Solved Logical Exercises for 1st Grade Mathematics

Master logical reasoning: patterns, sequences, comparisons, and problem-solving strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Pattern Recognition
Exercise 1
Complete the pattern: 🌟 🔵 🌟 🔵 🌟 ___ ___
Definition:

Pattern Recognition: Identifying repeating sequences or arrangements of shapes, colors, or numbers.

Pattern identification method:
  1. Look at the sequence carefully
  2. Find the repeating unit
  3. Continue the pattern
  4. Verify the sequence makes sense
Step 1: Observe the given sequence

🌟 🔵 🌟 🔵 🌟 ___ ___

Step 2: Identify the repeating unit

The pattern alternates between star (🌟) and blue circle (🔵)

Unit: 🌟 🔵

Step 3: Continue the pattern

After 🌟, the next shape should be 🔵

After 🔵, the next shape should be 🌟

Step 4: Complete the sequence

🌟 🔵 🌟 🔵 🌟 🔵 🌟

🌟 🔵 🌟 🔵 🌟 🔵 🌟
Final answer:

The missing shapes are: 🔵 🌟

Applied rules:

• Repetition: Look for repeating units in the sequence

• Alternation: Patterns often alternate between elements

• Continuation: Extend the identified pattern consistently

2 Number Sequence
Exercise 2
What number comes next? 2, 4, 6, 8, ___, ___
Definition:

Number Sequence: A list of numbers following a specific rule or pattern.

Step 1: Analyze the given numbers

2, 4, 6, 8, ___, ___

Step 2: Find the pattern

4 - 2 = 2

6 - 4 = 2

8 - 6 = 2

The pattern is adding 2 each time (counting by twos)

Step 3: Continue the sequence

8 + 2 = 10

10 + 2 = 12

Step 4: Complete the sequence

2, 4, 6, 8, 10, 12

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

The missing numbers are: 10, 12

Applied rules:

• Counting by twos: Adding 2 to each previous number

• Difference analysis: Find the consistent difference between numbers

• Even numbers: All numbers in the sequence are even

3 Comparison Logic
Exercise 3
Sarah has 5 apples. Tom has 3 apples. Who has more apples? How many more?
Definition:

Comparison: Determining which quantity is greater, lesser, or equal.

Step 1: Identify the quantities

Sarah has 5 apples

Tom has 3 apples

Step 2: Compare the numbers

5 > 3 (5 is greater than 3)

Step 3: Find the difference

5 - 3 = 2

Step 4: State the answer

Sarah has more apples than Tom

Sarah has 2 more apples than Tom

Sarah has more apples (2 more than Tom)
Final answer:

Sarah has more apples. She has 2 more apples than Tom.

Applied rules:

• Greater than: 5 > 3 means 5 is greater than 3

• Subtraction: Find difference by subtracting smaller number from larger

• Comparison symbols: > (greater than), < (less than), = (equal)

Logical Reasoning Concepts and Methods
Pattern: A-B-A-B...
Alternating Pattern
Comparison
5 > 3, 2 < 7
Greater/Less Than
Sequence
2, 4, 6, 8...
Counting by Twos
Difference
5 - 3 = 2
How Many More
Key definitions:

Pattern: A repeated design or sequence that follows a rule

Sequence: Numbers arranged in a particular order

Comparison: Looking at two or more things to see differences or similarities

Logical reasoning steps:
  1. Observe: Look carefully at the problem
  2. Identify: Find the pattern or relationship
  3. Apply: Use the rule to solve the problem
  4. Verify: Check if your answer makes sense
Tip 1: Look for colors, shapes, or numbers that repeat in a pattern.
Tip 2: Count the difference between numbers to find the pattern.
Tip 3: Use > (greater than) and < (less than) symbols for comparisons.
Common patterns: ABAB, AABB, ABCABC, counting by 2s, 5s, 10s.
Problem-solving: Always read the question carefully and answer what is asked.
Solution: Exercises 4 to 5
4 Classification
Exercise 4
Which one doesn't belong? Circle the odd one out:
🍎 🍌 🐶 🍊 🍇
Definition:

Classification: Grouping items based on shared characteristics.

