Grade 5 · Redistribute data without changing the total · 275 of 750
Redistribute data without changing the total: first measured amount: 4; second measured amount: 5; third measured amount: 12
Three measured amounts at a classroom activity are 4, 5, and 12 units. Find the fixed total and the exact equal share, 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
Three measured amounts at a classroom activity are 4, 5, and 12 units. First find the fixed total and the exact equal share. Then answer: What is the exact equal share, and how can it be checked?
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A starting point
The arithmetic mean is the common amount obtained by redistributing a fixed total equally. Each group's amount may change during sharing, but the combined total remains unchanged.
Work through the reasoning
Step 1
Identify the quantities and the task
Three measured amounts at a classroom activity are 4, 5, and 12 units. The first task is to find the fixed total and the exact equal share. The arithmetic mean is the common amount obtained by redistributing a fixed total equally. Each group's amount may change during sharing, but the combined total remains unchanged.
Step 2
Calculate the original result
Mean = (4 + 5 + 12) / 3 = 7.000 approximately. The total is 21. Each equal share is exactly 21/3 units, even when the decimal representation repeats.
Step 3
Complete the follow-up calculation
What is the exact equal share, and how can it be checked? 7/1 units per group. Multiplying this by 3 recovers the total 21.
The answer
Mean = (4 + 5 + 12) / 3 = 7.000 approximately. The total is 21. Each equal share is exactly 21/3 units, even when the decimal representation repeats. Follow-up: 7/1 units per group. Multiplying this by 3 recovers the total 21.
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
Three measured amounts at a classroom activity are 4, 5, and 12 units. The arithmetic mean is the common amount obtained by redistributing a fixed total equally. Each group's amount may change during sharing, but the combined total remains unchanged. The total is 21. Each equal share is exactly 21/3 units, even when the decimal representation repeats.
Mean = (4 + 5 + 12) / 3 = 7.000 approximately
03 · Reflect and transfer
Explain what changes and why.
Move the timeline to redistribute amounts toward three equal bars. Check that no material is created or lost while the bar heights become equal. 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.