Little Newtons · Class 35 · Fractions · Grades 1–2
Fractions on a Number Line (Little Newtons Class 35, Grades 1–2) — 25 Practice Questions with Hidden Answers
To show a fraction on a number line from 0 to 1: the DENOMINATOR (bottom number) tells you how many equal parts to split the line into, and the NUMERATOR (top number) tells you how many ticks to count from 0. For example, 3/4 means split 0 to 1 into 4 equal parts, then count over 3 ticks — that’s where 3/4 lives. This Little Newtons Class 35 pack teaches grade 1–2 students how to read and place fractions on a number line, how to spot equivalent fractions using parallel number lines, and gives 25 practice questions with click-to-reveal step-by-step answers.
This class is part of the Little Newtons arc at SOMATH — School of Math on the Upper West Side. Class 35 is the first “fractions” class of the year — the moment children realize that numbers live BETWEEN 0 and 1, not only at 0, 1, 2, 3…. It’s the class that changes how a child sees a number line for the rest of their math life. Taught in-person at 226 W 79th St. Call (646) 668-6151 or book a free 30-minute evaluation to see if your grade 1–2 child is a fit.
What’s in this class pack
- What is a fraction, and what does it look like on a number line?
- How to place a fraction on a number line (the 3 steps)
- How to read a fraction that’s already on a number line
- Equivalent fractions on parallel number lines
- Comparing fractions with a number line
- The 5 most common grade 1–2 number-line mistakes
- 25 practice questions with hidden answers
- Answer key summary
- Frequently asked questions
1. What is a fraction, and what does it look like on a number line?
A fraction is a number between 0 and 1 (usually)
Before Class 35, a child sees a number line as a list of counting numbers: 0, 1, 2, 3, 4…. In Class 35, we zoom in on the space between two counting numbers (usually between 0 and 1) and discover that there are numbers hiding there. Those numbers are called fractions.
A fraction has two parts:
- The denominator (bottom number) — how many equal parts the whole is split into.
- The numerator (top number) — how many of those parts we’re counting.
Say “the bottom splits, the top counts.” If you say that sentence out loud every time you look at a fraction, you will never mix them up.
Every fraction that’s smaller than 1 has a home on this line. We just need to know where.
2. How to place a fraction on a number line (the 3 steps)
The 3 steps
- Draw the line. A straight line with 0 on the left and 1 on the right.
- Split into equal parts. Look at the denominator. That’s how many equal parts you split the line into. For 3/4, split into 4 equal parts (4 pieces ⇒ 3 tick marks between 0 and 1, plus the endpoints).
- Count from 0. Look at the numerator. Starting at 0, count over that many tick marks. That’s where the fraction lives.
Example: 3/4. Split into 4 equal parts. Count 3 ticks from 0. Land on the 3rd tick.
3. How to read a fraction that’s already on a number line
Sometimes the number line is already drawn and there’s a dot on it. You have to figure out what fraction the dot is. Same idea, in reverse:
Reading a fraction from a number line
- Count the equal parts between 0 and 1 — that becomes the denominator (bottom number).
- Count the ticks from 0 to the dot — that becomes the numerator (top number).
- Write the fraction: numerator on top, denominator on bottom.
4. Equivalent fractions on parallel number lines
Two fractions are equivalent when they land on the exact same point on the number line. Different numbers, same amount. Grade 1–2 doesn’t need to write big rules for this — they just need to see it.
| Fraction | Equivalent fractions on other number lines |
|---|---|
| 1/2 | 2/4, 3/6, 4/8, 5/10… |
| 1/3 | 2/6, 3/9, 4/12… |
| 1/4 | 2/8, 3/12… |
| 2/3 | 4/6, 6/9, 8/12… |
| 3/4 | 6/8, 9/12… |
The pattern is: multiply both the top and the bottom by the same number. That’s a Kid Einsteins (grade 3–4) skill. For Little Newtons, seeing that they land at the same point is enough.
5. Comparing fractions with a number line
Between two fractions, the bigger one is the fraction that’s farther from 0 (farther to the right) on the number line. This is the whole reason we teach fractions on a number line first — the comparison is visual and immediate.
If the two fractions have the same denominator, comparing is easy: just look at which numerator is bigger. On a 5-line, 4/5 is farther right than 2/5 because 4 > 2.
If the two fractions have different denominators, we rewrite one to match the other. For example, to compare 5/6 and 2/3, rewrite 2/3 as 4/6 (both live at the same point on a 6-line). Now they’re on the same number line: 5/6 vs. 4/6. 5/6 is farther right ⇒ 5/6 > 2/3.
