Grade 3 · Number & Operations—Fractions · MAT-03-NF-003
Locate Unit Fractions on a Number Line
Represent locate unit fractions 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 unit fractions on a number line with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving locate unit fractions 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 Unit Fractions on a Number Line
A unit fraction is a distance from 0 on a number line, not only a shaded piece of a shape.
A reliable reasoning strategy
Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Representations that should agree
Each step on the partitioned line has length 1/b, so repeated steps create larger 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.
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.
From 0 to 1, the line is split into 2 equal intervals. What value is at the first tick after 0?
One interval has length 1/2, so the point is 1/2.Dividing one whole unit into 2 equal intervals makes every interval length 1/2.
From 0 to 1, the line is split into 3 equal intervals. What value is at the first partition point after 0?
One interval has length 1/3, so the point is 1/3.Dividing one whole unit into 3 equal intervals makes every interval length 1/3.
From 0 to 1, the line is split into 4 equal intervals. What value is at the one equal jump from 0?
One interval has length 1/4, so the point is 1/4.Dividing one whole unit into 4 equal intervals makes every interval length 1/4.
From 0 to 1, the line is split into 5 equal intervals. What value is at the endpoint of one unit-fraction step?
One interval has length 1/5, so the point is 1/5.Dividing one whole unit into 5 equal intervals makes every interval length 1/5.
From 0 to 1, the line is split into 6 equal intervals. What value is at the location reached after one equal interval?
One interval has length 1/6, so the point is 1/6.Dividing one whole unit into 6 equal intervals makes every interval length 1/6.
From 0 to 1, the line is split into 7 equal intervals. What value is at the first tick after 0?
One interval has length 1/7, so the point is 1/7.Dividing one whole unit into 7 equal intervals makes every interval length 1/7.
From 0 to 1, the line is split into 8 equal intervals. What value is at the first partition point after 0?
One interval has length 1/8, so the point is 1/8.Dividing one whole unit into 8 equal intervals makes every interval length 1/8.
From 0 to 1, the line is split into 9 equal intervals. What value is at the one equal jump from 0?
One interval has length 1/9, so the point is 1/9.Dividing one whole unit into 9 equal intervals makes every interval length 1/9.
From 0 to 1, the line is split into 10 equal intervals. What value is at the endpoint of one unit-fraction step?
One interval has length 1/10, so the point is 1/10.Dividing one whole unit into 10 equal intervals makes every interval length 1/10.
From 0 to 1, the line is split into 12 equal intervals. What value is at the location reached after one equal interval?
One interval has length 1/12, so the point is 1/12.Dividing one whole unit into 12 equal intervals makes every interval length 1/12.
From 0 to 1, the line is split into 3 equal intervals. What value is at the first tick after 0?
One interval has length 1/3, so the point is 1/3.Dividing one whole unit into 3 equal intervals makes every interval length 1/3.
From 0 to 1, the line is split into 4 equal intervals. What value is at the first partition point after 0?
One interval has length 1/4, so the point is 1/4.Dividing one whole unit into 4 equal intervals makes every interval length 1/4.
From 0 to 1, the line is split into 5 equal intervals. What value is at the one equal jump from 0?
One interval has length 1/5, so the point is 1/5.Dividing one whole unit into 5 equal intervals makes every interval length 1/5.
From 0 to 1, the line is split into 6 equal intervals. What value is at the endpoint of one unit-fraction step?
One interval has length 1/6, so the point is 1/6.Dividing one whole unit into 6 equal intervals makes every interval length 1/6.
From 0 to 1, the line is split into 8 equal intervals. What value is at the location reached after one equal interval?
One interval has length 1/8, so the point is 1/8.Dividing one whole unit into 8 equal intervals makes every interval length 1/8.
From 0 to 1, the line is split into 10 equal intervals. What value is at the first tick after 0?
One interval has length 1/10, so the point is 1/10.Dividing one whole unit into 10 equal intervals makes every interval length 1/10.
From 0 to 1, the line is split into 12 equal intervals. What value is at the first partition point after 0?
