Turning real situations into algebra
A phone contract, a taxi fare, and a football league table can all be described by the same kind of formula — once you know how to spot the pattern.
Part of your national curriculum
- Algebra: Model situations or procedures by translating them into algebraic expressions or formulae
Lesson overview
What you'll learn in this lesson
Model situations or procedures by translating them into algebraic expressions or formulae
Key learning points
- • From words to expressions
- • Worked example
- • Building your own formula
This lesson at a glance
- 27 minutes
- 16 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 16
Visual introductionPicture this
Turning real situations into algebra
A phone contract, a taxi fare, and a football league table can all be described by the same kind of formula — once you know how to spot the pattern.
In a nutshell
Model situations or procedures by translating them into algebraic expressions or formulae
Learning cycle
Part 2 of 16
Learning cycle 1 of 2
Part 1 · From words to expressions
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 16
Learn
From words to expressions
A taxi charges £3 plus £2 per mile. If m is the number of miles, the cost formula is C = 3 + 2m. Each part of the sentence maps directly onto a term in the expression.
Reset break
Part 4 of 16
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 16
Learn
Worked example
Using C = 3 + 2m, find the cost of a 7-mile journey: C = 3 + 2 × 7 = 3 + 14 = £17. Substituting a number into the formula gives a real answer.
Quick check
Part 6 of 16
Quick check
Part 7 of 16
Reset break
Part 8 of 16
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 16
Learning cycle 2 of 2
Part 2 · Building your own formula
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 16
Learn
Building your own formula
A gym charges a £15 joining fee plus £8 per month for n months. The total cost formula is T = 15 + 8n. Checking with n = 4: T = 15 + 32 = £47.
Quick check
Part 11 of 16
Quick check
A gym costs £15 joining fee plus £8 per month (n). What is the cost for 4 months?
Reset break
Part 12 of 16
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 16
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 14 of 16
Game · Recall cards
A taxi costs £3 plus £2 per mile (m). Which formula matches?
Card 1 of 3
Mastery quiz
Part 15 of 16
Marked quiz
End of lesson quiz: Turning real situations into algebra
3 questions, marked with the reasoning shown. No timer.
1. A taxi costs £3 plus £2 per mile (m). Which formula matches?
2. Using C = 3 + 2m, what is the cost of a 7-mile journey?
3. A gym costs £15 joining fee plus £8 per month (n). What is the cost for 4 months?
Lesson round-up
Part 16 of 16
Lesson round-up
Ready when you are
Quiz score
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Points this lesson
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Best run
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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 16 · Watch & discover
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Model situations or procedures by translating them into algebraic expressions or formulae