Chapter 11 — Mathematical Thinking
Mathematics is not only about counting and solving calculations. It also helps us think carefully, notice patterns, find answers and make decisions.
In this chapter, you will learn how to think about numbers, find missing numbers, solve simple logical problems and use mathematics in everyday situations. You will also practise different skills together.
Why This Chapter Matters
Mathematical thinking helps us understand problems and choose the correct way to solve them. Instead of only remembering answers, we learn to look for clues, compare information and think step by step.
Thinking carefully helps us find answers and check whether they make sense.
These skills are useful in mathematics and in everyday life. They also prepare you for more advanced problem solving in later classes.
What You Will Learn
- How to think about numbers in different ways.
- How to notice simple number relationships.
- How to find missing numbers.
- How to use clues to solve simple problems.
- How to solve simple logical problems.
- How mathematics is used in everyday situations.
- How to combine different mathematical skills.
- How to check your answers.
Before You Begin
Before starting this chapter, you should be comfortable with counting, comparing numbers, simple addition and subtraction, patterns and basic information from earlier chapters.
You will use these skills together to think about numbers and solve simple problems in different situations.
Understanding the Learning Sequence
The lessons begin with thinking about numbers and their relationships. You will then learn to find missing numbers, use clues to solve simple logical problems, apply mathematics to everyday situations and finally practise different skills together.
This sequence gradually develops your ability to use what you know to understand and solve new problems.
Lessons in This Chapter
Complete the lessons in the order shown below.
Important Ideas
- Numbers can be compared, ordered and related in different ways.
- Patterns can help us find what comes next.
- A missing number can be found by looking at the numbers around it.
- Clues can help us solve simple problems.
- Careful thinking helps us avoid mistakes.
- Mathematics can be used in many everyday situations.
- Different mathematical skills can be used together.
- Checking an answer helps us know whether it makes sense.
Chapter Practice
- Which number comes after 19?
- Which number is greater: 7 or 5?
- Find the missing number: 3, 4, __, 6.
- Find the missing number: 10, __, 12.
- What comes next: 2, 4, 6, __?
- If you have 5 apples and get 2 more, how many apples do you have?
- If you have 8 pencils and give away 3, how many pencils remain?
- Which is heavier: a school bag or a pencil?
- You have ₹10 and spend ₹5. How much money is left?
- Why should you check your answer after solving a problem?
Quick Revision
Mathematical thinking means using numbers, patterns, clues and relationships to understand and solve problems. We can find missing numbers by looking carefully at the numbers around them.
Mathematics is also useful in everyday situations such as counting objects, using money, comparing things, measuring and solving simple problems. Checking our answers helps us make sure our thinking is correct.
Continue Learning
Start with Lesson 1 — Thinking About Numbers and complete the lessons in sequence.