What is the missing number?
Arithmetic Sequence: Numbers that increase by the same amount each time
- Look at the first few numbers
- Find the difference between consecutive numbers
- Apply the same difference to find the next number
We have: 7, 14, 21, 28, __, 42
14 - 7 = 7, 21 - 14 = 7, 28 - 21 = 7
The pattern is adding 7 each time!
28 + 7 = 35, and 35 + 7 = 42 ✓
The sequence is: 7, 14, 21, 28, 35, 42
• Pattern Recognition: Find the consistent change between numbers
• Consistent Addition: Same number added each time
• Verification: Check that the pattern continues correctly
If the pattern continues, how much will she save on Saturday?
Increasing Pattern: Numbers that get bigger following a rule
$2
$4
$6
$8
$10
?
Monday: $2, Tuesday: $4, Wednesday: $6
$4 - $2 = $2, $6 - $4 = $2
She saves $2 more each day!
Thursday: $6 + $2 = $8
Friday: $8 + $2 = $10
Saturday: $10 + $2 = $12
Emma will save $12 on Saturday
• Daily Increase: Same number added each day
• Sequential Counting: Continue the pattern day by day
• Verification: Check that the pattern holds consistently
What shape comes next in the 13th position?
Repeating Pattern: Shapes that repeat in the same order
The pattern repeats every 3 shapes: Star, Heart, Diamond
To find the 13th shape: 13 ÷ 3 = 4 remainder 1
This means after 4 full cycles, we're at the 1st position in the next cycle
The 1st position in the pattern is Star (⭐)
The shape in the 13th position is a Star
• Repeating Unit: Identify what part repeats
• Division Method: Use division to find position in cycle
• Modulo Operation: Remainder tells us the position in the repeating unit
Definition: A sequence of numbers that follows a rule where the same amount is added or subtracted each time.
Example: 5, 10, 15, 20 (add 5 each time)
Definition: A sequence of shapes, colors, or objects that repeats in the same order.
Example: Red, Blue, Green, Red, Blue, Green...
Definition: The instruction that tells you how to continue a pattern.
Example: "Add 3 to each number" or "Repeat triangle, circle, square"
Method: Look at the numbers before and after the blank to find the pattern.
Example: 2, 4, 6, _, 10 (the missing number is 8)
Method: Divide the position number by the length of the repeating unit. The remainder tells you the position in the unit.
Example: In ABABAB..., position 7: 7÷2=3r1, so it's A
- Look at the numbers before and after the blank
- Calculate the difference between consecutive known numbers
- Apply the same difference to find the missing number
- Verify by checking the entire sequence
- Identify the starting number(s)
- Determine how much is added each time
- Continue adding the same amount
- Verify by checking the pattern consistency
- Identify the repeating unit (how many items repeat)
- Divide the target position by the unit length
- Use the remainder to find the position in the unit
- Match the remainder to the corresponding item
Pattern: 3, 6, 9, __, 15
Difference: 6-3=3, 9-6=3
Missing: 9+3=12
Answer: 12
Pattern: Circle, Square, Triangle, Circle, __, Triangle
Unit: Circle, Square, Triangle
Position 5: 5÷3=1r2
Answer: Square
Pattern: 10, 15, 20, 25, ... (find 20th term)
Rule: Start at 10, add 5 each time
Formula: 10 + (position-1)×5
Answer: 10 + 19×5 = 105
Pattern: ABCCABCCABCC... (find 31st letter)
Unit: ABCC (length 4)
31÷4=7r3
3rd in unit is C
Answer: C
• Pattern Memory: "Same difference means addition pattern"
• Position Rule: "Divide position by unit length, remainder shows where in cycle"
• Verification: "Always check your answer by continuing the pattern"
• Visual Aid: "Draw circles around the repeating unit"
• Count Aloud: "Say the pattern out loud to hear the rhythm"
• Same Difference: In arithmetic sequences, subtract to find the common difference
• Repeating Unit: For shape patterns, identify the smallest repeating group
• Position Finding: Use division to find where in a cycle a position falls
• Verification: Always check that your answer follows the pattern
• Consistency: The same rule must apply to every part of the pattern