Longer problems that join two or more topics, such as area and cost, Pythagoras and money, ratio and algebra, in Foundation and Higher versions.
What you will learn
- Break a long problem into steps across different topics
- Round in the direction the situation needs
- Set up an equation from a ratio or a sequence
- Check that the final answer makes sense
Break it into steps
A long problem is often two or three shorter questions joined together.
Find the chain:
- paint a wall, 2 coats, 1 tin covers 8 m²
- area of the wall minus the window
- double it for two coats
- divide by the cover of a tin, and round up
- multiply by the price of a tin
Label each result ("area", "tins", "cost") so you can find it again.
- Fencing: the perimeter of a rectangle is 2 × length + 2 × width. Take off any gate, then divide by the length of a panel: 40 m of fence in 2.5 m panels needs 16 panels.
- Painting: the area to paint is the wall's length × height minus the window's. Two coats need twice the area.
- Journeys: time = distance ÷ speed. 90 km at 60 km/h takes 1.5 hours, which is 90 minutes. Add any break, then add the total to the start time.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Break it into steps
- Round for the situation
- Equations hiding in problems
- Check it makes sense
- Try it: An easy one first
8 practice questions, marked as you go; about 35 minutes in all.
In this unit: Problem solving and proof
Reasoning and problem solving: multi-step money problems, angle chains with reasons, interpreting and justifying with statistics, algebraic proof, and mixed problems across topics.