The Mantra · Four Steps
1 · Circle
2 · Tool
3 · Write
4 · Check
Step 1 · The Map
Understand
Read the question twice. Circle the numbers, underline what is really asked. If you don't understand, every step after is wasted.
Cube S5: circle 3 cm, 1 cm, "no red paint". It really asks: how many cubes hide inside, never touching the outside?
Step 2 · The Map
Plan
Choose your tool before calculating: draw a picture, make a list, use a table, write an equation, or guess & check. Without a plan you are only guessing.
Coin Q3: plan HOW to count before counting — every amount is a multiple of 5, from 5¢ up to 55¢.
Step 3 · The Map
Solve
Write one step per line, clearly. If you can't read your own work, you can't check it — and you earn no method marks.
Cube S6: 3−2=1, then 1×1×1=1. One clean line per operation.
Step 4 · The Map
Look Back
Is the answer sensible? Right units? Answer sentence written? Can you extend it to a whole family? Small slips survive if you never look back.
Check 26 painted + 1 bare = 27 total. Or: 3 cm→1, 4 cm→8, 5 cm→27 ⇒ rule (n−2)³.
Mindset
Exercise vs Problem
Judge by the method, not the topic. Method known at once → Exercise. Must plan how to start → Problem. Competitions are won on the problems.
"12 × 8" = Exercise. "How many 2-digit numbers from 1,2,3,4?" = Problem (needs a careful list).
Tool · Draw
Draw a Picture / Peel the Shell
Hard to imagine? Draw it. For the painted cube, peel one layer off each end of every edge → the hidden core = (n−2)×(n−2)×(n−2).
3 cm cube: peel 1 layer each side → core 1×1×1 = 1. 5 cm cube: core 3×3×3 = 27.
Tool · Pattern
Find a Pattern
Finish one problem, then grow a family. 3 cm→1, 4 cm→8, 5 cm→27, so an n cm cube hides (n−2)³ unpainted cubes. That is Step 4 at work.
Once you own (n−2)³, any cube size answers itself — no more drawing.
Tool · List
Make an Organized List
Plan how to count before you count. List amounts smallest→largest. Here every amount is a multiple of 5, from 5¢ up to 55¢ — no skipped step, nothing missed.
5,10,15,…,55 ⇒ exactly 11 different amounts. Order is the anti-mistake machine.
Tool · Verify
Check It Twice
First list smallest→largest, then list again largest→smallest. Compare: same amounts? No extras, no missing? A different order catches the slips.
Coin S11: two passes in opposite order expose any amount you skipped.
Trap
Count the Cuts, Not the Pieces
4 pieces = 3 cuts. Each cut takes the same time. 6 pieces = 5 cuts. Trap: 6 × 4 = 24 counts one cut too many!
12 min ÷ 3 cuts = 4 min/cut. 5 cuts × 4 = 20 min. Remember: pieces = cuts + 1.
Big Idea
Tools Calculate. Brains Solve.
A calculator is fast and accurate — but it never chooses the method. The method is always your map: the four steps. You are the helmsman; the tool is the paddle.
Even with a calculator, you still do Step 2 (Plan) first. That is where the marks are.