Solved Exercises on Number Patterns in Grade 1

Master number sequences: counting patterns, skip counting, growing patterns, and algebraic thinking through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Skip Counting by 2s
Exercise 1
Complete the pattern by counting by 2s:
2, 4, 6, 8, 10, ?, ?, ?
Definition:

Skip Counting: Counting by a number other than 1 (counting by 2s, 5s, 10s, etc.).

Skip Counting Method:
  1. Identify the number being added each time
  2. Add that same number to get the next term
  3. Continue the pattern consistently
  4. Verify by checking the difference between terms
2
4
6
8
10
?
?
?
Step 1: Identify the pattern

2 → 4 (+2), 4 → 6 (+2), 6 → 8 (+2), 8 → 10 (+2)

Rule: Add 2 to get the next number

Step 2: Apply the rule

10 + 2 = 12, then 12 + 2 = 14, then 14 + 2 = 16

Step 3: Verify the pattern

2, 4, 6, 8, 10, 12, 14, 16 (all even numbers counting by 2s)

2, 4, 6, 8, 10, 12, 14, 16
Final answer:

The missing numbers are: 12, 14, 16

Applied rules:

• Constant Addition: Adding the same number repeatedly

• Even Numbers: Counting by 2s starting from 2

• Arithmetic Sequence: Constant difference between consecutive terms

2 Growing Number Pattern
Exercise 2
Complete the growing pattern:
1, 3, 5, 7, 9, ?, ?, ?
Definition:

Growing Pattern: Numbers increase by a consistent amount (arithmetic sequence).

1
3
5
7
9
?
?
?
Step 1: Find the pattern

1 → 3 (+2), 3 → 5 (+2), 5 → 7 (+2), 7 → 9 (+2)

All odd numbers counting by 2s

Step 2: Continue the sequence

9 + 2 = 11, 11 + 2 = 13, 13 + 2 = 15

Step 3: Verify

1, 3, 5, 7, 9, 11, 13, 15 (consecutive odd numbers)

1, 3, 5, 7, 9, 11, 13, 15
Final answer:

The missing numbers are: 11, 13, 15

Applied rules:

• Odd Numbers: Numbers not divisible by 2

• Arithmetic Progression: Same difference between terms

• Pattern Recognition: Identify the increment

3 Increasing Pattern by 5s
Exercise 3
Complete the pattern by counting by 5s:
5, 10, 15, 20, 25, ?, ?, ?
Definition:

Counting by 5s: A skip counting pattern where each number increases by 5.

5
10
15
20
25
?
?
?
Step 1: Identify the rule

5 → 10 (+5), 10 → 15 (+5), 15 → 20 (+5), 20 → 25 (+5)

Rule: Add 5 to get the next number

Step 2: Apply the rule

25 + 5 = 30, 30 + 5 = 35, 35 + 5 = 40

Step 3: Verify the pattern

5, 10, 15, 20, 25, 30, 35, 40 (multiples of 5)

5, 10, 15, 20, 25, 30, 35, 40
Final answer:

The missing numbers are: 30, 35, 40

Applied rules:

• Counting by 5s: Each number ends in 0 or 5

• Multiples of 5: Numbers divisible by 5

• Arithmetic Sequence: Constant difference of 5

Number Patterns Summary
Key Definitions

• Number Pattern: A sequence of numbers that follows a specific rule

• Arithmetic Sequence: Numbers that increase or decrease by the same amount

• Skip Counting: Counting by a number other than 1 (2s, 5s, 10s)

• Even Numbers: Numbers divisible by 2 (2, 4, 6, 8...)

• Odd Numbers: Numbers not divisible by 2 (1, 3, 5, 7...)

Next Term = Previous Term + Constant
Arithmetic Pattern Rule
Counting by 2s
2, 4, 6, 8...
Even Numbers
Counting by 5s
5, 10, 15, 20...
Multiples of 5
Counting by 10s
10, 20, 30, 40...
Multiples of 10
Pattern Recognition Tips

• Look for the difference between consecutive numbers

• Check if the pattern repeats or grows

• Count by the difference to continue the pattern

• Verify your answer by checking multiple pairs

Common Patterns

• Counting by 2s: +2 each time

• Counting by 5s: +5 each time

• Counting by 10s: +10 each time

• Backwards: Subtract the same number

Solution: Exercises 4 to 5
4 Decreasing Number Pattern
Exercise 4
Complete the decreasing pattern:
20, 18, 16, 14, 12, ?, ?, ?
Definition:

Decreasing Pattern: Numbers that decrease by a consistent amount.

20
18
16
14
12
?
?
?
Step 1: Find the pattern

20 → 18 (-2), 18 → 16 (-2), 16 → 14 (-2), 14 → 12 (-2)

Rule: Subtract 2 from each number

Step 2: Continue the sequence

12 - 2 = 10, 10 - 2 = 8, 8 - 2 = 6

Step 3: Verify

20, 18, 16, 14, 12, 10, 8, 6 (even numbers counting backwards by 2s)

20, 18, 16, 14, 12, 10, 8, 6
Final answer:

The missing numbers are: 10, 8, 6

Applied rules:

• Constant Subtraction: Subtracting the same number repeatedly

• Reverse Pattern: Opposite of increasing pattern

• Even Numbers: Counting backwards by 2s

5 Mixed Pattern Challenge
Exercise 5
Complete the mixed pattern:
10, 15, 20, 12, 17, 22, 14, ?, ?, ?
Definition:

Mixed Pattern: Multiple rules applied alternately or in groups.

