Grade 3 · Number & Operations—Fractions · MAT-03-NF-004
Locate Fractions a/b on a Number Line
Represent locate fractions a/b on a number line with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent locate fractions a/b on a number line with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving locate fractions a/b on a number line 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 Locate Fractions a/b on a Number Line
A fraction a/b is located by taking a steps of size 1/b from zero.
A reliable reasoning strategy
Partition each whole into b equal intervals, then count a intervals from 0.
Representations that should agree
Fractions greater than one continue naturally past 1 using the same unit-fraction step size. 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.
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.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- 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 number line is marked in steps of 1/3. Where do 1 equal steps from 0 land?
1 × 1/3 = 1/3.1 equal intervals of length 1/3 accumulate to 1/3.
A number line is marked in steps of 1/3. Where do 2 equal steps from 0 land?
2 × 1/3 = 2/3.2 equal intervals of length 1/3 accumulate to 2/3.
A number line is marked in steps of 1/4. Where do 3 equal steps from 0 land?
3 × 1/4 = 3/4.3 equal intervals of length 1/4 accumulate to 3/4.
A number line is marked in steps of 1/4. Where do 5 equal steps from 0 land?
5 × 1/4 = 5/4.5 equal intervals of length 1/4 accumulate to 5/4, which lies beyond 1.
A number line is marked in steps of 1/2. Where do 3 equal steps from 0 land?
3 × 1/2 = 3/2.3 equal intervals of length 1/2 accumulate to 3/2, which lies beyond 1.
A number line is marked in steps of 1/2. Where do 5 equal steps from 0 land?
5 × 1/2 = 5/2.5 equal intervals of length 1/2 accumulate to 5/2, which lies beyond 1.
A number line is marked in steps of 1/3. Where do 7 equal steps from 0 land?
7 × 1/3 = 7/3.7 equal intervals of length 1/3 accumulate to 7/3, which lies beyond 1.
A number line is marked in steps of 1/5. Where do 4 equal steps from 0 land?
4 × 1/5 = 4/5.4 equal intervals of length 1/5 accumulate to 4/5.
A number line is marked in steps of 1/5. Where do 6 equal steps from 0 land?
6 × 1/5 = 6/5.6 equal intervals of length 1/5 accumulate to 6/5, which lies beyond 1.
A number line is marked in steps of 1/8. Where do 7 equal steps from 0 land?
7 × 1/8 = 7/8.7 equal intervals of length 1/8 accumulate to 7/8.
A number line is marked in steps of 1/8. Where do 9 equal steps from 0 land?
9 × 1/8 = 9/8.9 equal intervals of length 1/8 accumulate to 9/8, which lies beyond 1.
A number line is marked in steps of 1/6. Where do 5 equal steps from 0 land?
5 × 1/6 = 5/6.5 equal intervals of length 1/6 accumulate to 5/6.
A number line is marked in steps of 1/6. Where do 7 equal steps from 0 land?
7 × 1/6 = 7/6.7 equal intervals of length 1/6 accumulate to 7/6, which lies beyond 1.
A number line is marked in steps of 1/3. Where do 4 equal steps from 0 land?
4 × 1/3 = 4/3.4 equal intervals of length 1/3 accumulate to 4/3, which lies beyond 1.
A number line is marked in steps of 1/3. Where do 8 equal steps from 0 land?
8 × 1/3 = 8/3.8 equal intervals of length 1/3 accumulate to 8/3, which lies beyond 1.
A number line is marked in steps of 1/5. Where do 3 equal steps from 0 land?
3 × 1/5 = 3/5.3 equal intervals of length 1/5 accumulate to 3/5.
A number line is marked in steps of 1/10. Where do 9 equal steps from 0 land?
9 × 1/10 = 9/10.9 equal intervals of length 1/10 accumulate to 9/10.
A number line is marked in steps of 1/10. Where do 11 equal steps from 0 land?
