Grade 3 · Mathematical Practice & Problem Solving · MAT-03-MP-001
Model Grade 3 Problems with Mathematics
Represent model grade 3 problems with mathematics with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent model grade 3 problems with mathematics with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving model grade 3 problems with mathematics 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 Model Grade 3 Problems with Mathematics
A mathematical model represents important quantities and relationships with drawings, tables, equations, graphs, or diagrams.
A reliable reasoning strategy
Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Representations that should agree
A strong model can reveal whether multiplication, division, fractions, measurement, or another idea is appropriate. 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.
Choose an equation for 3 bags with 5 apples in each bag and state the total.
3 × 5 = 15Equal groups are represented by multiplication.
Choose an equation for 4 bags with 7 apples in each bag and state the total.
4 × 7 = 28Equal groups are represented by multiplication.
Choose an equation for 5 bags with 9 apples in each bag and state the total.
5 × 9 = 45Equal groups are represented by multiplication.
Choose an equation for 6 bags with 4 apples in each bag and state the total.
6 × 4 = 24Equal groups are represented by multiplication.
Choose an equation for 7 bags with 6 apples in each bag and state the total.
7 × 6 = 42Equal groups are represented by multiplication.
Choose an equation for 2 bags with 8 apples in each bag and state the total.
2 × 8 = 16Equal groups are represented by multiplication.
Choose an equation for 3 bags with 3 apples in each bag and state the total.
3 × 3 = 9Equal groups are represented by multiplication.
Choose an equation for 4 bags with 5 apples in each bag and state the total.
4 × 5 = 20Equal groups are represented by multiplication.
Choose an equation for 5 bags with 7 apples in each bag and state the total.
5 × 7 = 35Equal groups are represented by multiplication.
Choose an equation for 6 bags with 9 apples in each bag and state the total.
6 × 9 = 54Equal groups are represented by multiplication.
Choose an equation for 7 bags with 4 apples in each bag and state the total.
7 × 4 = 28Equal groups are represented by multiplication.
Choose an equation for 2 bags with 6 apples in each bag and state the total.
2 × 6 = 12Equal groups are represented by multiplication.
Choose an equation for 3 bags with 8 apples in each bag and state the total.
3 × 8 = 24Equal groups are represented by multiplication.
Choose an equation for 4 bags with 3 apples in each bag and state the total.
4 × 3 = 12Equal groups are represented by multiplication.
Choose an equation for 5 bags with 5 apples in each bag and state the total.
5 × 5 = 25Equal groups are represented by multiplication.
Choose an equation for 6 bags with 7 apples in each bag and state the total.
6 × 7 = 42Equal groups are represented by multiplication.
Choose an equation for 7 bags with 9 apples in each bag and state the total.
7 × 9 = 63Equal groups are represented by multiplication.
Choose an equation for 2 bags with 4 apples in each bag and state the total.
2 × 4 = 8Equal groups are represented by multiplication.
Choose an equation for 3 bags with 6 apples in each bag and state the total.
3 × 6 = 18Equal groups are represented by multiplication.
Choose an equation for 4 bags with 8 apples in each bag and state the total.
4 × 8 = 32Equal groups are represented by multiplication.
Practice
Guided practice with hints
01Choose an equation for 3 bags with 9 apples in each bag and state the total.
Hint: Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Answer: 3 × 9 = 27
02Choose an equation for 4 bags with 4 apples in each bag and state the total.
Hint: Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Answer: 4 × 4 = 16
03Choose an equation for 5 bags with 6 apples in each bag and state the total.
Hint: Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Answer: 5 × 6 = 30
04Choose an equation for 6 bags with 8 apples in each bag and state the total.
Hint: Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Answer: 6 × 8 = 48
05Choose an equation for 7 bags with 3 apples in each bag and state the total.
Hint: Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Answer: 7 × 3 = 21
06Choose an equation for 2 bags with 5 apples in each bag and state the total.
Hint: Choose a representation that exposes the structure of the problem, solve within the model, then interpret the result in context.
Answer: 2 × 5 = 10
Practice
Independent practice
01Choose an equation for 5 bags with 7 apples in each bag and state the total.
Answer: 5 × 7 = 35
02Choose an equation for 6 bags with 9 apples in each bag and state the total.
Answer: 6 × 9 = 54
03Choose an equation for 7 bags with 4 apples in each bag and state the total.
Answer: 7 × 4 = 28
04Choose an equation for 2 bags with 6 apples in each bag and state the total.
Answer: 2 × 6 = 12
05Choose an equation for 3 bags with 8 apples in each bag and state the total.
Answer: 3 × 8 = 24
06Choose an equation for 4 bags with 3 apples in each bag and state the total.
Answer: 4 × 3 = 12
07Choose an equation for 5 bags with 5 apples in each bag and state the total.
Answer: 5 × 5 = 25
08Choose an equation for 6 bags with 7 apples in each bag and state the total.
Answer: 6 × 7 = 42
Common mistakes
Learn to catch the error, not just the answer.
Include only quantities and relationships needed to answer the question.
Reconnect the answer to model grade 3 problems with mathematics and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Translate real situations into solvable mathematical structures.
- Use model grade 3 problems with mathematics to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Choose an equation for 7 bags with 5 apples in each bag and state the total.
7 × 5 = 35
Choose an equation for 2 bags with 7 apples in each bag and state the total.
2 × 7 = 14
Choose an equation for 3 bags with 9 apples in each bag and state the total.
3 × 9 = 27
Choose an equation for 4 bags with 4 apples in each bag and state the total.
4 × 4 = 16
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Model Grade 3 Problems with Mathematics Challenge
Solve and explain Grade 3 problems involving model grade 3 problems with mathematics without relying on answer guessing.
Practice
Mastery check
01Choose an equation for 3 bags with 3 apples in each bag and state the total.
Answer: 3 × 3 = 9
02Choose an equation for 4 bags with 5 apples in each bag and state the total.
Answer: 4 × 5 = 20
03Choose an equation for 5 bags with 7 apples in each bag and state the total.
Answer: 5 × 7 = 35
04Choose an equation for 6 bags with 9 apples in each bag and state the total.
Answer: 6 × 9 = 54
05Choose an equation for 7 bags with 4 apples in each bag and state the total.
Answer: 7 × 4 = 28
06Choose an equation for 2 bags with 6 apples in each bag and state the total.
Answer: 2 × 6 = 12
07Choose an equation for 3 bags with 8 apples in each bag and state the total.
Answer: 3 × 8 = 24
08Choose an equation for 4 bags with 3 apples in each bag and state the total.
Answer: 4 × 3 = 12
Terminology
Words to know
- mathematical model
- A mathematical representation of a real or imagined situation.
- representation
- A way to show a mathematical idea, such as a diagram or equation.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, MP.1, MP.4
Primary standards alignment for Model Grade 3 Problems with Mathematics.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.