Fraction Architect Guide
Fraction Architect Guide
Lesson: Fraction Face-Off (6th Grade Review)
TEACHER RESOURCE
Objective
Students will master the "Common Denominator Strategy" to compare and order complex fractions. This foundational skill bridges the gap between basic fraction operations and future ratio/proportion units.
Pacing
- • Warm-up: 5 min
- • Video/Vocab: 10 min
- • Activity: 25 min
- • Closure: 5 min
Video Facilitation Guide
0:17
The Problem Pose
"Why can't we just say 4 is bigger than 3, so 4/5 is bigger than 3/4?"
Goal: Discuss why the size of the "slices" (denominators) matters before we compare the "number of slices" (numerators).
1:05
The Decimal Prediction
"Before he checks, what would these look like as money or decimals?"
Goal: Encourage students to relate 3/4 to $0.75 and 4/5 to $0.80 for a real-world sanity check.
2:17
The Whiteboard Challenge
"Pause and solve 5/9 vs 4/7 on your own."
Goal: Immediate application of the cross-multiplication method for finding common denominators.
Activity Key: Yardstick Timeline
Below is the correct order (Least to Greatest) for the 10 fraction cards. Use this to check student strings during the activity.
1. 3/8 (0.375)
2. 1/2 (0.500)
3. 5/9 (0.555...)
4. 4/7 (0.571...)
5. 3/5 (0.600)
6. 2/3 (0.666...)
7. 7/10 (0.700)
8. 8/11 (0.727...)
9. 5/6 (0.833...)
10. 11/12 (0.916...)
Closure Facilitation
When groups present, ask them specifically about the 4/7 vs 5/9 and 8/11 vs 7/10 gaps. These are the most difficult to distinguish visually and require the common denominator math learned today.
Fraction Face Off Slides
¾
⅘
⅚
⅔
Fraction Face Off
Which Side are You On?
6th Grade Math Review
Warm Up: Quick Fire
Convert to Decimals
1/2 = ?
1/4 = ?
3/4 = ?
Pro Tip:
Think of fractions like money! 1/4 is a quarter ($0.25). 3/4 is three quarters ($0.75).
Challenge:
What is 1/5 as a decimal?
The Blueprint
NUMERATOR
The "Top Number". Tells us how many parts we have.
DENOMINATOR
The "Bottom Number". Tells us the size of the whole.
EQUIVALENT
Fractions that look different but have the same value.
Which Side is Greater?
3
4
VS
4
5
It's hard to tell when the sizes (denominators) are different!
Mastering the Method
Embedded media
Watch for the "Common Denominator Strategy"
The 2-Step Strategy
1
Build Common Denominators
Multiply each fraction by the other fraction's denominator (over itself).
\( \frac{3}{4} \times \frac{5}{5} = \frac{15}{20} \)
2
Compare the Numerators
Now that the pieces are the same size, the bigger top number wins!
16 is greater than 15, so \( \frac{16}{20} \) is bigger.
Ordering the Timeline
Grab 10 Fraction Cards & Clothespins
Find Common Denominators to Compare
Order from LEAST to GREATEST on your string
WATCH OUT FOR THESE!
5/9 & 4/7
They are extremely close! You'll need the math to prove it.
Final Justification
"Identify the two fractions on your timeline that are closest together. Explain to the class exactly how you proved which one was larger."
Denominator
Equivalent
Inequality
Fraction Combat Scratchpad
Fraction Face-Off
The Timeline Scratchpad
Group Members:
Date:
Use this space to prove your placements! When two fractions are close, you must find a common denominator to determine which is greater. Show your work clearly for the class.
1 Battle Zone: 5/9 vs 4/7
Find Common Denominator
5/9
×
=
4/7
×
=
Therefore:
5/9
?
4/7
2 Battle Zone: Choose Two Close Fractions
Student Choice
Show Work Here
Show Work Here
Our Verdict:
Challenge: Can you convert your final "Verdict" to decimals to prove it again?
