Number Patterns

Grade 4 · mathematics · 87 practice problems · read aloud

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🔢 Number Patterns

What is a Number Pattern?

A number pattern is a sequence of numbers that follows a specific rule. Finding patterns helps us predict what comes next, which is useful for solving problems and understanding math in the real world, like counting money or telling time!

How to Find the Pattern: Step-by-Step

  1. Look at the numbers: Write them down. Example: 2, 4, 6, 8, __
  2. Find the change: Ask yourself: Is the sequence increasing (going up) or decreasing (going down)? From 2 to 4, it goes up.
  3. Identify the rule: How much is it changing by? +2 each time. The rule is "add 2".
  4. Apply the rule: Use the rule on the last number to find the missing one. 8 + 2 = 10.
  5. Check your work: Make sure the rule works for all the numbers in the pattern.

Visual Examples

Example 1: Adding

Pattern: 5, 10, 15, 20, __

🔍 The numbers are increasing. From 5 to 10, we add 5. Let's check: 10 + 5 = 15, 15 + 5 = 20. The rule is "add 5".

✅ Solution: 20 + 5 = 25

Example 2: Subtracting

Pattern: 85, 80, 75, 70, __

🔍 The numbers are decreasing. From 85 to 80, we subtract 5. The rule is "subtract 5".

✅ Solution: 70 - 5 = 65

⚠️ Common Mistakes

  • Not checking the whole pattern: A rule might work for the first two numbers but not the rest. Always check at least three numbers!
  • Mixing up operations: Don't just assume it's always adding. Look carefully for subtracting or other rules.
  • Forgetting to write the rule: Saying the rule in your own words helps you understand it.

💡 Tips & Tricks

  • Find the gap: Subtract a number from the one that comes after it to find the rule. (e.g., 10 - 5 = 5, so the rule is +5).
  • Look for "skip-counting": Patterns are often just skip-counting by 2s, 5s, or 10s.
  • Draw it: Use a number line or draw dots to see the pattern visually.

Practice Makes Perfect!

Try these ideas to get better at spotting patterns:

  • Create your own patterns for a friend to solve.
  • Look for patterns in everyday life—like house numbers or scores in a game.
  • Practice with worksheets or online math games focused on number sequences.

Try this one: What is the missing number? 3, 7, 11, 15, __ (Hint: Find the gap!)

Practice problems

6 of the 87, worked through step by step — try them before opening the answer.

1 245 × 6 = ?

Hint: Multiply the ones place first, then the tens place, and finally the hundreds place, remembering to carry over when needed.

Show the answer

Answer: 1470

  1. Write the multiplication vertically for clarity. 245 × 6
  2. Multiply the ones place. 6 × 5 = 30 Write down 0 in the ones place, and carry over 3 to the tens place. 245 × 6 ----- 0 (carry 3)
  3. Multiply the tens place. 6 × 4 = 24 Add the carried-over 3: 24 + 3 = 27 Write down 7 in the tens place, and carry over 2 to the hundreds place. 245 × 6 ----- 70 (carry 2)
  4. Multiply the hundreds place. 6 × 2 = 12 Add the carried-over 2: 12 + 2 = 14 Write down 4 in the hundreds place and 1 in the thousands place. 245 × 6 ----- 1470
  5. Combine the result. The final answer is 1470. Therefore, 245 × 6 = 1470.

Let's multiply 245 by 6 step by step.

2 256 ÷ 4 = ?

Hint: Think about how many times the divisor fits into the dividend. You can break the number into smaller parts to make it easier.

Show the answer

Answer: 64

  1. Understand the problem. We are dividing 256 into 4 equal parts.
  2. Break down 256 into parts that are easier to divide by 4. 256 = 200 + 56.
  3. Divide 200 by 4. 200 ÷ 4 = 50.
  4. Divide 56 by 4. 56 ÷ 4 = 14.
  5. Add the two results together. 50 + 14 = 64.
  6. Check: 4 × 64 = 256, which matches the original number. So, the final answer is 64.

Let's solve 256 ÷ 4 step by step.

3 256 ÷ 8 = ?

Hint: Think about how many times the divisor fits into the dividend. You might find it helpful to break down the dividend into smaller, more manageable parts.

Show the answer

Answer: 32

  1. Understand the problem. We are dividing 256 into 8 equal groups. We want to find how many are in each group.
  2. Break down the number 256. We can think of 256 as 240 + 16. This is helpful because both 240 and 16 are easy to divide by 8.
  3. Divide 240 by 8. We know that 24 ÷ 8 = 3. Therefore, 240 ÷ 8 = 30. So, 240 split into 8 groups gives 30 in each group.
  4. Divide 16 by 8. We know that 16 ÷ 8 = 2. So, 16 split into 8 groups gives 2 in each group.
  5. Add the two results together. From the 240 part we got 30, and from the 16 part we got 2. 30 + 2 = 32.
  6. Conclusion. Therefore, 256 ÷ 8 = 32. We can check our work: 8 × 32 = 256, which is correct.

Let's solve 256 ÷ 8 step by step.

4 256 ÷ 16 = ?

Hint: Think about how many times the divisor fits into the dividend. You can break down the division into smaller steps.

Show the answer

Answer: 16

  1. Understand the problem. We are dividing 256 into groups of 16. We want to know how many groups of 16 are in 256.
  2. One way to solve is to break 256 into parts that are easier to divide by 16. Notice that 256 = 16 × 16. We can check this by recalling that 16 × 10 = 160 and 16 × 6 = 96. 160 + 96 = 256.
  3. Another way is to use long division in your mind. 16 times 10 is 160. 256 − 160 = 96. Now, 96 ÷ 16 = 6. So total = 10 + 6 = 16.
  4. Check the multiplication: 16 × 16 = 16 × (10 + 6) = 160 + 96 = 256. This matches the original number, so the division is correct. Therefore, 256 ÷ 16 = 16.

Let's solve 256 ÷ 16 step by step.

5 324 ÷ 12 = ?

Hint: Break down the division into smaller, manageable parts using multiplication facts you know.

Show the answer

Answer: 27

  1. We are solving 324 ÷ 12.
  2. Think about how many times 12 fits into 324. We can break 324 into parts that are easier to divide.
  3. First, 12 × 20 = 240. Subtract 240 from 324: 324 - 240 = 84.
  4. Now, see how many times 12 fits into 84. 12 × 7 = 84.
  5. Add the partial results: 20 + 7 = 27.
  6. Therefore, 324 ÷ 12 = 27.

6 (48 + 32) ÷ 8 = ?

Hint: Remember to perform the operation inside the parentheses first before dividing

Show the answer

Answer: 10

  1. Calculate inside the parentheses: 48 + 32 = 80
  2. Divide the result by 8: 80 ÷ 8 = 10

The answer is 10.

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