🔑 Key Concepts
- A part-to-part ratio compares two parts of a group, such as boys to girls.
- The total is found by adding the parts together.
- A ratio table can show how both parts increase together.
- Adding a total column helps students see how the total number increases proportionally.
- Always answer the question being asked. Sometimes the question asks for one part, and sometimes it asks for the total.
✏️ Worked Examples
🧠 Math Vocabulary
- Part-to-part ratio: a ratio that compares one part of a group to another part of the same group.
- Total: the complete amount found by adding all parts together.
- Ratio table: a table that organizes equivalent ratios.
- Equivalent ratios: ratios that describe the same relationship.
- Scale factor: the number used to multiply each part of a ratio.
💡 Main Idea
When a problem gives a part-to-part ratio and asks for the total, use the ratio table to find the missing part first. Then add the parts together. A total column is helpful because it shows how the whole group increases as the parts increase.
📚 What You Should Already Know
Students should know how to read a ratio in the correct order, create equivalent ratios, use multiplication patterns, and add the parts of a group to find the total.
🚀 What Comes Next
After solving part-to-part ratio problems with totals, students can use similar reasoning with proportions, double number lines, percent problems, and real-world proportional relationships.
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