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5 Classrooms Sharing 4 Packages: How Fraction Models and Answers Change
Mathematics
Grade 5 of Primary School
Question Content
Look at the Example. Suppose only 5 classrooms share 4 packages. How would the model in the Example change? How would the answer change?
Correct Answer
1. Model change: Represent 4 packages (each as a whole) divided into 5 equal parts total, with each classroom getting 1/5 of each package, so 4*(1/5) = 4/5 of a package. Visually, if the original model used whole shapes for packages, you would split each of the 4 whole shapes into 5 equal sections, and assign one section from each shape to a classroom. 2. Answer change: Each classroom would receive 4/5 of a package instead of the original example's answer (which was likely a larger fraction or whole number based on more packages per classroom).
Detailed Solution Steps
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Step 1: Identify the division context: We are dividing 4 packages equally among 5 classrooms, which is represented by the division expression 4 ÷ 5.
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Step 2: Analyze the model change: If the original example used a model like fraction bars or circles for packages, we now need 4 full 'package' shapes, each split into 5 equal parts. Each classroom will get one part from each of the 4 packages.
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Step 3: Calculate the new answer: Using the rule for dividing a whole number by a whole number (a ÷ b = a/b for non-zero b), 4 ÷ 5 = 4/5. Compare this to the original example's answer: since we have fewer packages per classroom than a 1:1 ratio, the new answer is a proper fraction less than 1, which is smaller than the original example's result (which would have been ≥1 if more packages per classroom or equal to 1 if same number of packages and classrooms).
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Step 4: Summarize the model and answer changes clearly, linking the visual model to the fractional result.
Knowledge Points Involved
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Division of Whole Numbers as Fractions
When dividing a whole number a by a whole number b (b ≠ 0), the result is the fraction a/b, which represents the equal share each group receives. This is used to solve equal distribution problems, like splitting objects or resources among groups.
2
Fraction Models for Division
Visual models (such as fraction bars, circles, or area models) are used to represent division of whole numbers as fractions. Each whole (package, in this case) is split into equal parts corresponding to the number of groups, and the total share per group is the sum of one part from each whole.
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Comparing Fractional Results
When solving similar distribution problems with different numbers of items and groups, we can compare the resulting fractions to see how the share per group changes. Fewer items per more groups results in a smaller fractional share.
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