parents’ symposium 2018 solid figures, fun with problem ......the figure below shows a cuboid...

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Parents’ Symposium 2018

Fun with Problem Solving

Questions involving visualization of solid figures

Cubes and cuboid

•Questions on calculating the maximum number of cubes that can be packed into a container of a given dimension

•Usually not an issue when the given cube is a 1-cm cube.

What is the greatest number of 1-cm cubes

that can be packed in the box?

Length5 cm

Height 4 cm1 cm

1 cm

1 cm

Ans: 60 cubes

Calculation

Volume of cuboid = (5 x 3 x 4) cm³

= 60 cm³

Volume of a 1-cm cube = (1 x 1 x 1) cm³

= 1 cm³

Number of cubes = 60 ÷ 1

= 60 cubes

Ans: 60 cubes

What if the cube is not a 1-cm cube?

Can you foresee what might go wrong?

Common error

•Error occur when the cube is not a 1-cm cube.

•Students cannot divide the volume of the container with the volume of the cube.

•There may be gaps which cannot fit in any cubes.

What is the greatest number of 2-cm

cubes that can be packed in the cuboid?

2 cm2 cm

2 cm

Length9 cm

Height

7 cm

Ans: 24 cubes

Calculation

Volume of cuboid = (9 x 5 x 7) cm³

= 315 cm³

Volume of a 2-cm cube = (2 x 2 x 2) cm³

= 8 cm³

Number of cubes = 315 ÷ 8

= 39.3 cubes

Ans: 39 cubes

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Activity 1

ACTIVITY 1

•There are some wooden cubes and a container on your tables.

•Stack the wooden cubes into the container. How many wooden cubes can fit into the container?

•Notice that there are gaps that cannot be fitted in by the wooden cubes.

•Using division method (divide volume of cuboid by volume of cubes) does not work.

•How to solve without physical manipulatives?

ACTIVITY 1

•Measure the length, breadth and height of the container and the cube.

•Divide the length, breadth and height of the container with that of the cube respectively.

•Multiply only the whole number of the length, breadth and height to get the answer

SOLVING WITHOUT MANIPULATIVES

11 cm

6 cm

8 cm

How many 2-cm cubes can fill the

cuboid?

2 cm

Length: 11 ÷ 2 = 5R1

Breadth: 6 ÷ 2 = 3

Height: 8 ÷ 2 = 4

Ignore all ‘remainders’:

Number of cubes

= 5 x 3 x 4

= 60 cubes

Ans: 60 cubes

15 cm

6 cm

5 cm

How many 2-cm cubes can fill the above rectangular box?

2 cm Length: 15 ÷ 2 = 7R1

Breadth: 6 ÷ 2 = 3

Height: 5 ÷ 2 = 2R1

Ignore all remainders:

Number of cubes

= 7 x 3 x 2 = 42 cubes

Ans: 42 cubes

How many 5-cm cubes can be put into a box 36 cm long by 25

cm wide by 14 cm high ?

15 cm

36 cm

25 cm

5-cm cube

A wooden box is 30 cm by 20 cm by 15 cm.

It is filled with 2-cm cubes.

How many 2-cm cubes can be put into the box ?

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Activity 2

The outside of the box including the base is painted. How many cubes touch the inside of the box?

* Share your strategies

7 units4 units

5 units

ACTIVITY 2

7 units4 units

5 units

ACTIVITY 2

•You can use the inter-link cubes on the table and build the structure.

7 units4 units

5 units

ACTIVITY 2

Base: 7 x 4 = 28

Left & right sides: 4 x 4 x 2 = 32

Front & back: 5 x 4 x 2 = 40

Total: 28 + 32 + 40 = 100 cubes

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Activity 3

The figure below shows a cuboid which is made of some identical 2-cm cubes. When three cubes are removed and the remaining cubes are painted red, including the base of the cuboid, a)how many 2-cm cubes will have only one face painted red?b)what is the total surface area which is painted red?

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Instructions Use the wooden cubes and blue/white

stickers on the table to help you to visualize the solutions to the questions.

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Log into ‘Nearpod’&

Key in your answers

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Code

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Solution to Activity 3

3Back / Left /

Bottom

Back / Bottom

2

Back / Right / Bottom 3

Back / Left 2

Back1 Back / Right 2

Back / Left / Top/ Front

4 3Front/ Top/ Back

Front/ Back/ Right /

Top

4

2Bottom/

leftBotttom

1Bottom/

Right

2

Top/ left

2

Top

1

Top/ Right

2

Front/ Bottom /

Left3 Front/ Bottom

2Front/

Bottom / Right

3

Front/ Left

2Front

1

Front/ Right 2

Front/ Back /

Left / Top4Front/ Top / Back3

Front/ Back / Top/ Right

4

a)There are 4 cubes that have only one face painted red.

1 + 1 + 1 + 1 = 4

Total number of red painted faces

= 24 + 10 + 24 = 58

Total red surface area= 58 × 2 cm × 2 cm= 232 cm²

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Activity 4

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Instructions Use the nets sets on the table to help

you to visualize the solutions to the questions.

Parents’ Symposium 2018

Solid Figures,Nets &

Area

Key in answers at Nearpod

YES

Is this the net of a cube?

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

Is this the net of a cube?

YES

NO

Is this the net of a cube?

Bottom

Top

Back

Front

Left

Is this the net of a cube?

Bottom Top

BackLeft

Right

NO

Is this the net of a cube?

Bottom

Top

Back

Front

Left

NO

Is this the net of a cube?

Bottom Top

Back

Left Right

NO

Is this the net of a cube?

Bottom Top

Back

Left Right

NO

Is this the net of a cube?

Bottom Top

Front

Left Right

NO

Is this the net of a cube?

Bottom

Not possible to fold

Back

Front

Left Right

NO

Is this the net of a cube?

TopRight LeftBottom

NO