Essential Strategies Series
Mental Math Strategies
The Essential Shortcut Playbook for Middle School Success
69 Strategies5 VolumesMastery ChecksCompetition Prep
Grades 5–8
·Competition Ready
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About This Book
Master fast calculation techniques that top students use every day. Each chapter teaches a single shortcut, proves why it works, then builds mastery with progressively harder practice sets. Perfect for test prep, competition warm-ups, or everyday class work.
Table of Contents
1
Basic Divisibility Rules
2
Powers of Two
3
Last-Digit Divisibility Tests — Easy Primes
4
Triangular Numbers
5
The 1/7 Repeating Decimal Cycle
6
Decimal Digits of p/11
7
Cyclic Last-Digit Patterns in Powers
8
The 9-9-10 Rule
9
Percent Building Blocks
10
Left-to-Right Addition
11
Compensation — Addition and Subtraction
12
Friendly Number Anchors — 25, 50, 75, 100
13
Mental Multiplication by Simple Fractions
14
Difference of Squares
15
Cross-Product for Proportions
16
Percentage Change
17
Sum of an Arithmetic Sequence
18
Halving and Doubling
19
Special Number Multipliers
20
Squares — Special Cases
21
Ratio Scaling
22
Estimation with Compatible Numbers
23
Modular Clock Arithmetic
24
Division by 9 and 11 via Digit Sums
25
Squares Near 50 and Near 100
26
Factor Decomposition
27
Squaring Any Two-Digit Number
28
Average via Anchor
29
Speed Multiplication Methods — x6, x7, x8
30
Square Root Linearization
31
GCF by Repeated Subtraction
32
Last-Digit Divisibility Tests — Medium Primes
33
Casting Out Nines
34
Prime Factorization Strategies
35
Number of Divisors
36
LCM from GCF
37
Place-Value Column Method
38
Compensation in Multiplication
39
Halving Chains and Reciprocal Division
40
Cube Root Estimation
41
Sum of Divisors
42
Last-Digit Divisibility Tests — Hard Primes
43
The Euclidean Algorithm for GCF
44
Vedic Cross-Multiplication
45
Squaring Any Three-Digit Number
46
Vedic Division
47
The Doomsday Algorithm — Day of the Week for Any Date
48
Square Roots by Long Division — Perfect Squares
49
Lattice Multiplication
50
Square Roots by Long Division — Non-Perfect Squares
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Why This Book?
Infinite Variations
Every practice set uses our AI-powered generator — the same numbers never appear twice.
Answers and Worked Methods
Every problem has an answer, and a full step-by-step solution for its method — nothing is left as just a number.
Competition Aligned
Difficulty and style are calibrated to AMC 8 and MathCounts standards.
Print Ready
Professionally typeset with LaTeX — sharp on any standard printer.