HavenHub Academy • Edition 5 • Workbook

Unit 5: The Slice

Mastery Level: Just Judge

Lesson 5.1: Same Denominators (The Fair Race)

Problem 1. Circle the larger fraction:
$\frac{2}{5}$    or    $\frac{4}{5}$
Problem 2. Circle the smaller fraction:
$\frac{7}{8}$    or    $\frac{3}{8}$
Problem 3. Use > or < to compare:
$\frac{1}{6}$ _____ $\frac{5}{6}$
Problem 4. Order from smallest to biggest:
$\frac{3}{4}$, $\frac{1}{4}$, $\frac{4}{4}$, $\frac{2}{4}$
________________________________________________________
Problem 5. True or False: $\frac{10}{10}$ is bigger than $\frac{1}{10}$. ________
Problem 6. Draw two pizzas cut into 4 slices. Shade 1/4 in one and 3/4 in the other. Circle the winner.
DRAW HERE
Verification Node 5.1 "I testify that when the families are the same, more pieces always equals more treasure."

Student Signature: __________________________

Lesson 5.2: Same Numerators (The Paradox)

Problem 7. Circle the larger fraction:
$\frac{1}{2}$    or    $\frac{1}{10}$
Problem 8. Circle the smaller fraction:
$\frac{1}{3}$    or    $\frac{1}{100}$
Problem 9. Use > or < to compare:
$\frac{1}{8}$ _____ $\frac{1}{4}$
Problem 10. Order from smallest to biggest:
$\frac{1}{10}$, $\frac{1}{2}$, $\frac{1}{5}$, $\frac{1}{100}$
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Problem 11. Why is $\frac{1}{2}$ bigger than $\frac{1}{10}$?
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Problem 12. Circle the winner: $\frac{2}{3}$ or $\frac{2}{10}$.
Problem 13. Circle the winner: $\frac{5}{100}$ or $\frac{5}{10}$.
Problem 14. Draw a picture that proves $\frac{1}{2} > \frac{1}{4}$.
DRAW HERE
Problem 15. If I share my candy with 1,000 people, is my slice big or small? ________

Lesson 5.3: The Anchor (1/2)

Problem 16. Is $\frac{7}{8}$ more or less than half? ________
Problem 17. Is $\frac{1}{10}$ more or less than half? ________
Problem 18. Circle the fractions that are BIGGER than half:
$\frac{3}{4}$     $\frac{1}{8}$     $\frac{9}{10}$     $\frac{4}{10}$     $\frac{2}{3}$
Problem 19. Circle the fractions that are SMALLER than half:
$\frac{1}{5}$     $\frac{4}{5}$     $\frac{1}{12}$     $\frac{11}{12}$     $\frac{2}{100}$
Problem 20. How many eighths make exactly half? ____
Problem 21. How many tenths make exactly half? ____
Problem 22. If a fraction has a bottom number of 20, what is the half-way number? ____
Problem 23. Use the Anchor to compare: $\frac{1}{10}$ _____ $\frac{9}{10}$.
Problem 24. Use the Anchor to compare: $\frac{3}{4}$ _____ $\frac{1}{3}$.
Problem 25. Draw a line. Mark the middle (1/2). Now place $\frac{1}{10}$ and $\frac{9}{10}$ on the line.
DRAW LINE HERE

Lesson 5.4 & 5.5: Final Judgment

Problem 26. Use the Tug-of-War (Cross-Multiply) to compare:
$\frac{2}{3}$    and    $\frac{3}{5}$
(5 × 2) = ____     (3 × 3) = ____
Winner: ________
Problem 27. Use the Tug-of-War:
$\frac{1}{2}$    and    $\frac{2}{3}$
(3 × 1) = ____     (2 × 2) = ____
Winner: ________
Problem 28. Compare $\frac{3}{4}$ and $\frac{5}{6}$.
Winner: ________
Problem 29. Order from smallest to biggest:
$\frac{1}{100}$, $\frac{99}{100}$, $\frac{1}{2}$, $\frac{1}{4}$
________________________________________________________
Problem 30. Challenge: Order these five:
$\frac{1}{2}, \frac{1}{10}, \frac{9}{10}, \frac{1}{4}, \frac{3}{4}$
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📜 The Scribe's Vow of Discernment

"I, __________________________, do solemnly promise to judge all things with an understanding heart. I will not be fooled by large numbers or shiny masks. I will look for the true portion and honor the Anchor of Truth in all my judgments."

Signed on this day, ______________________.

