Competency Based Worksheet
Class:- VII Subject: Maths
Competencies
Knowledge of Concepts
Understanding the Concepts
Ability to compute
Problem Solving
Term 2 2024-2025
Chapters
Rational Numbers
Perimeter and Area
Algebraic Expressions
Exponents and Powers
Symmetry
Visualising solid shapes
From Term 1
Fractions and Decimals
Simple Equations
Chapters
Rational Numbers
Perimeter and Area
Algebraic Expressions
Exponents and Powers
Symmetry
Visualising solid shapes
Fractions and Decimals
Simple Equations
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ Rational Numbers DATE: _____________
Competency : Knowledge of Concepts
Distance Travelled by Buses
Two buses, Bus A and Bus B, start from the same station but travel in opposite directions. Bus A travels a distance of 35, and Bus B travels a distance of 710 km.
Questions:
What is the total distance between the two buses after they travel?
Is the distance travelled by Bus B greater than that of Bus A? If yes, by how much?
Express the distance travelled by both buses in decimal form.
If the station is considered as the origin (0), what would be the positions of Bus A and Bus B?
Competency : Understanding the Concepts
Recipe Measurements
A recipe requires 34 cup of sugar and 13 cup of milk.
Questions:
What is the total amount of sugar and milk combined in the recipe?
If you add only 12 cup of milk instead of 13, what would be the new total amount?
.
Which ingredient has a greater quantity in the recipe, and by how much?
If you double the recipe, what will be the total amount of sugar and milk?
Competency : Ability to Compute
Temperature Changes
During a winter morning, the temperature in a town was recorded as −412 °C. By noon, the temperature rose by 56°C.
Questions:
What was the temperature at noon?
If the temperature further increased by 712 °C, what would be the new temperature?
How much more does the temperature need to increase to reach 0 °C?
Express the temperature changes in decimal form for easier understanding.
Competency : Problem Solving
Garden Watering
A gardener waters 13 of the garden in the morning and another 14 in the evening. The remaining part of the garden does not need watering.
Questions:
What fraction of the garden did the gardener water in total?
What fraction of the garden does not need watering?
If the gardener decides to water an additional 18 of the garden in the evening, what will be the new total fraction watered?
Express the fraction of the garden watered and unwatered in decimal form.
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ Perimeter and Area DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Ravi has a rectangular garden with a length of 12 metres and a width of 8 metres. He wants to build a fence around it and also plant grass within the entire area of the garden.
Questions:
What is the formula for the perimeter of a rectangle? _____________
What is the formula for the area of a rectangle? _____________
Using the given dimensions, calculate the perimeter of Ravi’s garden.
Calculate the area of Ravi’s garden.
Explain the difference between perimeter and area.
Competency : Understanding the Concepts
Understanding Perimeter and Area of Different Shapes
Seema is planning a design for a square-shaped patio and a triangular flower bed. The side of the square patio is 5 metres, and the triangular flower bed has a base of 4 metres and a height of 3 metres.
Questions:
What is the formula for the perimeter of a square? _____________
What is the formula for the area of a square? ___________
Using the given dimensions, calculate the perimeter and area of Seema’s square patio.
What is the formula for the area of a triangle?
Calculate the area of Seema’s triangular flower bed using the given dimensions.
Competency : Ability to Compute
Application of Concepts to Real-Life Problems
A farmer has a square plot with a side length of 15 metres and wants to add a rectangular shed on one side of it. The shed will have a length of 10 metres and a width of 4 metres. He needs to calculate the area of the plot and the shed separately.
Questions:
Calculate the perimeter of the farmer’s square plot.
Calculate the area of the square plot.
What is the perimeter of the rectangular shed?
Calculate the area of the rectangular shed.
If the farmer decides to fence both the plot and the shed separately, what would be the total length of the fencing required?
Competency : Problem Solving
Building a Garden and Fence
Amit wants to build a rectangular garden in his backyard. The length of the garden is 18 metres, and the width is 12 metres. He plans to surround the garden with a fence and also wants to cover the entire garden with grass.
Questions:
Calculate the perimeter of the garden to determine how much fencing material Amit will need.
Calculate the area of the garden to find out how much grass will be needed to cover it.
If the cost of fencing is 50 rupees per metre and the cost of grass is 10 rupees per square metre, calculate the total cost for the fencing and the grass.
If Amit has only 5000 rupees, will he be able to cover the expenses for the garden? Explain.
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ ALGEBRAIC EXPRESSIONS DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Case 1: Weekly Grocery Shopping
Case Scenario:
Sam's weekly grocery shopping bill consists of various items, and he records the cost of some items using algebraic expressions. Let the cost of one bag of rice be rrr rupees, the cost of one pack of milk be mmm rupees, and the cost of one packet of sugar be sss rupees. He buys 3 bags of rice, 2 packs of milk, and 5 packets of sugar.
Questions:
Write an algebraic expression for the total cost of Sam’s grocery shopping.
If the cost of one bag of rice is 120 rupees, one pack of milk costs 50 rupees, and one packet of sugar costs 30 rupees, find the total cost.
How would the expression change if Sam buys 4 bags of rice, 3 packs of milk, and 6 packets of sugar?
Competency : Understanding the Concepts
Case 2: Buying Books for the Library
Case Scenario:
The library wants to buy books for the new semester. The cost of one textbook is denoted by xxx rupees. The library buys 3 textbooks for mathematics, 5 textbooks for science, and 4 textbooks for history.
Questions:
Write an algebraic expression for the total cost of the books the library buys.
If the cost of one textbook is 150 rupees, find the total cost of the books.
If the cost of one textbook increases to 200 rupees, how would the total cost change?
Competency : Ability to Compute
Case 1: Discount on Shopping Items
Case Scenario:
Ravi is shopping for clothes. He buys 3 pairs of shoes and 2 shirts.
The cost of one pair of shoes is represented by the algebraic expression 3p3p3p, where ppp is the price of one pair of shoes.
The cost of one shirt is represented by the expression 2s2s2s, where sss is the price of one shirt.
Questions:
Write an algebraic expression for the total cost of shoes and shirts.
If the price of one pair of shoes is 1200 rupees and the price of one shirt is 800 rupees, find the total cost.
If the price of one pair of shoes increases to 1500 rupees, how will the total cost change?
Competency : Problem Solving
Cost of Pizza for a Party
Sanya is ordering pizzas for a party. She orders p pizzas, and each pizza costs 250 rupees.
Additionally, she will be ordering drinks that cost 50 rupees each, and she plans to buy d drinks.
The total cost for the party is the cost of the pizzas and drinks combined.
Questions:
Write an algebraic expression for the total cost of pizzas and drinks for the party.
If Sanya orders 10 pizzas and 15 drinks, what will the total cost be?
If the price of each pizza increases to 300 rupees, how will the total cost change?
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ EXPONENTS AND POWERS DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Case 2: Interest Earned on a Deposit
Case Scenario:
A bank offers a compound interest scheme where the principal amount doubles every year. The principal amount is initially 1000 rupees. The amount of money after t years is given by the formula 1000×2t, where t is the number of years.
Questions:
Write the expression for the amount of money after t years.
What will be the total amount after 3 years?
What will be the total amount after 5 years?
Competency : Understanding the Concepts
Case 1: Growth of a Plant
Case Scenario:
In a science experiment, a researcher is observing the growth of a plant. The plant’s height doubles every week. Initially, the height of the plant is 5 cm. The height of the plant after ‘t’ weeks is given by the expression 5× 2t, where ‘t’ represents the number of weeks.
Questions:
Write the expression for the height of the plant after t weeks.
How tall will the plant be after 3 weeks?
What will be the height of the plant after 5 weeks?
Competency : Ability to Compute
Distance Travelled by Light
Light travels at an exponential speed. The distance travelled by light doubles every minute. Initially, light travels 1 metre per minute. The distance travelled after t minutes is given by the expression 1×2t, where t represents the number of minutes.
Questions:
Write the expression for the distance travelled by light after ttt minutes.
What will the distance travelled by light be after 3 minutes?
What will the distance travelled by light be after 5 minutes?
Competency : Problem Solving
Saving for a Vacation
A person saves money in a bank account that doubles every year. Initially, the person saves 2000 rupees. The amount of money saved after t years is given by the expression 2000×2t, where t is the number of years.
Questions:
Write the expression for the total savings after t years.
How much money will be saved after 3 years?
How much money will be saved after 5 years?
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ SYMMETRY DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Symmetry in Letters and Numbers
The letter "A" has vertical symmetry, meaning if you draw a line down the middle, both halves are identical. On the other hand, the number "8" has both vertical and horizontal symmetry.
Questions:
Which type of symmetry does the letter "A" exhibit?
Does the number "8" exhibit any symmetry? If so, what type?
How do the letters "O" and "H" differ in terms of symmetry?
Competency : Understanding the Concepts
Symmetry in a Square Tile Pattern
A tile pattern is designed using square tiles. Each square tile has four lines of symmetry — two vertical lines, one horizontal line, and two diagonal lines.
Questions:
How many lines of symmetry does a square have?
Why are these lines of symmetry important when designing tile patterns?
How would the symmetry change if the tiles were rectangular instead of square?
How many lines of symmetry does a regular hexagon have?
Competency : Ability to Compute
Symmetry in a Square
A square with side length 6 cm is drawn, and we need to compute the number of lines of symmetry and the perimeter.
Questions:
How many lines of symmetry does a square have?
Compute the perimeter of the square.
If the side length of the square is halved, what would the new perimeter be?
Competency : Problem Solving
Symmetry in a Mirror Reflection
You are standing in front of a mirror, and your reflection appears to be a perfect mirror image of yourself. The mirror serves as the axis of symmetry.
Questions:
What type of symmetry is shown in the mirror reflection?
If you move to the right by 2 steps, how will your reflection in the mirror change?
What happens if the mirror is rotated 90°? Will the reflection still be symmetric?
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ VISUALIZING SOLID SHAPES DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Viewing Different Sections by Slicing
A student is given a cone and is asked to visualise what happens when the cone is sliced in different ways. The student must describe the shape formed from different types of slices.
Questions:
What shape does a horizontal slice of a cone produce?
What shape does a vertical slice through the apex of a cone produce?
What would a slice parallel to the axis of the cone look like?
Competency : Understanding the Concepts
Shadow Play and Projection
A student is exploring how light and 3D shapes interact by placing a cube under a light source and observing the shadow.
Questions:
1. What will be the shape of the shadow of the cube if the light is placed directly above the cube?
(A) Circle (B) Square (C) Triangle (D) Rectangle
2. What will happen to the shadow of the cube if the light source is moved to the side of the cube?
A) The shadow will become elongated and may look like a rectangle.
(B) The shadow will stay as a square but become smaller.
(C) The shadow will look like a triangle.
(D) The shadow will disappear completely.
3. How can you predict the shape of the shadow when projecting a 3D object onto a 2D surface?
(A) By only knowing the size of the object
(B) By analysing the shape and angle of the light source
(C) By knowing the material of the object
(D) By knowing the colour of the object
Competency : Ability to Compute
Identifying the Shape Formed by Slicing a Cone
A cone has a height of 12 cm and a radius of 6 cm. The student needs to compute the shape formed when the cone is sliced vertically through its apex.
Questions:
What shape is formed when a cone is sliced vertically through its apex?
If the height of the cone is 12 cm and the radius is 6 cm, what is the base of the triangle formed by the slice?
What is the area of the triangle formed by the vertical slice of the cone?
Competency : Problem Solving
Solving the Cube’s Net and Surface Area
A student is given a cube with a side length of 5 cm. The student is tasked with finding the net of the cube and solving for its surface area.
Questions:
What is the net of a cube, and how can you draw it?
How many faces, edges, and vertices does a cube have?
What is the surface area of the cube with side length 5 cm?
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ FRACTIONS AND DECIMALS DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Word Problem Involving Fractions and Decimals
A garden is in the shape of a rectangle. The length of the garden is 212 metres and the width is 4 metres. The area of the garden needs to be calculated.
Questions:
Convert 212 to an improper fraction.
Find the area of the garden using the formula for area of a rectangle: Area = Length × Width.
Competency : Understanding the Concepts
Cake Sharing
A cake is cut into 12 equal slices. Ravi, Seema, and Neha are sharing the cake. Ravi eats 14 of the cake, Seema eats 13 of the cake, and Neha eats 16 of the cake.
Questions:
How many slices of the cake does Ravi eat?
(A) 2 (B) 3 (C) 4 (D) 6
How many slices are left after all three finish eating?
(A) 4 (B) 5 (C) 3 (D) 6
What fraction of the cake is left?
Competency : Ability to Compute
Shopping with Decimals
Arjun went shopping and purchased the following items: A book for ₹150.75; A pen for ₹12.50; A notebook for ₹45.25 ; Arjun has ₹500 with him.
Questions:
1.What is the total cost of all items Arjun bought?
a) ₹208.50 b) ₹208.75 c) ₹207.50 d) ₹210.50
2.How much money will Arjun have left after buying these items?
a) ₹290.25 b) ₹291.50 c) ₹291.25 d) ₹292.75
3. If Arjun buys another pen for ₹12.50, what will be the new total cost?
a) ₹221.25 b) ₹220.25 c) ₹222.00 d) ₹225.25
4. What is the difference between the price of the book and the notebook?
a) ₹95.50 b) ₹105.50 c) ₹102.00 d) ₹105.75
Competency : Problem Solving
Travel Distance Calculation
A cyclist travels 15.75 km in the first hour and 12.25 km in the second hour.
Questions:
How far did the cyclist travel in two hours?
a) 25 km b) 27.5 km
c) 28 km
d) 30 km
2.If the cyclist needs to travel a total of 50 km, how much distance is left?
a) 22.5 km b) 23 km c) 21 km d) 24 km
3.If the cyclist travels another 10.5 km in the next hour, what is the total distance covered now?
a) 37 km b) 38 km c) 40.25 km d) 48 km
4. To complete the 50 km journey, how much more distance does the cyclist need to cover after travelling 40.25 km?
a) 10.25 km b) 9.75 km c) 9.5 km d) 10 km
Competency Based Worksheet
Class:- VII Subject: Maths
NAME: _____________ SIMPLE EQUATIONS DATE: _____________
COMPETENCIES : Knowledge of Concepts, Understanding the Concepts, Ability to Compute, Problem Solving
Competency : Knowledge of Concepts
Number Puzzles
Ankit is thinking of a number. He adds 7 to this number and then doubles the result. He tells his friend that the answer is 24. Let the unknown number be xxx.
Questions:
1.Which of the following equations represents the situation described?
a) 2x+7=24 b) 2(x+7)=24 c) x+7=24 d) x+14=24
2.Solve 2(x+7)=242(x + 7) = 242(x+7)=24 to find the number Ankit is thinking of.
a) 3 b) 5 c) 7 d) 8
3. If Ankit adds 5 to the same number and doubles the result, what will the new answer be?
a) 20 b) 22 c) 18 d) 24
4. If the number Ankit is thinking of is tripled and increased by 6, what equation would represent this?
a) 3x+6 b) 3(x+6) c) x+6 d) 3+6x
Competency : Understanding the Concepts
Plant Growth
A plant grows by xxx cm each day. After 5 days, the plant has grown 30 cm.
Questions:
1. Which equation represents the growth of the plant over 5 days?
a) 5x=30 b) x+5=30 c) 5x+30=0 d) x−5=30
2. Solve 5x=30 to find the daily growth of the plant.
a) 4 cm b) 5 cm c) 6 cm d) 7 cm
3. How much will the plant grow in 10 days at the same rate?
a) 60 cm b) 65 cm c) 70 cm d) 75 cm
4. If the daily growth increases by 2 cm, what will be the total growth in 7 days?
a) 56 cm b) 64 cm c) 70 cm d) 84 cm
Competency : Ability to Compute
School Supplies Purchase
Rahul buys notebooks and pens for school. Each notebook costs ₹12, and each pen costs ₹5. He buys x notebooks and 3 pens and spends a total of ₹66.
Questions:
1.Which equation represents the total cost Rahul spent on notebooks and pens?
a) 12+5x=66 b) 12x+5×3=66 c) 12x+3=66 d) 12x+5x=66
2. Solve the equation 12x+15=6612x + 15 = 6612x+15=66 to find the number of notebooks Rahul bought.
a) 4 b) 3 c) 5 d) 6
3. If Rahul had bought 5 notebooks instead, what would be the total cost?
a) ₹75 b) ₹70 c) ₹80 d) ₹85
4.If the cost of each pen increases to ₹7, how much would Rahul spend for 4 notebooks and 3 pens?
a) ₹80 b) ₹83 c) ₹85 d) ₹88
Competency : Problem Solving
Money Distribution
Riya has ₹150. She gives ₹x to her friend and is left with ₹100.
Questions:
1.Which equation represents the amount Riya gave to her friend?
a) x+100=150 b) x−100=150 c) 150+x=100 d) x+50=100
2. Solve the equation x+100=150 to find how much Riya gave to her friend.
a) ₹30 b) ₹40 c) ₹50 d) ₹60
3. After giving money to her friend, how much is Riya left with?
a) ₹100 b) ₹50 c) ₹150 d) ₹200
4. If Riya gives another ₹20 to her friend, what is the new amount she has left?
a) ₹30 b) ₹80 c) ₹70 d) ₹90
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