Grade 3 · Operations & Algebraic Thinking · MAT-03-OA-012
Solve Two-Step Word Problems
Represent solve two-step word problems with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent solve two-step word problems with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving solve two-step word problems accurately and explain why the method works.
- Check results for reasonableness using a second representation, inverse relationship, benchmark, or property when appropriate.
Prerequisite check
Make sure the foundation is ready.
Checks conceptual readiness before new Grade 3 reasoning.
Checks whether prior skills are available for use, not only recalled by name.
Learn
Build the idea from meaning, not memorization.
Meaning of Solve Two-Step Word Problems
Two-step problems require two connected operations, and the first result becomes information for the second step.
A reliable reasoning strategy
Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Representations that should agree
Parentheses or separate equations can show which operation happens first. A correct model, equation, verbal explanation, or diagram should preserve the same quantities and relationships.
How to check the result
Check whether the answer fits the quantities, units, and structure of the problem. Use a second representation or inverse relationship when available, and explain what would make an answer unreasonable.
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.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
3 boxes hold 5 pencils each, then 3 loose pencils are added. How many pencils altogether?
3 × 5 = 15; 15 + 3 = 18Find the boxed pencils first, then add the loose pencils.
4 teams collect 7 cans each, then 4 cans are removed from the total. How many remain?
4 × 7 = 28; 28 - 4 = 24Find the equal-group total before subtracting the removed amount.
5 boxes hold 3 pencils each, then 5 loose pencils are added. How many pencils altogether?
5 × 3 = 15; 15 + 5 = 20Find the boxed pencils first, then add the loose pencils.
6 teams collect 5 cans each, then 6 cans are removed from the total. How many remain?
6 × 5 = 30; 30 - 6 = 24Find the equal-group total before subtracting the removed amount.
2 boxes hold 7 pencils each, then 7 loose pencils are added. How many pencils altogether?
2 × 7 = 14; 14 + 7 = 21Find the boxed pencils first, then add the loose pencils.
3 teams collect 3 cans each, then 8 cans are removed from the total. How many remain?
3 × 3 = 9; 9 - 8 = 1Find the equal-group total before subtracting the removed amount.
4 boxes hold 5 pencils each, then 2 loose pencils are added. How many pencils altogether?
4 × 5 = 20; 20 + 2 = 22Find the boxed pencils first, then add the loose pencils.
5 teams collect 7 cans each, then 3 cans are removed from the total. How many remain?
5 × 7 = 35; 35 - 3 = 32Find the equal-group total before subtracting the removed amount.
6 boxes hold 3 pencils each, then 4 loose pencils are added. How many pencils altogether?
6 × 3 = 18; 18 + 4 = 22Find the boxed pencils first, then add the loose pencils.
2 teams collect 5 cans each, then 5 cans are removed from the total. How many remain?
2 × 5 = 10; 10 - 5 = 5Find the equal-group total before subtracting the removed amount.
3 boxes hold 7 pencils each, then 6 loose pencils are added. How many pencils altogether?
3 × 7 = 21; 21 + 6 = 27Find the boxed pencils first, then add the loose pencils.
4 teams collect 3 cans each, then 7 cans are removed from the total. How many remain?
4 × 3 = 12; 12 - 7 = 5Find the equal-group total before subtracting the removed amount.
5 boxes hold 5 pencils each, then 8 loose pencils are added. How many pencils altogether?
5 × 5 = 25; 25 + 8 = 33Find the boxed pencils first, then add the loose pencils.
6 teams collect 7 cans each, then 2 cans are removed from the total. How many remain?
6 × 7 = 42; 42 - 2 = 40Find the equal-group total before subtracting the removed amount.
2 boxes hold 3 pencils each, then 3 loose pencils are added. How many pencils altogether?
2 × 3 = 6; 6 + 3 = 9Find the boxed pencils first, then add the loose pencils.
3 teams collect 5 cans each, then 4 cans are removed from the total. How many remain?
3 × 5 = 15; 15 - 4 = 11Find the equal-group total before subtracting the removed amount.
4 boxes hold 7 pencils each, then 5 loose pencils are added. How many pencils altogether?
