Solved Exercises on Completing Patterns in Grade 2

Master completing patterns: recognizing, extending, and creating patterns with numbers, shapes, and colors through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Shape Pattern Completion
Exercise 1
Complete the pattern:
🔵 🟡 🔵 🟡 🔵 🟡 ___
🔄
Definition: A pattern is a sequence that repeats in a predictable way.
Pattern Completion Method:
  1. Look at the given sequence
  2. Find the repeating unit
  3. Continue the pattern
  4. Verify your answer
🔵
🟡
🔵
🟡
🔵
🟡
→
?
Step 1: Observe the pattern

Look at the sequence: 🔵 🟡 🔵 🟡 🔵 🟡

Step 2: Identify the repeating unit

The pattern alternates between blue circle (🔵) and yellow circle (🟡)

The repeating unit is: 🔵 🟡

Step 3: Continue the pattern

After 🔵 🟡 🔵 🟡 🔵 🟡, the next element should be 🔵

🔵
🟡
🔵
🟡
🔵
🟡
🔵
Final answer:

The missing element is: 🔵

Applied rules:

• Repetition: Patterns repeat the same sequence

• Alternation: AB patterns alternate between two elements

• Continuation: Follow the established pattern

2 Number Pattern Completion
Exercise 2
What comes next in this pattern?
2, 4, 6, 8, 10, ___
🔢
Definition: A number pattern follows a mathematical rule to determine the next number.
2
4
6
8
10
→
?
Step 1: Analyze the pattern

Look at the numbers: 2, 4, 6, 8, 10

Step 2: Find the pattern rule

Each number increases by 2: 2+2=4, 4+2=6, 6+2=8, 8+2=10

This is skip counting by 2s

Step 3: Continue the pattern

After 10, add 2: 10 + 2 = 12

2
4
6
8
10
12
Final answer:

The missing number is: 12

Applied rules:

• Addition Pattern: Each number increases by the same amount

• Arithmetic Sequence: Numbers increase by a constant difference

• Continuation: Apply the same rule to find the next number

3 Color Pattern Completion
Exercise 3
Complete the pattern:
🔴 🟢 🔵 🔴 🟢 🔵 ___ ___
🎨
Definition: A color pattern repeats a sequence of colors in a specific order.
🔴
🟢
🔵
🔴
🟢
🔵
→
?
?
Step 1: Identify the color sequence

Pattern: Red (🔴), Green (🟢), Blue (🔵)

Step 2: Determine the repeating unit

The repeating unit is: 🔴 🟢 🔵

Step 3: Continue the pattern

After 🔴 🟢 🔵 🔴 🟢 🔵, the next two colors should be 🔴 🟢

🔴
🟢
🔵
🔴
🟢
🔵
🔴
🟢
Final answer:

The missing elements are: 🔴 🟢

Applied rules:

• ABC Pattern: Cycles through three different elements

• Consistency: The order must remain the same

• Extension: Repeat the exact sequence

Rules and Methods for Completing Patterns
Pattern(n) = Base Element + (n-1) × Step
Number Pattern Formula
Pattern Types
AB, ABC, ABAB, ABCABC
Repeating sequences
Pattern Rule
Find → Repeat → Extend
Pattern solving method
Pattern Length
Unit Size × Repetitions
Pattern complexity
Key Definitions:

Pattern: A sequence that repeats in a predictable way

Repeating Unit: The smallest group that repeats to form the pattern

Pattern Rule: The specific way elements repeat

Number Pattern: A sequence of numbers that follows a rule

Shape Pattern: A sequence of shapes that repeats

Color Pattern: A sequence of colors that repeats

Pattern Completion Steps:
  1. Observe: Look carefully at the given sequence
  2. Identify: Find the repeating unit or rule
  3. Verify: Make sure the pattern repeats consistently
  4. Extend: Continue the pattern using the rule
  5. Check: Verify your answer fits the pattern
Tip 1: Count how many elements are in the repeating unit.
Tip 2: Write down the pattern rule in words.
Tip 3: For number patterns, find the difference between consecutive numbers.
Tip 4: Draw brackets around each complete repeating unit.
Tip 5: Check your answer by reading the full pattern.
Pattern Types: AB (2 elements), ABC (3 elements), AABB (paired), ABCD (4 elements)
Number Patterns: Addition (+2, +3), Subtraction (-2, -3), Multiplication (×2, ×3), Skip counting (2s, 5s, 10s)
Pattern Rules to Remember:

• AB Pattern: Alternating between two elements (🔴 🔵 🔴 🔵)

• ABC Pattern: Cycling through three different elements (🔴 🟢 🔵)

• Number Patterns: Add or subtract the same amount each time

• Shape Patterns: Same shapes repeat in the same order

• Consistency: The rule stays the same throughout

Solution: Exercises 4 to 5
4 Growing Number Pattern
Exercise 4
Complete the pattern:
5, 10, 15, 20, 25, ___
📈
Definition: A growing pattern increases by the same amount each time.
5
10
15
20
25
→
?
Step 1: Look at the numbers

Sequence: 5, 10, 15, 20, 25

Step 2: Find the pattern rule

Each number increases by 5: 5+5=10, 10+5=15, 15+5=20, 20+5=25

This is skip counting by 5s

Step 3: Continue the pattern

After 25, add 5: 25 + 5 = 30

5
10
15
20
25
30
Final answer:

The missing number is: 30

Applied rules:

• Growing Pattern: Numbers increase by the same amount

• Constant Difference: The difference between consecutive numbers is the same

• Continuation: Apply the same rule to find the next number

5 Complex Shape Pattern
Exercise 5
Complete the pattern:
⬜ 🔺 ⬜ 🔺 🔺 ⬜ 🔺 🔺 🔺 ___
🔄
Definition: A complex pattern may have varying numbers of elements in each cycle.
⬜
🔺
⬜
🔺
🔺
⬜
🔺
🔺
🔺
→
?
Step 1: Analyze the pattern carefully

