Pattern Analysis

Grade 5 · mathematics · 88 practice problems · read aloud

🔊 Listen to this explanation

🔍 What is Pattern Analysis?

Pattern analysis is the math detective work of finding the rule or order in a sequence of numbers or shapes. It's super useful because it helps us predict what comes next, solve puzzles, and understand how things in our world are organized!

🛠️ How to Solve Pattern Problems: A Step-by-Step Guide

  1. Look Carefully: Examine the first few numbers or shapes in the sequence.
  2. Find the Change: Ask yourself: "Is it increasing or decreasing? By how much?"
  3. Test Your Rule: Apply the rule you think you've found to the next item in the pattern. Does it work?
  4. Predict & Check: Use your rule to find the missing number or the next item in the sequence.

📚 Visual Examples

Example 1: Number Pattern

Pattern: 2, 4, 6, 8, __, 12

  1. Look: 2 → 4 → 6 → 8
  2. Find the Change: The numbers are increasing by 2 each time. (+2 rule)
  3. Predict: After 8 comes 8 + 2 = 10.
  4. Check: 10 + 2 = 12. It works! ✅

Answer: The missing number is 10.

Example 2: Shape Pattern

Pattern: △, □, ○, △, □, __, △

  1. Look: The shapes repeat in a cycle: Triangle (△), Square (□), Circle (○).
  2. Find the Rule: The core repeating unit is: △, □, ○.
  3. Predict: After the square (□), the next shape in the cycle is the circle (○).

Answer: The missing shape is ○.

⚠️ Common Mistakes to Avoid

  • Only looking at the first two numbers: A pattern might start +2, +2, then change to +3! Always check at least 3 steps.
  • Forgetting patterns can repeat: Not all patterns grow; some just cycle (like the days of the week).
  • Guessing without checking: Always test your rule on a part of the pattern you already know to make sure it's correct.

💡 Tips & Tricks

  • Talk it out: Say the pattern aloud. "Plus two, plus two..." This can help you hear the rule.
  • Write the changes: Between the numbers, write down +3, +3, +3 to see the consistent rule.
  • Look for famous patterns: Know your even numbers (2,4,6,8), odd numbers (1,3,5,7), and multiples (5,10,15,20).

🎯 How to Practice

  • Create your own number patterns for a friend to solve.
  • Look for patterns in everyday life—like the tiles on the floor or the numbers on a clock.
  • Ask your teacher for worksheets or find online games about "number sequences" or "growing patterns."

Practice problems

6 of the 88, worked through step by step — try them before opening the answer.

1 √(144) = ?

Hint: Think about which number multiplied by itself gives the number under the square root symbol.

Show the answer

Answer: 12

  1. Understand what the square root means. The square root of a number is a value that, when multiplied by itself, gives the original number.
  2. Write the problem. We need to find: √(144) = ?
  3. Think of a number that multiplied by itself equals 144. Let's test some possibilities: - 10 × 10 = 100 (too small) - 11 × 11 = 121 (still too small) - 12 × 12 = 144 (this matches exactly)
  4. Check the result. 12 × 12 = 144, so √(144) = 12.
  5. Final answer. The square root of 144 is 12.

We are asked to find the square root of 144.

2 √(625) = ?

Hint: Think about what number multiplied by itself gives the number under the square root symbol.

Show the answer

Answer: 25

  1. We are looking for a number that, when multiplied by itself, equals 625.
  2. Consider that 20 × 20 = 400, which is less than 625.
  3. Consider that 25 × 25 = 625.
  4. Since 25 × 25 = 625, the square root of 625 is 25.

The answer is 25.

3 12.5 × 4.2 = ?

Hint: When multiplying decimals, first multiply as if they were whole numbers, then count the total decimal places in both factors to determine where to place the decimal point in your answer.

Show the answer

Answer: 52.5

  1. Remove decimals temporarily to work with whole numbers. 12.5 has 1 decimal place (the .5). 4.2 has 1 decimal place (the .2). So together, there are 1 + 1 = 2 decimal places total in the original problem. We will put them back at the end.
  2. Multiply the numbers as if they were whole numbers: 125 × 42.
  3. Break it into simpler parts. First, 125 × 40 = 125 × 4 × 10 = 500 × 10 = 5000. Second, 125 × 2 = 250.
  4. Add the results: 5000 + 250 = 5250.
  5. Now put back the decimal point. Since we ignored 2 decimal places total earlier (from 12.5 and 4.2), we need to move the decimal point 2 places to the left in our result. 5250 becomes 52.50.
  6. Simplify: 52.50 is the same as 52.5. Final answer: 52.5

Let's multiply 12.5 by 4.2 step by step.

4 (3/4 + 1/2) × 8 = ?

Hint: First find a common denominator to add the fractions, then multiply the result by the whole number.

Show the answer

Answer: 10

  1. Simplify inside the parentheses first. We have 3/4 + 1/2. To add these, find a common denominator. The common denominator of 4 and 2 is 4. 1/2 = 2/4. So: 3/4 + 2/4 = 5/4.
  2. Now the expression is (5/4) × 8.
  3. Multiply 5/4 by 8. This is the same as 5 × (8/4). 8/4 = 2. So: 5 × 2 = 10. Final answer: 10

Let's solve step by step.

5 (3/4 + 1/2) × 12 = ?

Hint: First find a common denominator to add the fractions, then multiply the result by the whole number.

Show the answer

Answer: 15

  1. Add the fractions 3/4 + 1/2
  2. Find a common denominator for 4 and 2, which is 4
  3. Convert 1/2 to 2/4
  4. Add 3/4 + 2/4 = 5/4
  5. Multiply 5/4 × 12
  6. 5/4 × 12 = (5 × 12)/4 = 60/4
  7. Simplify 60/4 = 15

The answer is 15.

6 (2/3 + 1/6) × 12 = ?

Hint: First find a common denominator to add the fractions, then multiply the result by the whole number.

Show the answer

Answer: 10

  1. Add the fractions: 2/3 + 1/6
  2. Find a common denominator: 2/3 = 4/6
  3. Add the fractions: 4/6 + 1/6 = 5/6
  4. Multiply by 12: 5/6 × 12 = (5 × 12)/6 = 60/6
  5. Simplify: 60 ÷ 6 = 10

The answer is 10.

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