30-Page Mind Games

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. The rule is “add 15 minutes,” so the missing time is 8:45. At a game, points might double: 1, 2, 4, 8,. The next score is 16. The expected outcome is a number that follows the same rule as the numbers around it.

Apply It

Solve each everyday pattern.

1. A plant grows 2 centimeters each week: 4 cm, 6 cm, 8 cm, cm. Missing amount: ________

2. You save 5 coins each day: 5, 10, 15,, 25. Missing amount: ________

3. A timer counts down: 30, 25, 20,, 10. Missing number: ________

4. A game gives double points each round: 2, 4, 8,. Missing points: ________

5. A clock chimes every 10 minutes: 2:00, 2:10,, 2:30. Missing time: ________

Write the rule beside each answer. You are finished when all five answers and all five rules are written.

Mini Mission

Make your own missing-number line. Choose one rule: add 3, take away 4, double, or use “add 2, take away 1.”

Start with this number: __________

Your number line: ________, ______, ______, ______, ________

Hide one number with a box: ________, ______, [], ______, ________

Write the rule: ________________________________________

Swap your puzzle with a partner, family member, or stuffed-animal assistant. (Stuffed animals are excellent at staying focused.) The other solver is finished when they write the missing number and the rule.

Reflect and Plan Your Next Move

You’ve practiced spotting changes, choosing a rule, and checking both sides of a blank. Now pause and notice which clue helps you most.

1. Which rule is easiest for you to spot: adding, taking away, doubling, halving, or a two-step rule? Give one number line as proof. ________________________________________________ ______________________________________________ ________________________________________________

2. What will you do first when a missing-number puzzle looks difficult? Write two steps you can follow. ________________________________________________ ______________________________________________ ________________________________________________

3. Create one new puzzle with exactly one missing number. Then solve it yourself and show your check. ________________________________________________ ______________________________________________ ________________________________________________

Before you put down your pencil, look at one puzzle you solved. Point to the first change, name the rule, and follow it all the way across. That simple check turns a guess into a smart answer.

End of chapter one. 4 more chapters in the full book.