Grade 5 · Count fractional portions in whole units · 260 of 750
Count fractional portions in whole units: whole units available: 2; equal portions per whole: 4
At a classroom activity, 2 whole units of a material are portioned into pieces of size 1/4. Find the number of portions in the original amount, 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
At a classroom activity, 2 whole units of a material are portioned into pieces of size 1/4. First find the number of portions in the original amount. Then answer: How many such portions would fit in one additional whole unit?
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A starting point
Division by a unit fraction asks how many small portions fit in the available whole amount. Each whole contains the denominator's number of portions, so smaller portions produce a larger count.
Work through the reasoning
Step 1
Identify the quantities and the task
At a classroom activity, 2 whole units of a material are portioned into pieces of size 1/4. The first task is to find the number of portions in the original amount. Division by a unit fraction asks how many small portions fit in the available whole amount. Each whole contains the denominator's number of portions, so smaller portions produce a larger count.
Step 2
Calculate the original result
2 ÷ (1/4) = 8. 8 portions fit exactly. Multiplying that count by 1/4 reconstructs the original 2 units.
Step 3
Complete the follow-up calculation
How many such portions would fit in one additional whole unit? 12 portions in total, 4 more than before.
The answer
2 ÷ (1/4) = 8. 8 portions fit exactly. Multiplying that count by 1/4 reconstructs the original 2 units. Follow-up: 12 portions in total, 4 more than before.
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.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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The mathematical idea
At a classroom activity, 2 whole units of a material are portioned into pieces of size 1/4. Division by a unit fraction asks how many small portions fit in the available whole amount. Each whole contains the denominator's number of portions, so smaller portions produce a larger count. 8 portions fit exactly. Multiplying that count by 1/4 reconstructs the original 2 units.
2 ÷ (1/4) = 8
03 · Reflect and transfer
Explain what changes and why.
Count the equal portions across every whole strip. A new strip repeats the same fractional unit rather than defining a larger whole. 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.