6. The 5 most common grade 1–2 number-line mistakes
- Unequal parts. If the ticks aren’t evenly spaced, the fraction is wrong. Fix: fold a paper strip and use it as a template so every jump is the same length.
- Counting 0 as the first tick. 0 is the starting line, not a count. The counting starts with the first jump AWAY from 0. So on a 4-line, the 1st tick after 0 is 1/4, not 0/4.
- Flipping numerator and denominator. Kids sometimes read 3/4 as “3 splits, count 4.” That’s backwards. Say “the bottom splits, the top counts” every time.
- Counting endpoints as ticks between them. On a 4-line from 0 to 1, there are 4 EQUAL PARTS but only 3 tick marks between 0 and 1 (plus the two endpoints). Kids sometimes count 5 tick marks and get confused. Fix: count the PARTS (spaces), not the marks.
- Thinking a bigger denominator makes a bigger fraction. 1/10 is smaller than 1/2, even though 10 is bigger than 2. The denominator counts how many pieces we cut the whole into — more pieces means each piece is SMALLER.
7. 25 practice questions with hidden answers
The 25 questions below march from reading a fraction that’s already on a number line, to placing a fraction on a blank number line, to spotting equivalent fractions, to comparing, and finish with real-life word problems.
Prefer a printable version?
A clean 5-page PDF with just the 25 questions and space to show work — the step-by-step answers stay online for the teacher or parent to check.
Download the 25-question practice packetPart 1 — Reading fractions on a number line (Q1–Q5)
“What fraction is this point?”
Q1
A number line goes from 0 to 1 and is split into 4 equal parts. Starting at 0, count 1 tick. What fraction is that point?
Answer: 1/4
The whole is split into 4 equal parts ⇒ denominator 4. We counted 1 tick from 0 ⇒ numerator 1. So the point is 1/4.
Q2
A number line from 0 to 1 is split into 3 equal parts. Starting at 0, count 2 ticks. What fraction is that point?
Answer: 2/3
Whole split into 3 ⇒ denominator 3. Counted 2 ticks from 0 ⇒ numerator 2. Fraction = 2/3.
Q3
A number line from 0 to 1 is split into 6 equal parts. What fraction lands exactly at the middle?
Answer: 3/6 (which is the same as 1/2)
Half of 6 equal parts is 3 parts. So the middle is at the 3rd tick from 0 ⇒ 3/6. And 3/6 = 1/2 — they land at the same point.
Q4
A number line from 0 to 1 is split into 8 equal parts. What fraction lands right before 1 (the very last tick)?
Answer: 7/8
Denominator 8 ⇒ whole split into 8 equal parts. The last tick BEFORE 1 is the 7th tick from 0 ⇒ numerator 7. Fraction = 7/8. (The 8th tick is 1 itself.)
Q5
A number line from 0 to 1 is split into 2 equal parts. What fraction is the tick between 0 and 1?
Answer: 1/2
Whole split into 2 ⇒ denominator 2. One tick from 0 to the middle ⇒ numerator 1. Fraction = 1/2. This is the classic “half.”
Part 2 — Placing fractions on a number line (Q6–Q10)
“Where does this fraction go?”
Q6
Draw a number line from 0 to 1 with 4 equal parts. Which tick is 3/4?
Answer: The 3rd tick from 0.
Denominator 4 ⇒ the line is already split into 4 equal parts. Numerator 3 ⇒ count 3 ticks from 0. The 3rd tick IS 3/4.
Q7
Draw a number line from 0 to 1 with 5 equal parts. Which tick is 2/5?
Answer: The 2nd tick from 0.
Denominator 5 ⇒ 5 equal parts. Numerator 2 ⇒ count 2 ticks. Land on the 2nd tick.
Q8
On a number line split into 3 equal parts from 0 to 1, where does 1/3 land?
Answer: The 1st tick after 0.
Denominator 3 ⇒ 3 equal parts. Numerator 1 ⇒ count 1 tick from 0. Land on the 1st tick.
Q9
On a number line split into 6 equal parts from 0 to 1, where does 5/6 land?
Answer: The 5th tick from 0.
Denominator 6 ⇒ 6 equal parts. Numerator 5 ⇒ count 5 ticks from 0. Land on the 5th tick (one before 1).
Q10
On a number line split into 4 equal parts from 0 to 1, where does 0/4 land?
Answer: At 0.
