MATHEMATICS LESSON

Grade 7 Lesson: Term 2

SURFACE AREA AND VOLUME OF 3-D OBJECTS

GET DIRECTORATE

MATHEMATICS LESSON

GRADE 7

2. CONCEPTS AND SKILLS TO BE ACHIEVED

By the end of the lesson, learners should know and be able to:

2.1. use appropriate formulae to calculate the surface area, volume and

capacity of a cube

2.2. use appropriate formulae to calculate the surface area, volume and

capacity of rectangular prisms

2.3. describe the interrelationship between surface area and volume of cubes

2.4. describe the interrelationship between surface area and volume of

rectangular prism

2.5. solve problems involving surface area, volume and capacity

2.6 use and convert between appropriate SI-units, including:

𝑚𝑚2 ↔ 𝑐𝑚2, 𝑐𝑚2 ↔ 𝑚2, 𝑚𝑚3 ↔ 𝑐𝑚3and 𝑐𝑚3 ↔ 𝑚3

2.7. use equivalence between units when solving problems:

1 cm3 ↔ 1 ml and 1 m3 ↔ 1 kl

TOPIC: SURFACE AREA AND VOLUME OF 3-D OBJECTS

Lesson: Surface area and volume

3. RESOURCES DBE workbook 1, textbooks. Sasol-Inzalo learner book

ONLINE RESOURCES

https://drive.google.com/open?id=1Qw6gZzmSxQ-

ypsHmqx1LHnVbA2HsKX79

https://www.thelearningtrust.org/asp-treasure-box

4. PRIOR KNOWLEDGE

Area, Volume and capacity of the rectangular prisms done in previous

grades.

5. INTRODUCTION (Suggested time: 10 Minutes)

Consider the cube below which is made from small cubes of 1𝑐𝑚 by 1𝑐𝑚 by 1𝑐𝑚:

One face of the cube

1. Use the Cube above to answer the following questions.

a) How many small cubes make up the big cube?

b) What is the volume of the big cube?

c) How many small cubes make up the first layer of the big cube?

d) How many cubes make up the length of each edge of the big cube?

e) Use the formula to calculate the area of the bottom face (base) of the big cube.

f) How many layers (height of the big cube) does the big cube have?

g) Is there no other way that we can use to find the volume of the prism without counting the number

of cubes which makes up the prism?

2. Calculate the area of each face of the big cube.

A cube has six (6) identical faces, see the net alongside

6. LESSON PRESENTATION/DEVELOPMENT (Suggested time: 20 minutes)

Activity 1:

Calculate the volume of the following cubes.=

Note: After learners’ calculations and teacher’s feedback no (b) is emphasised as a formula for

calculating volume of any given cube.

Activity 2: Calculate the surface area of the cubes below.

A formula for calculating surface area of any given cube, is:

7. CLASSWORK (Suggested time: 15 minutes) Learners complete the exercises:

a) Use the cube alongside and calculate using appropriate formulae its: i. Volume

ii. surface area

b) The dimensions of a 3-D object are: 7 𝑐𝑚 × 7 𝑐𝑚 × 7 𝑐𝑚. Calculate its

i. Volume

ii. surface area

5 𝑐𝑚

Volume of a cube = S³

3 𝑐𝑚

Surface area of a cube= 6S²

3 𝑐𝑚

8. CONSOLIDATION/CONCLUSION & HOMEWORK (Suggested time: 5 minutes)

Emphasise that:

Volume of an object is the amount of space it occupies.

Formula thereof is

Surface area of an object is the total area of the areas of the faces.

Formula thereof is

9. Homework: The solutions can be found at the end of the lesson.

COMPLETE THE EXERCISES BEOFE YOU WORK THROUGH THE SOLUTIONS.