10
15
20
12
17
22
14
?
?
?
Step 1: Identify sub-patterns

Looking at positions: 1st, 4th, 7th: 10, 12, 14 (increasing by 2)

Looking at positions: 2nd, 5th: 15, 17 (increasing by 2)

Looking at positions: 3rd, 6th: 20, 22 (increasing by 2)

Step 2: Continue each sub-pattern

8th position (next 1st pattern): 14 + 2 = 16

9th position (next 2nd pattern): 17 + 2 = 19

10th position (next 3rd pattern): 22 + 2 = 24

Step 3: Verify the pattern

Grouped pattern: (10, 15, 20), (12, 17, 22), (14, 19, 24)

Each group increases by 2 in each position

10, 15, 20, 12, 17, 22, 14, 19, 24
Final answer:

The missing numbers are: 19, 24

Applied rules:

• Sub-pattern Recognition: Identifying multiple patterns within one sequence

• Position Analysis: Looking at every nth term to find patterns

• Grouped Sequences: Patterns that repeat in groups

Detailed Concepts and Methods
Pattern Rule = Starting Number + (Position × Increment)
General Pattern Formula
Key definitions:

Number Pattern: A sequence of numbers that follows a specific rule or order.

Arithmetic Sequence: Numbers that increase or decrease by the same amount.

Skip Counting: Counting by a number other than 1 (2s, 5s, 10s).

Pattern Finding Strategy:
  1. Observe: Look at the given numbers carefully
  2. Compare: Find the difference between consecutive numbers
  3. Identify: Determine the consistent rule or pattern
  4. Test: Apply the rule to see if it works for all given numbers
  5. Apply: Use the rule to find missing numbers
  6. Verify: Check that your answer fits the pattern
Tip 1: Use your fingers to count if needed - it helps visualize the pattern.
Tip 2: Write down the differences between numbers to see the pattern.
Tip 3: Start with simple patterns (by 2s) before trying harder ones (by 3s).
Tip 4: Draw a number line to see how numbers increase or decrease.
Common errors: Forgetting the direction (up vs down), miscalculating the difference, not checking the pattern works for all numbers.
Success strategies: Always check your answer by applying the rule to all numbers, practice with physical objects.
Essential Rules to Remember:

• Counting by 2s: Even numbers (2, 4, 6, 8...) or odd numbers (1, 3, 5, 7...)

• Counting by 5s: Numbers ending in 0 or 5 (5, 10, 15, 20...)

• Counting by 10s: Numbers ending in 0 (10, 20, 30, 40...)

• Arithmetic Sequence: Same difference between consecutive terms

• Pattern Consistency: The rule applies to every element in the sequence

Pattern Analysis Visualization
Number Pattern Types
Let's analyze different number pattern types and their characteristics:
Counting by 2s
2
4
6
8
10
12

+2 each time (even numbers)

Counting by 5s
5
10
15
20
25
30

+5 each time (multiples of 5)

Counting by 10s
10
20
30
40
50
60

+10 each time (multiples of 10)

Backward Counting
20
18
16
14
12
10

-2 each time (decreasing pattern)

Pattern Recognition Skills: These exercises develop foundational mathematical reasoning, preparing students for more complex arithmetic operations and algebraic thinking in higher grades.

Questions & Answers

Question: I get confused when numbers go backward in a pattern. How do I know when to add and when to subtract?

Answer: Great question! Here's how to tell:

  • Increasing pattern: Numbers get bigger (like 2, 4, 6, 8) → Add
  • Decreasing pattern: Numbers get smaller (like 10, 8, 6, 4) → Subtract

Look at the first two numbers: if the second number is larger than the first, you add. If the second number is smaller than the first, you subtract.

Example: 20, 18... since 18 is smaller than 20, you subtract: 20 - 2 = 18.

Always compare the first number to the second to determine the direction!

Question: My students struggle with skip counting by 5s. What visual aids can help them?

Answer: Here are effective visual strategies for skip counting by 5s:

  • Money connection: Use nickels (5¢) to show counting by 5s
  • Finger counting: Count fingers on hands (5 fingers per hand)
  • Number line: Mark jumps of 5 on a visual number line
  • Grouping objects: Put objects in groups of 5 and count the groups

Notice that numbers counting by 5s always end in 0 or 5: 5, 10, 15, 20, 25, 30...

Connect skip counting to real-world applications like telling time (minutes on clock) or counting money!

Question: How can I help my child practice number patterns at home in a fun way?

Answer: Here are engaging home activities for number pattern practice:

  • Stair climbing: Count stairs by 2s or 5s while going up/down
  • Snack patterns: Arrange crackers or fruit pieces in number sequences
  • Music patterns: Create rhythm patterns that follow number sequences
  • Calendar patterns: Look for date patterns (every 7 days = week)

Play "Pattern Detective": Find number patterns in everyday life (house numbers, clock times, etc.)

Keep sessions short (10-15 minutes) and make them game-like with rewards for participation!

Question: What happens when a pattern has more than one possible rule? How do I know which one is right?

Answer: In 1st grade number patterns, there's usually one clear, simple rule. Here's how to determine the correct answer:

  • Look for the simplest rule: Adding or subtracting a small number
  • Check all given elements: Your rule should work for every part of the shown pattern
  • Consider the grade level: Patterns should match 1st grade complexity

For example, in 2, 4, 6, 8, ?, the simplest rule is "add 2," giving 10 as the answer.

If you think there might be multiple answers, go with the one that uses the most basic mathematical operation!

Question: Why do we learn number patterns? When will I use them?

Answer: Number patterns are super useful for many things:

  • Telling time: Minutes go by 5s (5, 10, 15, 20...)
  • Counting money: Nickels are worth 5¢ each
  • Measurement: Rulers show patterns of inches or centimeters
  • Future math: Multiplication is just skip counting!

Patterns help your brain get ready for multiplication, division, and algebra later on.

They also help you solve problems faster by seeing the rules that numbers follow!