Appendix-A
LESSON PLAN BASED ON CONSTRUCTIVIST APPROACH
Date: dd-mm-yy
Class: VIII
Subject: Mathematics
Age of the pupils: 14 yrs
Topic: Area of Total Surface of Cuboid
Duration: 40 minutes
Unit: Area of Total Surface of 3-D Figures
1. Defining a cuboid
2. Deriving the formula for finding lateral surface area as well as total surface
of a cuboid
3. Apply the formula in world problems
INSTRUCTIONAL OBJECTIVES (In Behavioural terms)
Remembering
(i)
Students will be able to know the meaning of the term ‘cuboid’.
(ii)
Students will be able to identify the formulae for finding area of the
lateral surface as well as total surface of a cuboid.
(iii)
They will be able to recall the formulae for finding out area of the total
surfaces as well as lateral surfaces of a cuboid.
Understanding
(i)
Students will be able to define the formulae for finding area of the lateral
surface as well as total surface of a cuboid.
(ii)
Students will be able to interpret the formulae for finding out area of the
lateral surface as well as total surface of a cuboid.
Applying
(i)
Students will be able to recognize the shape and figures of cuboidal
object.
(ii)
Students will be able to give example of articles of cuboidal shape other
than shown in the class.
222
(iii)
Students will be able to apply the formulae for determining area of the
curved surfaces and total surfaces of a cuboid.
(iv)
Students will be able to solve problems related to the area of the surfaces
of a cuboid with speed and accuracy.
Analysing
(i)
Students will be able to differentiate lateral surface and total surface area
of cuboid.
(ii)
Students will be able to distinguish the formulae for finding out area of
the lateral surface as well as total surface of a cuboid.
(iii)
Students will be able to construct the 3 D figure distinctly showing and
naming its identical faces.
Evaluating
(i)
Students will be able to derive the formulae for finding out area of the
lateral surface as well as total surface of a cuboid.
(ii)
Students will be able to determine the area of the cuboidal objects that
need more material to cover less lateral surface as well as total surface.
Creating
(i)
Students will be able to imagine different dimensions for covering less
surface area.
(ii)
Students will be able to elaborate the derivation of lateral surface area as
well as total surface of cuboid to lateral surface area as well as total
surface area of a cube.
Teaching Objects
(i)
Chalk Board, chalk, duster and pointer etc.
(ii)
Cuboidal objects like packaging of soap, toothpaste and other objects.
223
Prerequisite: Before starting teaching, teacher distributed students in to group of
five students according to their ability. Through an activity teacher tries to
create interest among students.
Previous Knowledge
(i)
Students are familiar with rectangular figurers as well as formulae of
determining the area of such figures.
(ii)
Students are able to give examples of two dimensional and three
dimensional figures and objects.
ENGAGEMENT (Using Previous Knowledge)
Teacher: Ask to draw some geometrical figures on their note book and ask to name
the figures. (Determines students' current understanding (prior knowledge) of
concept or idea)
Students: Draw Rectangle, Square, Cuboid, Cube , Cylinder etc. on their notebook
along with their names.
Teacher: Is there any difference between 2 D and 3 D shapes? (Invites students to
express what they think)
Students: 2 D figure has two dimensions viz. length and breadth, 3 D figure has
three dimensions viz. length, breadth and height.
Teacher: Shows some packaging of soap and toothpaste and ask the shape of the
box. (Piques student's curiosity and generates interest)
Teacher: What is the shape of the box and faces of box?
Student: Shape of the box is Cuboid and shape of the face is Rectangular.
Teacher: Are all the six faces having same dimensions?
Students: No, only three pairs are identical.
Teacher: So, how many identical pairs are there? (Invites students to express
what they think)
Students: There are three rectangular identical faces of different length, breadth
and height.
224
EXPLORATION
Teacher: Give some packaging of soap, toothpaste and box to all the group of
students and ask them to separate all the faces. (Provide new concrete (hands-on)
experience to examine, manipulate, and explore the phenomena)
Student: Start the activity
Teacher: Ask to give numbering on the faces and denote length, breadth and
height.
Students: Students give numbers on the faces I, II, III, IV, V and VI and denote l,b,h
Teacher: What is the formula to find the area of the rectangular figure?
Students: Length × Breadth
Teacher: Ask to find the area of all six faces. (Provides time for students to
puzzle through problems)
Students: Calculate the area of all six faces separately.
Teacher: If we want to calculate total area of this packaging than what will we do?
(Asks probing questions to help students make sense of their experiences)
Students: We should add the area of all six faces.
Teacher: Ask to do the same. (Encourages student-to-student interaction and
observes and listens to the students as they interact)
Students: Add the area of all six faces.
Teacher: What did you get?
Students: l×b+ b×h +h×l+l×b+ b×h +h×l
Teacher: Add common terms and tell what did you get?
Students: 2 (l×b+ b×h +h×l)
225
Teacher: So you have driven the formula to calculate area of total surfaces of
cuboid. (Appreciates and motivates)
Students: Students feel satisfaction and it increases their self confidence.
Teacher: Ask to remove one identical pair of dimensions length and breadth from
your box. What did you get?
Students: A box which doesn’t have top and bottom.
Teacher: Now subtract the area of this identical pair of rectangular shape having
length and breadth as dimensions. What did you get?
Students: 2 (l×b+ b×h +h×l)- 2 (l×b)
= 2( b×h +h×l)
=2h ( b+l)
Teacher: So you have driven the formula to calculate area of four surfaces of
cuboid. (Appreciates and motivates)
Students: Yes
EXPLANATION
Teacher: In above activity you have driven two formulas to find area of six
surfaces and four surfaces excluding top and bottom of the cuboidal box.
Students: Yes
Teacher: So area of six surfaces of the cuboidal box is known as Total Surface
Area of cuboid and area of four surfaces excluding top and bottom of the cuboidal
box is known as lateral surface area. (Introduces terminology and alternative
explanations after students express their ideas)
Total Surface Area: 2 (l×b+ b×h +h×l)
Lateral Surface Area: 2 h ( b +l)
ELABORATION
Teacher planned the same activity to elaborate the concepts of surface areas of
cuboid to surface areas of cube. Teacher shows the packaging of cubical box.
(Focuses students' attention on conceptual connections between new and
former experiences)
226
Teacher: What is this?
Students: It is a cubical box.
Teacher: How it is different from cuboid? (Asks questions that help students
draw reasonable conclusions from evidence and data)
Students: It is a special case of cuboid whose all sides have equal length.
Teacher: Good, Repeat the same activity for the cube having length of each side is
l. (Encourages students to use what they have learned to explain a new events
or idea)
Students: Repeat the activity and cut-out six identical faces of the cube and derive
the formula of Total Surface Area and Lateral Surface Area
Total Surface Area= 2 (l × l + l × l + l × l)
= 2 × 3 × l2
= 6 l2
Lateral Surface Area= 2 l ( l + l)
= 2×l×2l
= 4 l2
Teacher: So you have driven the formula to calculate area of four surfaces of cube.
(Appreciates and motivates)
Students: Yes
Teacher: Now you can evaluate the Total Surface Area and Lateral Surface Area of
cube and cuboid. (Reinforces students' use of mathematical terms and
descriptions previously introduced)
Students: Yes
Teacher: Measure length, width and height of your classroom and find
(a) The total surface area of the room.
(b) The lateral surface area of this room.
(c) The total area of the room which is to be white washed.
Students: Solve the given problem by associating new knowledge to present
situation.
227
EVALUATION
In beginning teacher evaluate the previous knowledge of the students, he/she
keeps eyes on activities done by the students during exploration and at the end
he/she evaluate students level of understanding, applying, analysing, evaluating and
creating about the lesson through some questions.
Questions
1. Differentiate Total Surface Area and Lateral Surface Area.
2. How will you arrange 12 cubes of equal length to form a cuboid of smallest
surface area?
3. Can we say that the total surface area of cuboid = lateral surface area + 2 × area
of base?
4. If we interchange the length of the base and the height of a cuboid (Fig I) to get
another cuboid (Fig II) will its lateral surface area changed. Elaborate your
answer.
5. The internal measures of a cuboidal room are 12 m × 8 m × 4 m. Find the total
cost of whitewashing all four walls of a room, if the cost of white washing is Rs
5 per m2. What will be the cost of white washing if the ceiling of the room is
also white washed.
228
Appendix-B
LESSON PLAN BASED ON TRADITIONAL APPROACH
Date: dd-mm-yy
Class: VIII
Subject: Mathematics
Age of the pupils: 13-14 yrs
Topic: Area of Total Surface of Cuboid
Duration: 40 minutes
Unit: Area of Total Surface of 3-D Figures
1. Defining cuboid.
2. Deriving the formula for finding area of the total surface of cuboid.
3. Solving the problem based on the use of formula.
Instructional Objectives (In Behavioural terms)
Remembering
(iv)
Students will be able to know the meaning of the term ‘cuboid’.
(v)
Students will be able to identify the formulae for finding area of the
lateral surface as well as total surface of a cuboid.
(vi)
They will be able to recall the formulae for finding out area of the total
surfaces as well as lateral surfaces of a cuboid.
Understanding
(iii)
Students will be able to define the formulae for finding area of the lateral
surface as well as total surface of a cuboid.
(iv)
Students will be able to interpret the formulae for finding out area of the
lateral surface as well as total surface of a cuboid.
Applying
(v)
Students will be able to recognize the shape and figures of cuboidal
object.
229
(vi)
Students will be able to give example of articles of cuboidal shape other
than shown in the class.
(vii)
Students will be able to apply the formulae for determining area of the
curved surfaces and total surfaces of a cuboid.
(viii)
Students will be able to solve problems related to the area of the surfaces
of a cuboid with speed and accuracy.
Analysing
(iv)
Students will be able to differentiate lateral surface and total surface area
of cuboid.
(v)
Students will be able to distinguish the formulae for finding out area of
the lateral surface as well as total surface of a cuboid.
(vi)
Students will be able to construct the 3 D figure distinctly showing and
naming its identical faces.
Evaluating
(iii)
Students will be able to derive the formulae for finding out area of the
lateral surface as well as total surface of a cuboid.
(iv)
Students will be able to determine the area of the cuboidal objects that
need more material to cover less lateral surface as well as total surface.
Creating
(iii)
Students will be able to imagine different dimensions for covering less
surface area.
(iv)
Students will be able to elaborate the derivation of lateral surface area as
well as total surface of cuboid to lateral surface area as well as total
surface area of a cube.
230
Previous Knowledge
(i)
Students are familiar with rectangular figurers and the method as well as
formulae of determining the area of such figures.
(ii)
Students are able to give examples of two dimensional and three
dimensional figures and objects.
Teaching Objects
(i)
Chalk Board, chalk, duster and pointer etc.
(ii)
Cuboidal objects like packaging of soap, toothpaste and other objects.
Previous Knowledge Testing
Teacher Activity
Student Activity
1. By making a rectangle on chalk
1. Rectangle
board teacher asks about the
shape.
2. What is the formula to find the
2. Length × Breadth
area of the rectangular figure?
3. Give me an example of 3 D figure.
3. Cuboid, Cube etc.
4. What is the formula to find the
area of the cuboid?
4. No answer
Announcement of the Topic: Today, we will find out the formula to find the
area of cuboid.
231
Presentation
Teaching
Teacher’s Activity
Students’ Activity Chalk
Points/Skills
Defining
Board
Summary
With the help of a Students look at Cuboid has six faces
cuboidal box, Teacher the box and try to
shows the parts of the recognize the box
box
l
Explanation
Teacher
makes
the
identical pairs of the
h
cuboid and tells the
student
about
its
measurement.
(It
is
written
Students look at
on the board
chalkboard)
h
Teacher tells that it has
three identical pairs of
rectangular shape.
b
b
l
One identical pair has
length and height as
measurement of sides.
One identical pair has
length and breadth as
measurement of sides.
One identical pair has
breadth and height as
measurement of sides.
What is the formula for
232
What is the formula
finding
Questioning
area
of
a l×b
rectangular figure?
for finding area of a
rectangular figure?
Now, we calculate the
area of all pairs of
cuboid.
It is l×b
l×b
b×h
b×h
h×l
h×l
Because they are the
Explanation
pairs so we add them
two times and we get
l×b+ b×h +h×l+ l×b+ Students note
down in their
b×h +h×l
l×b+
b×h
+h×l+
l×b+ b×h +h×l
note-books.
Area of cuboid=2(l×b+
Area
b×h +h×l)
cuboid=2(l×b+
(It is written on the
+h×l)
of
b×h
chalk board).
Write the problem on
Applying
formula
the board.
Students note
What is the formula
down the same
for
form of a cuboid whose
problem in their
surface
external measures are
notebook.
cuboid?
to An aquarium is in the
solve problem.
80 cm × 30 cm × 40 cm.
The base, side faces and
back face are to be
covered with a
coloured paper. Find the
area of the paper
needed?
( Problem is solved by
233
finding
area
total
of
a
the teacher on chalk
board.)
The length of the
Students copy the
aquarium = l = 80 cm
solution from
Width of the
chalkboard
aquarium = b = 30 cm
Height of the
aquarium = h = 40 cm
Area of the base = l ×
b = 80 × 30 = 2400
cm2
Area of the side face
Differentiate
Total
Teacher
tells
surface difference
the Students listen
between and note in their
area and Lateral lateral surface area and notebook
surface area
Total surface area.
carefully
= b × h = 30 × 40 =
1200 cm2
Area of the back face
= l × h = 80 × 40 =
3200 cm2
Explaining
The side walls (the faces
Required area = Area
excluding the top and
of the base + area of
bottom) make the lateral
the back face
surface
+ (2 × area of a side
area
of
the
cuboid. For example, the
face)
total area of all the four
= 2400 + 3200 + (2 ×
walls of the cuboidal
1200) = 8000 cm2
room in which you are
sitting
is
the
lateral
surface area of the room.
Hence,
the
surface area of a cuboid Students note the
2(h × l + b × h) or 2h
is given by 2(h × l + b × formula to find
(l + b).
h) or 2h (l + b).
Application of
lateral
lateral surface
area of cuboid
the formula for
finding L.S.A.
If
the
l=30 m
l=30 m
length What is given in the b=10m
b=10m
234
breadth
and problem?
h=8m
h=8m
height of a box
Lateral surface
is 30, 10 and
area
What will you find?
8m
=2( b×h +h×l)
respectively.
Find L.S.A.?
Substituting the
Lateral surface area
Recapitulation
known values in
=2(10×8 +8×30)
(Evaluation)
the formula of
=2(80+ 240)
Ask students to apply Lateral surface
=2(320)
the formula and put all area
=640m2
the
values
which
is =2(10×8 +8×30)
=2(80+ 240)
given in the problem
=2(320)
=640m2
So today we have learnt
T.S.A. and L.S.A. of
cuboid.
Recapitulation
What is the formula for 2h ( b+l)
finding lateral surface
area of a cuboid?
2(l×b+ b×h
What is the formula for
finding total surface area +h×l)
of a cuboid?
Evaluation
Solve
the
problem written
on chalkboard.
Write a problem on Students look at
If the length breadth
chalkboard i.e. If the the board and
and height of a box is
length
breadth
and note the problem
40,
20
and
height of a box is 40, 20 in their notebook.
respectively.
and 10m respectively.
T.S.A.?
Find T.S.A.?
235
10m
Find
(Recapitulation) What is given in the l= 40 m
problem?
b=20m
h=10m
What is to be finding Total surface area
=2(l×b+ b×h
out?
+h×l)
Ask students to apply Substituting the
the formula and put all known values in
the
values
which
given in the problem
is the formula of
Total surface area
=2(40×20+
20×10 +10×40)
=2(800+ 200
+400)
=2(1400)
=2800m2
Home Assignment
1. The internal measures of a cuboidal room are 12 m × 8 m × 4 m. Find the total
cost of whitewashing all four walls of a room, if the cost of white washing is Rs
5 per m2. What will be the cost of white washing if the ceiling of the room is
whitewashed?
2. A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a
tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to
cover 100 such suitcases?
236
Appendix-C
MATHEMATICS ACHIEVEMENT TEST: PILOT STUDY
Fill your particulars before start.
Name …………………………… Roll No………………
School ……………………………………………………………………….
Grade- VIII
Boy/Girl
Age………….
Rural/Urban
Time: 40 Minutes
INSTRUCTIONS
1. All questions are compulsory.
2.
3.
4.
5.
MM: 30
Question 1-5 carry 1 marks each
Question 6-11 carry 2 marks each
Question 12-14 carry 3 marks each
Question 15 carry 4 marks
Q1. Area of Trapezium = ½ × (___________) × Distance between Parallel sides.
Q2. All of faces of a ___________ box are squares.
Q3. Total surface area of a cube of side 8 cm is ___________.
Q4. If the volume of a cube is 64 cm3, the edges of this cube will be______.
Q5. Volume of Cylinder = ______×height.
Q6. The area of rhombus is 240 cm2 and one of the diagonal is 16 cm calculate the
length of another diagonal.
Q7. Find the lateral surface area of a cuboid having length, breadth, height as 6 cm, 4
cm and 2 cm respectively.
Q8. A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of
metal. How much sheet of metal is required?
Q9. If volume of a room is 72000 m3 then how many boxes each of volume 6 m3 can be
placed in this room?
Q10. If we interchange the length of the base and the height of a cuboid (Fig I) to get
another cuboid (Fig II) will its lateral surface area changed. Elaborate your answer.
237
Q11. If each edge of a cube is doubled how many time its volume increased.
Q12. A company sells biscuits. For packing purpose they are using cuboidal boxes:box
A →3 cm × 8 cm × 20 cm, box B → 4 cm × 12 cm × 10 cm. What size of the box will
be economical for the company? Why? Can you suggest any other size (dimensions)
which has the same volume but is more economical than these?
Q13. The ratio of two parallel side of trapezium is 1:3 and the distance between them is
10 cm. If the area of the trapezium is 340 cm2 then find the length of the parallel sides.
Q14. If each edge of a cube is doubled how many time its volume increased.
14cm
14cm
_____22cm_____
Q15. There is a pentagonal shaped park as shown in the figure (I). For finding its area
Bhawna (Fig. II) and Komal (Fig. III) divided it in two different ways.
15 m
30m
15 m
Fig. (I)
Bhawna
Fig. (II)
Komal
Fig. (III)
Compute the area of this park using both ways. Can you suggest some other way of
finding its area?
238
ANSWER KEY
Mathematics Achievement Test: Pilot Study
Question No
Answer
1.
Sum of parallel sides
2.
Cube
3.
384 cm2
4.
4cm
5.
6.
30 cm
7.
40 cm2
8.
440cm2
9.
12000 Boxes
10.
Yes
11.
8 times
12.
13.
B is more economic than A,
(6,8,10) may be other combination of box
51 cm
14.
539 cm3
15.
337.5 m2
239
Appendix- D
MATHEMATICS ACHIEVEMENT TEST: PRELIMINARY DRAFT
Student’s Data
Fill your particulars before start.
Name ……………………………
Roll No………………
School ……………………………………………………………………….
Grade- VIII
Boy/Girl
Age………….
Rural/Urban
Time: 3 Hours
INSTRUCTIONS
1.
2.
3.
4.
5.
MM: 110
All questions are compulsory.
Question 1-18 carry 1 marks each.
Question 19-36 carry 2 marks each.
Question 37-43 carry 3 marks each.
Question 44-50 carry 5marks each.
1)
Additive inverse of (-7/9) is ____________.
2)
The product of two rational numbers is always a ___________________.
3)
(a/b + b/c)+ e/f = a/b + (b/c+ e/f) is close under ______________________.
4)
Multiplicative inverse of 10-5 is _________.
5)
Value of (3-1+4-1+5-1)0 is _______________.
6)
A ____________ polygon is both equiangular and equilateral.
7)
A hexagonal prism has _____________ as its base.
8)
A trapezium is a quadrilateral with a pair of _____________ sides.
9)
The sum of the measures of the exterior angles of a pentagon is _______.
10)
Rhombus has all properties of ___________________.
11)
Area of general quadrilateral= ½ d (___________).
12)
Total surface area of a cube of side 8 cm is ___________.
13)
Area of four walls of a room =________________________________.
240
14)
If base area and height are 50 cm2, 8 cm respectively then volume of cylinder is
= _____________.
15)
(x+a) (x+b)= _________________ .
16)
a-m / a-n =______________.
17)
Value of (2/3) -2 is = _____________
18)
Algebraic terms with the same variables and same exponents are called
__________ terms.
19)
Is 8/9 is the multiplicative inverse of -11/8 ? Why or why not?
20)
Without calculation verify that (5/8 ÷ 10/3) and (10/3 ÷5/8) are same or not.
Write the reason in context of yes or no.
21)
The sum of two numbers is 4. If one of the numbers is -5/7 then find the other.