1. Use the cube alongside and calculate using formulae its: i. Volume

ii. surface area

2. The dimensions of a 3-D object are: 2,5 𝑐𝑚 × 2,5 𝑐𝑚 × 2,5 𝑐𝑚. Calculate its:

i. Volume

ii. surface area

MEMORANDUM : DAY 1:

ACTIVITY SOLUTION

5. INTRODUCTION 1(a) 27 cubes

(b) 27 cm3

(c) 9 cubes

(d) 3 cubes

(e) Area of base = 𝑠2 = (3 𝑐𝑚)2 = 9 𝑐𝑚2

(f) 3 lae

(g) Yes, Area of the cube x number of layers = Area of

base x height

= 𝑠2 × 𝑠

= 9 𝑐𝑚2 × 3 𝑐𝑚

= 27 𝑐𝑚3

Volume of a cube = S³

Surface area a cube= 6S²

4 𝑐𝑚

2. Surface area of a cube = Total of Area of all faces

= 9 𝑐𝑚2 + 9 𝑐𝑚2 + 9 𝑐𝑚2 + 9 𝑐𝑚2 + 9 𝑐𝑚2 +

9 𝑐𝑚2

= 6 × 9 𝑐𝑚2

= 54 𝑐𝑚2

Hence the surface area of a cube = 6 × 𝑠2

6.PRESENTATION/DEVELOPMENT

Aktivity1(a) Volume = 𝑠3

= (3 𝑐𝑚)3

= 27 𝑐𝑚3

(b) Volume = 𝑠 × 𝑠 × 𝑠

= 𝑠3

Aktivity 2(a) Surface area = 𝑠2 × 6

= (3 𝑐𝑚)2 × 6

= 9 𝑐𝑚2 × 6

= 54 𝑐𝑚2

(b) Surface area = 𝑠 × 𝑠 × 6

= 6 𝑠2

7. CLASSWORK

(a) i V= 125 cm3

ii BO = 150 cm2

(b)i V = 343 cm3

ii BO = 294 cm2

9.HOMEWORK

1 (i) V= l x b x h = 4 cm x 4 cm x 4cm = 64 cm3

(ii) SA = 6(l x l) = 6 x 16 cm2 = 96 cm2

2 (i) V = l x l x l; 2,5 cm x 2,5 cm x 2,5 cm = 15,625 cm3

(ii) SA = 6(l x l); 6(2,5 cm x 2,5 cm) = 37,5 cm2

PRIOR KNOWLEDGE Area, volume and capacity of the rectangular prisms done in previous

grades.

INTRODUCTION (Suggested time: 10 Minutes)

Consider the following rectangular prism made from small cubes of 1 𝑐𝑚 × 1 𝑐𝑚 × 1 𝑐𝑚 and its

faces.

N.B.: Remember each of these faces has a replica.

1. Use the rectangular prism above to answer the following questions.

a) How many small cubes make up the rectangular prism?

b) What is the volume of the rectangular prism?

c) How many small cubes make up the first layer of the rectangular prism?

d) How many cubes make up the length and breadth of the first layer (base)?

e) Use the formula to calculate the area of the bottom face (base) of the rectangular prism.

f) How many layers (height of the rectangular prism) does the prism have?

g) Is there no other way that we can use to find the volume of the prism without counting

the number of cubes which makes up the prism?

2. Calculate the area of each pair of faces of the rectangular prism.

3. What is the total surface area of the rectangular prism?

Activity 1: What is the volume of these rectangular prisms?

(a) (b) (c) h

8cm 3cm

3cm 2cm

5cm 2cm

(i) (iii) (ii)

a) 3 cm × 2 cm × 8 cm

b) 5 cm × 2 cm × 3 cm

c) l × b × h =

After learners’ calculations and teacher’s feedback no (c) is emphasised as a formula for calculating

any given rectangular prism.

Activity 2: What is the surface area of these rectangular prisms?

(a) (b) (c) h

8cm 3cm

3cm 2cm

5cm 2cm

(c) is emphasised as a formula for calculating any given rectangular prisms

a) Emphasise that:

Volume of a rectangular prism is 𝑙 x 𝑏 x ℎ

Surface area of a rectangular prism is 2(𝑙ℎ + 𝑏ℎ + 𝑙𝑏)

b) Homework: Educators must choose appropriate exercises from the textbook.

