HavenHub Academy • Edition 5 • Workbook
Unit 4: The Alias
Mastery Level: Discerning Steward
Lesson 4.1: The Paper Alias
Problem 1. Circle the pair of strips that show an Alias (the same amount colored).
[Drawings of 1/2 and 2/4 strips]
Problem 2. Color $\frac{1}{2}$ of the first bar and $\frac{3}{6}$ of the second bar. Are they equal?
[Two bars]
Answer: __________
Problem 3. Write the Alias for $\frac{1}{2}$ that uses Fourths.
$\frac{1}{2} = \frac{ }{4}$
Problem 4. Write the Alias for $\frac{1}{3}$ that uses Sixths.
$\frac{1}{3} = \frac{ }{6}$
Problem 5. True or False: $\frac{2}{3}$ is an alias for $\frac{4}{6}$. ________
Problem 6. Draw a circle divided into 4 parts. Shade 2. Then draw a line to make it 8 parts. What is the new fraction?
DRAW HERE
Answer: __________
Verification Node 4.1
"I testify that even when a fraction changes its name, the amount of space it fills remains the same."
Student Signature: __________________________
Lesson 4.2 & 4.3: The Law of One
Problem 7. Create an alias by multiplying by $\frac{2}{2}$:
$\frac{1}{4} \times \frac{2}{2} = $ _______
Problem 8. Create an alias by multiplying by $\frac{3}{3}$:
$\frac{1}{5} \times \frac{3}{3} = $ _______
Problem 9. Create an alias by multiplying by $\frac{10}{10}$:
$\frac{1}{2} \times \frac{10}{10} = $ _______
Problem 10. Complete the costume:
$\frac{2}{3} \times \frac{?}{?} = \frac{6}{9}$
Problem 11. Find three aliases for $\frac{1}{2}$:
1. _______ 2. _______ 3. _______
Problem 12. Why do we multiply by $\frac{2}{2}$ instead of just $\frac{2}{1}$?
__________________________________________________________________
Problem 13. Solve: $\frac{3}{5} \times \frac{4}{4} = $ _______
Problem 14. Solve: $\frac{5}{8} \times \frac{2}{2} = $ _______
Problem 15. Draw a visual proof that $\frac{1}{3} = \frac{2}{6}$.
DRAW HERE
Lesson 4.4: Simplifying (The Redaction)
Problem 16. Simplify by dividing by $\frac{2}{2}$:
$\frac{4}{10} \div \frac{2}{2} = $ _______
Problem 17. Simplify by dividing by $\frac{3}{3}$:
$\frac{3}{9} \div \frac{3}{3} = $ _______
Problem 18. Simplify to the "Simplest Name":
$\frac{5}{10} = $ _______ $\frac{8}{12} = $ _______
Problem 19. Circle the fraction that is already in its simplest form:
$\frac{2}{4}$ $\frac{3}{6}$ $\frac{1}{2}$ $\frac{5}{10}$
Problem 20. Redact $\frac{50}{100}$ to its smallest alias. _______
Problem 21. Redact $\frac{20}{40}$ to its smallest alias. _______
Problem 22. If I have $\frac{6}{12}$ of a cake, how much of the cake do I have in the simplest name? _______
Problem 23. Simplify $\frac{9}{12}$ by dividing by 3. _______
Problem 24. Simplify $\frac{10}{50}$ by dividing by 10. _______
Problem 25. Explain what happens to the size of the pieces when you simplify a fraction.
__________________________________________________________________
Lesson 4.5: Verification
Problem 26. Use the Tug-of-War (Cross-Multiply) to see if these are equal:
$\frac{1}{2}$ and $\frac{4}{8}$
(____ × ____) = ____ (____ × ____) = ____
Are they equal? _______
Problem 27. Use the Tug-of-War:
$\frac{2}{3}$ and $\frac{5}{6}$
(____ × ____) = ____ (____ × ____) = ____
Are they equal? _______
Problem 28. Find the missing number to make them equal:
$\frac{1}{4} = \frac{?}{12}$ Answer: ____
Problem 29. Find the missing number:
$\frac{3}{5} = \frac{6}{?}$ Answer: ____
Problem 30. Challenge: Is $\frac{1}{1}$ an alias for $\frac{1,000}{1,000}$? ________
📜 The Scribe's Vow of Identity
"I, __________________________, do solemnly promise to look past the surface of things to find the Truth. I will not be deceived by large numbers, but I will seek the heart of the fraction. I will use the Law of One to remain true to my calling."
Signed on this day, ______________________.
Bonus Challenge Problems
Problem 31. Write 3 equivalent fractions for 1/3: _______, _______, _______
Problem 32. Write 3 equivalent fractions for 2/5: _______, _______, _______
Problem 33. Simplify 15/25 to its simplest form: _______
Problem 34. Simplify 18/24 to its simplest form: _______
Problem 35. Are 3/4 and 9/12 equivalent? Show your work using cross-multiplication.
Problem 36. Are 2/3 and 4/7 equivalent? Show your work.
Problem 37. Fill in: 3/4 = ___/8 = ___/12 = ___/16
Problem 38. What is the greatest common factor of 12 and 16? _______
Problem 39. Simplify 12/16 using the GCF: _______
Problem 40. Explain why 5/5 × 3/4 = 3/4 (the value doesn't change).
