Advanced Integration
📋 What it is
Combine ratios, proportions, percent and scale in one rich problem.
🗣️ Coach says
The toughest problems blend it all: scale a recipe (proportion), convert units (rate), apply a discount (percent). Integration is choosing the right ratio-tool at each step and carrying the numbers through cleanly.
🧠 Memory hook
A big problem chains ratio-tools: scale → convert → percent. Keep the numbers tidy.
😂 Giggle
What did the similar triangle say to the bigger triangle?
"We may be different sizes, but we have the exact same angles on life!"
😲 Whoa!
Mixing paint colours to an exact shade at scale is a real integration of ratios, proportions and percents.
✅ Quick check: Scale a 2:3 recipe up 4× AND find 10% waste. Which tool for each part?
Say your answer out loud first — then reveal.
A proportion to scale (→ 8:12), then a percent for the 10% waste.
Synthesis chains proportional scaling with a percent calculation.
🧪 Try it! (2 minutes)
Scale a 1:2 mix to serve 12, then reduce it 25%. Use a proportion then a percent.