22)
Find m so that (–3) m+1 × (–3)5 = (–3)7
23)
Compare the size of a Red Blood cell which is 0.000007 m to that of a plant cell
which is 0.00001275 m.
24)
Find the angle measure x in the following figure.
xº
70 º
60 º
25)
How many sides does a regular polygon have if the measure of an exterior angle
is 24°?
26)
Indicate the front view, side view and top view of the given object.
27)
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of
metal. How much sheet of metal is required?
28)
A few notorious boys were chasing a cat of length 45 cm, breadth 20 cm and
height 22 cm. Suddenly she fell into a tub of water. Some of the water came out of the
tub, what was the volume of water that came out.
241
29)
If we interchange the length of the base and the height of a cuboid (Fig I) to get
another cuboid (Fig II) will its lateral surface area changed. Elaborate your answer.
30)
Construct a polynomial with x and y as variables having four terms.
31)
If the length of the rectangle is increased by 4 units, and breadth is decreased by
2 units, what will be the area of new rectangle?
32)
Simplify (a + b) (2a – 3b + c) – (2a – 3b) c.
33)
Simplify (2x+5)2 – (2x-5)2
34)
If 10a- 5b= 25 and ab=12 then 100a2+25b2=?
35)
Express 4-3 as a power with the base 2.
36)
Thickness of your hair is 6.07×10-6 mm; express it in decimal form.
37)
Use the Identity (x + a) (x + b) = x2 + (a + b) x + ab to find the solution of
501 × 502.
38)
Simplify:
3-5 × 10-3× 125
5 -7× 6-5
39)
What is the sum of the measures of the angles of a convex quadrilateral? Will
this property hold for concave quadrilateral? Elaborate your answer with one example
of concave quadrilateral.
40)
Diameter of cylinder A is 14 cm and height is 7 cm. Diameter of cylinder B is 7
cm, and the height is 14 cm. Without doing any calculations can you suggest whose
volume is greater? Verify it by finding the volume of both the cylinders. Check whether
the cylinder with greater volume also has greater surface area?
14 cm
7 cm
14cm
Cylinder A
242
Cylinder B
41) The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the
measure of each of the angles of the parallelogram.
42) Look at the following shape. Count and write number of faces, vertices and edges,
also verify Euler’s formula.
43) A rectangular paper of length 22cm and width 14 cm is rolled along its width on a
cylindrical can completely. Find the volume of the cylinder (Take22/7 for ).
14cm
14cm
22cm
44) A Company sells biscuits. For packing purpose they are using cuboidal boxes: box
A →3 cm × 8 cm × 20 cm, box B → 4 cm × 12 cm × 10 cm. What size of the box will
be economical for the company? Why? Can you suggest any other size (dimensions)
which has the same volume but is more economical than these?
45)
Verify that 1/8 × (-7/6 + 3/4) = (1/8 × -7/6) + (1/8 × 3/4).
46)
Using exponents expand 1025.63 in as many ways as you can.
47)
Verify Identity (I) (II) and (III) for a = 3, b = 2.
48)
Examine the table. There are some polygons. Find the sum of the angles and also
derive the formula to measure sum of the angles of a convex polygon.
Figure
Sides
Angle sum
3
4
5
243
6
49) Find three rational numbers between ¼ and ½ and place them on number line.
50) There is a pentagonal shaped park as shown in the figure (I). For finding its area
Ram (Fig. II) and Shyam (Fig. III) divided it in two different ways. Compute the area of
this park using both ways. Can you suggest some other way of finding its area?
30 m
15m
__15m ___
Fig. (I)
Fig. (II)
244
Fig.(III)
Appendix-E
MATHEMATICS ACHIEVEMENT TEST: FINAL DRAFT
Student’s Data
Fill your particulars before start.
Name ……………………………….. Roll. No.………………
School………………………………………
Time: 2½ Hours
MM: 80
Boy/Girl…………
INSTRUCTIONS
1.
2.
3.
4.
5.
Grade- VIII
All questions are compulsory.
Question 1-11 carry 1 marks each.
Question 12-23 carry 2 marks each.
Question 24-28carry 3 marks each.
Question 29-34 carry 5 marks each.
1. Additive inverse of (-7/9) is ____________.
2. Multiplicative inverse of 10-5 is _________.
3. Value of (3-1+4-1+5-1)0 is _______________.
4. A ____________ polygon is both equiangular and equilateral.
5. A hexagonal prism has _____________ as its base.
6. Rhombus has all properties of ___________________.
7. Total surface area of a cube of side 8 cm is ___________.
8.
Area of four walls of a room =________________________________.
9.
If base area and height are 50 cm2, 8 cm respectively then volume of cylinder is =
_____________.
10. a-m / a-n =______________.
11. Value of (2/3) -2 is = _____________
12. Is 8/9 is the multiplicative inverse of -11/8 ? Why or why not?
245
13. The sum of two numbers is 4. If one of the numbers is -5/7 then find the other.
14. How many sides does a regular polygon have if the measure of an exterior angle is
24°?
15. A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of
metal. How much sheet of metal is required?
16. A few notorious boys were chasing a cat of length 40 cm, breadth 25 cm and height
20 cm.
Suddenly she fell into a tub of water. Some of the water came out of the
tub, what was the volume of water that came out.
17. If we interchange the length of the base and the height of a cuboid (Fig I) to get
another cuboid (Fig II) will its lateral surface area changed. Elaborate your answer.
18. Construct a polynomial with x and y as variables having four terms.
19. Simplify (a + b) (2a – 3b + c) – (2a – 3b) c
20. Simplify (2x+5)2 – (2x-5)2
21. If 10a- 5b= 25 and ab=12 then 100a2+25b2=?
22. Express 4-3 as a power with the base 2
23. Thickness of your hair is 6.07×10-6 mm; express it in usual form (decimal form).
24. Use the Identity (x + a) (x + b) = x2 + (a + b) x + ab to find the solution of
501 × 502
25. Simplify:
3-5 × 10-3× 125
5-7× 6-5
246
26) The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find
the measure of each of the angles of the parallelogram.
27) Look at the following shape. Count and write number of faces, vertices and edges,
also verify Euler’s formula.
28) A rectangular paper of length 22cm and width 14 cm is rolled along its width on a
cylindrical can completely. Find the volume of the cylinder Take22/7 for ).
14cm
14cm
______22cm______
22cm
29) Verify that 1/8 × (-7/6 + 3/4) = (1/8 × -7/6) + (1/8 × 3/4).
30) Using exponents expand 1025.63 in as many ways as you can.
31) Verify Identity (I) (II) and (III) for a = 3, b = 2.
32) Examine the table. There are some polygons. Find the sum of the angles and also
derive the formula to measure sum of the angles of a convex polygon.
Figure
Sides
Angle
sum
3
4
33) Find three rational numbers between
5
¼
line.
247
and
6
½ and also place them on number
34) There is a pentagonal shaped park as shown in the figure (I). For finding its area
Bhawna and Komal divided it in two different ways. Compute the area of this park
using both ways. Can you suggest some other way of finding its area?
30 m
15m
15m
Fig. (I)
Fig. (II) Bhawna
248
Fig. (III) Komal
ANSWER KEY
Mathematics Achievement Test: Final Draft
Question No
Answer
1.
7/9
2.
105
3.
1
4.
Regular
5.
Hexagon
6.
Parallelogram
7.
384cm3
8.
Lateral Surface area of room
9.
400 cm3
10.
a-m+n
11.
9/4
12.
No
13.
33/4
14.
15
15.
440 m2
16.
19800 cm3
17.
Yes
18.
xy+xy2+ x 2y+ x 2y 2
19.
2a2-3b2 –ab-ac+4bc
20.
40 x
21.
1825
22.
(2)-6
23.
0.00000000607
24.
251502
25.
312500
26.
108º, 72º
27.
F=6, V=8, E=12, F+V-E=2
249
28.
539 cm3
29.
Verification
30.
1025.63×100 , 102.63×101
,10.2563×102 1.02563×10
3
,.102563×104 etc.
31.
Verification
32.
180º,360º,540º,720º Formula=(n-2)
180º
33.
3/12, 4/12,5/12, 6/12
34.
337.5cm2
250
Appendix- F
MATHEMATICS ACHIEVEMENT TEST : PARALLEL FORM
Student’s Data
Fill your particulars before start.
Name ……………………………
Roll No………………
School ……………………………………………………………………….
Grade- VIII
Boy/Girl
Age………….
Rural/Urban
Time: 2½ Hours
INSTRUCTIONS
1.
2.
3.
4.
5.
MM: 80
All questions are compulsory.
Question 1-11 carry 1 marks each.
Question 12-23 carry 2 marks each.
Question 24-28carry 3 marks each.
Question 29-34 carry 5marks each.
1) Additive inverse of (6/17) is ____________.
2) Multiplicative inverse of 108 is _________.
3) Value of (2-2+3-1+6-1)0 is _______________.
4) A regular polygon is both equiangular and_____________.
5) A triangular pyramid has _____________ as its base.
6) Rectangle has all properties of ___________________.
7) Lateral surface area of a cube of side 6 cm is ___________.
8) Area of four walls of a room =________________________________.
9) If base area and height are 25cm2, 6 cm respectively then volume of cylinder is =
_____________.
251
10) a-m × a-n =______________.
11) Value of (5/6) -2 is = _____________
12) Is 9/10 is the multiplicative inverse of --11/9 ? Why or why not?
13) The sum of two numbers is 7. If one of the numbers is 3/4 then find the other.
14) How many sides does a regular polygon have if each of its interior angle is 165°?
15) A closed cylindrical tank of radius 14 m and height 9 m is made from a sheet of
metal. How much sheet of metal is required?
16) A slab of ice length 45 cm, breadth 20 cm and height 22 cm fell into a tub of
water. Some of the water came out of the tub, what was the volume of water that
came out.
17) If we interchange the length of the base and the height of a sweet box to get
another box will its lateral surface area changed. Elaborate your answer.
18) Construct a trinomial with x and y as variables.
19) Simplify 3y (y -2x +5) + 2x(4x+3y –8) – (2x – 3y) z.
20) Simplify (5y-9)2 – (5y+9)2
21) If 5a- 3b = 12 and ab=8 then 25a2+9b2=?
22) Express 9-3 as a power with the base 3.
23) Thickness of thread is 9.03×10-8 mm; express it in usual form (decimal form).
24) Use the Identity (x + a) (x + b) = x2 + (a + b) x + ab to find the solution of 201 ×
205.
25) Simplify:
25 ×t-4× t8
5-3× 10-2
26) Two adjacent angles of a parallelogram have equal measure. Find the measure of
each of the angles of the parallelogram.
252
27) Look at the following shape. Count and write number of faces, vertices and
edges, also verify Euler’s formula.
28) A rectangular paper of length 11cm and width 7 cm is rolled along its width on a
cylindrical can completely. Find the volume of the cylinder (Take22/7 for ).
7 cm
7cm
______11cm______
29) Verify that 1/7 × (-5/9 + 2/7) = (1/7 × -5/9) + (1/7 × 2/7).
30) Using exponents expand 2065.89 in as many ways as you can.
31) Verify Identity (I) (II) and (III) for a = 4, b = 5.
32) Examine the table. There are some polygons. Find the sum of the angles and
also derive the formula to measure sum of the angles of a convex polygon.
Figure
Sides
3
4
5
6
Angle
sum
33) Find four rational number between1/5 and 1/7 and also place them on number
line.
253
34) There is a hexagonal MNOPQR of side 5 cm figure (I). For finding its area
Ramesh and Mohan divided it in two different ways. Compute the area of this figure
using both ways. Can you suggest some other way of finding its area?
i.
Fig(I)
Ramesh Way
254
Mohan Way
ANSWER KEY
Mathematics Achievement Test: Parallel Form
Question
Answer
No
1.
6/17
2.
10-8
3.
1
4.
Equilateral
5.
Triangle
6.
Parallelogram
7.
144cm3
8.
2(l+b)h
9.
150 cm3
10.
a-(m+n)
11.
36/25
12.
No
13.
25/4
14.
24
15.
2024 m2
16.
19800 cm3
17.
Yes
18.
xy2+ x 2y2+ x 3y 3
19.
8x2+3y2+15y-16x-z(2x+3y)
20.
-180y
21.
384
22.
(3)-6
23.
.0000000903
24.
41205
25.
3125000 t4
26.
108º, 72º
255
27.
F=6, V=8, E=12, F+V-E=2
28.
105.88 cm3
29.
Verification
30.
2065.89×100 , 206.589×101 , 20.6589×102
2.06589×10 3,.102563×104 etc.
31.
Verification
32.
180º,360º,540º,720º Formula=(n-2) 180º
33.
11/70, 23/140,12/70, 13/70
34.
64cm2
256
Appendix-G
MATHEMATICAL CREATIVITY TEST
Student’s Data
Fill your particulars before open the booklet.
Name …………………………………………………………
Roll No………………
School …………………………………………………………………..……………….
Grade- VIII
Age………….
Boy/Girl ……………
Rural/Urban…………
Time: 80 minutes
Directions for the Students
This mathematical creativity test is a part of an educational research aiming at assessing
your creativity in mathematics. Write responses what you think of without fear or hesitation. It
will help you to express your creative abilities in mathematics. The items in this booklet provide
you opportunities to think freely in mathematics, produce mathematical relationships, and solve
non-routine mathematics problems which have various different methods of solution and give
you the opportunity to pose some relevant problems toward a mathematical situation. Hence try
to respond to each item by the maximum number of unusual and different ideas. Let your mind
go far and deep in thinking up ideas. Keep in mind that ideas or responses should be yours not
your friend.
Developed by
Pooja Walia (J.R.F.-U.G.C.)
M.Sc. (Mathematics), M.Phil. (Education)
Department of Education
KurukshetraUniversity, Kurukshetra
DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO.
257
ITEM I
5 3
Write 1000 a b in different ways without changing the value.
Directions: A number can be presented by many ways e.g. you can write 6 as 3+3, 12-6, 2 × 3,
12/2, and 36/6. A problem related to presentation of numbers in different ways is given below.
You have to think and write as many expressions as you can.
E.g.: 1. 22. 5.2 10 × a3+2. b 4-1
2. (500+500). a5.b3
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
6.___________________________________________________________________________
Fluency………
Flexibility……….
Originality…………
ITEM II
Suppose you and your friend are playing a guessing game to determine the name of a
geometric figure. In this game, your friend will think of figure and you will ask him
questions about the figure. Your friend will respond. Your task is to put as many
questions as you can which should be answered in order to determine the name of the
figure.
E.g. 1) Is it a plane figure?
2) Does it have vertices?
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
Fluency………
Flexibility……….
Originality…………..
258
ITEM III
Write as many relationships as you can between 64 and 144.
Directions: When you see the numbers usually there is nothing to notice, but when you think
deeply about the numbers you will find many facts about a single number.
E.g. 25: It is an odd number.
It is a perfect square number.
It is divisible by 1, 5 & 25.
In the same pattern relate two numbers.
E.g.: Both are perfect square numbers.
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
Fluency………
Flexibility……….
Originality…………
ITEM IV
.
Write similarities and dissimilarities between the following figures. They are similar in
certain aspects and different in another.
E.g. Similarity: Both have diagonals.
Dissimilarity: The length of diagonals is equal in rectangle but it is not true in rhombus.
Rectangle
Rhombus
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
Fluency………
Flexibility……….
Originality…………
259
ITEM V
Write as many geometrical shapes, figures and concepts in relation to different objects
which you observe in day to day life.
Directions: In our daily life if we see the things around us some of them are related to
geometrical figure like Chapati (Roti)
has a circular shape and brick
has cuboidal
shape. Have you noticed something in your surrounding? If not, then think and
E.g. 1. Room floor has rectangular shape.
2. The rod of ceiling fan is perpendicular to ceiling.
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
Fluency………
Flexibility……….
Originality…………
ITEM VI
Select few numbers from the given numbers (1, 2, 3, 4, 8, 9, 16, 24, 27, 28, 32, 36, 40, 43,
44, 48, 49), showing some pattern or having relation with each other.
E.g. (2, 4, 8, 16, 24, 28, 32, 36, 40, 44, 48)
:
Even numbers
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
Fluency………
Flexibility……….
Originality…………
260
ITEM VII
Read the following mathematical situation carefully. Suppose you and your friend are playing
in the rectangular park having a length 160 m and breadth 120 m is surrounded by a footpath
having a width of 3 m. The cost of fencing is Rs. 35 per meter. It needs to be cemented at the
rate of Rs 120 per square meter. The cost of one bag of cement is Rs. 350. The grass lawn is
divided into four sections by two intersecting paths having width of 2 m. The path is also
required to be tiled. 9 tiles of 15×12 cm are required to cover 1 m2 area of footpath. There is one
flowering bed of 8 m × 8 m in one corner of each section of the grass lawn. Cost of planting
flower in 4 m2 areas is Rs. 100. Now, your task is to frame as many problems as you can from
the data given in problem as well as in diagram.
166 m
1.___________________________________________________________________________
2.___________________________________________________________________________
3.___________________________________________________________________________
4.___________________________________________________________________________
5.___________________________________________________________________________
6.___________________________________________________________________________
7.___________________________________________________________________________
8.___________________________________________________________________________
9.___________________________________________________________________________
10.__________________________________________________________________________
Fluency………
Flexibility……….
Originality…………
261
ITEM VIII
Suppose you have 12 pieces of wire of equal length. Name various geometrical
shapes/figures which can be made by using these 12 pieces of wires. Write also
the name of figure.
Directions: With the help of material you can make different shapes. Suppose you have 4
pieces of wire. You can make a square from those like this
. Space is provided for
shapes.
Fluency………
Flexibility……….
Originality…………
262
Appendix -H
ORIGINALITY SCORING KEY FOR MCT
ITEM I
Write 1000 a5b3 in different ways without changing the value.
Sr. Flexibility Category
Responses
Stud Score
No
ents
A
Simple form
B
Power form
a) Positive
b) Negative
c) Power in denominator
10×10×10×a×a×a×a×a×b×b
×b.
27
0
103×a2×a3×b3
(10-3)-1 a5b3
100000/102 a5b3
1010/105.102 a5b3
66
3
2
0
3
4
3
85
3
0
78
0
d) Power in variable
D
1000 a3 b2
Factor form : Break 1000 into 2×500, 4×250, 8×125
factor
Use of addition in constant
(200+400+400) a5b3 etc.
E
Use of subtraction in constant
(1500-500) a5b3 ,
67
0
F
Use of fraction in constant
(25000/25) a5b3 ,
71
0
G
a)Use of square root in
constant
√100 (1100-1000) a5b3
13
0
10(√10)2 a5b3
2
4
(5555×0+1000). a5b3 ,
(999+1+0) a5b3
6
0
C
H
b)Use of square & square
root both in one expression
Use of 0 in constant
I
Use of decimal in constant
(5000× .2) a5b3
1
5
J
Use of 0 as exponent
2º×2×50×10× a2×a3×b3
1000 a10-5 b10-7 c º
4
2
K
Use of addition in power of
variable
2×50×10× a4+1 ×b2+1
80
0
L
Use of subtraction in power
of variable
Use of fraction in
a) power of variable
2×50×10× a6-1×b9-6
83
0
31
0
M
2×50×10× a25/5×b18/6
263
[(10)1/5]15a50/10b30/10
1
5
Use of square root in power
of variable
Use of cube root in power of
variable
2×50×10× a √25×b √9
12
0
2×50×10× a 3√125×b 3√27
3
3
Use of decimal in power of
variable
Use root as denominator in
power of variable
2×50×10× a .25/ .5×b .12/
,5000/5 a2.5+2.5 b1.5+1.5
2×50×10× a 25/√ 25×b 9/ √9
4
2
1
5
R
Use of cube root in constant
Use of 5 root in constant
100 3√1000 a5b3
(5√1000 ab)5/b2
5
1
1
5
S
Use of cube in constant
(93+102+71) a5b3
17
0
T
Use of square and
other power in addition
Use of Multiplication in
power
Use of Negative Exponent in
power of variable
Use of Identity,
Additive Identity
Multiplicative Identity
(92+302+19) a5b3
(54+375) a5b3
(250×4) a(2×2)+1b3×3-6
103×2×3/6 a5b3
(1000) ×1/a-5×1/b-3
34
1
11
0
5
0
8
0
(92+302+19) a5+0b3+0
1000/1 a5×1b3×1
9
12
0
0
Use of variable other than a
&b
5000/5√5x/√5x a5b3
x º×103√a10√b6
(3√1000)3a(√x)2b√x where
√x=√ √9+√9+√9
5000/4+6/2 a15+10/2b3+3/2
500×2 a-5×-1 b-3×-1
-102×-10 a5b3
2
4
1
5
2
2
4
4
b) constant
N
O
P
Q
U
V
W
X
Y
Z
Use of substitute
Use of addition of fractions
Use of – sign
264
.4
ITEM II
Suppose you and your friend are playing a guessing game to determine the name of
a geometric figure. In this game, your friend will think of figure and you will ask
him questions about the figure. Your friend will respond. Your task is to put as
many questions as you can which should be answered in order to determine the
name of the figure.
Sr. Categor
Responses
Stude Score
No y
nts
.
A
Type of 1. What is the type of figure?
5
1
figure
2. Is it 2-dimensional figure?
46
0
3. Does it have plane surface?
4
2
4. Is it 3-dimensional figure?
42
0
5. Are all sides visible?
1
5
6. Does it can stable on the desk?
1
5
7. Is it Euclidean or Non Euclidean geometrical 1
5
figure?
1
B
Type of 1. What is the shape of the figure?
5
0
Shapes
2. Is it curved?
12
2
4
3. Is it circular?
1
5
4. Is it spherical?
5. Is it round?
12
0
2
6. Is it a figure with zero sides?
4
3
7. Does the figure pointed from the top/ bottom?
3
8. Does the figure pointed from corner?
5
1
9. Does it have no angle?
-C
Vertices,
Edges,
Faces
D
Sides
1. Does it have vertices?
2. How many vertices does it have?
3. Does it have edges?
4. How many edges does it have?
5. Does it have faces?
6. How many faces does it have?
7. What is the shape of its faces?
8. Does it have zero vertices?
9. Is centre of the figure equidistant from it vertices?
10. Can it satisfy Euler’s Formula?
11. Is it faces common or not?
12. Does it have zero edges?
13. Does it have zero Faces?
14. Is it a polyhedron?
1. Does it have any sides?
2. How many sides it have?
3. Does it have four sides?
4. Are opposite sides equal?
265
16
35
17
28
7
27
1
2
1
3
----5
34
4
26
0
0
0
0
0
0
5
4
5
3
1
0
2
0
5. Are all sides equal?
6. Are all sides unequal?
7. Are opposite sides parallel?
8. Are all sides’ non-parallel?
9. How many sides are equal?
10. How many sides are parallel?
11. Does it sides are perpendicular to each other?
E
Arc,
F
Straight
Lines
G
Angles
12. How many side are perpendicular to each other
13. Does the figure have more than four sides?
14. Is it a polygon?
15. Is it a Quadrilateral?
1. Does it have arc?
2. Does it have curve line?
1. Does it have/haven’t straight lines?
2. How many tangents can be drawn from it?
3. No. of lines draw from one vertex.
4. Does it have any transversal?
1. How many angles does it have?
2. Does it have three angles?
3. What kind of angles formed?
4. Obtuse Angle
5. Acute Angle
6. Right Angle
7. Reflex Angle
8. Complete Angle
9. Are opposite angles equal?
10. Does it have all angles equal?
11. Are opposite angles equal to 90 º?
12. Does it have all angles equal to 90 º?
13. Does it have all angles equal to 60 º?
14. Does it make angles equal to 90 º at intersection of
Diagonals?
15. Does it have alternate angle?
16. Does it have corresponding angles?
17. Does it have interior angle?
18. Does it have exterior angles?
19. Does it have V.O.A?
20. How many angles of rotational symmetry does it
have?
21. Is it equiangular?
22. Does any line make linear pair?
266
29
1
39
1
1
1
-1
7
---
0
5
0
5
5
5
1
8
3
2
1
1
33
3
3
5
6
19
1
-12
19
2
12
2
1
5
0
3
4
5
5
0
3
3
1
0
0
5
1
1
2
5
-1
---
5
5
4
1
5
0
0
0
4
0
4
5
5
8
10
5
3
1
1
2
2
5
5
0
0
1
3
5
5
4
4
1
1
Does it have perimeter? If yes than what is it?
13
Does it have area? If yes than what is it?
19
Does its area greater than perimeter?
1
Is circumference equal to perimeter?
1
Volume
Does it have volume?
20
Surface
Does it have surface area?
2
area
Does it have lateral surface area?
1
Does it have curved surface area?
2
Formula
Formula used to find perimeter.
10
Used
Formula used to find area
20
No. of formulas used for area
2
Formula used to find volume
4
Formula used to find surface area
1
Can we apply Heron’s Formula to find the area of 3
figure?
Required 1. Is diagonal required to find area?
1
dimensio 2. Is altitude required to find area?
1
ns
3. Is radius/diameter required to find area?
3
to find 4. Is one side required to find area?
4
area
Closed & 1. Is it closed figure?
11
Open
2. Is it open figure?
5
Construc 1. Can we draw it on paper?
3
tion
2. Can we draw it free hand?
3
method
3. Can we draw it by compass?
3
&Used
4. Can we draw it by scale?
2
Equipme 5. Can we make it by paper folding?
1
nt
6. Is it made by joining two plane figures?
3
Divided 1. Is diagonal divided the figure into two triangles?
4
into Parts 2. How many triangles/parts can be cut from it?
4
0
0
5
5
0
4
5
4
0
0
4
2
5
3
Diagonal
&
Transver
0
0
0
H
Circumfe
rence,
diameter,
radius,
centre
I
Regular,
Convex
&
Concave
Perimete
r&
Area
J
K
L
M
N
O
P
Q
R
1.
2.
3.
4.
5.
6.
7.
1.
2.
3.
Does it have circumference?
Does it have radius?
Does it have diameter?
Does it have centre point?
Is it centre equidistant from all dimensions?
Can we draw infinite lines from its centre?
Is any line passes through it?
Is it regular figure?
Is it concave figure?
Is it convex figure?
1.
2.
3.
4.
1.
1.
2.
3.
1.
2.
3.
4.
5.
6.
1. Does it have any diagonals?
2. How many diagonals does it have?
3. Length of diagonal is equal or not.
267
19
15
18
5
5
3
2
0
1
3
3
3
4
5
3
2
2
sal
S
Dimensi
ons
T
Bisector
Median
4.
5.
6.
7.
8.
1.
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
6.
1.
1.
2.
3.
1.
1.
U
Theorem
V
Orthocen
tre
Perpendi
cular
Sum of 1. What is the angle sum property?
Angles
2. What is the sum of all/interior angles?
3. Is the sum of interior angles is 360º?
4. What is the sum of exterior angles?
5. Is the sum of all angle 180º?
6. Does the sum of adjacent angle is 180º?
7. Is the sum of all angle 540º?
8. Is the sum of all angle 720º?
Symmetr 1. Can it have line of symmetry?
y
2. Can it have congruency with its own parts?
Congrue
ncy
W
X
0
0
0
5
11
Are diagonals intersecting?
13
Are diagonals perpendicular to each other?
6
Are diagonals bisecting each other?
1
Does it have any transversal?
Does diagonal lies inside the figure?
What are the length, breadth &height?
24
Ratio of length and breadth?
5
Does it have hypotenuse?
2
Does it have one base?
4
Does it have altitude?
3
Is it full in size or half?
1
Does it have angle bisectors?
11
How many bisectors does it have?
1
Does bisector of angles meets at a point on the 3
base.
1
Does bisector of angles meets at Centre?
4
Does bisector intersect at 90º?
1
Does it have bisectors of sides?
2
Does it have median?
Which theorem can we apply on it?
5
Does it follow Congruence Theorem?
1
Does it follow Pythagoras Theorem?
5
Does it have orthocentre?
1
Does it have any perpendicular in it /on base?
7
268
0
1
4
2
3
5
0
5
3
5
2
5
4
1
5
1
5
0
--14
9
4
5
2
----4
2
0
0
2
1
4
2
4
Y
Truncate
d
&
Similarit
y
with
other
figures
Z
Live
Example
Sr.
No
.
A
Categor
y
B
C
D
E
F
1. Can it be truncated into Cone?
2. Is the figure derived from other figure?
3. Does it have any similarities with other figures e.g.
square, rectangle
4. Is it used to make other shapes?
5. Does any other figure also exist in it?
6. Is it a combination of two or more than two shapes
e.g. cylinder?
1
1
3
5
5
3
--2
6
1
4
0
5
1. What is the live example of such figure?
20
2. How does it look like?
29
3. Does it look like –e.g. ---------------?
--ITEM III
Write as many relationships as you can between 64 and 144.
Responses
Position
1. Both are less than 150.
2. Both are greater than 60.
3. Both lie between 50 -150.
4. Both have equal difference from 104.
Nature
1. Both are Composite numbers.
depend
2. Square roots of both are Composite numbers.
on
3. Both are not Prime numbers.
division 4. Both are not odd numbers.
Common 1. Both contain 4 at unit places.
digit
2. Square of both contains 6 at unit places.
3. Both are double digit number.
Nature
1. Both are Natural numbers.
2. Both are Whole numbers.
3. Both are Integers.
4. Both are Positive Integers.
5. Both are Real numbers.
6. Both are Rational numbers.
7. Both can be written in p/q form.
8. Both lies on number line.
9. Both lies on right side on number line.
10. Both are not irrational numbers.
11. Both are not fractional numbers.
12. Square root of both has same nature.
Perfect
1. Both are perfect square numbers.
square
2. 4, 16 are the factors of both which are perfect
square.
Divisible 1. Both are divisible by 1.
2. Both are divisible by 2.
269
0
0
Stud Score
ents
3
14
1
1
25
1
9
3
45
1
2
38
33
10
16
26
26
6
9
4
3
--2
28
1
3
0
5
5
0
5
0
3
0
5
4
0
0
0
0
0
0
0
0
2
3
23
77
0
0
4
0
5
0
0
0
70
56
22
--5
4
5
2
2
12
2
2
1
1
1
1
2
1
4
4
0
4
4
5
5
5
1
1
1
5
5
5
H
Theorem
I
J
Formula
Polynom
ial
3. Both are divisible by 4.
4. Both are divisible by 8.
5. Both are divisible by 16.
1. 1 is the factor of both.
2. 2 is the factor of both.
3. 4 is the factor of both.
4. 8 is the factor of both.
5. 16 is the factor of both.
6. Both are factors of 576.
7. Both have more than 6 factors.
8. 16 is the H.C.F. of both.
9. 4 is the H.C.F. of their square root of both.
10. Smallest factor is 1.
11. Their half have common factor 2.
Prime Factorisation Theorem applies on both to find
square root.
Both follow Euclid De’lemma of Division Algorithm.
Both are polynomial of degree 0.
Both are constant term.
K
Area
Both can be area of a square.
2
4
L
Even
numbers.
