Grade 5 · Measurement & Data · MAT-05-MD-006
Make Line Plots with Fraction Data
Represent and solve make line plots with fraction data problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve make line plots with fraction data problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for make line plots with fraction data works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Make Line Plots with Fraction Data depends on treating fractions as numbers built from equal-sized units. The numerator counts those units and the denominator defines their size; operations are valid only when the units being combined are compatible.
Represent the idea
The Math Box uses data graph as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
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 one example of make line plots with fraction data in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
A line plot has 1 marks above 2 1/4. What is the frequency at that value?
Frequency = 1Each mark represents one measurement located at that number-line position.
A line plot has 2 marks above 2 2/4. What is the frequency at that value?
Frequency = 2Each mark represents one measurement located at that number-line position.
A line plot has 3 marks above 2 3/4. What is the frequency at that value?
Frequency = 3Each mark represents one measurement located at that number-line position.
A line plot has 4 marks above 2 1/4. What is the frequency at that value?
Frequency = 4Each mark represents one measurement located at that number-line position.
A line plot has 5 marks above 3 1/4. What is the frequency at that value?
Frequency = 5Each mark represents one measurement located at that number-line position.
A line plot has 6 marks above 3 2/4. What is the frequency at that value?
Frequency = 6Each mark represents one measurement located at that number-line position.
A line plot has 1 marks above 3 3/4. What is the frequency at that value?
Frequency = 1Each mark represents one measurement located at that number-line position.
A line plot has 2 marks above 3 1/4. What is the frequency at that value?
Frequency = 2Each mark represents one measurement located at that number-line position.
A line plot has 3 marks above 4 1/4. What is the frequency at that value?
Frequency = 3Each mark represents one measurement located at that number-line position.
A line plot has 4 marks above 4 2/4. What is the frequency at that value?
Frequency = 4Each mark represents one measurement located at that number-line position.
A line plot has 5 marks above 4 3/4. What is the frequency at that value?
Frequency = 5Each mark represents one measurement located at that number-line position.
A line plot has 6 marks above 4 1/4. What is the frequency at that value?
Frequency = 6Each mark represents one measurement located at that number-line position.
A line plot has 1 marks above 5 1/4. What is the frequency at that value?
Frequency = 1Each mark represents one measurement located at that number-line position.
A line plot has 2 marks above 5 2/4. What is the frequency at that value?
Frequency = 2Each mark represents one measurement located at that number-line position.
A line plot has 3 marks above 5 3/4. What is the frequency at that value?
Frequency = 3Each mark represents one measurement located at that number-line position.
A line plot has 4 marks above 5 1/4. What is the frequency at that value?
Frequency = 4Each mark represents one measurement located at that number-line position.
A line plot has 5 marks above 6 1/4. What is the frequency at that value?
Frequency = 5Each mark represents one measurement located at that number-line position.
A line plot has 6 marks above 6 2/4. What is the frequency at that value?
Frequency = 6Each mark represents one measurement located at that number-line position.
A line plot has 1 marks above 6 3/4. What is the frequency at that value?
Frequency = 1Each mark represents one measurement located at that number-line position.
A line plot has 2 marks above 6 1/4. What is the frequency at that value?
Frequency = 2Each mark represents one measurement located at that number-line position.
Practice
Guided practice with hints
01A line plot has 3 marks above 7 1/4. What is the frequency at that value?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Frequency = 3
02A line plot has 4 marks above 7 2/4. What is the frequency at that value?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Frequency = 4
03A line plot has 5 marks above 7 3/4. What is the frequency at that value?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Frequency = 5
04A line plot has 6 marks above 7 1/4. What is the frequency at that value?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Frequency = 6
05A line plot has 1 marks above 8 1/4. What is the frequency at that value?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Frequency = 1
06A line plot has 2 marks above 8 2/4. What is the frequency at that value?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: Frequency = 2
Practice
Independent practice
01A line plot has 3 marks above 8 3/4. What is the frequency at that value?
Answer: Frequency = 3
02A line plot has 4 marks above 8 1/4. What is the frequency at that value?
Answer: Frequency = 4
03A line plot has 5 marks above 9 1/4. What is the frequency at that value?
Answer: Frequency = 5
04A line plot has 6 marks above 9 2/4. What is the frequency at that value?
Answer: Frequency = 6
05A line plot has 1 marks above 9 3/4. What is the frequency at that value?
Answer: Frequency = 1
06A line plot has 2 marks above 9 1/4. What is the frequency at that value?
Answer: Frequency = 2
07A line plot has 3 marks above 10 1/4. What is the frequency at that value?
Answer: Frequency = 3
08A line plot has 4 marks above 10 2/4. What is the frequency at that value?
Answer: Frequency = 4
Common mistakes
Learn to catch the error, not just the answer.
Track the size of the fractional unit first; fractions can be combined only when the units are compatible.
Compare complete fraction values with a model, benchmark, common denominator, or cross-product reasoning.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Scale recipes, measurements, money, and data while preserving the meaning of the unit.
- Compare quantities that are not whole numbers in science, construction, shopping, and measurement.
Challenge problems
A line plot has 5 marks above 10 3/4. What is the frequency at that value?
Frequency = 5
A line plot has 6 marks above 10 1/4. What is the frequency at that value?
Frequency = 6
A line plot has 1 marks above 11 1/4. What is the frequency at that value?
Frequency = 1
A line plot has 2 marks above 11 2/4. What is the frequency at that value?
Frequency = 2
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain make line plots with fraction data problems accurately, then check each result with a second method.
Practice
Mastery check
01A line plot has 3 marks above 11 3/4. What is the frequency at that value?
Answer: Frequency = 3
02A line plot has 4 marks above 11 1/4. What is the frequency at that value?
Answer: Frequency = 4
03A line plot has 5 marks above 12 1/4. What is the frequency at that value?
Answer: Frequency = 5
04A line plot has 6 marks above 12 2/4. What is the frequency at that value?
Answer: Frequency = 6
05A line plot has 1 marks above 12 3/4. What is the frequency at that value?
Answer: Frequency = 1
06A line plot has 2 marks above 12 1/4. What is the frequency at that value?
Answer: Frequency = 2
07A line plot has 3 marks above 13 1/4. What is the frequency at that value?
Answer: Frequency = 3
08A line plot has 4 marks above 13 2/4. What is the frequency at that value?
Answer: Frequency = 4
Terminology
Words to know
- numerator
- The number of selected equal parts or unit fractions.
- denominator
- The number of equal parts that make one whole.
- equivalent fractions
- Different fraction names for the same numerical value.
- benchmark
- A familiar reference value such as 0, 1/2, or 1 used for comparison.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.