What is Working Backwards? | Simple Explanation for Class 5

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What is Working Backwards (Problem Solving)?

Grade Level:

Class 5

Maths, Computing, AI, Logic, Algorithms

Definition

What is it?

Working Backwards is a problem-solving strategy where you start from the end result or goal and trace your steps back to the beginning. It helps you figure out how to reach a solution by undoing the operations or actions that led to the final state.

Simple Example

Quick Example

Imagine you have 10 laddoos left in a box. You know your family ate 5 laddoos in the morning and your friends ate 3 laddoos in the evening. To find out how many laddoos were there initially, you start with the 10 laddoos remaining and add back the ones that were eaten.

Worked Example

Step-by-Step

Sita wants to buy a new cricket bat that costs Rs. 850. She has already saved Rs. 300. Her aunt gave her Rs. 150 for her birthday. How much more money does Sita need to save?

Step 1: Identify the goal. Sita needs Rs. 850.
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Step 2: Identify what she has already. She has Rs. 300 saved.
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Step 3: Add the money she received. Rs. 300 (saved) + Rs. 150 (from aunt) = Rs. 450.
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Step 4: Now, work backwards from the total cost. Subtract the money she has from the total cost. Rs. 850 (total cost) - Rs. 450 (money she has) = Rs. 400.
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Answer: Sita needs to save Rs. 400 more.

Why It Matters

Working Backwards is a fundamental skill in Maths, helping you solve complex problems by simplifying them. It's used by computer programmers to debug code, by AI developers to design efficient algorithms, and by scientists to trace causes of events. Understanding this helps you think logically in many careers!

Common Mistakes

MISTAKE: Adding amounts instead of subtracting when working backwards. | CORRECTION: When moving backwards from a final state, you must perform the inverse operation. If something was added, you subtract; if something was multiplied, you divide.

MISTAKE: Not keeping track of all steps or missing an operation. | CORRECTION: Always write down each step clearly. Double-check that you've accounted for every piece of information and every action in reverse.

MISTAKE: Starting from the beginning and trying to guess the end. | CORRECTION: Remember the core idea: start with the known end result and systematically undo the steps to find the beginning.

Practice Questions

Try It Yourself

Rohan had some money. He spent Rs. 50 on a book and Rs. 30 on snacks. He now has Rs. 70 left. How much money did Rohan have initially? | ANSWER: Rs. 150

A bus started its journey with some passengers. At the first stop, 10 passengers got off and 5 got on. At the second stop, 3 passengers got off and 8 got on. If there are now 30 passengers on the bus, how many were there at the start? | ANSWER: 20 passengers

Deepak is thinking of a number. He multiplies it by 3, then adds 7, and finally divides the result by 2. If the final answer is 10, what was Deepak's original number? | ANSWER: 13/3 (or 4.33)

MCQ

Quick Quiz

Which of these situations would best be solved by Working Backwards?

Calculating the total cost of groceries.

Finding out how many runs a cricket team needs to win if they have a target score.

Figuring out the starting time of a movie if you know the end time and duration.

Counting the number of students in a class.

The Correct Answer Is:

Option C is correct because you start with the known end time and subtract the duration to find the unknown starting time. This is a classic working backwards problem. Options A, B, and D are straightforward calculations or direct observations.

Real World Connection

In the Real World

Imagine you're planning a train journey from Delhi to Mumbai. You know you need to reach Mumbai by 6 PM. If the journey takes 16 hours, and you need 2 hours to get to the station and board, you can work backwards from 6 PM to figure out what time you need to leave your home. This is also how delivery apps like Swiggy or Zomato might calculate when a chef needs to start cooking for an order to reach you on time!

Key Vocabulary

Key Terms

STRATEGY: A plan of action to achieve a goal. | INVERSE OPERATION: The opposite operation (e.g., addition is the inverse of subtraction). | FINAL RESULT: The end outcome or answer of a problem. | INITIAL STATE: The starting condition or value before any changes.

What's Next

What to Learn Next

Great job understanding Working Backwards! Next, you can explore 'Problem Solving with Multiple Steps'. This will help you tackle even more complex problems by breaking them down and applying strategies like Working Backwards to individual parts.