Grade 4 · Operations & Algebraic Thinking · MAT-04-OA-004
Solve Multi-Step Whole-Number Problems
Represent and solve solve multi-step whole-number problems problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve solve multi-step whole-number problems problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for solve multi-step whole-number problems works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Solve Multi-Step Whole-Number Problems is a operations & algebraic thinking idea built from precise quantities, representations, and operations. The mathematical goal is to preserve the meaning of each quantity while choosing a representation that makes the relationship visible.
Represent the idea
The Math Box uses equation balance as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- Build one example of solve multi step whole number problems in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
2 boxes hold 6 items each, then 3 more items are added. What is the total?
2 × 6 = 12; 12 + 3 = 15The equal groups are multiplied first; the separate extra amount is added afterward.
3 boxes hold 7 items each, then 4 more items are added. What is the total?
3 × 7 = 21; 21 + 4 = 25The equal groups are multiplied first; the separate extra amount is added afterward.
4 boxes hold 8 items each, then 5 more items are added. What is the total?
4 × 8 = 32; 32 + 5 = 37The equal groups are multiplied first; the separate extra amount is added afterward.
5 boxes hold 9 items each, then 6 more items are added. What is the total?
5 × 9 = 45; 45 + 6 = 51The equal groups are multiplied first; the separate extra amount is added afterward.
6 boxes hold 10 items each, then 7 more items are added. What is the total?
6 × 10 = 60; 60 + 7 = 67The equal groups are multiplied first; the separate extra amount is added afterward.
2 boxes hold 11 items each, then 8 more items are added. What is the total?
2 × 11 = 22; 22 + 8 = 30The equal groups are multiplied first; the separate extra amount is added afterward.
3 boxes hold 12 items each, then 9 more items are added. What is the total?
3 × 12 = 36; 36 + 9 = 45The equal groups are multiplied first; the separate extra amount is added afterward.
4 boxes hold 6 items each, then 10 more items are added. What is the total?
4 × 6 = 24; 24 + 10 = 34The equal groups are multiplied first; the separate extra amount is added afterward.
5 boxes hold 7 items each, then 11 more items are added. What is the total?
5 × 7 = 35; 35 + 11 = 46The equal groups are multiplied first; the separate extra amount is added afterward.
6 boxes hold 8 items each, then 3 more items are added. What is the total?
6 × 8 = 48; 48 + 3 = 51The equal groups are multiplied first; the separate extra amount is added afterward.
2 boxes hold 9 items each, then 4 more items are added. What is the total?
2 × 9 = 18; 18 + 4 = 22The equal groups are multiplied first; the separate extra amount is added afterward.
3 boxes hold 10 items each, then 5 more items are added. What is the total?
3 × 10 = 30; 30 + 5 = 35The equal groups are multiplied first; the separate extra amount is added afterward.
4 boxes hold 11 items each, then 6 more items are added. What is the total?
4 × 11 = 44; 44 + 6 = 50The equal groups are multiplied first; the separate extra amount is added afterward.
5 boxes hold 12 items each, then 7 more items are added. What is the total?
5 × 12 = 60; 60 + 7 = 67The equal groups are multiplied first; the separate extra amount is added afterward.
6 boxes hold 6 items each, then 8 more items are added. What is the total?
6 × 6 = 36; 36 + 8 = 44The equal groups are multiplied first; the separate extra amount is added afterward.
2 boxes hold 7 items each, then 9 more items are added. What is the total?
2 × 7 = 14; 14 + 9 = 23The equal groups are multiplied first; the separate extra amount is added afterward.
3 boxes hold 8 items each, then 10 more items are added. What is the total?
3 × 8 = 24; 24 + 10 = 34The equal groups are multiplied first; the separate extra amount is added afterward.
4 boxes hold 9 items each, then 11 more items are added. What is the total?
4 × 9 = 36; 36 + 11 = 47The equal groups are multiplied first; the separate extra amount is added afterward.
5 boxes hold 10 items each, then 3 more items are added. What is the total?
5 × 10 = 50; 50 + 3 = 53The equal groups are multiplied first; the separate extra amount is added afterward.
6 boxes hold 11 items each, then 4 more items are added. What is the total?
6 × 11 = 66; 66 + 4 = 70The equal groups are multiplied first; the separate extra amount is added afterward.