11 × 1/10 = 11/10.11 equal intervals of length 1/10 accumulate to 11/10, which lies beyond 1.
A number line is marked in steps of 1/12. Where do 5 equal steps from 0 land?
5 × 1/12 = 5/12.5 equal intervals of length 1/12 accumulate to 5/12.
A number line is marked in steps of 1/12. Where do 13 equal steps from 0 land?
13 × 1/12 = 13/12.13 equal intervals of length 1/12 accumulate to 13/12, which lies beyond 1.
Practice
Guided practice with hints
01On a number line marked in 3 equal parts per whole, what fraction is 4 steps from 0?
Hint: Partition each whole into b equal intervals, then count a intervals from 0.
Answer: 4/3
02On a number line marked in 4 equal parts per whole, what fraction is 3 steps from 0?
Hint: Partition each whole into b equal intervals, then count a intervals from 0.
Answer: 3/4
03On a number line marked in 6 equal parts per whole, what fraction is 6 steps from 0?
Hint: Partition each whole into b equal intervals, then count a intervals from 0.
Answer: 6/6
04On a number line marked in 8 equal parts per whole, what fraction is 8 steps from 0?
Hint: Partition each whole into b equal intervals, then count a intervals from 0.
Answer: 8/8
05On a number line marked in 2 equal parts per whole, what fraction is 3 steps from 0?
Hint: Partition each whole into b equal intervals, then count a intervals from 0.
Answer: 3/2
06On a number line marked in 3 equal parts per whole, what fraction is 1 steps from 0?
Hint: Partition each whole into b equal intervals, then count a intervals from 0.
Answer: 1/3
Practice
Independent practice
01On a number line marked in 3 equal parts per whole, what fraction is 4 steps from 0?
Answer: 4/3
02On a number line marked in 4 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/4
03On a number line marked in 6 equal parts per whole, what fraction is 5 steps from 0?
Answer: 5/6
04On a number line marked in 8 equal parts per whole, what fraction is 1 steps from 0?
Answer: 1/8
05On a number line marked in 2 equal parts per whole, what fraction is 2 steps from 0?
Answer: 2/2
06On a number line marked in 3 equal parts per whole, what fraction is 1 steps from 0?
Answer: 1/3
07On a number line marked in 4 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/4
08On a number line marked in 6 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/6
Common mistakes
Learn to catch the error, not just the answer.
Start at 0 and count spaces of size 1/b, not labels or marks alone.
Reconnect the answer to locate fractions a/b on a number line and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Read fractional measurements and distances.
- Use locate fractions a/b on a number line to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
On a number line marked in 3 equal parts per whole, what fraction is 4 steps from 0?
4/3
On a number line marked in 4 equal parts per whole, what fraction is 3 steps from 0?
3/4
On a number line marked in 6 equal parts per whole, what fraction is 4 steps from 0?
4/6
On a number line marked in 8 equal parts per whole, what fraction is 3 steps from 0?
3/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Locate Fractions a/b on a Number Line Challenge
Solve and explain Grade 3 problems involving locate fractions a/b on a number line without relying on answer guessing.
Practice
Mastery check
01On a number line marked in 3 equal parts per whole, what fraction is 4 steps from 0?
Answer: 4/3
02On a number line marked in 4 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/4
03On a number line marked in 6 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/6
04On a number line marked in 8 equal parts per whole, what fraction is 5 steps from 0?
Answer: 5/8
05On a number line marked in 2 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/2
06On a number line marked in 3 equal parts per whole, what fraction is 1 steps from 0?
Answer: 1/3
07On a number line marked in 4 equal parts per whole, what fraction is 3 steps from 0?
Answer: 3/4
08On a number line marked in 6 equal parts per whole, what fraction is 1 steps from 0?
Answer: 1/6
Terminology
Words to know
- fraction point
- The position of a fraction on a number line.
- interval
- The distance between two number-line points.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.NF.2.b
Primary standards alignment for Locate Fractions a/b on a Number Line.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.