Fraction Strip Warmup Worksheet
Expedition Stage 1 Number Line Warmup
Name:
Date:
Fraction Strip Warmup | Folding & Placing Unit Fractions
1 Fold, Shade, and Label the Fraction Strips
Each strip represents 1 whole unit (from 0 to 1)
1 Whole
1 Whole Unit
Halves
\( \frac{1}{2} \)
\( \frac{1}{2} \)
Fourths
\( \frac{1}{4} \)
Eighths
\( \frac{1}{8} \)
2 Plot the Unit Fractions on the Trail Number Lines
Draw a point \( \bullet \) and label where the fraction lands
A. Partition into 2 equal segments and plot \( \frac{1}{2} \) Length = 1 Whole
0
1
B. Partition into 4 equal segments and plot \( \frac{1}{4} \) Tip: Fold in half, then half again
0
1
C. Partition into 3 equal segments and plot \( \frac{1}{3} \) 3 equal hops from 0 to 1
0
1
3 Trail Truths: Compare Fraction Magnitudes
Use >, <, or =
\( \frac{1}{2} \)
\( \frac{1}{4} \)
Use >, <, or =
\( \frac{1}{8} \)
\( \frac{1}{3} \)
Use >, <, or =
\( \frac{1}{6} \)
\( \frac{1}{2} \)
Trail Explorer Rule: Why is \( \frac{1}{8} \) smaller than \( \frac{1}{2} \) even though 8 is bigger than 2?
Fraction Trail Board Game
Expedition Stage 2 2–4 Players • 15–20 Mins
Fraction Trail: Number Line Race
The Fraction Trail Race Board
Race your explorer from Base Camp (0) to Summit Peak (1 Whole) using unit fraction card values!
Goal
First to Reach 1.0 Wins!
Base & Summit Unit Benchmarks Action Zones
Track Scale: 24 Trail Units = 1 Whole
Base Camp Sector Distance: 0 to 8/24 (\( \frac{1}{3} \))
Start 0 Camp
1 \( \frac{1}{24} \)
2 \( \frac{1}{12} \)
3 \( \frac{1}{8} \) Pond
4 \( \frac{1}{6} \) Trail
5 Bonus +1 Step
6 \( \frac{1}{4} \) Ridge
7 \( \frac{7}{24} \)
8 \( \frac{1}{3} \) Canyon
Mid-Mountain Plateau Distance: 9/24 to 16/24 (\( \frac{2}{3} \))
9 \( \frac{3}{8} \) Cave
10 \( \frac{5}{12} \)
11 Fog -1 Step
12 \( \frac{1}{2} \) Haven
13 \( \frac{13}{24} \)
14 \( \frac{7}{12} \)
15 \( \frac{5}{8} \) Falls
16 \( \frac{2}{3} \) Glacier
Summit Climb Sector Distance: 17/24 to 24/24 (1 Whole)
17 Breeze +2 Steps
18 \( \frac{3}{4} \) Lookout
19 \( \frac{19}{24} \)
20 \( \frac{5}{6} \) Cliff
21 \( \frac{7}{8} \) Ridge
22 \( \frac{11}{12} \)
23 \( \frac{23}{24} \)
Summit 1.0 \( \frac{24}{24} \)
Trail Explorer Rules
- Start at 0: All players place their tokens on Base Camp (0).
- Draw & Step: On your turn, draw 1 Fraction Card from the deck. Convert your fraction to steps: \( \frac{1}{2}=12 \), \( \frac{1}{3}=8 \), \( \frac{1}{4}=6 \), \( \frac{1}{6}=4 \), \( \frac{1}{8}=3 \), \( \frac{1}{12}=2 \).
- Milestone Check: If you land on a Benchmark, announce where you are on the number line!
- Victory: First player to reach or pass 1 Whole (24) plants their flag and wins!
Player Tokens
Cut out tokens or use coins/math cubes.
P1
P2
P3
P4
Expedition Kit Printable Cards & Scorecard
Cut along dashed lines
Fraction Trail Action Deck
Cut out these 12 trail cards to form the draw pile. Shuffle and place face down at Base Camp.
Unit Advance \( \frac{1}{2} \) Move 12 Steps
Unit Advance \( \frac{1}{2} \) Move 12 Steps
Unit Advance \( \frac{1}{3} \) Move 8 Steps
Unit Advance \( \frac{1}{3} \) Move 8 Steps
Unit Advance \( \frac{1}{4} \) Move 6 Steps
Unit Advance \( \frac{1}{4} \) Move 6 Steps
Unit Advance \( \frac{1}{6} \) Move 4 Steps
Unit Advance \( \frac{1}{6} \) Move 4 Steps
Unit Advance \( \frac{1}{8} \) Move 3 Steps
Unit Advance \( \frac{1}{8} \) Move 3 Steps
Trail Scout Binoculars Hop forward \( \frac{1}{4} \) or swap places with another player!
