🔑 Key Concepts
- A ratio compares two quantities.
- A part-to-part ratio compares one part of a group to another part of the same group.
- A part-to-whole ratio compares one part of a group to the total amount.
- Fractions are a type of part-to-whole ratio because they compare a part to the whole.
- Always read the question carefully. Shaded to total is different from shaded to unshaded.
✏️ Worked Examples
🧠 Math Vocabulary
- Ratio: a comparison of two quantities.
- Part-to-part ratio: a ratio that compares one part of a group to another part of the same group.
- Part-to-whole ratio: a ratio that compares one part of a group to the total amount.
- Fraction: a number that compares a part to a whole. A fraction is a type of part-to-whole ratio.
- Total: the whole amount, including all parts of the group.
💡 Main Idea
When a question asks for a ratio, the words matter. Shaded to unshaded is a part-to-part comparison, but shaded to total is a part-to-whole comparison. Fractions are part-to-whole ratios because they compare part of a group to the entire group.
📚 What You Should Already Know
Students should know how to count shaded and unshaded parts, identify the total number of objects, write ratios in the correct order, and simplify ratios by dividing both numbers by a common factor.
🚀 What Comes Next
After connecting part-to-whole ratios with fractions, students can use this idea to understand equivalent ratios, percent, ratio tables, proportional relationships, and real-world comparison problems.
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