Grade 3 · Number & Operations—Fractions · MAT-03-NF-002
Build Fractions from Unit Fractions
Represent build fractions from unit fractions with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent build fractions from unit fractions with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving build fractions from unit fractions 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 Build Fractions from Unit Fractions
A fraction a/b is made from a copies of the unit fraction 1/b.
A reliable reasoning strategy
Keep the denominator fixed to define the part size, then count how many such parts are included.
Representations that should agree
Area models, set models, and number lines can all show repeated unit fractions. 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.
A whole has 3 equal parts and 2 are selected. What fraction is selected?
2 copies of 1/3 make 2/3.The denominator gives part size and the numerator counts selected parts.
A whole has 4 equal parts and 3 are selected. What fraction is selected?
3 copies of 1/4 make 3/4.The denominator gives part size and the numerator counts selected parts.
A whole has 6 equal parts and 4 are selected. What fraction is selected?
4 copies of 1/6 make 4/6.The denominator gives part size and the numerator counts selected parts.
A whole has 8 equal parts and 5 are selected. What fraction is selected?
5 copies of 1/8 make 5/8.The denominator gives part size and the numerator counts selected parts.
A whole has 2 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/2 make 1/2.The denominator gives part size and the numerator counts selected parts.
A whole has 3 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/3 make 1/3.The denominator gives part size and the numerator counts selected parts.
A whole has 4 equal parts and 2 are selected. What fraction is selected?
2 copies of 1/4 make 2/4.The denominator gives part size and the numerator counts selected parts.
A whole has 6 equal parts and 4 are selected. What fraction is selected?
4 copies of 1/6 make 4/6.The denominator gives part size and the numerator counts selected parts.
A whole has 8 equal parts and 3 are selected. What fraction is selected?
3 copies of 1/8 make 3/8.The denominator gives part size and the numerator counts selected parts.
A whole has 2 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/2 make 1/2.The denominator gives part size and the numerator counts selected parts.
A whole has 3 equal parts and 2 are selected. What fraction is selected?
2 copies of 1/3 make 2/3.The denominator gives part size and the numerator counts selected parts.
A whole has 4 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/4 make 1/4.The denominator gives part size and the numerator counts selected parts.
A whole has 6 equal parts and 4 are selected. What fraction is selected?
4 copies of 1/6 make 4/6.The denominator gives part size and the numerator counts selected parts.
A whole has 8 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/8 make 1/8.The denominator gives part size and the numerator counts selected parts.
A whole has 2 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/2 make 1/2.The denominator gives part size and the numerator counts selected parts.
A whole has 3 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/3 make 1/3.The denominator gives part size and the numerator counts selected parts.
A whole has 4 equal parts and 3 are selected. What fraction is selected?
3 copies of 1/4 make 3/4.The denominator gives part size and the numerator counts selected parts.
A whole has 6 equal parts and 4 are selected. What fraction is selected?
4 copies of 1/6 make 4/6.The denominator gives part size and the numerator counts selected parts.
A whole has 8 equal parts and 6 are selected. What fraction is selected?
6 copies of 1/8 make 6/8.The denominator gives part size and the numerator counts selected parts.
A whole has 2 equal parts and 1 are selected. What fraction is selected?
1 copies of 1/2 make 1/2.The denominator gives part size and the numerator counts selected parts.
Practice
Guided practice with hints
01A whole has 3 equal parts and 2 are selected. What fraction is selected?
Hint: Keep the denominator fixed to define the part size, then count how many such parts are included.
Answer: 2/3
02A whole has 4 equal parts and 3 are selected. What fraction is selected?
Hint: Keep the denominator fixed to define the part size, then count how many such parts are included.
Answer: 3/4
03A whole has 6 equal parts and 4 are selected. What fraction is selected?
Hint: Keep the denominator fixed to define the part size, then count how many such parts are included.
Answer: 4/6
04A whole has 8 equal parts and 7 are selected. What fraction is selected?
Hint: Keep the denominator fixed to define the part size, then count how many such parts are included.
Answer: 7/8
05A whole has 2 equal parts and 1 are selected. What fraction is selected?
Hint: Keep the denominator fixed to define the part size, then count how many such parts are included.
Answer: 1/2
06A whole has 3 equal parts and 1 are selected. What fraction is selected?
Hint: Keep the denominator fixed to define the part size, then count how many such parts are included.
Answer: 1/3
Practice
Independent practice
01A whole has 3 equal parts and 2 are selected. What fraction is selected?
Answer: 2/3
02A whole has 4 equal parts and 2 are selected. What fraction is selected?
Answer: 2/4
03A whole has 6 equal parts and 4 are selected. What fraction is selected?
Answer: 4/6
04A whole has 8 equal parts and 6 are selected. What fraction is selected?
Answer: 6/8
05A whole has 2 equal parts and 1 are selected. What fraction is selected?
Answer: 1/2
06A whole has 3 equal parts and 1 are selected. What fraction is selected?
Answer: 1/3
07A whole has 4 equal parts and 1 are selected. What fraction is selected?
Answer: 1/4
08A whole has 6 equal parts and 4 are selected. What fraction is selected?
Answer: 4/6
Common mistakes
Learn to catch the error, not just the answer.
Use the denominator for part size and the numerator for part count.
Reconnect the answer to build fractions from unit fractions and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Measure portions and describe selected equal parts precisely.
- Use build fractions from unit fractions to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
A whole has 3 equal parts and 2 are selected. What fraction is selected?
2/3
A whole has 4 equal parts and 1 are selected. What fraction is selected?
1/4
A whole has 6 equal parts and 4 are selected. What fraction is selected?
4/6
A whole has 8 equal parts and 5 are selected. What fraction is selected?
5/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Build Fractions from Unit Fractions Challenge
Solve and explain Grade 3 problems involving build fractions from unit fractions without relying on answer guessing.
Practice
Mastery check
01A whole has 3 equal parts and 2 are selected. What fraction is selected?
Answer: 2/3
02A whole has 4 equal parts and 3 are selected. What fraction is selected?
Answer: 3/4
03A whole has 6 equal parts and 4 are selected. What fraction is selected?
Answer: 4/6
04A whole has 8 equal parts and 4 are selected. What fraction is selected?
Answer: 4/8
05A whole has 2 equal parts and 1 are selected. What fraction is selected?
Answer: 1/2
06A whole has 3 equal parts and 1 are selected. What fraction is selected?
Answer: 1/3
07A whole has 4 equal parts and 2 are selected. What fraction is selected?
Answer: 2/4
08A whole has 6 equal parts and 4 are selected. What fraction is selected?
Answer: 4/6
Terminology
Words to know
- numerator
- The number of unit-fraction parts being counted.
- denominator
- The number of equal parts in the whole.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.NF.1
Primary standards alignment for Build Fractions from Unit Fractions.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.