Mission 3 · Unit 2

Fraction Meanings

6.NS.A.1 · Unit 2
Today's objective: Interpret a fraction as division and as a quantity of equal parts.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

The art teacher is mixing paint for a hallway mural. She has 3/4 of a gallon of blue paint and 5/8 of a gallon of yellow paint. She needs to figure out which color she has more of, how much paint she has in total, and where each amount falls on a number line from 0 to 1. Your team must represent both fractions at least three different ways and prove which is greater.

Mural Paint Mixing Which color do we have more of? 3/4 Blue 5/8 Yellow Bar Models 3/4 = 6/8 5/8 Number Line 0 4/8 1 5/8 3/4 Area Model: 3/4 Area Model: 5/8 3/4 > 5/8 because 6/8 > 5/8

Team Roles

Facilitator Reads the paint problem aloud, checks that the team creates all three representations, and manages the timer.
Model Builder Draws fraction bar models, an area model, and a number line. Labels every part carefully with the fraction name.
Precision Checker Checks that all parts are equal size in each model, verifies equivalent fractions, and confirms the comparison symbol is correct.
Reporter Prepares the defense: explains which fraction is greater and why, shows all three representations, and shares one correction the team made.

Investigation

The Problem

The art teacher has 3/4 gallon of blue paint and 5/8 gallon of yellow paint.

Your tasks:

  1. Represent 3/4 and 5/8 using a fraction bar model (equal parts shaded).
  2. Place both fractions on the same number line (0 to 1).
  3. Draw an area model for each fraction.
  4. Find an equivalent fraction so both have the same denominator.
  5. Compare: which amount of paint is greater? Write the comparison with < or >.
  6. Find the total paint: 3/4 + 5/8 = ?
0 0/8 1/8 2/8 3/8 1/2 4/8 5/8 6/8 7/8 1 8/8 5/8 yellow 3/4 = 6/8 blue 3/4 > 5/8

Step-by-Step Investigation Guide

  1. Draw a fraction bar for 3/4 Draw a rectangle. Divide it into 4 equal parts. Shade 3 of the 4 parts. Label it 3/4.

    What does each part represent? What does the shaded area represent?

  2. Draw a fraction bar for 5/8 Draw another rectangle the same size. Divide it into 8 equal parts. Shade 5 of the 8 parts. Label it 5/8.

    Why does this bar have more pieces than the 3/4 bar? Are the pieces the same size?

  3. Find a common denominator To compare fairly, both fractions need the same size pieces. Convert 3/4 to eighths: 3/4 = ?/8. Multiply both the numerator and denominator by 2.

    Why does multiplying top and bottom by the same number keep the fraction equal?

  4. Place both on a number line Draw a number line from 0 to 1. Divide it into 8 equal segments. Plot 5/8 and 6/8 (which is 3/4). Which point is farther right?

    On a number line, which direction means "greater"? How do you know?

  5. Compare and write the inequality Since 6/8 > 5/8, we know 3/4 > 5/8. The teacher has more blue paint. Write both the fraction comparison and an explanation.

    Can you also compare using decimals? What is 3/4 as a decimal? What is 5/8?

  6. Find the total paint Add: 6/8 + 5/8 = 11/8 = 1 3/8 gallons total. Show this on the number line (it goes past 1). Does the teacher have more than 1 gallon?

    What does it mean when a fraction is greater than 1? How do you write it as a mixed number?

Language Support

Key Vocabulary

Numerator: The top number - how many parts you have
Denominator: The bottom number - how many equal parts in the whole
Equivalent fraction: A different fraction that shows the same amount (3/4 = 6/8)
Number line: A straight line with marks showing numbers in order
Common denominator: When two fractions have the same bottom number
Mixed number: A whole number plus a fraction (like 1 3/8)

Sentence Frames

  • "___ is equivalent to ___ because I multiplied both the numerator and denominator by ___."
  • "On the number line, ___ is to the right of ___, so ___ is greater."
  • "The total paint is ___ because ___ + ___ = ___."
  • "I can see in my bar model that ___ is greater because more parts are shaded."

Multiple Representations

Fraction Bar

Rectangles divided into equal parts with shading to show each fraction.

Number Line

Plot both fractions on a line from 0 to 1. Farther right = greater.

Area Model

Shade parts of same-size rectangles. Compare the shaded areas visually.

Work Space

Fraction Bar for 3/4:



Fraction Bar for 5/8:



Number Line (0 to 1):



Area Models:



Comparison and Total: