Patterns: find the rule

From “add 3 each time” to a rule that finds any term, even the 100th. Read one step, play with it, then tap “I understand this”.

Your progress0 of 4

Build a pattern with matchsticks

Every figure in a pattern has a position (1st, 2nd, 3rd …). If you know the position, a good rule tells you how many matchsticks you need, without drawing.

Play · Change the numbers

The matchstick pattern

Choose a pattern and change the figure number.

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Find the rule in three steps

The jump between terms tells you which times table the rule starts with. Then you check how much to add or subtract.

Play · Step through it

The rule finder

Tap “Next step” to find the rule step by step.

Why does the jump tell you the times table?

When the position goes up by 1, “position × 4” goes up by 4 every time. So if the terms jump by 4 each time, the rule must have “× 4”. The + or − at the end just shifts the whole row up or down.

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Use the rule for far-away terms

With the rule you get the 100th term in one sum: position × 4 + 3 gives 100 × 4 + 3 = 403. Counting all the way there would take very long!

In Grade 7 we write the rule with a letter: T = 4n + 3, where n is the position. You can also work backwards: which position gives 83? (83 − 3) ÷ 4 = 20.

Watch out: don’t just double

The 10th term is not just the 5th term × 2. If the rule has + 3, you would add the 3 twice. Always use the rule.

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Play: rules and terms

Game

Rule game

Find the rule or use it.

Correct: 0

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Check yourself

Remember this: your summary

The jump between terms tells you which times table the rule starts with.
Compare the terms with that table and add or subtract.
Test the rule on a term you know.
The 10th term is not the 5th term × 2: use the rule.
In algebra: T = an + b. Work backwards to find the position.

Write these points in your maths book. Read them again the night before the test.

Quiz

Quick questions

Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.

You ticked all 4 steps! Now you are ready for the quiz.

Free PDF to downloadPrint the practice sheet and practise on paper. The memo is on page 2: try on your own first.

Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
Patterns and algebra8 pages · PDFPaper Memo

All 14 free Grade 7 maths papers →

Ready for more? The Grade 7 patterns quiz gives you new questions every time.

Start the patterns quiz All Grade 7 classes

For parents

One step a day is enough. Ten calm minutes work better than an hour the night before the test.
Build the matchstick pattern with real matches (or toothpicks) and keep a table. Then ask: “How many for 50?”
Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.

Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.