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Two-Variable Pattern Rules

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Two-Variable Pattern Rules

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📚 WALT: Create, continue and describe two-variable patterns

We Are Learning To: link the step number to the number of objects and explain the rule.

Success criteria: I can continue a pattern, complete a table, describe the increase or decrease, and use my rule to find a later term.

Use cubes or tiles if you need them. Look for what happens next.

1. Continue the growing spatial pattern. Draw step 4 and write how many squares it has.

Step 1: ■    Step 2: ■ ■ ■    Step 3: ■ ■ ■ ■ ■

Step 4:

Number of squares: ______    The pattern increases by ______ each step.

2. Continue this pattern to the next two terms. Draw or use numbers.

■ ■   →   ■ ■ ■ ■   →   ■ ■ ■ ■ ■ ■   →   ______   →   ______

The rule is: start at ______ and __________________________ each step.

3. Complete the number pattern. Show the increase or decrease between terms.

18   →   15   →   12   →   ______   →   ______

The rule is to __________________ each time.

✏️ Part 2: Link the two variables

Complete each two-variable record. The headings are colour-coded: 🔵 step number and 🟢 number of objects.

4. The pattern starts with 1 object and increases by 2 each step. Complete the record.

🔵 Step:    1    2    3    4    5

🟢 Objects:   1    3    5    ______    ______

Arrows: 1   →   3   →   5   →   ______   →   ______

5. Complete the record for a pattern that starts at 16 and decreases by 3 each step.

🔵 Step:    1    2    3    4

🟢 Objects:   16    ______    ______    ______

Rule: The number of objects __________________________________________.

6. Write the rule in words, numbers or a picture.

Step 1 has 2 objects, step 2 has 5 objects, and step 3 has 8 objects.

My rule is: __________________________________________________________

7. Challenge: Use your rule from Question 4 to find the number of objects at step 10. Explain how you know.

Step 10 has ______ objects.

🎨 Part 3: Design a pattern for a classmate

Support: You may use cubes, tiles, numbers or drawings. Keep your values mainly within 20.

Extension: Make the increase change each time, such as adding 1, then 2, then 3. Ask your classmate to find a later term.

8. Create a growing spatial or number pattern with at least four steps. Include arrows between terms.
9. Complete the linked record for your pattern.

🔵 Step:    1    2    3    4    Later step: ______

🟢 Objects:   ______    ______    ______    ______    ______

My rule: _____________________________________________________________

──────────── fold line ────────────

10. Write the answer and rule here for your classmate to check.

The later term is ______ because _____________________________________

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