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GRADES 1 to 12

DAILY LESSON LOG

School:

Grade Level:

Teacher:

Learning Area:

MATHEMATICS

Teaching Dates and Time:

WEEK 2

Quarter:

4TH QUARTER

MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

I. OBJECTIVES

The learner………..

Content Standard

demonstrates understanding of volume of solid figures and meter reading.

Performance Standard

is able to apply knowledge of volume of solid figures and meter reading in mathematical problems and real-life situations.

Learning Competencies / Objectives

finds the volume of cylinders

M6ME-IVb-97

finds the volume of cones

M6ME-IVb-97

finds the volume of pyramids

M6ME-IVb-97

finds the volume of spheres. M6ME-IVb-97

Finds the volume of a given cube and rectangular prism. M6ME-IVb-97

Measurement

III. LEARNING RESOURCES

References

Teacher’s Guide pages

21ST Century Mathletes

21ST Century Mathletes,

21ST Century Mathletes

Learner’s Materials pages

21st Century Mathletes 6

21st Century Mathletes 6,

21st Century Mathletes 6

21st Century Mathletes 6, p. 272-285

21st Century Mathletes 6

Textbook pages

21st Century Mathletes 6

Additional Materials from Learning Resource (LR) Portal

Other Learning Resources

Mathletes 6 textbook, power point presentation

IV. PROCEDURES

A.Reviewing previous lesson or presenting the new lesson

Mental Computation Drill: Pi x a number.

π2
π5
π10
π62
π32

Review:

Find the area of the ff. circles:

Image result for area of circle

Drill:

Find the product of the ff.

1/3 x 8
1/3 x 5
1/3 x 3.14 x 3
1/3 x 22/7 x 6
1/3 x 3.14 x 2

Review:

Look at the illustrations below. Which cylindrical will hold more water? Show your solutions.

Drill:

Find the product of the ff.

12 x 8 x 1/3
1/3 x 10 x 7
1/3 x 15 x 8
1/3 x 20 x 6
0.6 x 2 x 1/3

Review:

Find the volume of the ff:

Image result for volume of cone worksheet

Drill:

Find the product of the ff.

8 x 8 x 8
5 x 5 x 5
10 x 10 x 10
73
63

Drill: Find the area of the ff. circles

Image result for area of circle

4.What is the area of a circle with radius of 3 m ?

5. The diameter of a circle is 0.4m. What is the area?

Review:

Find the volume of the ff:

Image result for volume of pyramid worksheet answers

Drill: Finding the area of parallelogram,rectangle and square.

Image result for find the area of each parallelogram

Review: Find the volume of the ff.

Image result for find the volume of solid figures with dimension

Image result for how to find the volume of sphere Related image

Related image

B.Establishing a purpose for the lesson

Show 2 cylinders to the class and guess which has the greatest or least volume.

What kinds of things can you think of, in real life, when you hear the word cone? possible answers: ice cream cone,orange caution cone, birthday hat, and volcano.

Let them draw the objects. Have them define or describe a cone.

Original File Submitted and Formatted by DepEd Club Member - visit depedclub.com for more

Take a look at the following pyramids.

$C:\Users\eligootee\AppData\Local\Microsoft\Windows\INetCache\IE\G928TUTE\square_pyramid[1].gif$ $C:\Users\eligootee\AppData\Local\Microsoft\Windows\INetCache\IE\G928TUTE\pyramid[1].gif$

How are they different from the rectangular prisms?

Possible answer:

Pyramid has only 1 base while rectangular prism has two Bases. The bases are joined together by the sides

What are examples of spheres found all around us?
-The planet is a sphere.
-Basketballs and soccer balls are spheres

Show a transparent plastic container filled with balls. Ask pupils to guess the number of balls inside the container. Let a volunteer count the balls to find out the answer. Elicit from them how they can make a good guess of the total number of balls. Relate this to the concept of volume.

Image result for transparent box filled with marbles

C.Presenting Examples/Instances of new lesson

Volume of cylinders

The volume of a cylinder is the amount of space inside the cylinder. Finding the volume of cylinder is similar to finding the volume of any prism.

Given the radius and h, the volume of cylinders can be found by using the formula:

Volumecylinder = Area of base × height = pi × r2× hand you can use 3.14 for pi.

Example:

Find the volume of coffee in this mug at the right. (See p. 291)

Solution: πx r2xh

=3.14 x 62 x 12

=3.14 x 36 x 12

V= 1356.48 cm3

So, the volume of this mug is 1356.48 cm3

At Five-six convenience store, you can buy a Big Gulp or a Little Gulp juice. The Big Gulp comes in a can, while the Little Gulp is served in cone.

How many bases does a cone have? What is the shape of the base of the cone? The Big Gulp and Little Gulp containers have equal radii (plural of radius) and equal heights. So, it takes three Little Gulps to fill one Big Gulp.

What fraction of the volume of the Big Gulp is the volume of Little Gulp?

The volume of cones is 1/3 the volume of a cylinder with same base area (B) and height (h)

The formula for the volume of cone is 1/3 the base (B) times the height (h)

V=1/3 x Bxh or 1/3 x πr2xh

Look for a pattern in the volumes of the prism and pyramid pairs

Suppose you have a pyramid and a prism with the same base and the same height. By turning these solid figures into containers you can show a relationship between their volumes.

It takes 3 of the pyramid to fill the prism.

So the volume of the prism is three times the volume of the pyramid. This means that the volume of the pyramid is 1/3 the volume of the prism.

So the volume of a pyramid equals 1/3*Bh.

A sphere is the set of all points that are a given distance from a given point, the center.

To calculate volume of a sphere, use the formula in the blue box.

V= 4/3πr3

Volume is measured in cubic units.

Example: Find the volume of sphere below.

sphere 4

Solution:

V =

= (3.14)(6)3

= (678.24)

= 904.32 units3

Image result for How can you find the volume of a sphere?

Using concrete objects

Let a pupil fill a rectangular box with cubes.

Ask the pupils the following questions:

How many cubes did it take to fill the prism?

How many cubic units is the length/ the width? the height?

Define these situations as finding the volume of solids. Define volume as the number of cubic units used to fill up a space. Use correct unit of measure.

Using this definition, ask the pupils the volume of rectangular prism.

Let them state the formula for the volume of a rectangular prism as V=lxwxh.

D.Discussing new concepts and practicing new skills #1

Show a video of volume of cylinder.

Show a video of volume of cone

Show a video of volume of pyramid

Show a video of volume of sphere

Show a video of volume of rectangular prism

E.Discussing new concepts and practicing new skills #2

Group Activity:

1) Distribute a cylinder to each group.

2) Let them measure the height and the radius of each cylinder in cm.

3) Let them solve for the volume of their cylinders using the formula.

4) Group sharing follows afterwards.

Group Activity:

1) Distribute a cone to each group.

2) Let them measure the height and the radius of each cone in cm.

3) Let them solve for the volume of their cone using the formula.

4) Group sharing follows afterwards.

Group Activity:

Find the volume of the ff.

Group Activity:

Find the volume of the ff.

Example:

Image result for How can you find the volume of a sphere?

Image result for volume of sphere worksheet

Related image

4. Related image

Solve for the volume of these rectangular prisms, given their measurements.

1. l=9m

w=4m

h=3m

2. l= 10cm

w=7cm

h=15cm

3. s=12cm

4.l=14 m

w=10m

h=9m

5. s=6m

F.Developing mastery

(Leads to Formative Assessment)

Pair-share:

Find the volume of the ff.

Image result for find the volume of cylinder Related image

Related image Image result for find the volume of cylinder

Pair-share:

Find the volume of the ff.

Image result for volume of cone worksheet

What happens to the volume of a square pyramid when you double the side length of the base?

Solution:

Find the volume of each sphere.Round to the nearest tenth.

Related image

Pair-share: Find the volume of the ff.

G.Finding practical applications of concepts and skills in daily living

Individual practice:
1.Calculate the Volume of cylinder if r = 2 cm and h = 5 cm
Answer:
Volumecylinder = pi × r2× h
Volumecylinder = 3.14 × 22× 5
Volumecylinder = 3.14 × 4 × 5
Volumecylinder = 3.14 × 20
Volumecylinder = 62.8 cm3

2. Calculate the Volume of cylinder if r = 4 inches and h = 8 inches
Answer:
Volumecylinder = pi × r2× h
Volumecylinder = 3.14 × 42× 8
Volumecylinder = 3.14 × 16 × 8
Volumecylinder = 3.14 × 128
Volumecylinder = 401.92 inches3

Individual practice:

1: Find the volume of a cone, if radius is 4 cm and height is 9 cm.

Solution:

Radius r= 4 cm

Height h= 9 cm

Using the volume of a cone formula,

Volume of cone = $\frac{1}{3}\pi r^{2}h$

Volume of cone = 1/3 x 3.14 x 4² x 9 = 150.72 cm³

2: Find the volume of a cone which has the base radius of 8 cm and height 10.24cm

Solution: Given,

Radius r= 8 cm

height= 10.24 cm

Using the formula of volume of cone,

Volume of cone = $\frac{1}{3}\pi r^{2}h$

Volumeof cone = $\frac{1}{3}\times \frac{22}{7}\times 8^{2}\times 10.24=686.65cm^{3}$

Individual practice:

Ms. Adventure’s tea package has the shape of a regular triangular pyramid. To the nearest tenth of a cubic inch, how much tea can the package hold?

V = 1/3 Bh

V = 1/3 ( 1/2*bh) (h)

V = 1/3 ( 1/2 )(1.4) (1.2) (3)

V = 5.04/6

V = 0.84 in³

V = 0.8 in³

Image result for volume of pyramid worksheet

Individual practice: Find the volume of the ff.

Related image

Find the volume:

H.Making generalizations and abstractions about the lesson

How can you find the volume of a cylinder?

Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume.

How can you find the volume of a cone?

You can calculate the volume of a cone easily once you know its height and radius and can plug those measurements into the formula for finding the volume of a cone. The formula for finding the volume of a cone is

v = hπr2/3 or $\frac{1}{3}\pi r^{2}h$

How can you find the volume of a pyramid?

To calculate the volume of a pyramid, use the formula V=1/3lwh , where l and w are the length and width of the base, and h is the height. You can also use the equivalent formula V=1/3 Abh , where Ab is the area of the base and h is the height. The method varies slightly depending on whether the pyramid has a triangular or a rectangular base.

How can you find the volume of a sphere?

This is the equation: V = ⁴⁄₃πr³. ...
Find the radius. If you're given the radius, then you can move on to the next step. ...
Cube the radius. ...
Multiply the cubed radius by 4/3. ...
Multiply the equation by π.

How can you find the volume of a cube/ rectangular prism?

To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism

I.Evaluating Learning

Find the exact volume of each cylinder: