Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sample Questions / Previous Year Questions
SecA
1.Find the product of the Successor and Predecessor of 999
Sol
Solution: Successor is
SecB
2. The sum of two whole numbers is 56. If one of the numbers is 24, what is the other number?
Sol
Solution:
SecC
What is the product of the first three whole numbers?
Sol
Solution: 0 (because 0 × 1 × 2 = 0)
SecD
Find the value of 7 × (8 + 2) using the distributive property.
Sol
Solution: Using the distributive property: 7 × (8 + 2) = 7 × 8 + 7 × 2 = 56 + 14 =
Problem 1
Understanding Distance
Situation: A group of friends are marking their homes on a number line to understand the distance between them. The positions of their homes are as follows: Riya's home at 5, Amit's home at 12, and Sanya's home at 20.
Questions:
1. What is the distance between Riya's home and Amit's home on the number line?
2. What is the distance between Amit's home and Sanya's home on the number line?
3. How can understanding distances on a number line help in real-life situations, such as planning a visit to a friend’s house?
Sol
Solutions:
- Distance between Riya's home and Amit's home:
Distance = 12 − 5 = 7 units
- Distance between Amit's home and Sanya's home:
Distance = 20 − 12 = 8 units
- Importance of understanding distances:
Planning Visits: Helps in planning the best route and estimating travel time.
Geographical Awareness: Enhances understanding of spatial relationships and geography.
Mathematical Application: Demonstrates practical applications of mathematical concepts in everyday life.
Problem 2
Number Line and Time Management
Situation: A teacher asked her students to place their study hours on a number line. Ramesh studies from 3 to 5, Priya from 6 to 9, and Neha from 4 to 7.
Questions:
1. Represent the study hours of each student on a number line.
2. How much time in total does each student spend studying?
3.Discuss the value of time management and how representing study hours on a number line can help.
Sol
Solution
1. Representing on a number line:
Ramesh: From 3 to 5
Priya: From 6 to 9
Neha: From 4 to 7
(Students can draw a number line from 1 to 10 and mark the segments for each student.)
2. Total study time:
Ramesh: 5 − 3 = 25 - 3 =2 hours
Priya: 9−6=39 - 6 = 3 hours
Neha: 7 − 4 = 37 - 4 =3 hours
3. Value of time management:
Efficiency: Helps in allocating time effectively to various tasks.
Productivity: Ensures productive use of time, leading to better academic performance.
Stress Reduction: Proper planning reduces stress and enhances well-being.
Goal Setting: Visualizing time on a number line aids in setting and achieving study goals.
Problem3
Situation: A group of volunteers decides to clean a beach. Each volunteer can collect 2 bags of trash in a day, and there are 6 volunteers.
Questions:
1. Use a number line to determine how many bags of trash are collected in total.
2. Explain the value of environmental stewardship and how such activities benefit the community.
Sol
Solutions
1. Using a number line to show multiplication:
Start at 0.
Make 6 jumps of 2 units each to represent 6 volunteers each collecting 2 bags.
After the first jump, you land on 2.
After the second jump, you land on 4.
After the third jump, you land on 6.
After the fourth jump, you land on 8.
After the fifth jump, you land on 10.
After the sixth jump, you land on 12.
2 × 6 = 12 bags
2. Value of environmental stewardship:
Environmental Responsibility: Demonstrates responsibility towards maintaining a clean and healthy environment.
Community Service: Shows the importance of contributing to the community’s well-being.
Awareness: Raises awareness about the impact of pollution and the importance of proper waste management.
Collective Effort: Highlights the power of collective effort in making a significant impact.
This question uses a number line to visualize multiplication and emphasizes the values of environmental stewardship, community service, and collective effort.
Q1
1.Find the product of the greatest 3-digit number and the smallest 2-digit number.
Sol
Solution
The greatest 3-digit number =
The smallest 2-digit number =
∴ Product = 999 x 10 =
Q2
2.Which property do the following statements hold?
(a) 6 + 4 = 4 + 6
(b) 3 + 2 = whole number
Sol
Solution
(a) 6 + 4 = 4 + 6 holds commutative property of addition
(b) 3 + 2 = whole number holds closure property.
Q3
3.Give one example for each of the following properties for whole numbers.
(a) Closure property
(b) Commutative property
(c) Associative property
(d) Distributive property
Sol
Solution
(a) 3 + 4 =
(b) 4 + 5 = 5 + 4 Commutative property
(c) 3 + (5 + 7) = (3 + 5) + 7 Associative property
(d) 6 x (8 + 3) = 6 x 8 + 6 x 3 Distributive property.
1. The successor of 1 million is
2. Successor of a one digit number is always a one digit number.
3. Predecessor of a two digit number is always a two digit number.
4. Every whole number has its successor.
5. The smallest 4-digit number is the successor of the largest 3-digit number.
6. 1 is the identity for multiplication of whole numbers.
7. If a whole number is divided by another whole number, which is greater than the first one, the quotient is not equal to zero.
8. The product of two whole numbers need not be a whole number.
9. Sum of two whole numbers is always less than their product.
10. If the sum of two distinct whole numbers is odd, then their difference also must be odd.
1. The smallest whole number is
2. Successor of 106159 is
3. Predecessor of 100000 is
4.
5. The smallest 6 digit whole number ending in 5 is
6. Whole numbers are closed under
7. Division of a whole number by
8. Multiplication is distributive over
Q1
We can count the number of children in our school; we can also count the number of people in a city; we can count the number of people in India. The number of people in the whole world can also be counted. We may not be able to count the number of stars in the sky or the number of hair on our heads but if we are able, there would be a number for them also. We can then add one more to such a number and get a larger number. In that case we can even write the number of hair on two heads taken together. It is now perhaps obvious that there is no largest number. Apart from these questions shared above, there are many others that can come to our mind when we work with Whole Numbers.
(i) Write the predecessor and successor of 2023.
(ii) Is there any natural number that has no predecessor? If yes, then write that number.
(iii) How many whole numbers are there between 34 and 43?
Sol
Solutions:
(i) The predecessor of 2023 is
(ii) Yes, there is a natural number that has no predecessor, which is 1
(iii) The whole no. between 34 and 44 are 35, 36, 37, 38, 39, 40, 41, 42 and 43
or total numbers between 34 and 44 =(largest number-smallest number)-1
= ([[44§§34]]-[[34§§44]])-1=[[9]]Q2
Draw a line. Mark a point on it. Label it 0. Mark a second point to the right of 0. Label it 1. The distance between these points labelled as 0 and 1 is called unit distance. On this line, mark a point to the right of 1 and at unit distance from 1 and label it 2. In this way go on labelling points at unit distances as 3, 4, 5,... on the line. You can go to any whole number on the right in this manner.
Answer the following questions
(i) Find 2 x 6 using the number line.
(ii) Find 3 x 3 using the number line.
(iii) Show 3 + 4 = 7 in the numberline