Numerator 0 ⇒ count 0 ticks from 0. We haven’t moved. 0/4 = 0. Any fraction with numerator 0 is just 0.
Part 3 — Equivalent fractions on a number line (Q11–Q15)
“Which fractions land at the same point?”
Q11
Draw two number lines from 0 to 1. Split one into 2 equal parts. Split the other into 4 equal parts. Which fraction on the 4-line lands exactly at 1/2?
Answer: 2/4
1/2 is the middle of a 2-line. The middle of a 4-line is the 2nd tick from 0, which is 2/4. Same point ⇒ equivalent fractions.
Q12
Which fraction on a 6-line matches 1/2?
Answer: 3/6
Half of 6 equal parts is 3 parts. So the middle of a 6-line is the 3rd tick from 0 ⇒ 3/6 = 1/2.
Q13
Which fraction on a 6-line matches 1/3?
Answer: 2/6
On a 3-line, 1/3 is the 1st tick from 0. On a 6-line, 2/6 lands at the same spot (6 is 2 times 3, so each part of the 3-line splits into 2 parts on the 6-line). 1/3 = 2/6.
Q14
Which fraction on an 8-line matches 1/4?
Answer: 2/8
Each part of a 4-line is the same as two parts of an 8-line (8 is 2 times 4). So 1/4 = 2/8.
Q15
Which fraction on an 8-line matches 1/2?
Answer: 4/8
Half of 8 equal parts is 4 parts. The middle of an 8-line is the 4th tick from 0 ⇒ 4/8 = 1/2.
Part 4 — Comparing on a number line (Q16–Q20)
“Which is bigger, and how do we know?”
Q16
On a 4-line from 0 to 1, which is farther from 0: 1/4 or 3/4?
Answer: 3/4
Same denominator ⇒ just compare the numerators. 3 > 1, so 3/4 is farther from 0. On a number line, farther from 0 = bigger. So 3/4 > 1/4.
Q17
Which is bigger, 2/3 or 1/3? Show how you know using a number line split into 3 equal parts.
Answer: 2/3
On the same 3-line, 1/3 is the 1st tick from 0 and 2/3 is the 2nd tick from 0. 2/3 is farther right ⇒ bigger. 2/3 > 1/3.
Q18
Which is bigger, 3/4 or 1/2? Draw both on a number line from 0 to 1.
Answer: 3/4
Rewrite 1/2 as 2/4 (they live at the same point on a 4-line). On the 4-line, 2/4 is the 2nd tick and 3/4 is the 3rd tick. 3/4 is farther right ⇒ 3/4 > 1/2.
Q19
Which is bigger, 5/6 or 2/3?
Answer: 5/6
Rewrite 2/3 as 4/6 (each part of a 3-line splits into 2 parts of a 6-line). Now both are on the same 6-line: 5/6 vs. 4/6. 5/6 is farther right ⇒ 5/6 > 2/3.
Q20
Which is bigger, 7/8 or 3/4?
Answer: 7/8
Rewrite 3/4 as 6/8 (each part of a 4-line splits into 2 parts of an 8-line). Now both are on the same 8-line: 7/8 vs. 6/8. 7/8 is one tick farther right ⇒ 7/8 > 3/4.
Part 5 — Word and picture problems (Q21–Q25)
“Real-life number-line problems.”
Q21
A snail crawls from 0 to 1 meter on a straight path. The path is marked in 4 equal parts. The snail stops at the 3rd mark. What fraction of the path did it crawl?
Answer: 3/4 of the path.
The path is the whole, split into 4 equal parts ⇒ denominator 4. The snail is at the 3rd of 4 marks ⇒ numerator 3. Fraction crawled = 3/4.
Q22
A pizza-parlor ruler is 1 foot long and split into 6 equal parts. A stripe of paint runs from 0 to the 4th mark. What fraction of the ruler is painted?
Answer: 4/6 (which is the same as 2/3).
Whole split into 6 ⇒ denominator 6. Painted up to the 4th mark ⇒ numerator 4. Fraction = 4/6. On a 3-line, this is the same point as 2/3.
Q23
Emma jumps along a hopscotch line from 0 to 1 meter. She lands on the 2nd mark of a line split into 5 equal parts. What fraction shows her landing spot?
Answer: 2/5
Whole split into 5 ⇒ denominator 5. Landed on the 2nd tick ⇒ numerator 2. Fraction = 2/5.
Q24
Two friends run a 1-block race. The block is 8 equal parts long. Jake stops at 5/8 and Mia stops at 3/4. Who is farther from the start?
