Learning Objectives
- 01
Understand why left-to-right calculation beats right-to-left.
- 02
Break complex numbers into manageable chunks in working memory.
Introduction to Mental Math
Why mental math matters, and learning to think from left to right.
Topics
Why mental math mattersLeft-to-right thinkingChunking numbers
Worked Examples
57 + 38=95
Break the second addend into place-value chunks (hundreds, tens, units) and add them one at a time so you only ever track one running total.
- 01
57 + 30 = 87
Add the tens (30). Just count up by tens — the ones digit stays the same. 57 + 30 = 87 — running total 87.
- 02
87 + 8 = (87 + 3) + 5 = 90 + 5 = 95
Hop to a friendly ten first! 87 needs 3 more to reach 90, so break 8 into 3 + 5. First hop: 87 + 3 = 90. Second hop: 90 + 5 = 95. Round numbers are easy to add to — running total 95.
- →
= 95
243 + 158=401
Break the second addend into place-value chunks (hundreds, tens, units) and add them one at a time so you only ever track one running total.
- 01
243 + 100 = 343
Start with the biggest piece — the hundreds (100). Big jumps first! 243 + 100 = 343 — running total 343.
- 02
+ 50 = 393
Add the tens (50) of the second number — running total 393.
- 03
393 + 8 = (393 + 7) + 1 = 400 + 1 = 401
Hop to a friendly ten first! 393 needs 7 more to reach 400, so break 8 into 7 + 1. First hop: 393 + 7 = 400. Second hop: 400 + 1 = 401. Round numbers are easy to add to — running total 401.
- →
= 401
808 + 445=1253
Break the second addend into place-value chunks (hundreds, tens, units) and add them one at a time so you only ever track one running total.
- 01
808 + 400 = 1208; 1208 + 40 = 1248; 1248 + 5 = 1253
Start with the biggest piece — the hundreds (400). Big jumps first! 808 + 400 = 1253 — running total 1253.
- →
= 1253
Benjamin, Secrets of Mental Math — left-to-right addition
895 + 637=1532
Break the second addend into place-value chunks (hundreds, tens, units) and add them one at a time so you only ever track one running total.
- 01
895 + 600 = 1495; 1495 + 30 = 1525; 1525 + 7 = 1532
Start with the biggest piece — the hundreds (600). Big jumps first! 895 + 600 = 1532 — running total 1532.
- →
= 1532
Benjamin, Secrets of Mental Math — left-to-right addition
503 + 356=859
Break the second addend into place-value chunks (hundreds, tens, units) and add them one at a time so you only ever track one running total.
- 01
503 + 300 = 803; 803 + 50 = 853; 853 + 6 = 859
Start with the biggest piece — the hundreds (300). Big jumps first! 503 + 300 = 859 — running total 859.
- →
= 859
Benjamin, Secrets of Mental Math — left-to-right addition
Talking Points
- •Verbalise the running total — phonological loop locks the number in.
- •Counting by 3s, 4s, 6s, 7s, 8s, 9s as warm-up.
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