What does it mean?
Subtraction can describe taking away or finding a gap. For 642 − 120, removing one hundred and two tens is convenient. For 503 − 498, counting up five steps is much easier than a long written subtraction. Both meanings lead to the same difference.
Subtraction can mean removing an amount or finding a difference. Choose place-value removal for structured amounts and counting up when the numbers are close.
Learning goal: Subtract within 1,000 using an efficient place-value or counting-up strategy. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Number sense and multiplication if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
First compare the two numbers. If they are close, count up from the smaller to the larger using friendly landmarks. If the amount removed has clear hundreds and tens, subtract those parts. If you compensate by subtracting a larger round amount, add back the excess you removed. Label the jumps to keep their direction clear.
Key rule and when to use it
Subtraction can mean removing an amount or finding a difference. Nearby numbers often suit counting up; round subtrahends often suit compensation.
Worked examples, step by step
Example 1: Solve 642 - 120 by place value.
- Remove 1 hundred from 6 hundreds.
- Remove 2 tens from 4 tens.
- Keep the 2 ones.
- The result is 522.
Answer: 522
Example 2: Solve 503 - 498 by counting up.
- Start at 498.
- Count to 500: +2.
- Count to 503: +3.
- The total gap is 5.
Answer: 5
Example 3: Find 724 − 198 by compensation.
- Subtract the easier 200: 724 − 200 = 524.
- This removed two more than needed. Add them back: 524 + 2 = 526.
- Check: 526 + 198 = 724.
Common mistakes and important boundaries
Subtraction cannot generally swap its two numbers: 30 − 12 and 12 − 30 are not the same. When counting up, add the sizes of the jumps, not their landing numbers. If you subtract 200 instead of 198, you removed two too many, so add two back.
A point to explain
The learner may force a take-away strategy even when finding the distance is much easier.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Mental Subtraction: Count Up or Take Away — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
Which strategy is especially efficient for 503 - 498?
Show answer
count up from 498 to 503
Which representation clearly shows 642 - 120 by place value?
Show answer
base-ten/place-value model
642 - 120 = __
Show answer
522
785 - 300 = __
Show answer
485
503 - 498 = __
Show answer
5
Why can counting up be efficient for 701 - 696?
Show answer
The numbers are close, so the small distance between them is easy to find.
A child solves 870 - 240 as 630 but says they subtracted 24. What is wrong with the explanation?
Show answer
240 is 2 hundreds and 4 tens, not 24 ones.
Choose an efficient strategy and solve 602 - 597.
Show answer
5; count up from 597 to 602
Mental Subtraction: Count Up or Take Away — answer key
count up from 498 to 503
base-ten/place-value model
522
485
5
The numbers are close, so the small distance between them is easy to find.
240 is 2 hundreds and 4 tens, not 24 ones.
5; count up from 597 to 602
Questions students and parents ask
How do I subtract 199 mentally?
Subtract 200, then add 1 back because you removed one too much. For 450 − 199, this gives 250 + 1 = 251.
Why can counting up answer a subtraction?
It measures the distance from the smaller number to the larger. That distance is the difference, even though the jumps themselves are additions.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Number sense and multiplication. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Compare a close-number subtraction with a round-hundreds subtraction. Ask which approach makes each one simpler instead of insisting on one written method.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
- Number sense and multiplication
- Grade 3 Estimating Sums and Differences
- Grade 3 Odd and Even Numbers: Pairs and Patterns
- Grade 3 Mental Addition: Bridge Tens and Compensate
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About this guide
Based on BananaLearn’s Grade 3 course lesson “Subtraction Strategies”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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