Equal Pieces Discovery Activity
Grade 4 Math • Fraction Concepts
Equal Pieces Discovery Activity
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Big Question: Why can’t we just add the top numbers and bottom numbers together when fractions have different sized pieces?
1
The Bakery Dilemma: Maya and Noah's Pans
Maya and Noah each baked an identical pan of brownies. Maya has \( \frac{1}{2} \) of her pan left. Noah has \( \frac{1}{4} \) of his pan left.
Maya's Pan: \( \frac{1}{2} \) 1/2 Eaten 1 large slice out of 2
Noah's Pan: \( \frac{1}{4} \) 1/4 Eaten (3/4) 1 small slice out of 4
Alex says: "Maya has 1 piece and Noah has 1 piece. That's \( 1 + 1 = 2 \) pieces total. So together they have \( \frac{2}{6} \) of a pan!"
Look closely at the slices above. Why is Alex's thinking incorrect?
2
The Solution: Re-partitioning into Equal Sizes
To count pieces together, all pieces must be the exact same size. Draw a dashed vertical line down Maya’s half to slice it into fourths, just like Noah’s pan!
Step 1: Slice Maya's Half 1/4 1/4 \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \)
Step 2: Noah's Piece 1/4 \( \frac{1}{4} \) is already fourths
=
Step 3: Combined in 1 Pan 1/4 1/4 1/4 Total: 3 fourth-sized pieces
Complete the equation:
\( \frac{1}{2} + \frac{1}{4} \) becomes \( \frac{\underline{\hspace{0.8cm}}}{4} + \frac{1}{4} \) = \( \frac{\underline{\hspace{0.8cm}}}{4} \)
Page 1 • Visual Discovery Flip over for hands-on practice
P.2
Practice: Partitioning to Create Common Sizes
Use a pencil and straightedge
A Adding Thirds and Sixths: \( \frac{1}{3} + \frac{1}{6} \) Model 1
Notice the pieces are different lengths. Split each third in the top bar into 2 equal parts so they match the sixths below!
\( \frac{1}{3} \) Bar: 1/3 ← Draw lines to make sixths
\( \frac{1}{6} \) Bar: 1/6 Already in sixths
How many sixths equal \( \frac{1}{3} \)?
\( \frac{1}{3} = \frac{\underline{\hspace{1cm}}}{6} \)
Now add the common-sized pieces:
\( \frac{\underline{\hspace{0.8cm}}}{6} + \frac{1}{6} = \frac{\underline{\hspace{0.8cm}}}{6} \)
B Adding Halves and Eighths: \( \frac{1}{2} + \frac{3}{8} \) Model 2
Jordan wants to add \( \frac{1}{2} \) and \( \frac{3}{8} \). He needs eighth-sized pieces. Partition the top bar into 8 equal parts!
\( \frac{1}{2} \) Bar: 1/2 ← Partition half into 4 pieces
\( \frac{3}{8} \) Bar: 3/8 shaded Already in eighths
Rename \( \frac{1}{2} \) as eighths:
\( \frac{1}{2} = \frac{\underline{\hspace{1cm}}}{8} \)
Add the eighths together:
\( \frac{\underline{\hspace{0.8cm}}}{8} + \frac{3}{8} = \frac{\underline{\hspace{0.8cm}}}{8} \)
Math Detective: Spot the Error!
Sam solved this problem on his test: \( \frac{1}{4} + \frac{1}{2} = \frac{2}{6} \)
Explain what Sam did wrong using the words size and pieces:
The Golden Rule
Fill in the key conclusion:
Before we can add fraction pieces, they must be partitioned into sized parts so that we are counting the same !
Word bank: unit, equal, large, numerator
Page 2 • Synthesis & Application Great job exploring fraction pieces!