Step 1: Examine all items

🍎 (apple), 🍌 (banana), 🐶 (dog), 🍊 (orange), 🍇 (grapes)

Step 2: Find the common characteristic

🍎, 🍌, 🍊, 🍇 are all fruits

🐶 is an animal

Step 3: Identify the odd one out

The dog (🐶) doesn't belong because it's not a fruit

Step 4: Verify the answer

All others are fruits, only the dog is different

🐶 (dog) is the odd one out
Final answer:

The dog (🐶) doesn't belong because it's not a fruit.

Applied rules:

• Categorization: Group items by common features

• Differentiation: Find what makes one item unique

• Logical grouping: Fruits vs. animals

5 Problem Solving
Exercise 5
Mom bought 10 cookies. She gave 3 to her daughter and 2 to her son. How many cookies are left?
Definition:

Problem Solving: Using math skills to answer real-world questions.

Step 1: Identify what we know

Total cookies: 10

Given to daughter: 3

Given to son: 2

Step 2: Find total given away

3 + 2 = 5 cookies given away

Step 3: Subtract to find remaining

10 - 5 = 5 cookies left

Step 4: Verify the answer

3 + 2 + 5 = 10 ✓

5 cookies are left
Final answer:

There are 5 cookies left.

Applied rules:

• Addition: Combine amounts given away

• Subtraction: Take away from the total

• Verification: Check that parts add up to whole

Logical Reasoning Laws, Methods, and Definitions
Pattern = Rule × Repetition
Pattern Formation
Key definitions:

Logic: Using reasoning to solve problems and make decisions

Pattern: Something that repeats in a predictable way

Classification: Sorting items into groups based on similarities

Comparison: Looking at things to see how they are alike or different

Complete logical reasoning methodology:
  1. Read carefully: Understand what the problem is asking
  2. Look for clues: Find patterns, similarities, or differences
  3. Choose a strategy: Decide whether to count, compare, or classify
  4. Solve step-by-step: Work through the problem systematically
  5. Check your work: Make sure your answer makes sense
Tip 1: Draw pictures or use objects to help visualize the problem.
Tip 2: Count aloud or use your fingers when working with numbers.
Tip 3: Look for the "odd one out" by finding what's different.
Tip 4: When comparing, use > (greater than) and < (less than) symbols.
Common errors: Missing the pattern, miscounting, forgetting to verify answers.
Memory aids: Remember: More means >, Less means <, Same means =.
Essential rules to remember:

• Pattern recognition: Look for repeating units in sequences

• Comparison: Use >, <, or = to compare quantities

• Classification: Group items by shared characteristics

• Problem solving: Read carefully, plan, solve, check

• Verification: Always make sure your answer makes sense

Questions & Answers

Question: I don't understand how to find patterns. How do I know what comes next in a sequence?

Answer: Great question! Finding patterns is like being a detective:

  • Look closely: Examine the sequence item by item
  • Find the unit: Look for the smallest repeating part (like A-B-A-B)
  • Count differences: In number sequences, subtract consecutive numbers to find the pattern
  • Test your theory: Apply your rule to predict the next item

Example: In 2, 4, 6, 8..., the difference is always +2, so the next numbers are 10, 12, 14.

Practice with simple patterns first, then move to more complex ones!

Question: My child gets confused with greater than and less than symbols. Any tips to help remember which is which?

Answer: Yes! Here are some helpful memory tricks:

  • Alligator method: The symbol (>) looks like an alligator's mouth that wants to eat the bigger number
  • L Method: The symbol (<) looks like the letter L, and "Less than" starts with L
  • Arrow method: Both symbols point toward the smaller number

So 5 > 3 means 5 is greater than 3, and 3 < 5 means 3 is less than 5.

Practice with real objects: "I have 5 apples and you have 3 apples. Who has more?" Then connect to symbols.

Question: When I have to find the "odd one out," I get confused. How do I figure out which one doesn't belong?

Answer: Think of it as sorting items into groups! Here's how:

  • Look for categories: Are most items fruits? Animals? Colors?
  • Find the common feature: What do most items share?
  • Spot the difference: Which item is different?
  • Check your answer: Does your choice really not fit?

Example: 🍎, 🍌, 🐶, 🍊 - Most are fruits, so 🐶 (dog) is the odd one out.

Practice with everyday items around your house!