MEMORANDUM: DAY 2

ACTIVITY SOLUTION

11. INTRODUCTION

1(a) 210 cubes

(b) 210 𝑐𝑚3

(c) 30 cubes

(d) Length = 6 cubes and the breadth = 5 cubes

(e) Area of the base = 𝑙 × 𝑏 = 6 𝑐𝑚 × 5 𝑐𝑚 = 30 𝑐𝑚2

(f) 7 layers

(g) Yes,

Volume of a rectangular prism = l x b x h

Surface area of a rectangular prism = 2(𝑙ℎ + 𝑏ℎ + 𝑙𝑏)

Volume of the rectangular prism =Area of the base ×

number of layers

=Area of the base × height

= 𝑙 × 𝑏 × ℎ

= 6 𝑐𝑚 × 5 𝑐𝑚 × 7

= 210 𝑐𝑚3

2(a) 2(7𝑐𝑚 × 5𝑐𝑚)

= 2(35 𝑐𝑚²)

= 70 𝑐𝑚2

(b) 2(6𝑐𝑚 × 5𝑐𝑚)

= 2(30 𝑐𝑚²)

= 60 𝑐𝑚2

(c) 2(7𝑐𝑚 × 6𝑐𝑚)

= 2(42 𝑐𝑚²)

= 84 𝑐𝑚2

3. 70𝑐𝑚² + 60𝑐𝑚² + 84𝑐𝑚²= 214 𝑐𝑚²

12.LESSON

PRESENTATION/DEVELOPMENT

Activity 1(a) 48 cm³

(b) 30 cm3

(c) □ cubic units

Activity 2

2(8 𝑐𝑚 x 3 𝑐𝑚) + 2(8 𝑐𝑚 x 2 𝑐𝑚) + 2(3 𝑐𝑚 × 2 𝑐𝑚)

= 2(24 𝑐𝑚²) + 2(16 𝑐𝑚²) + 2(6 𝑐𝑚²)

= 48 𝑐𝑚² + 32 𝑐𝑚² + 12 𝑐𝑚²

= 92 𝑐𝑚²

(b) 2(5𝑐𝑚 x 3𝑐𝑚) + 2(3𝑐𝑚 x 2𝑐𝑚) + 2(5𝑐𝑚 × 2𝑐𝑚)

= 2(15 𝑐𝑚²) + 2(6 𝑐𝑚²) + 2(10 𝑐𝑚²)

= 30 𝑐𝑚² + 12 𝑐𝑚² + 20 𝑐𝑚²

= 62 𝑐𝑚²

(c) 2(𝑙 x ℎ) + 2(𝑏 × ℎ) + 2(𝑙 × 𝑏)

= 2(𝑙ℎ + 𝑏ℎ + 𝑙𝑏)

12. PRIOR KNOWLEDGE Surface area and volume of a cube

Learners must revise the following work done:

Determine the surface area and the volume of the following 3-D shapes in the table.

Name Object Volume Surface Area

Activity 1:

a) Complete the table: .

Size of Cube Volume Surface Area

1 𝑚 x 1 𝑚 x 1 𝑚

2 𝑚 x 2 𝑚 x 2 𝑚

3 𝑚 x 3 𝑚 x 3 𝑚

4 𝑚 x 4 𝑚 x 4 𝑚

5 𝑚 x 5 𝑚 x 5 𝑚

8 𝑚 x 8 𝑚 x 8 𝑚

b) Does the surface area increase or decrease as the length of the side of the cube increases?

c) Does the volume increase or decrease as the length of side of the cube increases?

d) Does volume or surface area increase more rapidly when the length of the side of the cube

increases?

15. CLASSWORK (Suggested time: 15 minutes) Consider the table above (i.e. in Activity 1)

a) Which length(s) of the side of the cube will make the volume and surface area the same?

b) Which lengths of the side of the cube will make the volume less than the surface area?

c) Which lengths of the side of the cube will make the surface area less than the volume?

Emphasise that: (Below, in red, are also the answers to no. 17 a, b and c above).

a). A cube that has length of 6 units will have the same volume as the surface area.

b). All lengths smaller than 6 units will have the volume smaller than the surface area.

c). All lengths bigger than 6 units will have the volume bigger than the surface area.