Practice
Guided practice with hints
012 boxes hold 12 items each, then 5 more items are added. What is the total?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2 × 12 = 24; 24 + 5 = 29
023 boxes hold 6 items each, then 6 more items are added. What is the total?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3 × 6 = 18; 18 + 6 = 24
034 boxes hold 7 items each, then 7 more items are added. What is the total?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4 × 7 = 28; 28 + 7 = 35
045 boxes hold 8 items each, then 8 more items are added. What is the total?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 5 × 8 = 40; 40 + 8 = 48
056 boxes hold 9 items each, then 9 more items are added. What is the total?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 6 × 9 = 54; 54 + 9 = 63
062 boxes hold 10 items each, then 10 more items are added. What is the total?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2 × 10 = 20; 20 + 10 = 30
Practice
Independent practice
013 boxes hold 11 items each, then 11 more items are added. What is the total?
Answer: 3 × 11 = 33; 33 + 11 = 44
024 boxes hold 12 items each, then 3 more items are added. What is the total?
Answer: 4 × 12 = 48; 48 + 3 = 51
035 boxes hold 6 items each, then 4 more items are added. What is the total?
Answer: 5 × 6 = 30; 30 + 4 = 34
046 boxes hold 7 items each, then 5 more items are added. What is the total?
Answer: 6 × 7 = 42; 42 + 5 = 47
052 boxes hold 6 items each, then 3 more items are added. What is the total?
Answer: 2 × 6 = 12; 12 + 3 = 15
063 boxes hold 7 items each, then 4 more items are added. What is the total?
Answer: 3 × 7 = 21; 21 + 4 = 25
074 boxes hold 8 items each, then 5 more items are added. What is the total?
Answer: 4 × 8 = 32; 32 + 5 = 37
085 boxes hold 9 items each, then 6 more items are added. What is the total?
Answer: 5 × 9 = 45; 45 + 6 = 51
Common mistakes
Learn to catch the error, not just the answer.
Identify what each number represents and how the quantities are related before selecting an operation.
Estimate, use an inverse operation, or compare with a second representation.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use solve multi-step whole-number problems when solving multi-step problems in measurement, data, money, design, or everyday quantitative decisions.
- Explain the result with units and a second check so another person can audit the reasoning.
Challenge problems
6 boxes hold 10 items each, then 7 more items are added. What is the total?
6 × 10 = 60; 60 + 7 = 67
2 boxes hold 11 items each, then 8 more items are added. What is the total?
2 × 11 = 22; 22 + 8 = 30
3 boxes hold 12 items each, then 9 more items are added. What is the total?
3 × 12 = 36; 36 + 9 = 45
4 boxes hold 6 items each, then 10 more items are added. What is the total?
4 × 6 = 24; 24 + 10 = 34
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain solve multi-step whole-number problems problems accurately, then check each result with a second method.
Practice
Mastery check
015 boxes hold 7 items each, then 11 more items are added. What is the total?
Answer: 5 × 7 = 35; 35 + 11 = 46
026 boxes hold 8 items each, then 3 more items are added. What is the total?
Answer: 6 × 8 = 48; 48 + 3 = 51
032 boxes hold 9 items each, then 4 more items are added. What is the total?
Answer: 2 × 9 = 18; 18 + 4 = 22
043 boxes hold 10 items each, then 5 more items are added. What is the total?
Answer: 3 × 10 = 30; 30 + 5 = 35
054 boxes hold 11 items each, then 6 more items are added. What is the total?
Answer: 4 × 11 = 44; 44 + 6 = 50
065 boxes hold 12 items each, then 7 more items are added. What is the total?
Answer: 5 × 12 = 60; 60 + 7 = 67
076 boxes hold 6 items each, then 8 more items are added. What is the total?
Answer: 6 × 6 = 36; 36 + 8 = 44
082 boxes hold 7 items each, then 9 more items are added. What is the total?
Answer: 2 × 7 = 14; 14 + 9 = 23
Terminology
Words to know
- representation
- A diagram, model, equation, table, graph, or other form showing a mathematical idea.
- strategy
- A purposeful method chosen to solve or analyze a problem.
- estimate
- A nearby value used to judge size or reasonableness.
- verify
- To confirm a result using a second calculation, representation, or logical check.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.