Open navigation menu
Mathematics
Unit rates, speed and proportion
Loading resource…
Loading resource…
Put goods on a scale to see that cost is proportional to quantity, read the number pairs on a double number line, answer unit-price questions, set your own prices and race cars to compare speeds.
Add a pair to the line
Enter both numbers, then choose Place point. A proportional pair becomes a point on the line.
Erases typed points and old points; keeps the current scale point, question points and the latest race point.
Point colours
- scale point
- typed point
- question point
- unit price point
Set 1/4
Unit price: how much does 1 orange cost, in thousand dong?
Model notes
- Unit price = cost : quantity; cost = quantity × unit price. Every pair on the double number line has the same ratio, so cost is proportional to quantity. Speed is a unit rate too: the kilometres covered in 1 hour.
- Prices in Shopping are made-up prices for the problems, in thousand dong (1 thousand dong = 1,000 dong), not market prices. Set the price lets you choose any 1–20 thousand dong for 1–20 pieces or kg, so it may differ from real prices.
- The resource rounds the same way for the scale, the line, the answers and the clock: money to 0.01 thousand dong (10 dong), quantities to 0.1 piece, masses to 0.01 kg, distances to 0.01 km, times to 0.01 h; an exact half rounds up. A pair is accepted when it is proportional after rounding.
- The line only shows 0–16 pieces (or 0–1.6 kg) and the track 0–200 km; these are limits of the resource, not of the arithmetic. Points outside the axes are not drawn.
- Points come from typing, the scale, the questions, the unit price and the race (in increasing priority). When two points share a top or a bottom value, the higher-priority point stays. When the scale changes or a new race finishes, the old point becomes an ordinary point that can be erased.
- A fruit bag holds 5 pieces and opens on the scale; a vegetable bag holds 3–4 pieces; a candy bag weighs 0.3–0.4 kg. The pictures of goods, bags and the scale are illustrations; read the numbers on the scale and the line.
- On the track each car moves at a constant speed (no speeding up or slowing down) and stops exactly at its flag; finish time = distance : speed. The model clock runs 2 hours per real second; with reduced motion the cars jump in 1-hour steps but the finish time stays exact.