MEMORANDUM: DAY 3

ACTIVITY SOLUTION

15. INTRODUCTION 𝑉 = 𝑠3

= 33𝑐𝑚3

= 27𝑐𝑚3

𝑆𝐴 = 6 × 𝑠2

= 6 × 32𝑐𝑚2

= 6 × 9𝑐𝑚2

= 54𝑐𝑚2

16. a) Size of Cube Volume Surface Area

1 𝑚 x 1 𝑚 x 1 𝑚 1𝑚3 6 × (1𝑚)2 = 6𝑚2

2 𝑚 x 2 𝑚 x 2 𝑚 8𝑚3 6 × (2𝑚)2 = 24𝑚2

3 𝑚 x 3 𝑚 x 3 𝑚 27𝑚3 54𝑚2

4 𝑚 x 4 𝑚 x 4 𝑚 64𝑚3 96𝑚2

5 𝑚 x 5 𝑚 x 5 𝑚 125𝑚3 150𝑚2

8 𝑚 x 8 𝑚 x 8 𝑚 512𝑚3 384𝑚2

b).Yes, the surface area of the cube increases as the length of the

side increases.

c) Yes, the volume increase as the length of the side of the cube

increases.

d) The volume increases more rapidly when the length of the side of

the cube increases.

17.CONSOLIDATION/ CONCLUSION & HOMEWORK

a). A cube that has length of 6 units will have the same volume as the

surface area.

b). All lengths smaller than 6 units will have the volume smaller than

the surface area.

c). All lengths bigger than 6 units will have the volume bigger than the surface area

17. PRIOR KNOWLEDGE Volume and capacity of a cube and

Volume and capacity rectangular prisms

Revise the following work.

Determine the surface area and the volume of the following 3-D object in the table.

Rectangular

Activity: Consider the 3-D objects below.

(i) (ii)

a) Calculate the volume of each of the rectangular prism?

b) Calculate the surface area of each of the rectangular prism?

c) Compare the two rectangular prisms in terms of volume and surface area?

Size of Rectangular Volume Surface Area

1 𝑚 x 1 𝑚 x 16 𝑚

1 𝑚 x 2 𝑚 x 8 𝑚

1 𝑚 x 4 𝑚 x 4 𝑚

2 𝑚 × 2 𝑚 × 4 𝑚

Note: 1 m x 1 m x 16 m has a one side with the greatest dimension

𝑏 = 2 𝑐𝑚 𝑙 = 4 𝑐𝑚

ℎ = 3 𝑐𝑚

6 𝑐𝑚

2 𝑐𝑚

2 𝑐𝑚 1 𝑐𝑚

1 𝑐𝑚

24 𝑐𝑚

20. CLASSWORK (Suggested time: 15 minutes) a) Calculate the volume of each of the rectangular prism with the following dimensions:

i. 6𝑚 × 2𝑚 × 3𝑚

ii. 4𝑚 × 3𝑚 × 3𝑚

iii. 9𝑚 × 2𝑚 × 2𝑚

b) Arrange the rectangular prisms from the one with smallest surface area to the one with biggest surface area.

21. CONSOLIDATION AND CONCLUSION (Suggested time: 5 minutes)

Emphasise that:

Rectangular prisms with the same volume and different dimensions have different surface area.

MEMORANDUM: DAY 4

ACTIVITY SOLUTION 20. INTRODUCTION

Rectangular

𝑉 = 𝑙 × 𝑏 × ℎ

= 4𝑐𝑚 × 2𝑐𝑚 ×

3𝑐𝑚

= 24𝑐𝑚3

𝑆𝐴 = 2𝑙ℎ + 2𝑏ℎ + 2𝑙𝑏

= 2(4 𝑐𝑚 × 3 𝑐𝑚) + 2(2 cm× 3 𝑐𝑚) +

2(4 𝑐𝑚 × 2 𝑐𝑚)

= 24 𝑐𝑚2 + 12 𝑐𝑚2 + 16 𝑐𝑚2

= 52𝑐𝑚2

21. LESSON PREPARATION/DEVELOPMENT

Activity: (a).

