It is a matter of understanding and reasonable compliance with safety and operational procedure. Read your kitchen safety manuals for your stove, show the kids how to work safely with knives, and explain proper technique.
My sons were both able to handle excavators and track hoes at eleven. Of course, professional operators were faster, but by fourteen, they were both fairly competent.
Safety first! Disregard feminist double talk: "Err on the side of caution." To inject random error into anything is an open invitation to accidents, permanent disability, and fatality. Rather, show that you actually understand the safe use of household implements and teach by the tried and proven, lesson and test method.
Show the kid, don't just say it. The kid will need a step stool to get to your appliances. Give the kid confidence, never fear.
Knives: show what it is supposed to do and how it actually works, how to sharpen and maintain them, proper cleaning techniques, safe storage and proper use. Show how to select and use cutting boards, use a sharpening steel, and safe cutting procedure.
Stoves: show what heat does, let the kid put his hand NEAR the burner, and that will give him a clue how hot it gets -- and reasons to handle hot pots and pans with proper heat protection: hot pads, insulated gloves, etc. Show actual cooking techniques, then let the kid cook something. Usually, it is best to start with boiling water for hard-boiled eggs. Then show how to make award-winning pancakes.
Cleanup: show how to load a home dishwasher, sort and put away the clean dishes, explain that it cleans by pressurized water near boiling, uses a non-foaming detergent (nothing else will work) and show what not to clean in the dishwasher: cast iron and some plastics.
Meal planning: ask what the family wants for dinner, and plan that out with the kid. Show how to use cookbooks, food safety, sanitation, and basic family nutrition. Show how to plan a balanced meal.
ABOVE ALL, AVOID THE TENDENCY TO YELL, "DON'T!"
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