Bonus Challenge Problems

Problem 31. Compare using >, <, or =: 5/8 ___ 7/12
Problem 32. Compare: 4/9 ___ 1/2
Problem 33. Compare: 7/10 ___ 2/3
Problem 34. Order from least to greatest: 3/8, 1/4, 5/8, 1/2: _____________
Problem 35. Which is closer to 1: 7/8 or 9/10? _______
Problem 36. Which is closer to 0: 1/10 or 1/100? _______
Problem 37. Is 5/11 above or below 1/2? _______
Problem 38. Is 8/15 above or below 1/2? _______
Problem 39. If I ate 3/4 of a pizza and my friend ate 5/6, who ate more? _______
Problem 40. Compare 2/3 and 3/4 using cross-multiplication: ___×___ = ___ and ___×___ = ___

More Practice

Problem 41. Order: 1/3, 1/2, 2/3, 5/6 (smallest to largest): _____________
Problem 42. Order: 3/10, 1/4, 2/5, 1/2 (smallest to largest): _____________
Problem 43. Circle all fractions greater than 1/2: 3/5, 4/9, 7/12, 2/3, 5/11
Problem 44. Circle all fractions less than 1/2: 5/12, 3/7, 4/10, 6/11, 2/5
Problem 45. Put in order (largest to smallest): 1/2, 1/3, 1/4, 1/5, 1/10: _____________
Problem 46. True or False: 3/6 = 1/2 _______
Problem 47. True or False: 4/7 > 1/2 _______
Problem 48. Compare: 11/20 ___ 1/2
Problem 49. Which fraction is exactly equal to 1/2? Circle: 5/10, 6/11, 7/15, 4/9
Problem 50. Explain in your own words how to use 1/2 as an anchor for comparing fractions.

UNIT 5 SIGNET CHALLENGE

Task 1: Classify as above or below 1/2:

7/12: _______    3/8: _______    5/9: _______    4/10: _______

Task 2: Order from smallest to largest:

2/3, 1/4, 5/8, 1/2, 3/10: _________________________________

Task 3: Teach someone the Anchor Method:

I taught: _______________ Signature: _______________

Mentor's Signature: ___________________________ Date: ___________

Quick Reference: Comparison Strategies

Master's Checklist for Unit 5

Student Signature: ___________________________ Date: ___________

Scripture Connection

1 Kings 3:9 — "Give your servant a discerning heart to distinguish between right and wrong."

When Solomon asked God for wisdom, he asked for discernment—the ability to compare and judge correctly. Learning to compare fractions trains your mind in the same skill. May your judgments be righteous!

Word Problems: Real-World Comparisons

Problem 51. Sarah ate 2/3 of her sandwich. Tom ate 3/4 of his identical sandwich. Who ate more? Show your work using cross-multiplication.
_________________________________________________________________
Answer: _______________________
Problem 52. A recipe calls for 3/4 cup of flour. Another recipe calls for 5/8 cup. Which recipe uses more flour?
_________________________________________________________________
Answer: _______________________
Problem 53. Marcus walked 7/10 of a mile to school. His sister walked 3/4 of a mile. Who walked farther? How do you know?
_________________________________________________________________
Answer: _______________________
Problem 54. During art class, Lily used 5/6 of her paint and Ben used 4/5 of his paint. Who used a greater portion of their paint?
_________________________________________________________________
Answer: _______________________
Problem 55. A store has two sales: Store A offers 1/3 off, and Store B offers 2/5 off. Which store has the bigger discount?
_________________________________________________________________
Answer: _______________________

Unit 5 Glossary

Anchor: A reference point used for comparison. In fraction comparison, 1/2 is our primary anchor because it helps us quickly classify fractions as "more than half" or "less than half."

Cross-Multiplication: A method for comparing fractions by multiplying the numerator of one fraction by the denominator of the other. The side with the larger product indicates the larger fraction.

Discernment: The ability to judge wisely and distinguish between options. In mathematics, we discern which fraction is larger through careful comparison.

Denominator: The bottom number in a fraction, showing how many equal parts make the whole. When denominators are the same, we compare numerators directly.

Numerator: The top number in a fraction, showing how many parts we have. When numerators are the same, the fraction with the smaller denominator is larger.

Paradox: Something that seems contradictory but is true. The fraction paradox is that larger denominators create smaller pieces.

Tug-of-War: Our visual name for cross-multiplication, where we imagine two sides pulling against each other to see which fraction wins.

Reflection Journal

1. What was the most surprising thing you learned in Unit 5?

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2. Which comparison method do you find easiest to use? Why?

_______________________________________________________________

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3. Write your own word problem involving fraction comparison:

_______________________________________________________________

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4. How does learning to compare fractions help you make wise decisions in life?

_______________________________________________________________

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The Golden Thread of Discernment

"The tongue of the wise commends knowledge, but the mouths of fools pour out folly." — Proverbs 15:2

Throughout Unit 5, you have developed the skill of discernment—the ability to look beyond surface appearances and determine true value. This is the same wisdom that allowed Solomon to judge fairly between two mothers claiming the same child.

The fraction 1/100 may look impressive with its large denominator, but a wise judge knows that 1/2 represents far more. Similarly, in life, we must not be deceived by appearances but must look for true worth and genuine value in all things.

As you complete this unit, remember: the ability to discern rightly is a gift from God, developed through practice and prayer. May your mathematical discernment grow alongside your spiritual discernment.

© 2026 The HavenHub Academy • Edition 5 Workbook • Unit 5: The Slice • C.A.M.E. Framework V.2