Story Solver Reference Sheet
Story Solver Reference Sheet
Turn equal sharing story problems into Division Equations, Fractions, and Visual Models
The G - S - T Problem Decoder Key
Ask these 3 questions for every story problem:
T = Total TOP
What is being shared?
The whole amount, items, food, ribbon, or distance.
= Numerator (Dividend)
G = Groups BOTTOM
Who is sharing it?
The people, plates, bags, bowls, or equal parts.
= Denominator (Divisor)
S = Size ANSWER
How much does 1 get?
The fraction or amount each individual group receives.
= Quotient (Result)
Total (T) ÷ Groups (G) = Size (S)
⇔
Fraction Form:
Total (T) Groups (G)
= Size of 1 Share
1 Identify G, S, and T in the story
2 Write Division & Fraction equation
3 Draw and partition the model
Case 1 Total < Groups
Story: 3 mini pizzas are shared equally among 4 friends. How much does each friend get?
Total (T)
3 pizzas
Groups (G)
4 friends
Size (S)
? per friend
Division 3 ÷ 4
=
Fraction \( \frac{3}{4} \)
=
Answer \( \frac{3}{4} \) pizza
Visual Model (Cut each pizza into 4 parts): 1 piece each
Pizza 1
1/4
1/4
1/4
1/4
Pizza 2
1/4
1/4
1/4
1/4
Pizza 3
1/4
1/4
1/4
1/4
\( \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \mathbf{\frac{3}{4}} \) pizza per friend
Case 2 Total > Groups
Story: 5 granola bars are shared equally between 2 hikers. How much does each hiker get?
Total (T)
5 bars
Groups (G)
2 hikers
Size (S)
? per hiker
Division 5 ÷ 2
=
Improper \( \frac{5}{2} \)
=
Mixed Number \( 2\frac{1}{2} \) bars
Visual Model (Split 5 wholes among 2): 2 wholes + 1 half
Hiker 1:
Bar 1
Bar 2
\( \frac{1}{2} \)
\( \frac{1}{2} \)
\( 2\frac{1}{2} \)
Hiker 2:
Bar 3
Bar 4
\( \frac{1}{2} \)
\( \frac{1}{2} \)
\( 2\frac{1}{2} \)
\( 1 + 1 + \frac{1}{2} = \mathbf{2\frac{1}{2}} \) (or \( \mathbf{\frac{5}{2}} \)) bars per hiker
Scholar Trap Alert: Do NOT just put the bigger number first!
Always ask yourself: "What is getting sliced or shared?" That item is ALWAYS your Total (Numerator), even if it is smaller than the number of groups!
