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