Mountain Gust Tailwind Advance \( \frac{1}{6} \) and take another turn immediately!
Explorer Log: Record Your Trail Math
Each player writes down their card fraction and running location
| Turn | Card Drawn | Fraction Distance | New Trail Benchmark Position |
|---|
| Turn 1 | | | |
| Turn 2 | | | |
| Turn 3 | | | |
| Turn 4 | | | |
| Turn 5 | | | |
Trail Question: You need 6 steps to reach 1 Whole. Which single unit fraction card gets you there?
Unit Fractions Quick Quiz
Expedition Stage 3 Quick Assessment
Name:
Date:
Score: ____ / 20
Unit Fractions Quick Quiz Standards: 3.NF.1, 3.NF.2
1 What is always true about a unit fraction? (3 pts)
A The denominator is always 1.
B The numerator is always 1.
C The fraction is greater than 1 whole.
D It represents the entire whole strip.
2 Identify the fraction represented by point P on the number line below. (4 pts)
0
P
?
1
Point P =
3 Partition this number line into 6 equal parts and plot a point at \( \frac{1}{6} \). (4 pts)
0
1
4 Order these unit fractions from Least to Greatest: \( \frac{1}{2},\; \frac{1}{8},\; \frac{1}{4},\; \frac{1}{3} \) (4 pts)
Least
<
<
<
Greatest
5 Trail Reasoning & Explanation (5 pts)
Explorer Maya claims: "Hiking \( \frac{1}{8} \) of the mountain trail is longer than hiking \( \frac{1}{4} \) of the trail because 8 is bigger than 4." Is Maya correct? Explain why or why not using what you know about partitioning 1 whole.
Unit Fractions Quiz Key
Teacher Key Scoring & Diagnostic Guide
Total: 20 Points Mastery: 16+ / 20
Unit Fractions Quick Quiz: Answer Key
Item 1: Definition of Unit Fraction (3 pts) Correct: B
Answer: B (The numerator is always 1). A unit fraction represents exactly one of the equal parts that make up a whole (\( \frac{1}{b} \)).
Item 2: Reading the Number Line (4 pts) Point P = \( \frac{1}{3} \)
The line between 0 and 1 has 3 equal intervals (\( 0 \to \frac{1}{3} \to \frac{2}{3} \to 1 \)). Point P sits at the first tick mark, representing \( \frac{1}{3} \). Award 2 pts for identifying denominator 3; 2 pts for correct fraction \( \frac{1}{3} \).
Item 3: Partitioning into 6 Parts & Plotting \( \frac{1}{6} \) (4 pts) 5 tick marks + point at 1st
0
\( \frac{1}{6} \)
\( \frac{2}{6} \)
\( \frac{3}{6} \)
\( \frac{4}{6} \)
\( \frac{5}{6} \)
1
Rubric: 2 pts for roughly equal 6 intervals (5 internal tick marks); 2 pts for accurately placed and labeled point at \( \frac{1}{6} \).
Item 4: Ordering Fractions (4 pts) \( \frac{1}{8} < \frac{1}{4} < \frac{1}{3} < \frac{1}{2} \)
Full credit (4 pts) for exact sequence: \( \frac{1}{8} \) < \( \frac{1}{4} \) < \( \frac{1}{3} \) < \( \frac{1}{2} \). Partial credit: 2 pts if ordered in reverse (showing confusion between whole numbers and denominators).
Item 5: Conceptual Reasoning Rubric (5 pts) Maya is Incorrect
Exemplar Student Response: "No, Maya is incorrect. When 1 whole trail is cut into 8 equal pieces, each piece is much smaller than when it is cut into only 4 equal pieces. More cuts make smaller slices, so \( \frac{1}{8} < \frac{1}{4} \)."
5 pts (Exemplary): Clear negation + explains sharing/partitioning size relationship.
3-4 pts (Approaching): States Maya is wrong; states \( 1/4 \) is bigger but explanation is brief.
1-2 pts (Developing): Confuses numerator/denominator or agrees with Maya based on whole number rules.
Common Misconception Alert & Intervention
The "Bigger Denominator = Bigger Fraction" Fallacy: Students applying whole-number schemas will intuitively believe \( \frac{1}{8} > \frac{1}{4} \). Remediation: Have students hold up their folded warmup fraction strips. Put the \( \frac{1}{8} \) strip physically on top of the \( \frac{1}{4} \) strip so they see it is half as long. Emphasize that the denominator tells how many pieces the whole is cut into—more pieces means smaller slices.