Look for groups: ⬜ 🔺 | ⬜ 🔺 🔺 | ⬜ 🔺 🔺 🔺

Step 2: Identify the rule

Each group starts with a white square (⬜) followed by an increasing number of triangles (🔺)

Group 1: 1 triangle, Group 2: 2 triangles, Group 3: 3 triangles

Step 3: Continue the pattern

The next group should have 4 triangles: ⬜ 🔺 🔺 🔺 🔺

The first element of this group is ⬜

⬜
🔺
⬜
🔺
🔺
⬜
🔺
🔺
🔺
⬜
Final answer:

The missing element is: ⬜

Applied rules:

• Complex Pattern: May have varying numbers of elements per group

• Increasing Sequence: Elements may increase in quantity per group

• Group Recognition: Look for patterns within patterns

Complete Guide to Completing Patterns
Pattern(n) = Start + (n-1) × Difference
Arithmetic Sequence Formula
Key definitions:

Pattern: A sequence of elements that follows a predictable, repeating rule

Repeating Unit: The shortest sequence that, when repeated, creates the entire pattern

Pattern Rule: The specific mathematical relationship that governs the sequence

Number Pattern: A sequence of numbers that follows a mathematical rule

Shape Pattern: A sequence of shapes that repeats in a specific order

Color Pattern: A sequence of colors that follows a predictable order

Complete Pattern Analysis Method:
  1. Visual Inspection: Look at the overall sequence and note similarities and differences
  2. Unit Identification: Find the smallest group that appears to repeat
  3. Rule Verification: Confirm the unit repeats consistently throughout
  4. Extension Application: Apply the verified rule to continue the pattern
  5. Validation Check: Verify the extended pattern maintains the original rule
Tip 1: Use colors, numbers, or letters to label the pattern unit (e.g., A-B-A-B).
Tip 2: Draw a table showing position vs. element to identify the pattern mathematically.
Tip 3: For number patterns, find the difference between consecutive numbers.
Tip 4: Practice with physical objects like blocks or counters to build understanding.
Tip 5: Look for patterns in daily life (clothing designs, tiles, music) to reinforce learning.
Pattern Categories: AB (simple alternating), ABC (three-element cycle), AABB (paired repetition), ABCD (four-element cycle), growing patterns (increasing quantities).
Learning Benefits: Develops logical reasoning, prediction skills, mathematical thinking, and prepares for advanced algebraic concepts.
Common Mistakes: Miscounting the unit length, overlooking subtle differences, assuming the pattern changes mid-sequence.
Essential Pattern Rules:

• Consistency Rule: The pattern rule remains the same throughout the sequence

• Repetition Rule: The same sequence of elements repeats over and over

• Extension Rule: New elements must follow the established pattern rule

• Verification Rule: Always check that your extension maintains the pattern

• Unit Rule: Identify the shortest possible repeating unit

Real World Applications: Music rhythms, architectural designs, nature formations (flower petals, tree rings), computer programming, art and design.
Mathematical Connection: Paves the way for understanding sequences, functions, and algebraic relationships in higher grades.

Questions & Answers

Question: My child is struggling with number patterns like 2, 4, 6, 8, ___. What's the best way to teach them to find the pattern rule?

Answer: Here's an effective approach for teaching number pattern rules:

  • Use concrete objects: Have your child count physical items (blocks, counters) while saying the numbers
  • Focus on differences: Ask "How do we get from 2 to 4?" (add 2), "How do we get from 4 to 6?" (add 2)
  • Visual representation: Draw number lines or use hundreds charts to show the jumps
  • Verbalize the rule: "We're adding 2 each time" or "Skip counting by 2s"

Start with simple addition patterns (+1, +2, +5) before moving to more complex ones. Use manipulatives like snap cubes to physically show the pattern growth.

Encourage your child to predict the next few numbers before filling in the blank. This helps them internalize the pattern rule rather than just finding one answer.

Question: Sometimes I see patterns like 🔴 🔵 🔴 🔵 🔴 and I don't know if the next one should be 🔵 or another 🔴. How do I know?

Answer: Great question! Here's how to figure it out:

  • Look for the repeating unit: In 🔴 🔵 🔴 🔵 🔴, the pattern is alternating red and blue
  • Identify the sequence: Red (🔴), then Blue (🔵), then Red (🔴), then Blue (🔵), then Red (🔴)
  • Follow the order: After Red (🔴), the next color should be Blue (🔵)

Think of it like a song that repeats: "Red, Blue, Red, Blue, Red..." What comes next? It's Blue!

A helpful trick is to say the pattern out loud: "Red, Blue, Red, Blue, Red, Blue..." Now you can hear what comes next!

Question: How can I help my students who mix up different pattern types, like treating an ABC pattern as an AB pattern?

Answer: This is a common challenge! Here are effective strategies:

  1. Explicit naming: Call them by their names - "This is an AB pattern" or "This is an ABC pattern"
  2. Visual grouping: Use brackets or circles to group the complete repeating units: [🔴🔵] [🔴🔵] vs [🔴🟢🔵] [🔴🟢🔵]
  3. Pattern identification activities: Sort different patterns into AB and ABC categories
  4. Color coding: Use different colors to highlight each unique element in the pattern

Provide plenty of practice with both types separately before mixing them. Use manipulatives to physically group the elements, making the repeating unit tangible.

Create anchor charts showing examples of AB patterns vs ABC patterns so students can reference them. Emphasize that ABC patterns have THREE different elements that repeat, not just two!