UNIT 4 SIGNET CHALLENGE
Task 1: Create 4 equivalent fractions for 1/2:
_______, _______, _______, _______
Task 2: Simplify these to lowest terms:
10/20 = _______ 6/9 = _______ 8/12 = _______
Task 3: Teach someone what equivalent fractions are:
I taught: _______________ Signature: _______________
Mentor's Signature: ___________________________ Date: ___________
Additional Practice
Problem 41. Circle all fractions equivalent to 1/2: 2/4, 3/5, 5/10, 4/9, 50/100, 6/12
Problem 42. Circle all fractions equivalent to 2/3: 4/6, 3/5, 6/9, 8/12, 10/14, 20/30
Problem 43. Fill in: 2/3 = 4/___ = 6/___ = 8/___ = 10/___
Problem 44. Fill in: 3/5 = ___/10 = ___/15 = ___/20 = ___/25
Problem 45. Simplify: 24/36 = _______
Problem 46. Simplify: 14/21 = _______
Problem 47. Find the missing number: 4/5 = 16/___
Problem 48. Find the missing number: ___/8 = 6/24
Problem 49. Which fraction is NOT equivalent to 3/4? Circle: 6/8, 9/12, 12/15, 15/20
Problem 50. Explain in your own words why 3/3 = 1 and why multiplying by 3/3 doesn't change a value.
Reflection Questions
1. Why are equivalent fractions like "aliases" or "nicknames"?
__________________________________________________________________
2. How does multiplying by n/n preserve the value of a fraction?
__________________________________________________________________
3. How does Hebrews 13:8 ("Jesus Christ the same yesterday, today, and forever") connect to equivalent fractions?
__________________________________________________________________
Common Equivalent Fraction Families
The Halves: 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 50/100
The Thirds: 1/3 = 2/6 = 3/9 = 4/12 = 5/15
The Fourths: 1/4 = 2/8 = 3/12 = 4/16 = 25/100
The Fifths: 1/5 = 2/10 = 3/15 = 4/20 = 20/100
More Practice: Cross-Multiplication
Problem 51. Use cross-multiplication: Are 5/6 and 15/18 equivalent? Show work: ___×___ = ___ and ___×___ = ___. Answer: _______
Problem 52. Use cross-multiplication: Are 3/7 and 9/21 equivalent? Show work: ___×___ = ___ and ___×___ = ___. Answer: _______
Problem 53. Use cross-multiplication: Are 4/9 and 8/16 equivalent? Show work: ___×___ = ___ and ___×___ = ___. Answer: _______
Problem 54. A recipe calls for 2/3 cup of flour. You want to triple the recipe. How many cups of flour? Express as an equivalent fraction: _______
Problem 55. If 6/10 of the class passed a test, simplify this to show the fraction in simplest form: _______
Problem 56. You ate 3/4 of a pizza. Express this as eighths: _______
Problem 57. Express 25/100 as a simpler fraction: _______
Problem 58. Express 75/100 as a simpler fraction: _______
Problem 59. If 1/4 = 3/12, what multiplication happened to both parts? _______
Problem 60. Challenge: Find a fraction equivalent to 7/8 with a denominator of 24: _______
Scripture Connection
Hebrews 13:8 — "Jesus Christ is the same yesterday and today and forever."
Like equivalent fractions, Jesus may be known by different names (Shepherd, King, Savior, Lord) but His identity never changes. Learning about equivalence teaches us that truth can appear in different forms while remaining the same at its core.
Quick Reference: Key Concepts
- Equivalent fractions: Different fractions that represent the same value.
- Creating equivalents: Multiply both top and bottom by the same number.
- Simplifying: Divide both top and bottom by the same common factor.
- Cross-multiplication: Test for equivalence by multiplying diagonally.
Master's Checklist for Unit 4
- [ ] I can create equivalent fractions by multiplying by n/n.
- [ ] I can simplify fractions by dividing by common factors.
- [ ] I can use cross-multiplication to test for equivalence.
- [ ] I completed all 40 problems.
- [ ] I completed the Signet Challenge.
Student Signature: ___________________________ Date: ___________
The Golden Thread of Identity
"For I am the Lord, I change not." — Malachi 3:6
Throughout Unit 4, you discovered that fractions can wear many "costumes" while remaining true to their essential value. The fraction 1/2 can appear as 2/4, 3/6, 50/100, or countless other aliases—yet its heart remains unchanged. This is the mystery of identity: true worth does not depend on appearances.
As you master equivalent fractions, remember this truth: God sees past our outer appearances to our hearts. He values faithfulness over fame, integrity over image. May your mathematical journey teach you to look for the unchanging truth beneath the surface of all things.
Step-by-Step Guides
How to Create an Equivalent Fraction:
- Choose a number (e.g., 2, 3, 4)
- Multiply BOTH numerator and denominator by that number
- Write the new fraction
Example: 2/3 × 4/4 = 8/12
How to Simplify a Fraction:
- Find a common factor of numerator and denominator
- Divide both by that factor
- Repeat until no common factors remain
Example: 12/16 ÷ 4/4 = 3/4