A student places 3/4 on a number line from 0 to 1 by drawing 4 tick marks between 0 and 1 and then marking the 3rd tick mark. What error has the student made?
ANo error — marking the 3rd of 4 tick marks correctly gives 3/4
BThe student should have drawn 3 tick marks instead of 4
CThe student counted tick marks instead of intervals — 4 tick marks between 0 and 1 create 5 intervals, so the 3rd mark is actually at 3/5
DThe student should place 3/4 between 1 and 2, not between 0 and 1
This is the most common error with fractions on a number line. Four tick marks between 0 and 1 divide the segment into 5 equal intervals, not 4 — so the third mark is at 3/5. To place 3/4 correctly, you divide the space between 0 and 1 into 4 equal intervals (which requires only 3 interior tick marks) and count 3 of those intervals from 0. Always count spaces (intervals), not lines (tick marks).
Question 2 Multiple Choice
A number line is divided into fourths. A student places a point one interval past 1. What fraction names that point?
A1/4
B4/4
C5/4
DThe point cannot be named as a fraction because it is past 1
The number line divided into fourths keeps the same interval size past 1. After 4/4 (which equals 1), the next point is 5/4 — five intervals from 0. Option D reflects the misconception that fractions only live between 0 and 1. The number line shows that fractions greater than 1 (improper fractions) are legitimate numbers with specific locations.
Question 3 True / False
On a number line divided into fourths, the fraction 4/4 and the whole number 1 are at the exact same location.
TTrue
FFalse
Answer: True
Yes — 4/4 means 4 intervals of size 1/4, and four quarter-intervals exactly span from 0 to 1. This is one of the most important insights the number line model reveals: fractions and whole numbers share the same number line. 4/4 = 1 is visible as a location, not just as an abstract arithmetic fact.
Question 4 True / False
To place 3/4 on a number line, you should count the 3rd tick mark drawn between 0 and 1.
TTrue
FFalse
Answer: False
This is the classic counting-marks-instead-of-intervals error. The denominator (4) tells you how many equal intervals to divide the 0-to-1 segment into, and the numerator (3) tells you how many intervals to count from 0. The correct approach: divide the space between 0 and 1 into 4 equal parts, then count 3 intervals from 0. The number of tick marks you draw to create those intervals may differ from the numerator.
Question 5 Short Answer
How does placing fractions on a number line show that fractions are numbers, not just parts of shapes?
Think about your answer, then reveal below.
Model answer: On a number line, every fraction has a specific location — a fixed address — just like whole numbers do. This shows that 3/4 is a number that lives between 0 and 1 on the same number line as 0, 1, 2, and 3. It also shows that fractions extend beyond 1 (like 5/4), and that equivalent fractions (like 1/2 and 2/4) land at the same point. None of this is visible when fractions are only shown as shaded parts of shapes.
The shape model (shaded pieces) shows fractions as parts of a specific object — which suggests fractions depend on the object. The number line eliminates the object: 3/4 is just a point, existing on its own. This is what mathematicians mean when they say fractions are numbers. The number line also naturally handles fractions greater than 1 and makes equivalence visible as two different names for the same location.