(i) 𝑉 = 𝑙 × 𝑏 × ℎ (ii) 𝑉 = 𝑙 × 𝑏 × ℎ

= 6 𝑐𝑚 × 2 𝑐𝑚 × 2 𝑐𝑚 = 24 𝑐𝑚 × 1 𝑐𝑚 × 1 𝑐𝑚

= 24 𝑐𝑚³ = 24 𝑐𝑚³

(b). (i) 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = 2𝑙𝑏 + 2𝑙ℎ + 2𝑏ℎ

= 2 × 6 𝑐𝑚 × 2 𝑐𝑚 + 2 × 6 𝑐𝑚 × 2 𝑐𝑚 + 2 × 2 𝑐𝑚 × 2 𝑐𝑚

= 56 𝑐𝑚²

(ii) 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = 2𝑙𝑏 + 2𝑙ℎ + 2𝑏ℎ

= 2 × 24 𝑐𝑚 × 1 𝑐𝑚 + 2 × 24 𝑐𝑚 × 1 𝑐𝑚 + 2 × 1 𝑐𝑚 × 1 𝑐𝑚

= 98 𝑐𝑚²

(c). If the volume of different rectangular prisms is the same, then

the rectangular prism that has the greatest one dimension of

all other dimensions have the greatest surface area.

Size of Rectangular Volume Surface Area

1 𝑚 x 1 𝑚 x 16 𝑚 16 𝑚3 66 𝑚2

1 𝑚 x 2 𝑚 x 8 𝑚 16 𝑚3 52 𝑚2

1 𝑚 x 4 𝑚 x 4 𝑚 16 𝑚3 48 𝑚2

2 𝑚 × 2 𝑚 × 4 𝑚 16 𝑚3 40 𝑚2

22. CLASSWORK

(a). i V= l ×b ×h = 36 m3 (a). ii V= l ×b ×h = 36 m3

𝑏 = 2 𝑐𝑚 𝑙 = 4 𝑐𝑚

ℎ = 3 𝑐𝑚

(a). iii V= l ×b ×h = 36 m3

(b). (ii), (i), (iii)

22. PRIOR KNOWLEDGE formulae for surface area of a cube and rectangular prism

formulae for volume of a cube and rectangular prism

Revise the following formulae for calculating the surface area and volume of the 3-D objects in the

table below. Learners must name each 3-D object and give its formula.

NAME OF 3-D

OBJECT

SURFACE AREA /

VLOLUME FORMULAE

Surface area

Volume

Surface area

Volume

The surface area of any 3-D object is the sum of the areas of all its faces.

The volume of any 3-D object is given by area of the base × heght.

Example 1: Consider the following rectangular prism with inside measurements as shown:

a) Calculate its surface area.

b) Calculate its volume.

c) What is the capacity of rectangular prism in 𝑚𝑙?

Example 2: Consider the following cube:

a) Calculate its surface area.

b) Calculate its volume.

a) Emphasise that:

the volume of prism = area of the base × height

the surface area of the prism = the sum of the area of all its faces

the volume of a cube = 𝑠3 or 𝑙3

the volume of a rectangular prism = 𝑙 × 𝑏 × ℎ

b) Homework:

Educators choose appropriate exercises from the textbook.

MEMORANDUM: DAY 5

ACTIVITY SOLUTION 25. INTRODUCTION

NAME OF 3-D OBJECT

SURFACE

AREA /

VLOLUME

FORMULAE

Surface area

𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 = 6 × 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑜𝑛𝑒 𝑓𝑎𝑐𝑒

= 6 × 𝑠2

Volume

𝑉 = 𝑠3

RECTANGULAR PRISM

Surface area

𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = 2 × 𝑙𝑏 + 2 × 𝑙ℎ + 2 × 𝑏ℎ

= 2(𝑙𝑏 + 𝑙ℎ + 𝑏ℎ)

Volume

𝑉 = 𝑙 × 𝑏 × ℎ

26. LESSON

PRESENTATION/DEVELOPMENT

Example 1: (a).

Surface area = 2(𝑙𝑏 + 𝑙ℎ + 𝑏ℎ) = 2(8 𝑐𝑚 × 5 𝑐𝑚 + 8 𝑐𝑚 × 2 𝑐𝑚 + 5 𝑐𝑚 ×2 𝑐𝑚) = 2(40 𝑐𝑚2 + 16 𝑐𝑚2 + 10 𝑐𝑚2) = 2(66 𝑐𝑚2) = 132 𝑐𝑚2

(b). Volume = 𝑙 × 𝑏 × ℎ = 8 𝑐𝑚 × 5 𝑐𝑚 × 2 𝑐𝑚

= 80 𝑐𝑚3

(c). Capacity = 80 𝑚𝑙

Example 2 (a).