One interval has length 1/12, so the point is 1/12.Dividing one whole unit into 12 equal intervals makes every interval length 1/12.
From 0 to 1, the line is split into 7 equal intervals. What value is at the one equal jump from 0?
One interval has length 1/7, so the point is 1/7.Dividing one whole unit into 7 equal intervals makes every interval length 1/7.
From 0 to 1, the line is split into 9 equal intervals. What value is at the endpoint of one unit-fraction step?
One interval has length 1/9, so the point is 1/9.Dividing one whole unit into 9 equal intervals makes every interval length 1/9.
From 0 to 1, the line is split into 11 equal intervals. What value is at the location reached after one equal interval?
One interval has length 1/11, so the point is 1/11.Dividing one whole unit into 11 equal intervals makes every interval length 1/11.
Practice
Guided practice with hints
01The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
Hint: Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Answer: 1/3
02The interval 0 to 1 is split into 4 equal spaces. What number is at the first partition point after 0?
Hint: Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Answer: 1/4
03The interval 0 to 1 is split into 6 equal spaces. What number is at the first partition point after 0?
Hint: Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Answer: 1/6
04The interval 0 to 1 is split into 8 equal spaces. What number is at the first partition point after 0?
Hint: Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Answer: 1/8
05The interval 0 to 1 is split into 2 equal spaces. What number is at the first partition point after 0?
Hint: Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Answer: 1/2
06The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
Hint: Define 0 to 1 as one whole, divide that interval into equal parts, and locate the first partition point.
Answer: 1/3
Practice
Independent practice
01The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
Answer: 1/3
02The interval 0 to 1 is split into 4 equal spaces. What number is at the first partition point after 0?
Answer: 1/4
03The interval 0 to 1 is split into 6 equal spaces. What number is at the first partition point after 0?
Answer: 1/6
04The interval 0 to 1 is split into 8 equal spaces. What number is at the first partition point after 0?
Answer: 1/8
05The interval 0 to 1 is split into 2 equal spaces. What number is at the first partition point after 0?
Answer: 1/2
06The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
Answer: 1/3
07The interval 0 to 1 is split into 4 equal spaces. What number is at the first partition point after 0?
Answer: 1/4
08The interval 0 to 1 is split into 6 equal spaces. What number is at the first partition point after 0?
Answer: 1/6
Common mistakes
Learn to catch the error, not just the answer.
Partition the whole interval from 0 to 1 into equal lengths.
Reconnect the answer to locate unit fractions 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
- Measure fractional distances along a path or ruler.
- Use locate unit fractions on a number line to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
1/3
The interval 0 to 1 is split into 4 equal spaces. What number is at the first partition point after 0?
1/4
The interval 0 to 1 is split into 6 equal spaces. What number is at the first partition point after 0?
1/6
The interval 0 to 1 is split into 8 equal spaces. What number is at the first partition point after 0?
1/8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Locate Unit Fractions on a Number Line Challenge
Solve and explain Grade 3 problems involving locate unit fractions on a number line without relying on answer guessing.
Practice
Mastery check
01The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
Answer: 1/3
02The interval 0 to 1 is split into 4 equal spaces. What number is at the first partition point after 0?
Answer: 1/4
03The interval 0 to 1 is split into 6 equal spaces. What number is at the first partition point after 0?
Answer: 1/6
04The interval 0 to 1 is split into 8 equal spaces. What number is at the first partition point after 0?
Answer: 1/8
05The interval 0 to 1 is split into 2 equal spaces. What number is at the first partition point after 0?
Answer: 1/2
06The interval 0 to 1 is split into 3 equal spaces. What number is at the first partition point after 0?
Answer: 1/3
07The interval 0 to 1 is split into 4 equal spaces. What number is at the first partition point after 0?
Answer: 1/4
08The interval 0 to 1 is split into 6 equal spaces. What number is at the first partition point after 0?
Answer: 1/6
Terminology
Words to know
- number line
- A line on which positions represent numbers.
- unit interval
- The distance from 0 to 1 used as one whole.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.NF.2.a
Primary standards alignment for Locate Unit Fractions on a Number Line.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.