Summer Study Guide – Entering Grades 4 or 5


Much of grades three and four center on multiplication and, by extension, division. Multiplication is necessary for:

  • fractions.
  • recognizing function rules.
  • simplifying algebraic equations.
  • simplifying radicals.
  • factoring trinomials.

Multiplication is important all the way through high school math and critical on timed tests.

The best help you can give your child is to ensure that he or she fully masters multiplication. Besides handing your child worksheets and flashcards, how can you do this? Here are some suggestions:

Write out the times tables.

Give your child a paper with 15 lines for each set of multiples they will be practicing. Go all the way up to having your child list the 15 multiples of 15.

You’ll be thankful later when they’re doing word problems involving time, such as the SATs, ACTs, and even middle and H.S. entrance exams.

There is no doing too much of this. Fluency with all of the numbers in a given times table will pay off in division and factoring.

Have them say the times tables out loud.

Again, go up to 15 multiples of each number. And include 12s, 13s, 14s, and 15s.
Give them repeated addition problems.

Having your child connect that `9 + 9 + 9 + 9 + 9 + 9 = 9 times 6` will help them recognize when multiplication is called for in word problems.

It will also encourage some children to remember their multiplication facts because they don’t want to add `9` six times.

Multi-digit multiplication.

Depending on your child’s skill level, have them practice two-digit by one-digit, two-digit by two-digit, and three-digit by three-digit problems. If your child is intimidated by this, start with problems like `40 times 2` and `20 times 3`.

Factor Check.

Ask them if certain numbers are in certain times tables.

This activity prepares them for long division and also can aid in their number sense. “Is `38` in the `5` times table?” should be met with an immediate, “No!” if a child has a true understanding of the multiples of `5`.

Division as Missing Factor.

Give division problems as a missing factor problem.

Asking `8 times [ ? ] = 32` encourages your child to use what they already know to do the problem.

In addition, they can write the corresponding division equations that go with the problem.

Word Problems.

Give them word problems involving multiplication and division. For an added challenge, you can give problems that require both operations.

You can also offer ones that require adding or subtracting combined with multiplication and division.

Ex: “The six fourth grade classes are going on a trip. Each class has 16 students. 4 teachers and 8 chaperones are accompanying them. They are taking vans that can hold 9 people each. How many vans do they need?”

Math Triangles

Just like with addition and subtraction, math triangles are a great tool for mixing up multiplication and division practice; see the diagrams below. The two numbers at the bottom multiply to the number at the top. If you fill in the bottom numbers, it’s a multiplication problem for your child. If you fill in the top and one number at the bottom, it’s a division problem for your child.

Based on your child’s skill, you can make these problems easier or harder.

Summer Study Plan

3nd and 4rd graders should spend roughly 25-35 minutes, twice a week during the summer to make sure their skills don’t deteriorate by next year.

If they had difficulty with math during the school year, they should spend 30-40 minutes, 3 times per week. By the end of the summer, they should be able to solve these kinds of problems quickly and correctly.


IXL has an online library of grade-specific problems, broken down by topic:

Alternatively, has well formatted, easy-to-print worksheets, also broken down by topic. The sheets are organized and given titles like “multiple by 10” and “missing dividend or divsior”. See

I prefer the printed worksheets, as computers can be distracting.

Need Help?

If you need help organizing an effective summer study plan or just want someone to sit down with your kids and make math fun, give us a call at 718.552.0300. We’re always happy to help.

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Elizabeth Campbell

Elizabeth Campbell

Liz has a B.A. in Mathematics and has been tutoring and teaching math in New York City since 2005, working with students as young as four, as experienced as thirty-somethings, and at every age in between.Having tutored students at private, charter, and public schools, she is familiar with a host of math curricula.
She has also taught high school math and has prepared students for a variety of standardized tests, including the ISEE, SHSAT, Regents, Common Core, and SAT. Because of her experience across age and grade levels, she knows how concepts learned in earlier grades connect to what students will need to know in later ones.
Elizabeth Campbell

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