What Math Should a 3rd to 5th Grader Know?

I sat down to help my third grader with a worksheet and caught myself completely unsure of what she was even supposed to know. Was long division a third-grade thing or a fourth-grade thing? Were fractions supposed to be solid by now? I was trying to coach a game without knowing the rules.

So here is the map I wish I had taped to the fridge. In short: third grade is the year multiplication, division, and fractions arrive. Fourth grade is multi-digit operations and the start of decimals. Fifth grade is decimals in full and operations with fractions. Almost all of it is aligned to the Common Core math standards that most U.S. states follow. Here is the grade-by-grade version.

What math should a 3rd grader know?

Third grade is the engine room. The two ideas that matter most are multiplication and fractions, and they show up here for the first time in a serious way.

• Multiply and divide within 100, and know products of one-digit numbers from memory by the end of the year.
• Understand a fraction as a number on the number line, recognize simple equivalent fractions, and compare fractions with the same numerator or denominator.
• Add and subtract within 1,000 using place value.
• Round to the nearest 10 and 100.
• Measure area and perimeter, tell time to the minute, and read bar and picture graphs.

If a child leaves third grade shaky on multiplication facts or thinking of fractions as "a piece of pizza" rather than a number, that is the gap to close before fourth grade builds on top of it.

What math should a 4th grader know?

Fourth grade scales everything up. The numbers get bigger and fractions start doing real work.

• Multiply a four-digit number by a one-digit number, and two two-digit numbers; divide up to four digits by one digit with remainders.
• Generate equivalent fractions, compare fractions with unlike denominators, and add and subtract fractions with like denominators.
• Multiply a fraction by a whole number.
• Understand decimal notation for fractions, and compare decimals to the hundredths.
• Find factors and multiples, recognize prime and composite numbers, and measure and classify angles.

What math should a 5th grader know?

Fifth grade is the decimals year, and it is the last stop before middle-school math. This is where the bill comes due for any earlier fraction gaps.

• Add, subtract, multiply, and divide decimals to the hundredths.
• Add and subtract fractions with unlike denominators, and multiply and divide fractions.
• Fluently multiply multi-digit whole numbers and divide with two-digit divisors.
• Understand place value to the thousandths and powers of 10, and use grouping symbols in expressions.
• Find the volume of rectangular prisms and plot points on the coordinate plane.

Knowing the standard is not the same as mastering it

Here is the trap. A list like this can make you feel either reassured or panicked, and both feelings can be wrong. The standards describe what istaught. They say nothing about what your specific child has actually learned. A kid can sit through every fractions lesson and still not believe, deep down, that one-half and two-fourths are the same number.

And remember the framing that makes all of this useful: a gap is not a verdict, it is a coordinate. If your fifth grader is strong on decimals but wobbly on dividing fractions, that is not "bad at math." It is one nameable skill to go get. The whole point is to find what they have not learned yet.

How to check what actually stuck

The fastest way to turn this map into something useful is to measure against it. A short adaptive math assessment adjusts its difficulty to each answer, so in about eight minutes it finds the level your child can sustain and breaks the result down by topic, calibrated to NWEA MAP and iReady. Instead of "third-grade math," you get "solid on multiplication, shaky on fractions," which is the only version that tells you what to do next.

Tape the map to the fridge if it helps. Then go find out which parts your child already owns and which one to work on this month. That is a much better use of a Tuesday night than guessing, which is exactly what I was doing. If you want the longer version of how that measurement works, it is all in how Test My Kid works.