What does it mean?
A two-step story changes a quantity more than once or asks you to combine two relationships. The answer to the first calculation becomes information for the next. Writing “505 pens available” is more useful than writing just 505 because it tells you what the second operation acts on.
A two-step problem needs an ordered model. The first answer should be labelled because it becomes information for the second step.
Learning goal: Solve two-step additive problems by identifying the order of relationships, labelling the intermediate quantity and checking the final answer. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Multiplication word problems with models and explained answers 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
Name the quantity you are following. List the changes in the order given, choose an operation for each, and label the intermediate result. Read the last sentence again before answering: it might ask for a final stock, a difference or a total collected. Check the direction of each change against the story.
Key rule and when to use it
Identify what changes first, calculate that quantity and label it. Then apply the next change and check whether the final amount fits the story.
Worked examples, step by step
Example 1: 320 pens, 185 more arrive, then 96 are sold.
- Step 1: 320 + 185 = 505 pens available.
- Label 505 as the new stock.
- Step 2: 505 - 96 = 409.
- Check that the final amount is below 505.
Answer: 409
Example 2: 850 books, 126 borrowed, then 74 returned.
- Step 1: 850 - 126 = 724 books left.
- Label 724.
- Step 2: 724 + 74 = 798.
- Check that returning books increases the intermediate amount.
Answer: 798
Example 3: A library has 460 books, receives 125, then lends 78. How many remain on its shelves?
- After receiving books: 460 + 125 = 585 books.
- After lending books: 585 − 78 = 507 books.
- 507 is below the intermediate 585. Check 507 + 78 − 125 = 460.
Common mistakes and important boundaries
A different calculation order can sometimes give the same result without following the story chronologically. For example, (400 + 175) − 90 and 400 + (175 − 90) are both 485. Explain the regrouping rather than saying it is mathematically wrong. A story model should still make clear where the 90 is removed.
A point to explain
The learner may perform two calculations without checking whether the first result is the quantity needed next.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Two-Step Addition and Subtraction Word Problems — 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: __________
A class collects 235 cans on Monday and 184 on Tuesday, then 96 are recycled. What must be found first?
Show answer
the total collected before recycling
A tank has 700 L. 185 L are used, then 240 L are added. Which operation order matches the story?
Show answer
subtract 185, then add 240
A shop has 320 pens. It receives 185 more, then sells 96. How many pens remain?
Show answer
409
A team scores 248 points, then 175 more. A penalty deducts 68 points. What is the final score?
Show answer
355
A library has 850 books. 126 are borrowed. Later 74 are returned. How many books are now in the library?
Show answer
798
Why should the intermediate answer be labelled in a two-step problem?
Show answer
It shows what the first calculation represents and whether it is the quantity needed for step two.
Does (400 + 175) − 90 have the same value as 400 + (175 − 90)? Explain.
Answer and a way to check
Yes; both equal 485.
Regrouping these additions and subtractions preserves the value. A story model should still label the combined stock before the removal.
An exhibition has 265 visitors inside. Then 138 arrive and 174 leave. How many visitors remain?
Show answer
229
Two-Step Addition and Subtraction Word Problems — answer key
the total collected before recycling
subtract 185, then add 240
409
355
798
It shows what the first calculation represents and whether it is the quantity needed for step two.
Yes; both equal 485. Regrouping these additions and subtractions preserves the value. A story model should still label the combined stock before the removal.
229
Questions students and parents ask
Must I always add before subtracting?
No. A story about 700 litres, then using 185 and adding 240, is modelled by 700 − 185 + 240. The changes in the story determine the operations.
Do words such as “more” always mean add?
No. Read what is unknown. “A has 20 more than B; A has 70” requires subtraction to find B. Describe the relationship before picking an operation.
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 Multiplication word problems with models and explained answers. 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
Ask your child what the first answer means and why it is needed next. A small labelled flow diagram can make the sequence easier to follow.
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
About this guide
Based on BananaLearn’s Grade 3 course lesson “Two-Step Additive Problems”. 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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