Answer: Mia.
Rewrite 3/4 as 6/8 (both on the 8-line). Now compare on the same line: Jake at 5/8 vs. Mia at 6/8. 6/8 is one tick farther right ⇒ Mia is farther from the start.
Q25
A ribbon is 1 meter long and cut into 4 equal pieces. Alex takes 1 piece and Sam takes 2 pieces. On a number line from 0 to 1, mark the point that shows how much they took together as a fraction.
Answer: 3/4
Alex’s piece = 1/4. Sam’s pieces = 2/4. Together = 1/4 + 2/4 = 3/4. On a 4-line, mark the 3rd tick from 0.
8. Answer key summary
| Q | Answer | Q | Answer | Q | Answer |
|---|---|---|---|---|---|
| 1 | 1/4 | 10 | 0 | 19 | 5/6 |
| 2 | 2/3 | 11 | 2/4 | 20 | 7/8 |
| 3 | 3/6 = 1/2 | 12 | 3/6 | 21 | 3/4 |
| 4 | 7/8 | 13 | 2/6 | 22 | 4/6 = 2/3 |
| 5 | 1/2 | 14 | 2/8 | 23 | 2/5 |
| 6 | 3rd tick (3/4) | 15 | 4/8 | 24 | Mia (6/8 > 5/8) |
| 7 | 2nd tick (2/5) | 16 | 3/4 | 25 | 3/4 |
| 8 | 1st tick (1/3) | 17 | 2/3 | ||
| 9 | 5th tick (5/6) | 18 | 3/4 |
9. Frequently asked questions
How do you show a fraction on a number line?
Three steps. (1) Draw a straight line with 0 on the left and 1 on the right. (2) Split the space into equal parts — the denominator tells you how many. If the fraction is 3/4, split into 4 equal parts. (3) Starting at 0, count over as many ticks as the numerator. For 3/4, count 3 ticks from 0. The most common grade 1–2 mistake is making the parts unequal — the number line only works when every jump is the same size.
What is the numerator and what is the denominator on a number line?
On a number line from 0 to 1, the denominator (bottom number) is how many equal parts you split the line into. The numerator (top number) is how many of those parts you count over from 0. For 2/3: denominator 3 ⇒ split into 3 equal parts; numerator 2 ⇒ count over 2 ticks. Say it out loud: “the bottom splits, the top counts.”
How do you know two fractions are equivalent using a number line?
Draw the two fractions on TWO parallel number lines from 0 to 1. If they land at the exact same point, they’re equivalent — they name the same amount with different numbers. Example: 1/2, 2/4, and 3/6 all land in the middle. Same point ⇒ same fraction.
How do you compare fractions using a number line?
The bigger fraction is the one farther from 0 (to the right). If the denominators are different, rewrite one to match the other. Example: 3/4 vs. 2/3. Rewrite both on a 12-line: 9/12 vs. 8/12. 9/12 is farther right ⇒ 3/4 > 2/3. For grade 1–2 we usually stick to same-denominator comparisons (fast) or simple rewrites like 1/2 = 2/4.
Why is my grade 1 or 2 child confused about fractions on a number line?
Three usual reasons. (1) The parts aren’t equal — use a folded paper strip as a template. (2) They count 0 as the first tick — 0 is the start, not a count. (3) They flip numerator and denominator — say “bottom splits, top counts” every time. Fix any one of these and most confusion disappears.
What is 1/2 on a number line?
1/2 is the exact middle point between 0 and 1. To see this, split the space into 2 equal parts. The tick in the middle IS 1/2. Same point as 2/4, 3/6, and 4/8.
What comes next in the Little Newtons arc after this class?
Class 35 sets up the fraction unit. Class 36 is comparing fractions with the same denominator. Class 37 is simple two-step word problems. Fractions come back in more depth in the Kid Einsteins arc (grades 3–4), where students learn equivalent fractions with different denominators, adding and subtracting fractions, and fractions as division.
About SOMATH — School of Math
SOMATH — School of Math is a math-focused school on the Upper West Side of Manhattan for students in grades 1–12. Class 35 is part of the Little Newtons arc (grades 1–2), taught in small groups by cofounder Marcelo Ambrozio (Northwestern-trained, 15+ years teaching NYC math) and the SOMATH team.
Location: 226 W 79th St, 1st Floor, New York, NY 10024 · Upper West Side
Phone: (646) 668-6151 · Email: hello@schoolofmath.us
Book: Free evaluation · Schedule · Home
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