Surface area = 6 × 𝑠2

= 6 × (5 𝑐𝑚)2

= 6 × 25 𝑐𝑚2

= 150 𝑐𝑚2

(b). Volume = 𝑠3

= (5 𝑐𝑚)3

= 125 𝑐𝑚3

26. PRIOR KNOWLEDGE

Volume and capacity of a cube and rectangular prisms done in the

previous lessons.

substitution

Revise the following formulae for calculating the surface area and volume of the 3-D objects on the

table below. Ask learners to name each 3-D object and give its formulae (previous lesson).

NAME OF 3D

OBJECT

SURFACE AREA /

VLOLUME FORMULAE

Surface area

Volume

Surface area

Volume

The surface area of any 3-D object is the sum of the areas of all its faces.

The volume of any 3-D object is given by area of the base × heght.

Teaching activities

Present the following examples in activity 1 to learners:

Activity 1:

Example 1:

a) The volume of a prism is 350 𝑚3. What is the height of the prism if its length is 10 𝑚 and its breadth is 5 𝑚?

b) Calculate the volume of a prism with a surface base of 48 𝑚2 and a height of 4 𝑚.

Example 2

a) Calculate the capacity of a rectangular prism with the following inside measurements: length = 3 𝑚,

breadth 2 𝑚 and height = 1,5 𝑚

b) A water tank has a square base with internal edge lengths of 15 𝑐𝑚. What is the height of the tank

when the maximum capacity of the tank is 11 250 𝑐𝑚3?

Activity 2

The volume of a cube is 64 𝑐𝑚3. a) Determine the length of each side face. b) Determine the surface area of the cube.

Emphasise that:

the volume of prism = area of the base × height

the surface area of the prism = the sum of the area of all its faces

the volume of a cube = 𝑠3 or 𝑙3

the volume of a rectangular prism = 𝑙 × 𝑏 × ℎ

the amount of space inside the prism is called its capacity

the amount of space occupied by a prism is called its volume

MEMORANDUM: DAY 6

ACTIVITY SOLUTION Activity 1, example

1(a). 𝑙 × 𝑏 × ℎ = 𝑉

10 𝑚 × 5 𝑚 × ℎ = 350 𝑚3

50 𝑚2 × ℎ = 350 𝑚3

ℎ = 7 𝑚

(b). 𝑉 = 𝑙 × 𝑏 × ℎ

= 48 𝑚2 × 4 𝑚

= 192 𝑐𝑚3

Activity 1, example

2(a). 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 𝑙 × 𝑏 × ℎ

= 3 𝑚 × 2 𝑚 × 1,5 𝑚

= 9 𝑚3

(b). 𝑙 × 𝑏 × ℎ = 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦

15 𝑐𝑚 × 15 𝑐𝑚 × ℎ = 11 250 𝑐𝑚3

225 𝑐𝑚2 × ℎ = 11 250 𝑐𝑚3

ℎ = 50 𝑐𝑚

Activity 2

2(a) Side length of one face = √64 𝑐𝑚33= 4 𝑐𝑚

(b) Surface area of the cube = 6 × 𝑠2

= 6 × (4 𝑐𝑚)2

= 6 × 16 𝑐𝑚2

= 96 𝑐𝑚2

𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑏𝑎𝑠𝑒 = 𝑙 × 𝑏 = 48 𝑚2

Solve by inspection by asking: 224 multiplied by what will be 11 250

30. PRIOR KNOWLEDGE

Volume and capacity of a cube and rectangular prisms done in the

previous lessons.

Conversion between appropriate units done in area and perimeter

of 2-D shapes.

Revise the conversion between appropriate SI- units as shown in the table below:

Hence, we see from the table that:

1 𝑐𝑚2 = 100 𝑚𝑚2 1 𝑚𝑚2 = 0,01 𝑐𝑚2

1 𝑚2 = 10 000 𝑐𝑚2 1 𝑐𝑚2 = 0,0001 𝑚2

POSING A PROBLEM: How many 𝑚𝑚3 would fit into 𝑐𝑚3?

How many 𝑐𝑚3 would fit into 𝑚3?

To convert Do this To convert Do this

𝑐𝑚 𝑡𝑜 𝑚𝑚 × 10 𝑚𝑚 𝑡𝑜 𝑐𝑚 ÷ 10

𝑚 𝑡𝑜 𝑐𝑚 × 100 𝑐𝑚 𝑡𝑜 𝑚 ÷ 100

𝑐𝑚2 𝑡𝑜 𝑚𝑚2 × 100 𝑚𝑚2 𝑡𝑜 𝑐𝑚2 ÷ 100

𝑚2 𝑡𝑜 𝑐𝑚2 × 10 000 𝑐𝑚2 𝑡𝑜 𝑚2 ÷ 10 000

Emphasise that:

To convert Do this To convert Do this

𝑐𝑚3𝑡𝑜 𝑚𝑚3 × 1 000 𝑚𝑚3 to 𝑐𝑚3 ÷ 1 000

𝑚3𝑡𝑜 𝑐𝑚3 × 1 000 000 𝑐𝑚3 to 𝑚3 ÷ 1 000 000

Learners must complete example 4, below.

Example 1: Convert 𝑐𝑚3 to 𝑚𝑚3

Example 2: Work out how many 𝑚𝑚3 are equal to 1 𝑐𝑚3?

Example 3: Convert 𝑚𝑚3 to 𝑐𝑚3

Example 4:

1. Write the following volumes in 𝑐𝑚3:

a) 3000 𝑚𝑚3

b) 50 𝑚𝑚3

c) 4 450 𝑚𝑚3

d) 2,23 𝑚3

2. Write the following volumes in 𝑚3:

a) 500 000 𝑐𝑚3

b) 350 000 𝑐𝑚3

c) 4 000 000 𝑐𝑚3

MEMORANDUM: DAY 7

ACTIVITY SOLUTION 34. LESSON PRESENTATION/ DEVELOPMENT

Example 1 Solution: To convert 1 𝑐𝑚3 to 𝑚𝑚3 is the same as

finding out how many 𝑚𝑚3 would fit into 1 𝑐𝑚3?

Consider the sketch below which shows cube A with a length edge of 1 𝑚. Also shown is cube B with an

edge length of 1 𝑐𝑚.

How many small cubes can fit into the large cube?

100 small cubes can fit along the length of the

base of cube A (because there are 100 𝑐𝑚 in 1

𝑚).

100 small cubes can fit along the breadth of the

base of cube A.

100 small cubes can fit along the height of cube A.

The total number of 1 𝑐𝑚3 cubes in 1 𝑚3 = 100 ×

100 × 10 =

1000 000

1 𝑚3 = 1 000 000 𝑐𝑚3

Example 2 1𝑐𝑚3 = 1 𝑐𝑚 × 1 𝑐𝑚 × 1 𝑐𝑚

= 10 𝑚𝑚 × 10 𝑚𝑚 × 10 𝑚𝑚

= 1 000 𝑚𝑚3

Example 3 Solution: 1 𝑚𝑚3 = 1 𝑚𝑚 × 1 𝑚𝑚 × 1 𝑚𝑚

= 0,01 𝑐𝑚 × 0,01 𝑐𝑚 × 0,01 𝑐𝑚

= 0,001 𝑐𝑚3

Example 4 1. Write the following volumes in 𝑐𝑚3:

𝑎) 3000 𝑚𝑚3 = 3 𝑐𝑚3

𝑏) 50 𝑚𝑚3 = 0,05 𝑐𝑚3

c) 450 𝑚𝑚3 = 4,45 𝑐𝑚3

d) 2,23 𝑚3 = 2 230 000 𝑐𝑚3

2. Write the following volumes in 𝑚3:

𝑎) 500 000 𝑐𝑚3 = 0,5 𝑚3

𝑏) 350 000 𝑐𝑚3 = 0,35 𝑚3

c) 4 000 000 𝑐𝑚3 = 4 𝑚3

34. PRIOR KNOWLEDGE Conversion between appropriate SI-units done in the previous

lesson

Activity 1: Learners revise the definition of the following concepts:

Volume: The amount of space occupied by a 3-D object.

Capacity: The amount of space inside a 3-D object.