4 × 7 = 28; 28 + 5 = 33Find the boxed pencils first, then add the loose pencils.
5 teams collect 3 cans each, then 6 cans are removed from the total. How many remain?
5 × 3 = 15; 15 - 6 = 9Find the equal-group total before subtracting the removed amount.
6 boxes hold 5 pencils each, then 7 loose pencils are added. How many pencils altogether?
6 × 5 = 30; 30 + 7 = 37Find the boxed pencils first, then add the loose pencils.
2 teams collect 7 cans each, then 8 cans are removed from the total. How many remain?
2 × 7 = 14; 14 - 8 = 6Find the equal-group total before subtracting the removed amount.
Practice
Guided practice with hints
013 boxes hold 5 pencils each, then 5 loose pencils are added. How many pencils altogether?
Hint: Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Answer: 20
024 teams collect 7 cans each, then 6 cans are removed from the total. How many remain?
Hint: Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Answer: 22
035 boxes hold 3 pencils each, then 7 loose pencils are added. How many pencils altogether?
Hint: Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Answer: 22
046 teams collect 5 cans each, then 8 cans are removed from the total. How many remain?
Hint: Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Answer: 22
052 boxes hold 7 pencils each, then 2 loose pencils are added. How many pencils altogether?
Hint: Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Answer: 16
063 teams collect 3 cans each, then 3 cans are removed from the total. How many remain?
Hint: Plan the sequence before calculating; estimate to check whether the final answer is reasonable.
Answer: 6
Practice
Independent practice
013 boxes hold 3 pencils each, then 4 loose pencils are added. How many pencils altogether?
Answer: 13
024 teams collect 5 cans each, then 5 cans are removed from the total. How many remain?
Answer: 15
035 boxes hold 7 pencils each, then 6 loose pencils are added. How many pencils altogether?
Answer: 41
046 teams collect 3 cans each, then 7 cans are removed from the total. How many remain?
Answer: 11
052 boxes hold 5 pencils each, then 8 loose pencils are added. How many pencils altogether?
Answer: 18
063 teams collect 7 cans each, then 2 cans are removed from the total. How many remain?
Answer: 19
074 boxes hold 3 pencils each, then 3 loose pencils are added. How many pencils altogether?
Answer: 15
085 teams collect 5 cans each, then 4 cans are removed from the total. How many remain?
Answer: 21
Common mistakes
Learn to catch the error, not just the answer.
After each calculation, reread the question and decide whether another step is still required.
Reconnect the answer to solve two-step word problems and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine equal groups with addition, subtraction, or sharing in real situations.
- Use solve two-step word problems to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
3 boxes hold 7 pencils each, then 3 loose pencils are added. How many pencils altogether?
24
4 teams collect 3 cans each, then 4 cans are removed from the total. How many remain?
8
5 boxes hold 5 pencils each, then 5 loose pencils are added. How many pencils altogether?
30
6 teams collect 7 cans each, then 6 cans are removed from the total. How many remain?
36
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Solve Two-Step Word Problems Challenge
Solve and explain Grade 3 problems involving solve two-step word problems without relying on answer guessing.
Practice
Mastery check
013 boxes hold 5 pencils each, then 2 loose pencils are added. How many pencils altogether?
Answer: 17
024 teams collect 7 cans each, then 3 cans are removed from the total. How many remain?
Answer: 25
035 boxes hold 3 pencils each, then 4 loose pencils are added. How many pencils altogether?
Answer: 19
046 teams collect 5 cans each, then 5 cans are removed from the total. How many remain?
Answer: 25
052 boxes hold 7 pencils each, then 6 loose pencils are added. How many pencils altogether?
Answer: 20
063 teams collect 3 cans each, then 7 cans are removed from the total. How many remain?
Answer: 2
074 boxes hold 5 pencils each, then 8 loose pencils are added. How many pencils altogether?
Answer: 28
085 teams collect 7 cans each, then 2 cans are removed from the total. How many remain?
Answer: 33
Terminology
Words to know
- two-step problem
- A problem requiring two connected calculations.
- intermediate result
- The answer from the first step used in the next step.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.OA.8
Primary standards alignment for Solve Two-Step Word Problems.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.