Today is rung 10 of 15 on this topic
Ratios, rates and proportional reasoning
Can do: Uses ratio tables and unit rates to solve problems, and knows when a situation is proportional.
Why it matters
Proportional reasoning is the most important idea in middle school maths — it underpins percent, scale, slope, similarity, density and speed.
What it looks like when it's wobbly
Adds instead of scaling: if 3 pens cost $6, they think 5 pens cost $8 by adding 2.
⏱️ Two-minute check
"If 4 tickets cost $30, what do 10 cost?" and "Which is better value: 500 g for $3 or 800 g for $4.60?"
Solid looks like: $75, and the second with a unit rate calculated.
The full activity for this topic · 20 minutes
Unit Price at the Shop
- 1Take three products with different pack sizes and work out price per 100 g for each.
- 2Compare and decide which is actually the best value.
- 3Build a ratio table for one product: 1, 2, 5, 10 units, filling in prices.
- 4Ask what stays constant — the unit rate — and mark it on the table.
- 5Try a non-proportional situation, like a taxi with a flat fee, and see why the table breaks.
If it's too hard
Double and halve within a ratio table before jumping to arbitrary values.
If it's too easy
Compare three products in different units, and handle a special offer that breaks proportionality.
Say this
"What's the cost of exactly one? Once you have that, every other quantity is easy."