Terms: The numbers in a pattern

Rule: The instruction for finding the next term

First term: The starting number

Addition Rule: Add the same number each time

Example: Add 5 → 3, 8, 13, 18, 23...

Subtraction Rule: Subtract the same number each time

Example: Subtract 7 → 100, 93, 86, 79, 72...

Multiplication Rule: Multiply by the same number each time

Example: Multiply by 2 → 5, 10, 20, 40, 80...

Division Rule: Divide by the same number each time

Example: Divide by 3 → 81, 27, 9, 3, 1...

Combined Rules: More than one operation

Example: Add 3, then subtract 1 → 10, 13, 12, 15, 14...

Step 1: Look at the given numbers

Step 2: Find the difference or relationship between consecutive terms

Step 3: Identify the rule (add, subtract, multiply, divide)

Step 4: Apply the rule to find missing numbers

Step 5: Check your answer by applying the rule again

Example 1: Complete the pattern: 7, 12, 17, 22, __, __

Example 2: Complete: 80, 72, 64, __, __, 40

Example 3: Rule: Start at 5, add 1, then add 2, then add 3, and so on

1. Compare Rules: Are the rules the same or different?

2. Compare Terms: Which pattern has larger/smaller numbers?

3. Compare Growth Rate: Which pattern increases/decreases faster?

4. Compare Relationships: Is one pattern related to the other?

Step 1: Write both patterns

Step 2: Find the rule for each pattern

Step 3: Compare corresponding terms (1st to 1st, 2nd to 2nd, etc.)

Step 4: Look for relationships or patterns between the two sequences

Example 1: Compare these patterns

Example 2: Compare related patterns

Example 3: Using a table to compare

1. Constant Addition Pattern

Add the same number each time

Example: 10, 15, 20, 25, 30... (Add 5)

2. Increasing Addition Pattern

The amount you add increases each time

Example: 2, 3, 5, 8, 12... (Add 1, add 2, add 3, add 4)

3. Multiplication Pattern

Multiply by the same number each time

Example: 2, 6, 18, 54... (Multiply by 3)

Find the difference between consecutive terms

Example 1: Complete: 13, 18, 23, 28, __, __, __

Example 2: Complete: 1, 3, 6, 10, 15, __, __

Next Term = Previous Term × Common Ratio

Divide any term by the previous term

Multiplier = Second Term ÷ First Term

Example 1: Complete: 4, 12, 36, __, __

Example 2: Complete: 5, 10, 20, 40, __, __

Example 3: Find the 6th term: 3, 15, 75, 375, ...

• Saving money regularly

• Growing plants or populations

• Building structures with blocks

• Seating arrangements at events

• Distance traveled at constant speed

Step 1: Read the problem carefully

Step 2: Identify the pattern in the situation

Step 3: Write the first few terms as numbers

Step 4: Find the rule

Step 5: Apply the rule to answer the question

Problem 1: "Maya saves $5 in week 1, $10 in week 2, $15 in week 3. If this pattern continues, how much will she save in week 6?"

Problem 2: "A bacteria colony doubles every hour. If there are 8 bacteria at 1:00 PM, how many will there be at 4:00 PM?"

Problem 3: "A theater has 20 seats in row 1, 25 seats in row 2, 30 seats in row 3. If this pattern continues, how many seats are in row 8?"

1. Look: Examine the given terms

2. Think: Ask yourself questions:

• Are numbers getting larger or smaller?

• Is there a constant difference?

• Is multiplication or division involved?

• Is the pattern more complex?

3. Test: Check if your rule works for all terms

4. Apply: Use the rule to complete the pattern

Problem 1: 100, 90, 80, 70, __, __

Problem 2: 2, 6, 18, 54, __, __

Problem 3: 1, 4, 9, 16, 25, __, __

Problem 4: 10, 12, 15, 19, 24, __, __

Problem 5: 5, 10, 8, 16, 14, 28, 26, __, __

✓ Always check your rule by testing it on all given terms

✓ Look for patterns in the differences between consecutive terms

✓ Increasing patterns: Terms get larger (add or multiply)

✓ Decreasing patterns: Terms get smaller (subtract or divide)

✓ Some patterns may have more than one rule (alternating patterns)

✓ Multiplication patterns grow much faster than addition patterns

✓ Write down your work step-by-step to avoid mistakes

✓ In word problems, identify the numbers before finding the pattern

✓ Practice makes perfect - the more patterns you solve, the easier they become!

For Addition/Subtraction Patterns:

Ask: "What do I add or subtract to get from one number to the next?"

For Multiplication/Division Patterns:

Ask: "What do I multiply or divide by to get from one number to the next?"

The "STOP" Method:

See the pattern

Test your rule

Operate to find next terms

Prove it works!

If stuck, try this:

1. Check if it's skip counting (2, 4, 6... or 5, 10, 15...)

2. Check if it's doubling (×2) or tripling (×3)

3. Check if there's an alternating pattern (two rules taking turns)