Grade 3 · Number & Operations—Fractions · MAT-03-NF-005
Generate Equivalent Fractions with Models
Represent generate equivalent fractions with models with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent generate equivalent fractions with models with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving generate equivalent fractions with models 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 Generate Equivalent Fractions with Models
Equivalent fractions name the same number even though they use different-sized unit parts.
A reliable reasoning strategy
Use area models or number lines to show two fractions landing on the same amount or point.
Representations that should agree
Partitioning every existing part into the same number of smaller equal parts changes numerator and denominator together but not value. 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.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- build a model
- change one quantity
- predict before calculating
- explain why the result changes
Worked examples
Twenty different ways to see the concept work.
Are 1/3 and 2/6 equivalent?
1/3 and 2/6 name the same point or area.A model or number line places both fractions at the same value.
Are 2/3 and 4/6 equivalent?
2/3 and 4/6 name the same point or area.A model or number line places both fractions at the same value.
Are 1/4 and 2/8 equivalent?
1/4 and 2/8 name the same point or area.A model or number line places both fractions at the same value.
Are 3/4 and 6/8 equivalent?
3/4 and 6/8 name the same point or area.A model or number line places both fractions at the same value.
Are 1/2 and 2/4 equivalent?
1/2 and 2/4 name the same point or area.A model or number line places both fractions at the same value.
Are 1/3 and 2/6 equivalent?
1/3 and 2/6 name the same point or area.A model or number line places both fractions at the same value.
Are 2/3 and 4/6 equivalent?
2/3 and 4/6 name the same point or area.A model or number line places both fractions at the same value.
Are 1/4 and 2/8 equivalent?
1/4 and 2/8 name the same point or area.A model or number line places both fractions at the same value.
Are 3/4 and 6/8 equivalent?
3/4 and 6/8 name the same point or area.A model or number line places both fractions at the same value.
Are 1/2 and 2/4 equivalent?
1/2 and 2/4 name the same point or area.A model or number line places both fractions at the same value.
Are 1/3 and 2/6 equivalent?
1/3 and 2/6 name the same point or area.A model or number line places both fractions at the same value.
Are 2/3 and 4/6 equivalent?
2/3 and 4/6 name the same point or area.A model or number line places both fractions at the same value.
Are 1/4 and 2/8 equivalent?
1/4 and 2/8 name the same point or area.A model or number line places both fractions at the same value.
Are 3/4 and 6/8 equivalent?
3/4 and 6/8 name the same point or area.A model or number line places both fractions at the same value.
Are 1/2 and 2/4 equivalent?
1/2 and 2/4 name the same point or area.A model or number line places both fractions at the same value.
Are 1/3 and 2/6 equivalent?
1/3 and 2/6 name the same point or area.A model or number line places both fractions at the same value.
Are 2/3 and 4/6 equivalent?
2/3 and 4/6 name the same point or area.A model or number line places both fractions at the same value.
Are 1/4 and 2/8 equivalent?
1/4 and 2/8 name the same point or area.A model or number line places both fractions at the same value.
Are 3/4 and 6/8 equivalent?
3/4 and 6/8 name the same point or area.A model or number line places both fractions at the same value.
Are 1/2 and 2/4 equivalent?
1/2 and 2/4 name the same point or area.A model or number line places both fractions at the same value.
Practice
Guided practice with hints
01Are 1/3 and 2/6 equivalent?
Hint: Use area models or number lines to show two fractions landing on the same amount or point.
Answer: Yes
02Are 2/3 and 4/6 equivalent?
Hint: Use area models or number lines to show two fractions landing on the same amount or point.
Answer: Yes
03Are 1/4 and 2/8 equivalent?
Hint: Use area models or number lines to show two fractions landing on the same amount or point.
Answer: Yes
04Are 3/4 and 6/8 equivalent?
Hint: Use area models or number lines to show two fractions landing on the same amount or point.
Answer: Yes
05Are 1/2 and 2/4 equivalent?
Hint: Use area models or number lines to show two fractions landing on the same amount or point.
Answer: Yes
06Are 1/3 and 2/6 equivalent?
Hint: Use area models or number lines to show two fractions landing on the same amount or point.
Answer: Yes
Practice
Independent practice
01Are 1/3 and 2/6 equivalent?
Answer: Yes
02Are 2/3 and 4/6 equivalent?
Answer: Yes
03Are 1/4 and 2/8 equivalent?
Answer: Yes
04Are 3/4 and 6/8 equivalent?
Answer: Yes
05Are 1/2 and 2/4 equivalent?
Answer: Yes
06Are 1/3 and 2/6 equivalent?
Answer: Yes
07Are 2/3 and 4/6 equivalent?
Answer: Yes
08Are 1/4 and 2/8 equivalent?
Answer: Yes
Common mistakes
Learn to catch the error, not just the answer.
Check whether both fractions represent the same location or portion of the same whole.
Reconnect the answer to generate equivalent fractions with models and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Use different fraction labels for the same measured quantity.
- Use generate equivalent fractions with models to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Are 1/3 and 2/6 equivalent?
Yes
Are 2/3 and 4/6 equivalent?
Yes
Are 1/4 and 2/8 equivalent?
Yes
Are 3/4 and 6/8 equivalent?
Yes
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Generate Equivalent Fractions with Models Challenge
Solve and explain Grade 3 problems involving generate equivalent fractions with models without relying on answer guessing.
Practice
Mastery check
01Are 1/3 and 2/6 equivalent?
Answer: Yes
02Are 2/3 and 4/6 equivalent?
Answer: Yes
03Are 1/4 and 2/8 equivalent?
Answer: Yes
04Are 3/4 and 6/8 equivalent?
Answer: Yes
05Are 1/2 and 2/4 equivalent?
Answer: Yes
06Are 1/3 and 2/6 equivalent?
Answer: Yes
07Are 2/3 and 4/6 equivalent?
Answer: Yes
08Are 1/4 and 2/8 equivalent?
Answer: Yes
Terminology
Words to know
- equivalent fractions
- Different fractions that represent the same number.
- equivalence
- Equality of value despite different forms.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.NF.3.a-b
Primary standards alignment for Generate Equivalent Fractions with Models.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.