Picture this: your child stares at a SASMO problem, pencil frozen. The question gives a final number and asks what happened first. Most students try to guess, but there is a smarter way. The working backwards method flips the problem around. Instead of starting at the beginning, you start at the end and reverse each step. This technique saves time, reduces mistakes, and builds confidence. For Grade 4 students preparing for the SASMO competition, it is one of the most powerful tools in their problem-solving kit.

What Is the Working Backwards Method?

The working backwards method is exactly what it sounds like. You take the final answer given in the problem and reverse every operation to find the starting value. If the problem says someone doubled a number and then added 5 to get 17, you start at 17, subtract 5, then divide by 2. That gives you 6, the original number.

This method works especially well for SASMO because many competition problems describe a sequence of events that leads to a final result. The question asks for the initial amount, the starting number, or the original quantity. Instead of guessing and checking, you can work step by step in reverse.

When Should You Use the SASMO Working Backwards Method?

Not every problem needs this approach. You want to use it when you see certain clues.

• The problem gives a final result or ending value.
• The problem describes a series of changes, like adding, subtracting, multiplying, or dividing.
• The question asks for the starting amount or original number.
• The problem involves age calculations, money transactions, or number puzzles with multiple steps.

For example, a typical SASMO question might say: “After giving away half of his marbles and then buying 12 more, Tom has 30 marbles. How many did he start with?” You can work backwards from 30. Reverse the “buying 12 more” by subtracting 12, which gives 18. Then reverse the “giving away half” by doubling, which gives 36. Tom started with 36 marbles.

How to Apply the Method in 3 Steps

Here is a simple process your child can follow during the SASMO competition.

1. Identify the final value. Read the problem carefully and circle the number that represents the outcome. This is your starting point for working backwards.

2. List the operations in order. Write down each step the problem describes from beginning to end. For example: start, add 5, multiply by 3, subtract 2, end with 19.

3. Reverse each operation. Starting from the final value, do the opposite of each step. If the original step was “add 5,” you subtract 5. If it was “multiply by 3,” you divide by 3. Continue until you reach the starting value.

Let us test this with a real SASMO style problem.

Problem: Jenny had some stickers. She gave half to her brother. Then she gave 6 stickers to her friend. Finally, she bought 10 more stickers. She now has 24 stickers. How many did she start with?

• Final value: 24
• Operations in order: start, divide by 2 (gave half), subtract 6 (gave to friend), add 10 (bought more), end with 24
• Reverse: Start at 24. Subtract 10 (reverse of buying) = 14. Add 6 (reverse of giving) = 20. Multiply by 2 (reverse of giving half) = 40.

Jenny started with 40 stickers. You can check by going forward: half of 40 is 20, give 6 leaves 14, buy 10 gives 24. It works.

Common Mistakes and How to Avoid Them

Students often make small errors when working backwards. The table below shows the most common mistakes and the fixes.

Practice Problems to Try at Home

The best way to master the SASMO working backwards method is to practice with real competition style questions. Here are a few to get started.

Problem 1: A number is multiplied by 4, then 7 is added. The result is 31. What is the number?

Problem 2: Sarah spent half of her money on lunch. Then she spent $8 on a book. She has $12 left. How much did she start with?

Problem 3: There were some students in a classroom. 5 students left, then 3 more arrived. There are now 18 students. How many were there at the start?

Answers: Problem 1: 6. Start with 31, subtract 7 gives 24, divide by 4 gives 6. Problem 2: $40. Start with $12, add $8 gives $20, multiply by 2 gives $40. Problem 3: 20. Start with 18, subtract 3 gives 15, add 5 gives 20.

Why This Method Works So Well for SASMO

The SASMO competition rewards students who can think logically and solve problems efficiently. The working backwards method fits perfectly with the types of questions that appear on the test. Many SASMO problems involve sequences of operations where the final result is known. By working backwards, your child avoids the guesswork that wastes time.

“Working backwards is like solving a puzzle by looking at the finished picture first. Every step you reverse brings you closer to the starting piece. It turns a confusing problem into a clear path.” This advice comes from experienced SASMO coaches who have seen students improve their scores by using this technique.

Combining Working Backwards with Other Techniques

The SASMO working backwards method does not exist in isolation. Your child can combine it with other strategies to solve even harder problems. For example, if a problem involves both forward and backward steps, your child might work backwards for part of the problem and then use a bar model for another part. You can learn more about the bar model method in our guide on how to solve SASMO word problems using the bar model method.

Another helpful technique is answer elimination. After working backwards to find a possible answer, your child can check it against the multiple choice options. If the answer matches one option, they can be confident. If not, they can try again. Read more about answer elimination techniques that boost your SASMO multiple choice accuracy.

How to Build Speed with This Method

Speed matters in the SASMO competition. Your child has a limited time to solve each problem. Here are some tips to get faster with the working backwards method.

• Practice with a timer. Set 2 minutes for each problem and try to finish before the buzzer.
• Write the steps clearly. Messy handwriting leads to mistakes.
• Use mental math for simple reversals. For example, if the last step is “add 5,” your child should instantly think “subtract 5” without writing it down.
• Check your work by going forward. After finding the starting number, run through the original steps to make sure the final value matches.

For more time management strategies, check out our guide on how to manage your time effectively during SASMO competition day.

When Working Backwards Does Not Work

No method works for every problem. The working backwards method struggles with problems that do not give a clear final value. For example, if a problem asks “which of these numbers could be the result?” you cannot start from a single end point. Similarly, problems with multiple possible paths or conditional steps are harder to reverse. In those cases, your child might need to use other strategies like guess and check or logical reasoning.

A Parent’s Role in Teaching This Method

You do not need to be a math expert to help your child learn the SASMO working backwards method. Start by reading a problem together and asking one question: “What is the final number?” Then ask, “What happened right before that?” Work backwards one step at a time. Let your child do the thinking. You just guide the questions.

If your child gets stuck, go back to the problem and read it aloud. Sometimes hearing the steps helps more than reading them. Celebrate small wins when your child solves a problem correctly. That builds the confidence they need for competition day.

For more parent tips, read our parents guide to supporting your SASMO competitor.

Putting It All Together

The SASMO working backwards method is a simple but powerful technique that every Grade 4 student should master. It turns confusing word problems into clear, step by step puzzles. With practice, your child will be able to spot working backwards problems instantly and solve them in under a minute. That means more time for the harder questions and a higher score overall.

Start with the practice problems in this guide. Then move on to past SASMO papers and try the method there. Before long, your child will wonder why they ever solved problems any other way.

Your Next Step Toward SASMO Success

Now that you understand the SASMO working backwards method, it is time to put it into action. Grab a pencil and a few practice problems. Work through them with your child using the three step process. If your child masters this technique, they will have a major advantage on competition day. And remember, every expert was once a beginner. With consistent practice, your child can become a confident problem solver ready for any SASMO challenge.

For a complete collection of practice problems arranged by grade level, visit our grade by grade SASMO problem sets page. Happy solving.