Grade 3 · Measurement & Data · MAT-03-MD-006
Make Line Plots with Fractional Units
Represent make line plots with fractional units with words, symbols, diagrams, or models appropriate to Grade 3.
Learning objectives
What you should be able to do
- Represent make line plots with fractional units with words, symbols, diagrams, or models appropriate to Grade 3.
- Solve problems involving make line plots with fractional units 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 Make Line Plots with Fractional Units
A line plot organizes measurements along a number line and shows how often each value occurs.
A reliable reasoning strategy
Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Representations that should agree
Fraction knowledge is essential because measured lengths may fall between whole-number marks. 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.
Data & Graph Lab
Adjust category values and read the graph numerically.
- 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 line plot has 2 X marks above 2 1/4. What is the frequency of 2 1/4?
2Each X represents one measurement at that value.
A line plot has 5 X marks above 3 1/2. What is the frequency of 3 1/2?
5Count the marks stacked above the value.
There are 4 marks above 1 3/4 and 1 mark above 2. How many measurements are shown?
4 + 1 = 5Total frequency is the sum of the marks.
A plot shows 3 marks at 4 1/4 and 6 marks at 4 1/2. Which value occurs more often?
4 1/2Six marks is a greater frequency than three marks.
A plot has 7 marks at 2 1/2 and 4 marks at 2 3/4. What is the difference in frequency?
7 − 4 = 3Subtract the smaller frequency from the larger.
A line plot uses quarter-unit intervals. What value comes after 3 1/2?
3 3/4Adding one quarter to 3 1/2 gives 3 3/4.
A line plot uses half-unit intervals. What value lies between 5 and 6?
5 1/2The midpoint on half-unit intervals is five and one-half.
A plot shows measurements 2 1/4, 2 1/4, 2 1/2, 2 3/4. How many marks belong above 2 1/4?
2The value 2 1/4 appears twice.
Data are 3, 3 1/2, 3 1/2, 4. Which value has the greatest frequency?
3 1/2It occurs twice while the others occur once.
A line plot has one mark at each of 1 1/4, 1 1/2, and 1 3/4. How many data points are represented?
3Each mark represents one observation.
There are 6 marks above 7 1/2. If two measurements are removed, how many marks remain?
6 − 2 = 4Removing two data points reduces frequency by two.
A plot has 3 marks above 2 and 3 marks above 2 1/2. Do the values have equal frequency?
Yes.Both positions have three observations.
A line plot has 2 marks at 1 1/4, 4 at 1 1/2, and 1 at 1 3/4. How many total measurements?
2 + 4 = 6; then 6 + 1 = 7Add all category frequencies.
Which point is farther right on a number-line plot: 3 1/4 or 3 3/4?
3 3/4Larger values lie farther to the right.
A plot uses quarter units. How many quarter-steps are there from 2 to 3?
4Four intervals of 1/4 make one whole unit.
A plot has 5 marks at 6 1/4 and 2 at 6 3/4. How many more measurements are at 6 1/4?
5 − 2 = 3Frequency difference is three.
A data set is 1 1/2, 2, 2, 2 1/2, 3. How many X marks should appear at 2?
2The value 2 occurs twice in the data set.
A line plot has no mark above 4 3/4. What is the frequency of that value?
0No observations were recorded at that position.
A plot shows 8 total X marks spread across four positions. What does 8 represent?
The total number of measurements.Each X corresponds to one observation.
Why must line-plot tick marks be equally spaced?
Equal spacing represents equal numerical intervals.Unequal spacing would distort the numerical distances between values.
Practice
Guided practice with hints
01A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
Hint: Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Answer: 2
02A line plot has 3 marks above 2 1/2. What is the frequency of 2 1/2?
Hint: Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Answer: 3
03A line plot has 4 marks above 2 3/4. What is the frequency of 2 3/4?
Hint: Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Answer: 4
04A line plot has 5 marks above 3. What is the frequency of 3?
Hint: Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Answer: 5
05A line plot has 1 marks above 2. What is the frequency of 2?
Hint: Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Answer: 1
06A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
Hint: Choose a scale that includes halves or fourths, place one mark for each measurement, then read frequencies and differences.
Answer: 2
Practice
Independent practice
01A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
Answer: 2
02A line plot has 3 marks above 2 1/2. What is the frequency of 2 1/2?
Answer: 3
03A line plot has 4 marks above 2 3/4. What is the frequency of 2 3/4?
Answer: 4
04A line plot has 5 marks above 3. What is the frequency of 3?
Answer: 5
05A line plot has 1 marks above 2. What is the frequency of 2?
Answer: 1
06A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
Answer: 2
07A line plot has 3 marks above 2 1/2. What is the frequency of 2 1/2?
Answer: 3
08A line plot has 4 marks above 2 3/4. What is the frequency of 2 3/4?
Answer: 4
Common mistakes
Learn to catch the error, not just the answer.
Build an evenly spaced number line before plotting any data.
Reconnect the answer to make line plots with fractional units and verify that the model, calculation, and label describe the same quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Summarize repeated length measurements.
- Use make line plots with fractional units to interpret or solve a Grade 3 situation with quantities, diagrams, measurements, or data.
Challenge problems
A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
2
A line plot has 3 marks above 2 1/2. What is the frequency of 2 1/2?
3
A line plot has 4 marks above 2 3/4. What is the frequency of 2 3/4?
4
A line plot has 5 marks above 3. What is the frequency of 3?
5
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Make Line Plots with Fractional Units Challenge
Solve and explain Grade 3 problems involving make line plots with fractional units without relying on answer guessing.
Practice
Mastery check
01A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
Answer: 2
02A line plot has 3 marks above 2 1/2. What is the frequency of 2 1/2?
Answer: 3
03A line plot has 4 marks above 2 3/4. What is the frequency of 2 3/4?
Answer: 4
04A line plot has 5 marks above 3. What is the frequency of 3?
Answer: 5
05A line plot has 1 marks above 2. What is the frequency of 2?
Answer: 1
06A line plot has 2 marks above 2 1/4. What is the frequency of 2 1/4?
Answer: 2
07A line plot has 3 marks above 2 1/2. What is the frequency of 2 1/2?
Answer: 3
08A line plot has 4 marks above 2 3/4. What is the frequency of 2 3/4?
Answer: 4
Terminology
Words to know
- line plot
- A display that marks frequencies above positions on a number line.
- frequency
- How many times a value occurs.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 3, 3.MD.4
Primary standards alignment for Make Line Plots with Fractional Units.2023 Mathematics Framework for California Public Schools
Instructional emphasis on reasoning, representations, problem solving, and equitable access.