Topics your child is likely to have trouble with in math, arranged by grade and/or topic.

This topic is currently under construction!

First and Second grades

Memorization of addition and subtraction facts is sometimes tough for young kids. :Liping Ma suggests having kids this age memorize sums and differences up to 20; i.e. they should have calculations such as 17-9=8 at their fingertips. This makes subtraction with borrowing go more smoothly.

Borrowing in subtraction is difficult for many children, and to a lesser extent so is 'carrying in addition*. Both are symptomatic of problems understanding place value.

Third

Multiplication itself is a fairly easy operation for kids to understand, but memorizing the multiplication tables is a critical thing to do, and difficult for some children.

Kids are introduced to fractions this year, and often find the basic idea very confusing. They may need help understanding the equivalence of fractions (e.g., 1/2 = 2/4) and simple rules such as 3 * 1/3 = 1.

Fourth

This is a big year in mathematics education in most places, when children are learning the algorithms which will allow them to do most mathematical computations by hand.

Long division is a difficult (but necessary!) algorithm for most children to master to automaticity. This can take a long time to master and needs frequent practice until it's mastered.

A sizeable number of kids have trouble with the multidigit multiplication algorithm during this year. A common problem is to use amounts carried over to the next column incorrectly. For example, in 34 x 34, the '1' from the '16' must be carried over and added to the result of 3x4 to make 13; but not infrequently a child will add the '1' to the 3 and then multiply by 4.

Fifth

Addition and subtraction of fractions is difficult for a lot of kids; many will naturally want to add and subtract the numerators and denominators independently. Multiplication and division of fractions will be much easier.

Related to the above, kids often have trouble both understanding and finding the least common denominators for two fractions to be added or subtracted.

Understanding the meaning of place value in decimal representations will often be difficult.

Purely computationally, kids will mix up the steps of adding and subtracting decimal numbers with the very different algorithm for multiplying decimal numbers.

Long division for decimal numbers seems not to be difficult provided the child can do long division.

Manipulation of negative numbers can be confusing but isn't usually a big hurdle.

Story problems are difficult in every grade because of the need to transform words into expressions, solve them, and transform back to words. Some of the problem is just due to attention problems in young children; every word problem contains those three steps at a minimum, and so they require good executive functioning just to carry them through to the end. Extensive practice is required, and the use of simple dimensional analysis to aid understanding can really be helpful (but must also be drilled).

Adding and subtracting mixed fractions is hard for kids. Take the opportunity to teach 'borrowing from the whole number' when doing subtractions such as

2 1/2 - 1 3/4,

since it strengthens a kid's understanding of borrowing in general.

Cross-multiplication, cancellation in fraction multiplication and other computational tricks are sometimes taught in this grade without sufficient explanation as to why they work, and sometimes the kids will simply 'learn them wrong' because they don't understand them. Keep an eye out for incorrectly applied tricks, and keep offering explanations as to why they work (deeper understanding will sometimes take a while to sink in).

Pre-algebra

The meaning of negative exponents are sometimes misunderstood. Kids will make mistakes simplifying expressions containing them. Zero exponents take some getting used to. Fractional exponents are very confusing.

Kids have to learn to get comfortable with moving back and forth between operations with negative numbers, and the familiar whole-number operations. They'll have trouble seeing at first, for example, that 6 - (-3) is the same as 6 + 3. With practice, though, they'll forget it was ever a problem.

The distributive law can be difficult to recognize in new applications. In pre-algebra, they'll apply this law (which they may know in their bones in the arithmetic setting from doing mental multiplication) to symbols, and it won't seem familiar. Treat it as a new topic in every new situation, but help the kid make the connections back to familiar settings.

Computational conversions between decimals, percents and fractions may not have been so hard for your kid to learn in fifth grade -- but the application of these conversions in story problems are often a sticking point. Does your kid really understand that 8% sales tax means that a little cost -- and only a little -- is being added onto the price of something? A lot of 8th graders still can't compute sales tax.

Algebra

Logarithms are EXTREMELY confusing. This is when many children just plain give up on math. Get them all the help they need with logs; don't let your kid slide over them.

Factoring polynomial expressions.

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