Activity 2: Learners must see the equivalence between units of volume and capacity by presenting

the following scenario:

Present the following examples to learners:

Examples:

1. Write the following volumes in 𝑚𝑙:

a) 2 000 𝑐𝑚3

b) 2,5 𝑙

c) 1 𝑙

2. Write the following volumes in 𝑘𝑙:

a) 6 500 𝑚3

b) 20 𝑙

c) 1 423 000 𝑐𝑚3

3. A glass can hold up to 250 𝑚𝑙 of water. What is the capacity of the glass:

a) in 𝑚𝑙?

b) in 𝑐𝑚3?

4. A glass tank has the following inside measurements: length = 250 𝑚𝑚, breadth =

120 𝑚𝑚 and height = 100 𝑚𝑚.

Calculate the capacity of the tank in millilitres.

a. Emphasise that:

1 𝑙 = 1 000 𝑚𝑙 and 1 𝑚𝑙 = 0,001 𝑙

1 𝑘𝑙 = 1 000𝑙 and 1 𝑙 = 0,001 𝑘𝑙

1 𝑙 = 1 000 𝑐𝑚3

1 𝑐𝑚3 = 1 𝑚𝑙 and 1 𝑚3 = 1 𝑘𝑙

b. Homework:

The primary purpose of Homework is to give each learner an opportunity to demonstrate mastery

of mathematics skills taught in class. Therefore, Homework should be purposeful and the principle

of ‘Less is more’ is recommended, i.e. give learners few high quality activities that address variety

of skills than many activities that do not enhance learners’ conceptual understanding. Carefully

select appropriate activities from the DBE workbooks and/or textbooks for learners’ homework. The

selected activities should address different cognitive levels.

MEMORANDUM: DAY 8

ACTIVITY SOLUTION

38. LESSON PRESENTATION/

DEVELOPMENT

Write the following volumes in 𝑚𝑙:

d) 2 000 𝑐𝑚3 2 000 𝑚𝑙

e) 2,5 𝑙 2 500 𝑚𝑙

f) 1 𝑙 1 000 𝑚𝑙

2. Write the following volumes in 𝑘𝑙:

𝑎) 6 500 𝑚3 6 500 𝑘𝑙

𝑏) 20 𝑙 0,02 𝑘𝑙

𝑐) 1 423 000 𝑐𝑚3 1,423 𝑘𝑙

a) in 𝑚𝑙? 250 𝑚𝑙

b) in 𝑐𝑚3? 250 𝑐𝑚3

4. Solution:

Capacity = 250 𝑚𝑚 × 120 𝑚𝑚 × 100 𝑚𝑚

= 3 000 000 𝑚𝑚3

= 3000 𝑐𝑚3

= 3000 𝑚𝑙

Capacity = 250 𝑚𝑚 × 120 𝑚𝑚 × 100 𝑚𝑚

= 25 𝑐𝑚 × 12 𝑐𝑚 × 10 𝑐𝑚

= 3000 𝑐𝑚3

= 3000 𝑚𝑙

Divide by 1 000

MATHEMATICS LESSON

Documents

Lesson 3 strategies in teaching mathematics

TEACHING AND LEARNING MATHEMATICS THROUGH LESSON …

Mathematics 9 Lesson 3: Quadratic Functions

Use with Lesson 4 MAFS.8.EE.3.7 Course 3, Lesson 2-4...

MATHEMATICS: TEACHER GUIDE: LESSON PLANS

COMMON CORE MATHEMATICS CURRICULUM Lesson 1 Problem Set...

NYSCOMMON CORE MATHEMATICS CURRICULUM Lesson 1 Problem ….....

Mathematics Education Mini Symposium on Lesson Study...

Lesson Plan Level 1: Mathematics Following directions VWI...

NYS COMMON CORE MATHEMATICS CURRICULUM Lesson … … ·...

· Web viewGRADE 8 TERM 3 LESSON PLAN MATHEMATICS 165...

A Lesson From The Mathematics & Science Center The...

GUIDANCE Lesson Study: Enhancing Mathematics Teaching...

Daily Lesson Plan for Mathematics

Daily Lesson Plan Mathematics

Binary Mathematics Sample Lesson