Denomin
ator
Same
1. Same number occurs at unit place when it is
number
divided by 2, 4 & 8.
at
unit
place
Not
1. Both are not divisible by any numbers except 1, 2,
divided
4, 8, and 16.
and
2. Both have terminating decimal representation
multiple
when divided by 5 and other numbers.
3. Both are not multiple of any numbers except 1, 2,
4, 8, and 16.
Addition 1. If we add or Subtract same number (even/odd) to
/
both then nature of both remains same.
Subtracti 2. If 4 is subtracted from both than divisible by 5.
on of a
number
Multiplic 1. If we multiply or
ation/Div 2. Divide by a number (even/odd) then nature of
ision by
number remains same.
92
4
1
-----
0
2
5
M
1. Both are even numbers.
2. Both are squares of even numbers.
3. Factors of both are even numbers.
4. Squares/Square root of both are even numbers.
Both have same denominator.
2
4
14
0
3
3
G
N
O
P
Q
Factors
270
---------
9
1
0
5
R
S
a number 3. Answer is same when divided by zero.
4. Quotient is also perfect square when divided by 16.
5. Sum of both digits of Quotient is odd when divided
by 2 & 3.
Multiple 1. Both are multiple of 1.
2. Both are multiple of 2.
3. Both are multiple of 4.
4. Both are multiple of 8.
5. Both are multiple of 16.
6. 576 is the L.C.M. of both.
7. 24 is the L.C.M. of square root of both.
Square
1. Square roots of both are divisible by 1, 2 & 4.
root
2. Square roots of both are factor of 24.
3. Square roots of both have factor of 1, 2 & 4.
4. Square roots of both are not perfect square.
5. Square roots of both are multiple of 4.
6
--1
0
1
9
4
8
7
1
1
14
1
1
1
5
0
2
0
0
5
5
0
5
5
5
5
ITEM IV
Two figures are given below. They are similar in certain aspects and different
in another. Write similarities and dissimilarities between the figures.
Rectangle
Categories of Similarity
Sr.
No.
A
Category
Sides
Responses
1.
2.
3.
4.
5.
6.
B
Vertices,
face
Stude Score
nts
Both have four sides.
62
0
Opposite sides of both figures are equal.
21
0
Both have two pair of parallel sides.
2
4
Opposite sides of both figures are parallel.
37
0
Both have six line segments including 4 sides and 5
1
2 diagonal.
1
5
Both made from straight lines.
1. Both have four vertices.
2. Both have one face.
3. Both have four edges
271
41
2
---
0
4
C
Diagonals
D
Point of
Intersection
E
Types of
Figures
Angles
G
Sum of
Angles
H
Divided
sections
Dimensions
J
Perimeter
and Area
K
Congruency
L
Symmetry
M
Total
triangles
Both have diagonals.
Both have two diagonals.
Diagonals of both figures intersect each other.
Diagonals bisect each other in both figures.
Diagonals works as transversal.
Both have point of intersection.
Diagonals meet at a point in centre.
1. Both are plane (2-D) figures.
2. Both have plane surface.
3. Both are Quadrilaterals.
4. Both are parallelogram.
5. Both are polygon.
6. Both are convex polygon.
7. Both are irregular polygon.
8. Both have some properties of Square.
9. Both are Trapezium also.
10. Both are not curved figure.
11. Both can be seen in practical life.
1. Both have four angles.
2. Opposite angles are equal in both figures.
3. Two pairs of vertically opposite angle formed in
both.
4. Corresponding angle formed in both.
5. Alternate angle formed in both.
1. Sum of interior angles is 360º.
2. Sum of corresponding angles is equal to180º.
3. Sum of angles is equal to 360º at the centre.
4. Sum of interior angles is equal in both.
5. Sum of all triangles formed by intersection of
diagonal is equal to 720º
in 1. Diagonals of both divided them in to four sections.
F
I
1.
2.
3.
4.
5.
1.
2.
1.
2.
1.
2.
3.
1.
1.
2.
3.
4.
1.
2.
Length is the variable in both.
Both don’t have height.
Both have perimeter.
Both have area.
Both don’t have volume.
Two Congruent triangles are formed
intersection of diagonals.
Both are symmetrical Figure.
Both have two line of symmetry.
Both have rotational symmetry.
Both can be divided symmetrical.
Both have 4 triangles in them.
Both have same number of triangles.
272
16
40
16
24
1
9
14
0
0
0
0
5
0
0
35
4
26
11
--1
1
3
1
--1
18
13
14
1
3
0
2
0
0
20
1
2
1
2
0
5
4
5
4
11
0
1
1
7
8
3
by 7
--4
2
1
26
20
5
5
3
5
5
0
0
0
5
3
5
5
0
0
3
0
2
4
5
0
0
N
O
P
Q
Closed
figure
Adjacent
angles
Method
used
Construction
Equipment
Both are closed figures.
6
0
Sum of adjacent angles is 180º in both figure.
4
2
Method used to find perimeter is same in both.
6
Perimeter = Sum of four sides
1. Same Construction Equipments used to make both 3
figure.
1
2. Both can make by joining four triangles
0
3
5
Category of Dissimilarity
R
S
T
Sides
Angles
Diagonals
1. All sides are equal in Rhombus but not in Rectangle. 65
2. The sides of Rectangle intersect at 90º but not in
Rhombus.
1
0
1. All the angles are equal in Rectangle but not in
Rhombus.
2. All the angles are 90º in Rectangle but not in
Rhombus.
3. Angles formed by intersection of diagonal are 90º in
Rhombus but not in Rectangle.
4. Triangles formed at the intersection of diagonal are
right angled triangles in Rhombus but not in
Rectangle.
1. Length of diagonals is equal in Rectangle but not in
Rhombus.
2. Diagonals intersect at 90º in Rhombus but not in
Rectangle.
3. Diagonals bisect their respective angles in Rhombus
but not in Rectangle.
1. Method used to find area is different in both.
2. Area is different.
3. Perimeter is different.
5
1
36
0
6
0
4
2
18
0
38
0
3
3
26
-----
0
U
Method
and
Formula
V
Convertible If length & breadth will be equal than Rectangle will 2
convert into square but not true in Rhombus.
Live
Rhombus is like a piece of Burfi but Rectangle is like 5
Example
front face of Cuboidal boxes.
Congruent All triangles are congruent in Rhombus but not in 2
Rectangle.
W
X
273
5
4
1
4
ITEM V
Write as many geometrical shapes, figures and concepts in relation to
different objects which you observe in day to day life.
Sr.No. Category
Responses
Students Score Responses
A
Blackboard
Bench
Cardboard
Chart
Chocolate
Cricket Pitch
Curtains
Desk
Doors
Face of
Notebook
Faces Of
Duster
Faces of
cuboidal things
Floors
Hanging Swing
I-Card
Ladder
Lecture Stand
Base
Map
Mirror
Monitor Batch
Name Slip
National Flag
Bread Piece
Carom Board
Floor
Handkerchief
Park
Photograph
50
6
1
9
2
1
3
5
3
Bottle
Bucket
Buiscuit Pack
Can
Chalk
11
1
0
5
16
0
B
C
Rectangular
Square
Cylindrical
0
0
5
0
4
Notice Board
Paper
Paperboard
Park
Photograph
1
6
16
6
1
12
5
0
0
0
5
0
5
1
1
5
2
1
11
4
5
0
Poster
Room Roof
Rupee Note
Scale
Screen: T.V.
Computer
Slab
Spectacles
Lense
Strature Bed
Switchboard
Table Top
Tiles
Traffic Sign
Board
Wall
Watch Dial
Window
Window
Glass
Roof
Shirt Pocket
Table /Stool
Tiles
Wall / poster
Watch Dial
Window
Letter Drum
Pillar
Pipe
Pipe Line
Railing Rod
1
5
274
Students Score
9
2
0
4
2
5
4
1
7
0
1
3
1
5
14
2
1
5
3
5
1
0
4
5
4
2
6
1
0
5
1
1
2
2
2
5
5
4
4
4
3
8
1
1
3
0
5
5
D
Cubical
E
Cuboidal
F
Frustum
Container
Curtains Rods
Deo Can
Drum
Dustbin
Electricity Pole
Flower Pot
Foil Roll
Fold Chart
Gas Cylinder
Glass
1
5
5
1
1
3
3
5
3
3
1
19
1
5
0
5
Chalk Box
Cube A.C.
Dice
Ice Cube
A.C.
Any Box
Bag
Battery
Bed
Book
Bus
Duster
Eraser
Sharpener
Geometry Box
Harmonium
Ice-Cream
Brick
2
2
14
3
3
18
4
4
0
3
3
0
Bucket
Chalk
1
11
1
8
5
0
5
0
19
0
1
1
5
5
275
Refill & Pen
Roller
Rolling Pin
Spring
Spring Roll
Straw
Trunk
of
Tree
Tube Light
Water
Camphor
Water Tank
Well
Wires
Puzzle Box
Room
Piece
of
Sugar
Laptop/Comp
Lecture
Stand
Leg
of
Benches
Mobile
Oven
Refrigerator
Room /House
Scenery
T.V.
Wall Brick
Wardrobe
Glass
26
2
7
0
4
0
1
4
1
1
11
1
1
5
2
5
5
0
5
5
2
5
1
4
1
5
2
4
1
5
2
4
9
2
1
3
3
4
2
0
4
5
3
3
1
5
G
Circular
Semi Circular
Quarter
Circular
Bangles
Button
C.D.
Camera Lens
Central Part of
Ceiling Fan
Chakla
Chapatti
Coin
Disc
Eye Ball /Lens
Fan Move
Hooks
of
Curtains
Human Body
Cell
Mirror
Pan
Opening Door
Protector
Hand Fan
12
7
3
0
0
3
1
1
4
1
5
5
2
5
H
Conical
Conical
Birthday Cap
I
Spherical /
Round
Balloon
Bulb
Eyeball
Frog
Globe
Hemispherical
J
Constructed
Material
5
1
1
1
5
5
1
5
2
1
4
5
9
0
Of 3
3
Bowl
Bun/Burger
Half
Cut
Orange/Lemon
House/Building
┴ to Ground
The Edges of
Bb
Wall of Room
Is ┴ to Floor
and roof
3
3
2
4
1
5
3
3
3
3
276
Papad
Pizza
Plate
Ring
Rubber Band
Spectacles
Frame
Stadium
Steering of
FourWheeler
Table top
Tap/Well
Head
Tata Sky
Top
of
Cylindrical
Things
Traffic Light
Watch’ Dial
Wheels
Of
Vehicles
6
4
6
2
1
0
2
0
4
5
2
2
6
4
4
0
1
20
19
5
0
0
24
0
2
12
14
1
4
0
0
5
1
1
5
5
Straight
2
Grills are ┴
To Case
Standing Rod 3
Pillar ┴ To
Ground
1
Crossing Of
Road
4
Ice-Cream
Cone
Tent
Orange
Planets
Playing Ball
Rasgoola
Thermacol
Balls
Tomb
of
Masjid
Umbrella
3
5
Electrical
Material
K
L
Furniture
Others
Pole Stand
Fan Rod is ┴
of Ceiling
Breadth
of
Desk is┴ to
Length
Cricket Wicket
Lecture Stand
1
3
5
3
Bulb is ┴ to 3
Wall
3
1
5
Legs of Chair 1
Table is ┴ to
itself
1
Table is ┴ to
Ground
5
Bristles
of 1
Comb are ┴
to Base
1
Curtains ┴ to
floor
Moving
5
1
1
1
1
5
5
5
5
Hand Pump
L of Paper to B
Stick
of 1
Umbrella
5
M
Vehicles
Standing
N
Human Being
3
O
P
Tree
Polygon
Pentagonal/
Concave
Human being 3
in
standing
position is ┴ to
Earth.
Tree to Ground 4
Park shape
Front Face of 1
Hut
Top Part of
Pencil
Nut
Bristles
of
Comb
Compartment
in Refrigerator
Cricket
Wickets
Door Side
Electricity
Wires
Ladder Rods
Leg of Bench
Lines of Pages
2
4
1
5
1
5
1
5
Q
Hexagonal
Octagon
R
Parallel
5
5
2
5
1
5
3
2
1
13
277
3
4
5
0
Opposite Sides
of
Things:
Brick
Opposite walls
of Room
Paper Side
Railway
Tracks
Road Side
Rods of Grills
Two Trees in
one Line
Veins of Leaf
Wall is II to
Man (Standing
position)
7
14
12
4
0
0
0
2
1
5
V
Eye Shape
Grapes
Pebbles
Toilet Seat
Track
of
0
Race
Right Angled Bingo
Mad 3
3
Sandwitches
Triangle
Angle
Slide Swing
Front Face of
Stairs Slope
conical things
2
4
TrafficSign
Parantha
1
5
Board
Pole of Swings 2
4
Triangular
Ramp
Flag
Distance
Grills have equal distance between them.
Our school is 3 km from our house.
Adjacent
My house is adjacent to my neighbour.
W
Point
X
Alphabets
S
T
U
Y
Z
AA
Oval/
Elliptical
1
Baseball
Earth Moves 4
Elliptically
Around Sun
15
Egg
5
2
Tip of Pen Shows Point.
Tip of Needle Shows Point.
D→ Seems Semi Circle
H→ Seems Parallel Lines
L → Seems Right Angle
N →Seems Transversal
X→ Seems intersection
O→ Seems oval
T→ Opposite T Seems ┴ perpendicular
Ray Straight Arrow
Lines
Curtain Rods
Electricity Poles
Electricity Wire
Hairs
Line Segment Rope
Thread1
Road is a Line Segment has two end points.
Quadrilaterals Blades of Fan
&Its Types
Field
Trapezium
Glass Of Car
Slant Roof
Rhombus
Lecture Stand
Kite
Burfi
Kite
Map
China Map is seems to be a Trapezium.
India Map is seems to be a Rhombus.
South region of India map is seems to be a
Triangle
278
4
0
1
5
1
5
1
10
5
0
2
2
4
4
1
5
1
5
4
1
2
5
1
1
5
5
2
1
1
4
5
5
3
2
2
2
1
1
1
2
3
4
4
4
5
5
5
4
2
7
3
5
1
2
7
4
0
3
1
5
4
0
BB
Curved &
Hairs
I-Card Corners
Path of Falling Stone
Crooked
River & Roads in hilly areas
Pyramidical
Hills
Pyramid in Egypt
Prism
Sand Dunes
Pencil
Surface
Benches has plane surface
Floor has plane surface
Paper has plane surface
Seesaw has plane surface
Circumference Moving fan symbolize circumference of a circle.
Radius
The blades of fan symbolize radius.
C.d. has its centre point and radius
Angles
Hands of watch make every type of angle
Acute Angle
Nose on Face
Right Angle
Stairs Corners
V. O. A
Slide Swing
Obtuse Angle
Two Pencils in Cross
Blades of Fan
Intersection
Scissors Legs
Linear Pair
Two Adjacent Sides of a Book Intersect
Seesaw Pair
At T Point Road Intersect Each Other
CC
DD
EE
FF
GG
1
2
1
1
1
2
1
5
4
5
5
5
4
5
2
4
2
1
1
1
4
5
5
5
1
5
1
9
5
0
1
1
1
2
1
5
5
5
4
5
ITEM VI
Select few numbers from the given numbers (1, 2, 3, 4, 8, 9, 16, 24, 27, 28, 32, 36, 40,
43, 44, 48, 49), showing some pattern or having relation with each other.
Sr. No.
Category
A
Collection of 1.
numbers
2.
3.
4.
5.
Nature
of 1.
numbers
2.
3.
4.
B
Responses
Even numbers
Prime numbers
Composite numbers
Odd numbers
Neither Prime nor composite (1)
Natural numbers
Whole numbers
Integers
Rational numbers,
279
Stud
ents
14
29
16
71
3
22
11
1
6
Score
0
0
0
0
3
0
0
5
0
5.
6.
7.
8.
C
D
E
F
G
H
I
J
K
Real numbers
Positive numbers
Can be written in p/q form
Present on number line
Consecutivel 1. Consecutive multiplied by 2 (1,2,4,8,16,32)
y multiplied 2. Consecutive multiplied by 3 (1,3,9,27)
by a number
3. Consecutive multiplied by 4 (1,4,16)
4. 2n , n belongs to 1-5
Collection of (1,4,9,16,36,49)
Perfect
square
number
Collection of
(1, 8, 27)
Perfect cube
number
Divisible
1. Divisible by 1
2. Divisible by 2
3. Divisible by 3
4. Divisible by 4
5. Divisible by (2&3)
6. Divisible by 5
7. Divisible by 6
8. Divisible by 7
9. Divisible by 8
10. Divisible by 9
11. Divisible by 11
12. Divisible by 16
13. Divisible by 24
Consecutive
1. (1,2,3,4)
number
2. (1,2)(3,4),(8,9)(27,28)(43,44) (48,49)
Having Equal Difference of 4(24,28,32,36,40,44,48)
difference
Difference of 8(1,8,16,24,32,40,48)
H.C.F.
1. H.C.F. is 2 (2,4,8,16)
2. H.C.F. is 12 (24,36)
3. H.C.F. is 3 (3,9,2,27,36)
Number & its (2,4), (3,9), (4,16)
square
Multiple
1. Multiple of 1
2. Multiple of 2
3. Multiple of 3
4. Multiple of 4
5. Multiple of 5
6. Multiple of 6
7. Multiple of 7
280
10
5
1
1
0
1
5
5
13
2
1
2
62
0
4
5
4
0
45
0
5
31
36
23
1
4
2
4
8
3
3
----5
4
7
1
0
1
0
0
0
5
2
4
2
0
3
3
3
3
0
13
17
12
2
1
---
0
0
0
4
5
1
2
0
5
L
M
N
O
P
Q
R
8. Multiple of 8
9. Multiple of 9
10. Multiple of 12
11. Multiple of 16
Collection of (2, 3, 4, 9, 16, 24, 28, 32, 36, 40, 43, 44, 48, 49)
non cubes
Collection of (2, 3, 8, 24, 27, 32, 40, 43, 44, 48)
non squares
Single
and 1. (1, 2, 3, 4, 8, 9)
Double digit 2. (16, 24, 27, 28, 32, 36, 40, 43, 44, 48, 49)
numbers.
Factors
1. Factors of 48
2. Factors of 36
3. Factors of 16
Position
1. Less than 10 (1, 2, 3, 4, 8, 9)
2. Greater than10 (16, 24, 27, 28, 32, 36, 40,
43, 44, 48, 49)
3. Lies b/w 10 and 50
4. Having 4 at one place
5. Having 4 at tenth place
6. Increasing Order
7. Decreasing Order
Not divisible Not divisible by 2
Not divisible by 3 etc.
Relation of 1. 4(1+3n) , n belongs to 0-3: (4,16,28,40)
reasoning
2. Same sum [(27,63) ,(16,43)]: (9,7)
3. Same multiply (16,32): 6
4
2
--2
1
2
4
1
5
3
2
3
4
3
1
3
3
5
3
3
1
3
5
--1
1
------
4
5
5
5
2
---
4
1
1
5
5
1
5
ITEM VII
Read the following mathematical situation carefully. You and your friend are playing in
the rectangular park having a length 160 m and breadth 120 m is surrounded by a
footpath having a width of 3 m. The cost of fencing is Rs. 35 per meter. It needs to be
cemented at the rate of Rs 120 per square meter. The cost of one bag of cement is Rs.
350. The grass lawn is divided into four sections by two intersecting paths having width
of 2 m. The path is also required to be tiled. 9 tiles of 15×12 cm are required to cover 1
m2 area of footpath. There is one flowering bed of 8 m × 8 m in one corner of each
section of the grass lawn. Cost of planting flower in 4 m2 areas is Rs. 100. Now, your
task is to frame as many problems as you can from the data given in the below diagram.
281
Area
1. Area of complete park
2. Area of park inner side.
3. Area of park outer side.
4. Area of footpath.
5. Area of flowering bed.
6. Area of four sections.
7. Area of park covered by grass.
8. Area of intersecting portion
9. Area of ¼ park
10. Area of dimensions taken by students
11. Area of tiles
Stud
ents
61
22
30
48
38
22
30
23
2
3
1
B
Perimeter
C
Cement
quantity
1. Perimeter of complete park
2. Perimeter of park inner side
3. Perimeter of park outer side
4. Perimeter of footpath.
5. Perimeter of flowering bed.
6. Perimeter of four sections.
7. Perimeter of park covered by grass.
8. Perimeter of intersecting portion.
1. How much bag of cement is required for cementing?
48
8
9
14
9
5
-1
31
0
0
0
0
0
1
--5
0
D
Cost
of 1. What will be the cost of cementing 36 m2 area of
cementing
footpath?
2. What would it cost for cementing if we supposed to
cement Whole Park?
3. What will be the cost of 80 bags?
Cost
of 1. What will be the cost of fencing the outer side of the
Fencing
park?
2. What will be the cost of fencing the flowering beds?
3. If the area of path is more than 6m2 than cost of
fencing.
Number of 1. How many tiles will be required to cover complete
Tiles
footpath?
Cost
of 1. What will be the cost of tiling 56 m2 area of footpath?
tiling
2. What is the cost of one tile?
Grassing
1. What will be the cost of grassing in all sections of
park?
Flowering
1. How many flowers are required to cover flowering
beds?
2. What will be the cost of planting in flowering beds?
No. of total 1. How many total Rectangular parks are there in park?
44
0
1
5
---18
0
1
1
5
5
33
0
24
4
9
0
2
0
9
0
54
1
0
5
E
F
G
H
I
J
Category
Responses
Score
S.N
o.
A
282
0
0
0
0
0
0
0
0
4
3
5
K
L
M
park
Subtraction
of outer –
inner park
Total
expenditure
Responses
related to
situation
thought by
the students
beyond the
data given
N
O
Labour
Labour cost
P
Profit/Loss
Discount
Q
R
Reduction
or
increment
in
Length/Bre
adth
Maintenanc
2. How many total square parks are there in park?
What is the area between inner boundary and outer
boundary?
What is the perimeter of path between inner boundary
and outer boundary?
Area covered with green grass only
What is the total cost of beautification of park?
1. What will be cost of grassing if it will grow in full
rectangular park?
2. What will be cost of watering the grass if Rs 16 is
required to water 2 m2 area of rectangular park?
3. Place for playing
4. Sitting percentage
5. Shading
6. Fountain setting
7. Colouring
8. Pond dug
9. Making football ground, Badminton court, pitch
10. Visiting cost
How many persons are required for any work?
1. What is the labour cost?
2. What is the labour cost of planting the flowers?
3. What is the labour cost of cementing?
1. If the cost of tiles is decreased then what will be the
profit?
2. If the cost of planting flowers will reduce 100 Rs. to
50 Rs. than find profit percentage?
3. Is there any discount available on cement bag?
1. Find effect on area of park if 10 m is subtracted from
length & breadth?
2. If park is divided by diagonal than find the length of
Diagonal?
3. What will effect on cementing cost if length is
decreased 4m.
4. What will effect on fencing cost if length is increased
6m.
5. Length of fence required to cover whole park
6. Required flowers if length of flowering beds is
reduced
7. Length of largest/Smallest path
8. If length is 166m and area of park is 2666 m2 than
find breadth?
1. How much Rs. is required to maintain whole park?
283
3
2
3
4
3
3
3
14
3
0
1
5
1
5
1
3
1
1
2
1
3
1
4
--1
2
2
5
3
5
5
4
5
3
5
2
-5
4
4
1
5
1
5
2
4
1
5
3
3
2
4
1
1
1
---
5
5
5
1
5
e
2. How much Rs. is required to maintain flowering beds?
3. How much Rs. is required to repair footpath?
1
1
5
5
ITEM VIII
You know that different geometrical shapes can be made by using different
material e.g. you can make a square by using four match sticks. Now suppose you
have 12 pieces of wire of equal length. Name various geometrical shapes/figures
which can be made by using wires.
Sr.
no.
A
B
C
D
E
F
Category
Mathematical
operations
1.
2.
3.
4.
5.
Lines and curves
1.
2.
3.
4.
5.
6.
7.
Combination of two 1.
lines
2.
3.
4.
5.
6.
2-DShapes
1.
2.
3.
4.
3-DShapes
1.
2.
3.
4.
5.
Quadrilaterals
1.
2.
3.
4.
5.
6.
Responses
Sign of +,
Sign of ×,
Sign of ÷,
Sign of - ,
Sign of →
Straight Line
Curved Line
Arc
Crooked
Line Segment
Horizontal Line
Vertical line
Parallel Lines
Intersecting Lines
Linear Pair
Perpendicular Lines
Transversal Line
Concurrent Lines
Rectangle
Rectangle with Diagonal
Square
Square with Diagonal
Cuboidal
Cubical
Prism
Rectangular Prism
Pyramid
Parallelogram
Trapezium
Rhombus
Rhombus with Diagonal
Quadrilaterals with Diagonal
Concave Quadrilaterals
284
Stude Score
nts
1
5
0
-0
-1
5
2
4
11
0
3
3
2
4
2
4
1
5
----37
0
25
0
10
0
30
0
1
5
1
5
8
0
1
5
65
0
2
4
11
0
20
0
3
3
4
2
4
2
37
0
34
0
34
0
3
3
2
4
---
G
Triangles
H
Polygon
I
Oval
J
Circular shape
K
L
Frustum
Angle representation
M
Quadrant
N
Combination of 2D
and circular shape
Combination of two
shapes
Angle made by
Transversal
O
P
Q
Sphere/
Hemisphere
7. Convex Quadrilaterals
8. Kite
1. Scalene Triangle
2. Right Angled Triangle
3. Equilateral Triangle
4. Isosceles Triangle
5. line of symmetry in Triangles
6. Triangle With Bisector
7. Median of Triangles
1. Hexagon
2. Hexagon with cross
3. Polygon
4. Pentagon
5. Septagon
6. Octagon
7. Decagon
Oval
----17
14
43
10
3
1
1
30
1
2
--------13
1. Circle
2. Circle with radius
3. Circle by adjoining of two semicircles
4. Quarter Circle
5. Semicircle
6. Diameter
7. Radius
Frustum
1. Right Angle
2. Obtuse Angle
3. Acute Angle
4. 180º
5. 360º
6. Angle Bisector
Quadrant
63
1
1
1
19
----1
21
5
4
4
1
3
---
0
5
5
5
0
1. Cone
2. Cylinder
Square + Triangle
36
44
8
0
0
0
1. Vertically Opposite Angles
2. Alternate Angle
3. Corresponding Angles
4. Interior Angles
5. Exterior Angles
1.Sphere
2. Hemisphere
9
8
5
1
2
1
---
0
0
1
5
4
5
285
0
0
0
0
3
5
5
0
5
4
0
5
0
1
2
2
5
3
Appendix -I
CREATIVE ABILITIY IN MATHEMATICS TEST
Name:_________________________________________________________________
Grade:__________ Age:__________ Boy /Girl __________
Directions
The items in the booklet give you a chance to use your imagination to think up ideas
and problems about mathematical situations. We want to find out how creative you are
in mathematics. Try to think of unusual, interesting, and exciting ideas – things no one
else in your class will think of. Let your mind go wild in thinking up ideas.
You will have the entire class time to complete this booklet. Make good use of your
time and work as fast as you can without rushing. If you run out of ideas for a certain
item go on to the next item. You may have difficulty with some of the items; however,
do not worry. You will not be graded on the answers that you write. Do your best!
Do you have any questions?
ITEM I
Directions
Patterns, chains, or sequences of numbers appear frequently in mathematics. It is fun to
find out how the numbers are related. For example look at the following chain:
2 5 8 11 ___ ___
The difference between each term is 3; therefore, the next two terms are 14 and 17. Now
look at the chain shown below and supply the next three numbers.
1 1 2 3 5 8 13 21 ___ ___ ___
ITEM II
Directions
Below are figures of various polygons with all the possible diagonals drawn (dotted
lines) from each vertex of the polygon. List as many things as you can of what happens
when you increase the number of sides of the polygon. For example: The number of
diagonals increases. The number of triangles formed by the number of diagonals
increases.
1.______________________________________________________________________
2.______________________________________________________________________
3. ______________________________________________________________________
4. ______________________________________________________________________
286
ITEM III
Directions
Suppose the chalkboard in your classroom was broken and everyone’s paper was thrown
away; consequently, you and your teacher could not draw any plane geometry figures such
as lines, triangles, squares, polygons, or any others. The only object remaining in the room
that you could draw on was a large ball or globe used for geography. List all the things
which could happen as a result of doing your geometry on this ball. Let your mind go wild
thinking up ideas. For example: If we start drawing a straight line on the ball, we will
eventually end up where we started. (Don’t worry about the maps of the countries on the
globe.)
1.______________________________________________________________________
2.______________________________________________________________________
3. ______________________________________________________________________
4. ______________________________________________________________________
5. ______________________________________________________________________
6. ______________________________________________________________________
7. ______________________________________________________________________
ITEM IV
Directions
Write down every step necessary to solve the following mathematical situation. Lines are
provided for you to write on; however there may be more lines than you actually need.
Suppose you have a barrel of water, a seven cup can, and an eight cup can. The cans have no
markings on them to indicate a smaller number of cups such as 3 cups. How can you
measure nine cups of water using only the seven cup can and the eight cup can?
1.______________________________________________________________________
2.______________________________________________________________________
3. ______________________________________________________________________
4. ______________________________________________________________________
5. ______________________________________________________________________
6. ______________________________________________________________________
7. ______________________________________________________________________
287
ITEM V
Directions
Suppose you were given the general problem of determining the names or identities of two
hidden geometric figures, and you were told that the two figures were related in some
manner. List as many other problems as you can which must be solved in order to determine
the names of the figures. For example: Are they solid figures such as a ball, a box, or a
pyramid? Are they plane figures such as a square, a triangle, or a parallelogram? If you need
more space, write on the back of this page.
1.______________________________________________________________________
2.______________________________________________________________________
3. ______________________________________________________________________
4. ______________________________________________________________________
5. ______________________________________________________________________
ITEM VI
Directions
The situation listed below contains much information involving numbers. Your task is to
make up as many problems as you can concerning the mathematical situation. You do not
need to solve the problems you write. For example, from the situation which follows: If the
company buys one airplane of each kind, how much will it cost? If you need more space to
write problems, use the back of this page.
An airline company is considering the purchase of 3 types of jet passenger airplanes, the
747, the 707 and the DC-10. The cost of each 747 is $15 million; $10 million for each DC
10; and $6 million for each 707. The company can spend a total of $250 million. After
expenses, the profits for the company are expected to be $800,000 for each 747,$500,000
for each DC-10, and $350,000 for each 707. It is predicted that there will be enough trained
pilots to man 25 new airplanes. The overhaul base for the airplanes can handle 45 of the 707
jets. In terms of their use of the maintenance facility, each DC 10 is equivalent to 1 1/3 of
the 707’s and each 747 is equivalent to 1 2/3 of the 707’s.
1.______________________________________________________________________
2.______________________________________________________________________
3. ______________________________________________________________________
4. ______________________________________________________________________
5. ______________________________________________________________________
6. ______________________________________________________________________
288
289