Grade 2 · Operations · MAT-02-OPS-009
Two-Step Addition and Subtraction Word Problems
Solve two-step word problems using addition and subtraction within 100.
Learning objectives
What you should be able to do
- Solve two-step word problems using addition and subtraction within 100.
- Represent each step with equations or diagrams.
- Explain why the order of the two steps matches the story.
Prerequisite check
Make sure the foundation is ready.
Checks problem-structure understanding before combining steps.
Learn
Build the idea from meaning, not memorization.
Two-step problems contain two connected relationships
A two-step story cannot usually be solved with one operation because the first result becomes information needed for the second step. Identify what must be found first and why.
Write one equation for each step
For a story with 28 books, 17 added, then 12 removed, first find 28+17=45. Then use 45−12=33. Separate equations keep the reasoning visible.
The story determines operation order
Addition does not always come before subtraction, nor subtraction before addition. Follow the sequence or logical dependency described in the situation.
Check the final answer against the story
Ask whether the quantity should end larger, smaller, or between earlier amounts. A reasonableness check can reveal a correct-looking calculation applied in the wrong order.
Interactive math lab
Change it. See what stays true.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- identify step1
- solve intermediate
- identify step2
- reverse check
Worked examples
Twenty different ways to see the concept work.
28 books +17, then12 removed.
28+17=45;45−12=33First join, then separate.
60 stickers−18, then+9.
60−18=42;42+9=51First separate, then join.
24 red+19 blue, then15 used.
24+19=43;43−15=28Combine parts before subtracting use.
75 total,22 given away, then8 added.
75−22=53;53+8=61Follow the story order.
35 children,12 leave,7 return.
35−12=23;23+7=30Each step changes the same quantity.
18 apples+26+15.
18+26=44;44+15=59Two addition steps.
90 points−24−16.
90−24=66;66−16=50Two subtraction steps.
42 pencils+13 then split off20.
42+13=55;55−20=35Intermediate total matters.
50 tickets−17 then+25.
33 then58Subtract then add.
31 birds+14;9 fly away.
45 then36Join then separate.
Start70, remove28, then remove12.
42 then30Two decreases.
Start27, add19, then add14.
46 then60Two increases.
A jar has65, 21 used, 18 replaced.
44 then62Subtract then add.
20 cats and18 dogs; 11 animals leave.
38 then27Combine categories, then subtract.
100 cards, 35 given, 22 returned.
65 then87Return increases after decrease.
Which first: total 25 red+17 blue, then give away9?
25+17 firstThe removal is from the combined set.
Can one equation show both steps compactly?
(28+17)−12=33Parentheses preserve step order.
Why not do 17−12 first in example1?
Those amounts describe different events on the running totalStory relationships must be respected.
Estimate example1.
About3030+20−10≈40; exact33 is plausible.
Check result33 from example1.
33+12=45 and45−17=28Reverse the steps.
Practice
Guided practice with hints
0140+18, then−12.
Hint: Find first total.
Answer: 46
0272−25, then+10.
Hint: Follow story order.
Answer: 57
0316+29+5.
Hint: Add first two, then third.
Answer: 50
0490−30−25.
Hint: Subtract sequentially.
Answer: 35
0530 red+22 blue, then18 removed.
Hint: Combine first.
Answer: 34
06Why show an intermediate result?
Hint: It becomes input to step two.
Answer: It makes the reasoning traceable.
Practice
Independent practice
0125+17−8
Answer: 34
0264−19+7
Answer: 52
0318+22+10
Answer: 50
0480−24−16
Answer: 40
0533+27−15
Answer: 45
0695−35+12
Answer: 72
0740+18−20
Answer: 38
08Explain first-step choice.
Answer: It must produce the quantity needed for the second relationship.
Common mistakes
Learn to catch the error, not just the answer.
Determine the role of each event; two-step stories can mix operations.
Use story sequence and dependencies.
Record it explicitly as the input to step two.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Track inventory through two changes.
- Follow two score or attendance changes in sequence.
Challenge problems
Write a two-step story for40+15−12=43.
Any valid join-then-separate story.
Can two different operation orders give different answers with same numbers?
Yes; order can matter when subtraction is involved.
Why is (20+10)−5 different in structure from20+(10−5)?
They group events differently even if sometimes totals coincide.
How can reverse operations check a two-step result?
Undo step two, then undo step one to recover the start.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Two-Step Trail
Choose and solve the correct two-operation path through a story.
Practice
Mastery check
0128+16−9
Answer: 35
0270−22+8
Answer: 56
0335+15+20
Answer: 70
0490−30−15
Answer: 45
05What is an intermediate result?
Answer: Step one's answer used in step two.
06Who determines operation order?
Answer: The structure of the story.
07Why write two equations?
Answer: To make each relationship and intermediate result visible.
08How can you check?
Answer: Reverse the two operations in reverse order.
Terminology
Words to know
- two-step problem
- A problem requiring two connected operations.
- intermediate result
- A result from one step needed in the next step.
- operation order
- The sequence in which calculations must occur.
- dependency
- When one step needs information produced by another.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.OA.A.1
One- and two-step addition/subtraction word problems.