Term to term rules matching| KS3 maths sequences | Teachit - Free Printable

The image you've uploaded is a teacher's resource for a mathematics activity focused on describing sequences using term-to-term rules. It includes instructions, teacher notes, and a table of answers. Let me break down the content and explain how it works.

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🔍 Overview of the Activity

This is a matching card game designed for students to practice identifying sequences based on their term-to-term rules (i.e., how each term changes from one to the next).

#### 🧩 How the Activity Works:
- There are 24 cards, arranged randomly.
- Students cut them out and match three cards per group:
1. The first four terms of a sequence (e.g., `4, 9, 14, 19, ...`)
2. The rule for generating the sequence (e.g., "First term 4, Add 5")
3. The next four terms in the sequence (e.g., `... 24, 29, 34, 39`)

Each group of three cards represents one complete sequence.

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✔ Answer Key Table Explained

Here’s the table provided with explanations:

| First Four Terms | Term-to-Term Rule | Next Four Terms |
|------------------|--------------------|------------------|
| 4, 9, 14, 19, ... | First term 4<br>Add 5 | ... 24, 29, 34, 39 |
| 11, 8, 5, 2, ... | First term 11<br>Subtract 3 | ... -1, -4, -7, -10 |
| 7, 10, 13, 16, ... | First term 7<br>Add 3 | ... 19, 22, 25, 28 |
| -8, -5, -2, 1, ... | First term -8<br>Add 3 | ... 4, 7, 10, 13 |
| 8, 4, 0, -4, ... | First term 8<br>Subtract 4 | ... -8, -12, -16, -20 |
| 3, 8, 13, 18, ... | First term 3<br>Add 5 | ... 23, 28, 33, 38 |
| 3, 7, 11, 15, ... | First term 3<br>Add 4 | ... 19, 23, 27, 31 |
| 8, 5, 2, -1, ... | First term 8<br>Subtract 3 | ... -4, -7, -10, -13 |

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🔎 How to Verify the Answers

Let’s walk through one example:

#### Example: `4, 9, 14, 19, ...`
- Rule: Start at 4, add 5 each time.
- Check:
4 → 4+5 = 9 → 9+5 = 14 → 14+5 = 19 ✔
- Next four terms:
19 + 5 = 24
24 + 5 = 29
29 + 5 = 34
34 + 5 = 39
So: `... 24, 29, 34, 39` ✔

Similarly, check another:

#### Example: `11, 8, 5, 2, ...`
- Rule: Start at 11, subtract 3 each time.
- 11 → 8 → 5 → 2 ✔
- Next:
2 - 3 = -1
-1 - 3 = -4
-4 - 3 = -7
-7 - 3 = -10
So: `... -1, -4, -7, -10` ✔

All entries follow this logic.

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📌 Teaching Purpose & Skills Developed

This activity helps students:
- Recognize arithmetic sequences (constant difference between terms).
- Understand term-to-term rules (how to get from one term to the next).
- Practice predicting future terms.
- Develop pattern recognition and logical reasoning.

It’s ideal for KS3 or GCSE level maths, focusing on foundational algebra skills.

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🔄 Extension Ideas (Optional)

To deepen learning, teachers could ask students to:
- Find the nth term formula (e.g., for `4, 9, 14, 19, ...`, the nth term is `5n - 1`).
- Create their own sequences with different rules.
- Explore non-linear sequences (though this activity focuses only on linear ones).

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✔ Conclusion

This worksheet is a well-designed, hands-on way for students to learn about sequences and term-to-term rules. The answer key confirms that all sequences are arithmetic with a constant common difference, and the next four terms are correctly calculated by applying the rule repeatedly.

If you're a teacher, you can use this as a group activity or plenary task. If you're a student, try matching the cards without looking at the answers first!

Let me know if you'd like a printable version or want help creating more sequences!