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed as the equation a^2 + b^2 = c^2, where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

For example, the set of integers 3, 4, and 5 is a Pythagorean triplet because 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25. This means that these integers can be used to form the sides of a right triangle with a right angle.

Other examples of Pythagorean triplets include 5, 12, 13, 8, 15, 17, and 7, 24, 25. These sets of integers can also be used to form right triangles with a right angle.

Pythagorean triplets are important in geometry because they allow us to easily construct right triangles with specific side lengths. They are also used in various mathematical and scientific applications, such as calculating distances and analyzing data.

 

 

Presentation

The topic is presented step by step

 

Step 1:

The class teacher revises the previous topics

 

Step 2.

He introduces the new topic

 

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

 

Evaluation :

1. What is a Pythagorean triplet? a. A set of three positive integers that can be used to form a right triangle with a right angle b. A set of three negative integers that can be used to form a right triangle with a right angle c. A set of three integers that can be used to form an equilateral triangle d. A set of three integers that can be used to form an isosceles triangle
2. Which of the following is an example of a Pythagorean triplet? a. 3, 4, 5 b. 5, 6, 7 c. 8, 15, 17 d. All of the above
3. Which of the following is NOT an example of a Pythagorean triplet? a. 7, 24, 25 b. 5, 12, 13 c. 6, 8, 10 d. 3, 4, 6
4. How many Pythagorean triplets are there? a. Two b. Three c. Four d. An infinite number
5. Can Pythagorean triplets be negative integers? a. Yes b. No c. Only if they are odd d. Only if they are even
6. What is the relationship between the sides of a right triangle in a Pythagorean triplet? a. The sum of the squares of the legs is equal to the square of the hypotenuse b. The product of the legs is equal to the hypotenuse c. The sum of the legs is equal to the hypotenuse d. The difference between the legs is equal to the hypotenuse
7. Can Pythagorean triplets be used to form right triangles with acute angles? a. Yes b. No c. Only if they are odd d. Only if they are even
8. Can Pythagorean triplets be used to form right triangles with obtuse angles? a. Yes b. No c. Only if they are odd d. Only if they are even
9. Are there Pythagorean triplets that are not integers? a. Yes b. No c. Only if they are odd d. Only if they are even

 

 

 

1. A set of three positive integers that can be used to form a right triangle with a right angle
2. All of the above
3. 6, 8, 10
4. An infinite number
5. No
6. The sum of the squares of the legs is equal to the square of the hypotenuse
7. Yes
8. Yes
9. No

Conclusion :

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where  the needs arise.