Planning, Deduction, and Numeracy Drills

Complex planning drill

Rule

You have positions:

A B C D

Goal:

D C B A

Allowed move: swap adjacent positions.

Minimum swaps?

Answer: 6

Reason:

Reverse order of 4 elements has 4 × 3 / 2 = 6 inversions.

Planning method

For any planning game:

1. Write current state.
2. Write target state.
3. Identify fixed pieces.
4. Move blockers first.
5. Count minimum moves if possible.

Deductive reasoning drill 1

Find next:

▲ ○ ▲ ○ ▲ ?

Answer: ○

Rule: alternating.

Deductive reasoning drill 2

Find next:

A, C, F, J, O, ?

Answer: U

Positions:

1, 3, 6, 10, 15

Differences:

+2, +3, +4, +5

Next +6 = 21 = U.

Deductive reasoning drill 3

Complete:

2, 6, 12, 20, 30, ?

Answer: 42

Pattern:

n² + n

or differences:

4, 6, 8, 10, 12

Numeracy shortcut drills

Multiplication by 25

n × 25 = n × 100 / 4

Examples:

• 36×25 = 900
• 48×25 = 1200
• 72×25 = 1800

Multiplication by 11

For two-digit number ab:

ab × 11 = a, a+b, b

Example:

34 × 11 = 374

If middle sum exceeds 9:

57 × 11 = 627

because 5+7=12, carry 1 to 5.

Percentage equivalents

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.67%
1/8	12.5%
1/10	10%
1/20	5%

10-minute game warmup

Before actual assessment:

1. 2 minutes: grid recall
2. 2 minutes: reverse digit recall
3. 2 minutes: simple arithmetic
4. 2 minutes: pattern series
5. 2 minutes: calm instruction reading