Decimals are one of the trickiest topics in upper-elementary math. The rules for adding, subtracting, and multiplying decimals look, to a child, like a bunch of weird new rituals: line up the decimal points, count the digits after the point, move the decimal in the quotient. These rules are not arbitrary — they all follow from place value — but a child who has been taught them as rules without meaning is in for a rough few years.
The shortcut most experienced teachers use is money. Nearly every child arrives in third or fourth grade with a working intuition for dollars and cents: they know that $1.75 is more than $1.25, that adding $0.40 to $0.60 gives $1.00, and that "a quarter" is worth twenty-five cents. This intuition is, mathematically speaking, decimal arithmetic. The child just hasn't been told yet.
To teach decimal addition, start with money questions: "You have $2.50 and find $1.25 more; how much do you have?" The child solves this without effort. Then rewrite the same problem as 2.50 + 1.25 and note that the answer is the same. Now ask the child what they *did* with the decimal points. They will say some version of "I just added the cents and the dollars separately". That is the place-value insight, and once they have said it, the abstract rule ("line up the decimal points") becomes obvious — it's the thing that makes the cents-and-dollars alignment line up automatically on paper.
Subtraction, multiplication by whole numbers, and division by whole numbers all extend naturally from money contexts. "Three friends split $12.60" is decimal division. "Six packs of gum at $0.75 each" is decimal multiplication.
Where money breaks down is decimal-by-decimal multiplication ("what is 0.4 times 0.3?") because we don't commonly multiply dollars by dollars. For that step, you need to return to the underlying place-value argument. But by the time the child gets there, they already believe that decimal arithmetic is just normal arithmetic with a decimal point in the right place — which is exactly the belief you want them to have.
In MathVenture, the Decimal Diner game uses a restaurant bill as the backdrop for every decimal problem. Every price is realistic, every tax is 10% (for easier mental math at first), every tip is 10 or 20%. The contexts are different but the mechanic is the one we've described: start with dollars and cents, then peel back the scaffolding.
A practical home routine that builds decimal fluency is letting the child read prices off a real receipt. Pick three or four items and ask the child to add them mentally. Round if the digits make rounding easy. Then check against the printed total. The "check against reality" step is what makes this work — there's no abstract right answer to argue about, just a number on a slip of paper. A few minutes of this once a week, in the car on the way home from the supermarket, beats half an hour of decimal worksheets.
The classic decimal misconception is that 0.45 is bigger than 0.5 because 45 > 5. A child who sees the digits as separate numbers, rather than as a single number, will reason their way into this mistake without ever noticing it. The fix is to come back to place value: the 4 in 0.45 is in the tenths column, and the 5 in 0.5 is also in the tenths column, so we are comparing four tenths to five tenths, and five tenths wins. Money is the easiest place to feel this — "would you rather have forty-five cents or fifty cents?" is not a hard question for any child, and once they have given the obvious answer you have the door open to the formal version.
Once decimals are stable, percentages are nearly free. A percent is just a fraction with a denominator of one hundred, and one hundred is what our money system is already built around. 25% of the bill is the same as a quarter of the bill is the same as 0.25 of the bill — three different costumes for the same number. Children who arrive at percentages with decimals in place pick them up in days. Children who arrive without find percentages to be one of the harder topics of the entire year. Spending time on decimals first is not a detour — it's the shortest path.