30-Page Mind Games

Spot the Missing Number

A number line can hide a secret. Look at the numbers around the empty space, find the rule, and place the number that belongs there. The rule might be “add 2,” “take away 5,” or “double the number.”

Grab a pencil. You’ll test the pattern, check your answer, and become a number detective.

Find the Rule

A pattern is a group of numbers that changes in a regular way. To find a missing number, compare numbers next to each other. Ask, “What happened to get from one number to the next?”

Try these common rules:

1. Adding: 4, 7, 10, 13. Each number goes up by 3.

2. Taking away: 20, 16, 12, 8. Each number goes down by 4.

3. Doubling: 2, 4, 8, 16. Each number is twice the one before it.

4. Halving: 32, 16, 8, 4. Each number is half the one before it.

The missing number must fit the rule on both sides when possible. For example, in 5, 10, __, 20, the rule is “add 5.” The missing number is 15. Check it: 5 + 5 = 10, 10 + 5 = 15, and 15 + 5 = 20.

Key takeaway: Find what changes between the numbers, then use that same rule to fill the empty space.

Sometimes the pattern moves up and down. Look carefully before guessing. In 3, 6, 5, 8, 7, __, the pattern is “add 3, take away 1.” After 7, add 3 to get 10.

Quick Check

Write the rule for each pattern.

1. 6, 9, 12, 15

Rule: ____________

2. 30, 25, 20, 15

Rule: ____________

3. 3, 6, 12, 24

Rule: ____________

4. 18, 9, 4.5, 2.25

Rule: ____________

Now fill in the missing number.

5. 8, 12, __, 20

Answer: __

6. 40, 35, __, 25

Answer: __

7. 5, 10, __, 40

Answer: __

Your Turn: The Missing-Number Trail

Materials needed: pencil and this page

Time required: 10 minutes

Follow the steps. Don’t rush past the checking part. That’s where sneaky mistakes get caught.

1. Read the whole number line.

2. Compare the first two numbers.

3. Decide whether the pattern adds, subtracts, doubles, halves, or uses two repeating rules.

4. Write the rule beside the line.

5. Fill in the missing number.

6. Check your answer by using the rule from the beginning to the end.

Completed example

> 7, 11, __, 19

> Rule: add 4

> Missing number: 15

> Check: 7, 11, 15, 19

Your Turn

1. 2, 5, __, 11

Rule: ____________

Missing number: __

Check: ___________

2. 24, 20, __, 12

Rule: ____________

Missing number: __

Check: ___________

3. 4, 8, __, 32

Rule: ____________

Missing number: __

Check: ___________

4. 64, 32, __, 8

Rule: ____________

Missing number: __

Check: ___________

5. 10, 13, 12, 15, 14, __

Rule: ____________

Missing number: __

Check: ___________

6. 1, 4, 7, __, 13

Rule: ____________

Missing number: __

Check: ___________

7. 50, 45, 40, __, 30

Rule: ____________

Missing number: __

Check: ___________

8. 3, 6, 5, 10, 9, __

Rule: ____________

Missing number: __

Check: ___________

Number Detective Challenge

This time, the blank can appear anywhere.

1. 6, __, 18, 24

Rule: ____________

Missing number: __

2. 45, 40, __, 30

Rule: ____________

Missing number: __

3. 2, 6, 18, __, 162

Rule: ____________

Missing number: __

4. 100, __, 64, 46

Rule: ____________

Missing number: __

5. 9, 12, 11, __, 13, 16

Rule: ____________

Missing number: __

When you finish, count your correct answers. You are done when you have completed all 13 lines and checked each rule.

Score box:

Correct answers: __ out of 13

If a line feels tricky, circle the two numbers closest to the blank. Compare those first. A small clue often unlocks the whole pattern.

Use Number Patterns Around You

Patterns show up in everyday jobs. A baker may place 6, 12, 18, and 24 cookies on trays. The rule is “add 6.” If one tray is missing, you can predict that it holds 30 cookies. Your answer is complete when the numbers rise by 6 each time.

A bus schedule may show times such as 8:00, 8:15, 8:30, __, and 9:00....