Grade 3 · Count equal fractional pieces · 627 of 750
Count equal fractional pieces: selected pieces: 3; equal pieces in each whole: 3
A supply strip for a classroom activity is cut into 3 equal pieces per whole, and 3 pieces are selected. Find the original selected amount as an exact fraction, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A supply strip for a classroom activity is cut into 3 equal pieces per whole, and 3 pieces are selected. First find the original selected amount as an exact fraction. Then answer: What fraction would one additional piece of the same size represent?
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A starting point
The denominator sets the size of one fractional unit. The numerator counts those units. Enough selected pieces can fill more than one whole, so fractions need not be less than one.
Work through the reasoning
Step 1
Identify the quantities and the task
A supply strip for a classroom activity is cut into 3 equal pieces per whole, and 3 pieces are selected. The first task is to find the original selected amount as an exact fraction. The denominator sets the size of one fractional unit. The numerator counts those units. Enough selected pieces can fill more than one whole, so fractions need not be less than one.
Step 2
Calculate the original result
3 pieces of 1/3 = 3/3. 3/3 has value 1.000 approximately. The exact fractional name remains valid even when its decimal does not terminate.
Step 3
Complete the follow-up calculation
What fraction would one additional piece of the same size represent? 4/3. The denominator stays 3 because the size of each piece does not change.
The answer
3 pieces of 1/3 = 3/3. 3/3 has value 1.000 approximately. The exact fractional name remains valid even when its decimal does not terminate. Follow-up: 4/3. The denominator stays 3 because the size of each piece does not change.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
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Watch the relationship
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The mathematical idea
A supply strip for a classroom activity is cut into 3 equal pieces per whole, and 3 pieces are selected. The denominator sets the size of one fractional unit. The numerator counts those units. Enough selected pieces can fill more than one whole, so fractions need not be less than one. 3/3 has value 1.000 approximately. The exact fractional name remains valid even when its decimal does not terminate.
3 pieces of 1/3 = 3/3
03 · Reflect and transfer
Explain what changes and why.
Color selected pieces in order, beginning a new equal-sized whole whenever the previous whole is full. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.