Should my child learn PEMDAS?

Eventually yes, but knowing the letters is not the same as understanding the idea, and children who memorize the mnemonic first often apply it wrongly, doing all division before any multiplication. Start with the single fact that multiplication is done before addition, get that automatic on expressions like these, and add the rest of the list when brackets and exponents actually appear.

Is the rule arbitrary, or is there a reason for it?

It is a convention, but not a pointless one. Multiplication is shorthand for repeated addition, so in 3 + 4 x 5 the 4 x 5 is one quantity, twenty, that happens to be written as a product. Giving it priority means expressions can be written without brackets around every product, which is why the convention stuck.

What grade is this, and what depends on it?

It is introduced in fifth grade, though two step word problems in third and fourth already quietly require it. Everything algebraic afterwards assumes it silently: 3 + 4n means 3 plus four lots of n, and a child still reading left to right will misinterpret expressions from the first day of algebra onward.

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Order Matters

Multiply before you add.

Grades 5 · Order of operations

How to play

1An expression appears, like 3 + 4 x 5.
2Tap the correct value.
3Do the multiplication first, then the addition. Left to right is a trap here.
4Keep your streak alive.

Try a few

3 + 4 x 5
Answer: 23
Find the multiplication and do it first: 4 x 5 is 20. Now the expression is 3 + 20, which is 23. Reading straight across instead gives 3 + 4 is 7, then 7 x 5 is 35, and 35 will be sitting there on screen as one of the choices, because it is the answer this game is built to catch. Both readings are arithmetic done correctly. Only one of them read the expression the way everyone agrees it should be read.
6 x 2 + 9
Answer: 21
The multiplication is at the front this time, so left to right happens to start in the right place: 6 x 2 is 12, then add 9 to get 21. The trap in this shape is doing the addition first, 2 + 9 is 11 and 6 x 11 is 66, which is three times too big. How far apart 21 and 66 are is the point: the order is not a technicality.
9 + 2 x 2
Answer: 13
Small numbers, same rule. 2 x 2 is 4, and 9 + 4 is 13. Left to right would give 11 x 2, which is 22. A child who can already see that 9 plus a small thing cannot reach 22 has a check on themselves that does not depend on remembering the convention at all, and estimating like that is worth encouraging alongside the rule.

Why this game helps

Reading left to right is how children read everything else, so applying it to 3 + 4 x 5 and getting 35 is a sensible mistake rather than a careless one. The convention that multiplication binds tighter than addition is genuinely arbitrary as a rule and genuinely necessary as an agreement: without it the same expression means different things to different people. Meeting the two readings side by side, and seeing that they disagree, is what makes the rule feel needed instead of imposed. Everything algebraic afterwards assumes it silently.

If your child finds this hard

There is really only one error in this game and it is reading left to right, the way children read everything else. It produces a specific wrong answer, the one you get by doing the addition first, and that answer is always among the four choices here. Say it out loud as an admission: left to right is the sensible guess, and math is the one place it does not apply. Children accept the rule faster when it is presented as an exception rather than as something they should have known.

Some children go the other way and decide the order never matters, or that the correct reading is itself the mistake. Settle it with a story instead of a rule. You have 3 dollars and buy 4 packs of stickers at 5 dollars each: the 4 and the 5 belong together, they make 20, and the 3 was never part of that purchase. The expression 3 + 4 x 5 is describing exactly that situation, and once the numbers mean something the grouping stops being arbitrary.

A practical habit that fixes this faster than chanting a mnemonic: before calculating anything, draw a loop around the multiplication with a finger or a pencil. 3 + 4 x 5 becomes 3 + (4 x 5) on the page, and the expression now tells you what to do without any recall. Note that this game uses only one addition and one multiplication, with no brackets, exponents or division, so the full priority list is not needed yet. One rule, applied every time, is the goal here.

Common questions

Should my child learn PEMDAS?: Eventually yes, but knowing the letters is not the same as understanding the idea, and children who memorize the mnemonic first often apply it wrongly, doing all division before any multiplication. Start with the single fact that multiplication is done before addition, get that automatic on expressions like these, and add the rest of the list when brackets and exponents actually appear.
Is the rule arbitrary, or is there a reason for it?: It is a convention, but not a pointless one. Multiplication is shorthand for repeated addition, so in 3 + 4 x 5 the 4 x 5 is one quantity, twenty, that happens to be written as a product. Giving it priority means expressions can be written without brackets around every product, which is why the convention stuck.
What grade is this, and what depends on it?: It is introduced in fifth grade, though two step word problems in third and fourth already quietly require it. Everything algebraic afterwards assumes it silently: 3 + 4n means 3 plus four lots of n, and a child still reading left to right will misinterpret expressions from the first day of algebra onward.

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