Grade 3 · Number & Operations—Fractions · MAT-03-NF-006
Express Whole Numbers as Fractions
Represent express whole numbers as fractions with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent express whole numbers as fractions with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving express whole numbers as 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 Express Whole Numbers as Fractions
A whole number can be written as a fraction when the numerator contains complete sets of denominator-sized parts.
A reliable reasoning strategy
One whole is b/b; two wholes are 2b/b, and the pattern continues.
Representations that should agree
Number lines make the connection visible because whole-number points can also carry fraction names. 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.
Write whole number 2 as a fraction with denominator 3.
2 = 6/3Each whole contains 3 copies of 1/3; 2 wholes contain 6 such parts.
Write whole number 3 as a fraction with denominator 4.
3 = 12/4Each whole contains 4 copies of 1/4; 3 wholes contain 12 such parts.
Write whole number 1 as a fraction with denominator 6.
1 = 6/6Each whole contains 6 copies of 1/6; 1 wholes contain 6 such parts.
Write whole number 2 as a fraction with denominator 8.
2 = 16/8Each whole contains 8 copies of 1/8; 2 wholes contain 16 such parts.
Write whole number 3 as a fraction with denominator 2.
3 = 6/2Each whole contains 2 copies of 1/2; 3 wholes contain 6 such parts.
Write whole number 1 as a fraction with denominator 3.
1 = 3/3Each whole contains 3 copies of 1/3; 1 wholes contain 3 such parts.
Write whole number 2 as a fraction with denominator 4.
2 = 8/4Each whole contains 4 copies of 1/4; 2 wholes contain 8 such parts.
Write whole number 3 as a fraction with denominator 6.
3 = 18/6Each whole contains 6 copies of 1/6; 3 wholes contain 18 such parts.
Write whole number 1 as a fraction with denominator 8.
1 = 8/8Each whole contains 8 copies of 1/8; 1 wholes contain 8 such parts.
Write whole number 2 as a fraction with denominator 2.
2 = 4/2Each whole contains 2 copies of 1/2; 2 wholes contain 4 such parts.
Write whole number 3 as a fraction with denominator 3.
3 = 9/3Each whole contains 3 copies of 1/3; 3 wholes contain 9 such parts.
Write whole number 1 as a fraction with denominator 4.
1 = 4/4Each whole contains 4 copies of 1/4; 1 wholes contain 4 such parts.
Write whole number 2 as a fraction with denominator 6.
2 = 12/6Each whole contains 6 copies of 1/6; 2 wholes contain 12 such parts.
Write whole number 3 as a fraction with denominator 8.
3 = 24/8Each whole contains 8 copies of 1/8; 3 wholes contain 24 such parts.
Write whole number 1 as a fraction with denominator 2.
1 = 2/2Each whole contains 2 copies of 1/2; 1 wholes contain 2 such parts.
Write whole number 2 as a fraction with denominator 3.
2 = 6/3Each whole contains 3 copies of 1/3; 2 wholes contain 6 such parts.
Write whole number 3 as a fraction with denominator 4.
3 = 12/4Each whole contains 4 copies of 1/4; 3 wholes contain 12 such parts.
Write whole number 1 as a fraction with denominator 6.
1 = 6/6Each whole contains 6 copies of 1/6; 1 wholes contain 6 such parts.
Write whole number 2 as a fraction with denominator 8.
2 = 16/8Each whole contains 8 copies of 1/8; 2 wholes contain 16 such parts.
Write whole number 3 as a fraction with denominator 2.
3 = 6/2Each whole contains 2 copies of 1/2; 3 wholes contain 6 such parts.
Practice
Guided practice with hints
01Write whole number 2 as a fraction with denominator 3.
Hint: One whole is b/b; two wholes are 2b/b, and the pattern continues.
Answer: 6/3
02Write whole number 3 as a fraction with denominator 4.
Hint: One whole is b/b; two wholes are 2b/b, and the pattern continues.
Answer: 12/4
03Write whole number 1 as a fraction with denominator 6.
Hint: One whole is b/b; two wholes are 2b/b, and the pattern continues.
Answer: 6/6
04Write whole number 2 as a fraction with denominator 8.
Hint: One whole is b/b; two wholes are 2b/b, and the pattern continues.
Answer: 16/8
05Write whole number 3 as a fraction with denominator 2.
Hint: One whole is b/b; two wholes are 2b/b, and the pattern continues.
Answer: 6/2
06Write whole number 1 as a fraction with denominator 3.
Hint: One whole is b/b; two wholes are 2b/b, and the pattern continues.
Answer: 3/3
Practice
Independent practice
01Write whole number 1 as a fraction with denominator 3.
Answer: 3/3
02Write whole number 2 as a fraction with denominator 4.
Answer: 8/4
03Write whole number 3 as a fraction with denominator 6.
Answer: 18/6
04Write whole number 1 as a fraction with denominator 8.
Answer: 8/8
05Write whole number 2 as a fraction with denominator 2.
Answer: 4/2
06Write whole number 3 as a fraction with denominator 3.
Answer: 9/3
07Write whole number 1 as a fraction with denominator 4.
Answer: 4/4
08Write whole number 2 as a fraction with denominator 6.
Answer: 12/6
Common mistakes
Learn to catch the error, not just the answer.
Count how many unit fractions fit into each whole and into all wholes being named.
Reconnect the answer to express whole numbers as fractions and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Translate between whole-number and fraction labels on measurements.
- Use express whole numbers as fractions to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
Write whole number 3 as a fraction with denominator 3.
9/3
Write whole number 1 as a fraction with denominator 4.
4/4
Write whole number 2 as a fraction with denominator 6.
12/6
Write whole number 3 as a fraction with denominator 8.
24/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Express Whole Numbers as Fractions Challenge
Solve and explain Grade 3 problems involving express whole numbers as fractions without relying on answer guessing.
Practice
Mastery check
01Write whole number 2 as a fraction with denominator 3.
Answer: 6/3
02Write whole number 3 as a fraction with denominator 4.
Answer: 12/4
03Write whole number 1 as a fraction with denominator 6.
Answer: 6/6
04Write whole number 2 as a fraction with denominator 8.
Answer: 16/8
05Write whole number 3 as a fraction with denominator 2.
Answer: 6/2
06Write whole number 1 as a fraction with denominator 3.
Answer: 3/3
07Write whole number 2 as a fraction with denominator 4.
Answer: 8/4
08Write whole number 3 as a fraction with denominator 6.
Answer: 18/6
Terminology
Words to know
- whole-number fraction
- A fraction whose value is a whole number.
- complete whole
- All equal parts needed to make one full unit.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.NF.3.c
Primary standards alignment for Express Whole Numbers as Fractions.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.