Learning Objectives
- 01
Demonstrate fluency across additions, ×11, and ×5-squares.
Weekly Practice Assessment
Timed drills across every Week 1 technique.
Goal · 50 mixed problems · 90% accuracy
Topics
Mixed timed drills
Worked Examples
51 × 3=153
Left-to-right multiplication (Benjamin): break the 2-digit number into tens + units, multiply each, add.
- 01
50 × 3 = 150
Tens first — biggest piece always goes first to keep the running total anchored.
- 02
1 × 3 = 3
Now the units piece.
- 03
150 + 3 = 153
Add the two partial products — left-to-right addition.
- →
= 153
Benjamin, Secrets of Mental Math — distribute by place
35²=1225
Squares-ending-in-5 shortcut (Benjamin, Secrets of Mental Math).
- 01
3 × 4 = 12
Drop the 5. Multiply the front digit(s) by the next number: 3 × 4 = 12.
- 02
12 | 25 → 1225
Stick "25" on the end. Every square ending in 5 ends in 25 — because (10a+5)² = 100·a(a+1) + 25.
- →
= 1225
Benjamin, Secrets of Mental Math — squaring numbers ending in 5
64 × 3=192
Left-to-right multiplication (Benjamin): break the 2-digit number into tens + units, multiply each, add.
- 01
60 × 3 = 180
Tens first — biggest piece always goes first to keep the running total anchored.
- 02
4 × 3 = 12
Now the units piece.
- 03
180 + 12 = 192
Add the two partial products — left-to-right addition.
- →
= 192
Benjamin, Secrets of Mental Math — distribute by place
95²=9025
Squares-ending-in-5 shortcut (Benjamin, Secrets of Mental Math).
- 01
9 × 10 = 90
Drop the 5. Multiply the front digit(s) by the next number: 9 × 10 = 90.
- 02
90 | 25 → 9025
Stick "25" on the end. Every square ending in 5 ends in 25 — because (10a+5)² = 100·a(a+1) + 25.
- →
= 9025
Benjamin, Secrets of Mental Math — squaring numbers ending in 5
22 × 6=132
Left-to-right multiplication (Benjamin): break the 2-digit number into tens + units, multiply each, add.
- 01
20 × 6 = 120
Tens first — biggest piece always goes first to keep the running total anchored.
- 02
2 × 6 = 12
Now the units piece.
- 03
120 + 12 = 132
Add the two partial products — left-to-right addition.
- →
= 132
Benjamin, Secrets of Mental Math — distribute by place
Talking Points
- •Target: 90% accuracy under timed pressure.
- •Log misses — they reveal which sub-skill still needs reps.
Week 1 · Fundamentals
Mental Math Fundamentals & Basic Operations
- →Develop left-to-right calculation habits
- →Strengthen multiplication table mastery
- →Learn fundamental mental shortcuts
Sample Problems · Week 1
One simple and one intermediate problem to preview the week.
Simple · Day 1
57 + 38=95
Intermediate · Day 3
314 × 11=3454