Rules for Patterns Using Words and Tables

Warning: Your screen size is quite small for viewing this. Rotate your device into landscape mode if you can.

1 Getting Started
2 Watch and Notice
3 Try It Together
4 Build the Table in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Illustration for Getting Started Here is a growing tile pattern: pattern 1, then pattern 2, then pattern 3, each one a little bigger than the last. Pattern 1 uses 3 tiles, pattern 2 uses 5 tiles, pattern 3 uses 7 tiles.

Big question

Now the big question: how many tiles would pattern 10 need? Could you work it out without drawing all ten patterns?

Teacher Notes

Display the three growing patterns as pupils settle. Give five seconds of quiet think-time before any hands go up, then take three hands-up answers. Do not confirm a correct answer yet — the point is to leave the question open so the table feels useful in the next step.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~8 mins

This machine takes a term-number in and hands back a value using a hidden rule. We feed in 1, 2 and 3, read off what comes out, and work out the rule each time. Watch the jump between the values.

Teacher Notes

First machine: values 3, 5, 7. Point at the jumps, 3 to 5 up 2, 5 to 7 up 2, so grows by 2 each term. Check term 1: 2 x 1 = 2 but we have 3, so 1 extra. Rule: tiles = 2 x term + 1.

Second: ask them to predict the jump before you send these through. Values 3, 6, 9, up 3 each time. Check term 1: 3 x 1 = 3, nothing extra. Rule: tiles = 3 x term.

Third: predict the jump again. Ask what number the values jump by. Values 3, 7, 11, 15, up in fours. Check term 1: 4 x 1 = 4 but we have 3, so 1 short, take one off. Rule: tiles = 4 x term - 1.

Revoice from a pupil: the step between values tells you the number you multiply by.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~10 mins

Today we work through this growing pattern together: term 1 gives 4, term 2 gives 7, term 3 gives 10. I will send the next term-numbers through the machine and build a two-row table on the board as the values land, while you watch and call out each value. Then we will agree on the rule in words together.

Find the rule: 4, 7, 10

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Send term 4 and term 5 through the machine; write each term-number and value into a two-row table on the board as it lands, so pupils see the table take shape before they copy it next step. Ask 'what is the step between values?' (3) before anyone names the full rule, then ask how many lots of the term that gives. Revoice a strong answer as 'so it is three times the term number, then add one'. Watch for pupils who say the rule is just add three — that continues the pattern but cannot leap to a far term; steer them to the three times the term form.

+15 XP

4 - Build the Table in Your Copy ~3 mins

COPYBOOK MOMENT

Illustration for Build the Table in Your Copy In your maths copy, draw a two-row table with the top row labelled term-number and the bottom row labelled value. Fill in terms 1 to 5 for our pattern, then write the rule as a sentence underneath the table.

Teacher Notes

Walk the room glancing for two things: the table is drawn with two clear rows, and the rule sentence underneath uses times the term number, not just add three. This is whole-class copybook practice, not marking.

+10 XP

5 - Class Challenge ~8 mins

Now we crack the rule for three of these patterns by sending term-numbers through the machine and watching the values. Once we have the rule, we will use it to leap straight to a far term, without drawing every step in between. Here are our three patterns:

Pattern A: term 1 gives 2, term 2 gives 4, term 3 gives 6.
Pattern B: term 1 gives 5, term 2 gives 8, term 3 gives 11.
Pattern C: term 1 gives 2, term 2 gives 6, term 3 gives 10 — and once we have the rule, we leap all the way to term 10.

Crack the hidden rule

Teacher Notes

These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining. The three patterns and their rules are:

Pattern A — 1→2, 2→4, 3→6. Step of 2, no adjustment, so the rule is value = 2 × term.
Pattern B — 1→5, 2→8, 3→11. Step of 3; term 1 gives 3 but we have 5, so add 2: value = 3 × term + 2.
Pattern C — 1→2, 2→6, 3→10. Step of 4; term 1 gives 4 but we have 2, so take 2 off: value = 4 × term − 2. Leap to term 10: 4 × 10 − 2 = 38.

For each challenge, have a pupil probe one more input to test their guess, then build and check the rule. After the rule is confirmed, ask the class 'so what would term 10 be?' so they practise leaping to a far term. Pattern C has a minus part — watch for pupils stopping at four times the term and forgetting to take 2 off.

+15 XP

6 - What Did We Notice? ~3 mins

MATHS TALK

How does the table help us see the rule that the picture hides? Which was easier for you: reading the rule from the row of patterns, or reading it from the table of numbers?

Teacher Notes

Listen for pupils naming the step between values as the clue to the multiplier. Revoice a strong answer: so once we know the step, we know the times-number, and the rest is just the adjustment. Head off the idea that add the step each time is a full rule — push them to see why times the term is what lets you leap to term 50 without listing every term in between.

+10 XP

7 - What's Next ~3 mins

What we learned

A two-row table of term-number against value lays a pattern out so its rule is easy to spot.
The step between values tells you the number to multiply the term by; the rest of the rule is the adjustment that sets where the pattern starts.
Once you have the rule in words, you can leap straight to any term without drawing every step.

Coming up

Next we look at the properties of operations and the distributive law — how multiplication shares out over addition, so a tricky product becomes two easy ones.

Teacher Notes

Keep this brisk. Recap the three bullets, then point forward to the distributive law lesson.

+5 XP

Pupil practice

Module 10 · Algebra: Patterns, Expressions and Equations Mixed

Lesson 105 · Rules for Patterns Using Words and Tables

Download Activity Book page (PDF)

End of lesson

123learn · Online learning platform

Unlock the full learning experience

You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

Hundreds of curriculum-aligned lessons

Interactive activities in every lesson

Printable resources & progress tracking

Get started

Copyright Notice
This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.

Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~8 mins

3 - Try It Together ~10 mins

Find the rule: 4, 7, 10

4 - Build the Table in Your Copy ~3 mins

5 - Class Challenge ~8 mins

Crack the hidden rule

6 - What Did We Notice? ~3 mins

7 - What's Next ~3 mins

What we learned

Unlock the full learning experience

XP