5th Grade Algebra: Problems and Practice Drills

The more practice your 5th grader gets with algebraic concepts, the more familiar he or she will become with manipulating variables and graphing. If your child needs pre-algebra practice, review the math drills and practice problems below, and try using them as a model for creating your own problems at home.

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What Do Students Study in 5th Grade Algebra?

In 5th grade, students continue their study of algebra by writing and solving expressions using symbols like parentheses. Students also continue to apply the order of operations to solve equations. For instance, for a problem such as (3 x 4) + 2, 5th graders know to solve the multiplication problem inside the parentheses first. The concepts learned in 5th grade are building blocks for skills that will be needed later when they study complex equations, such as the quadratic formula.

In addition, students learn to plot ordered pairs on a graph. Math review doesn't have to be limited to drills; help your 5th grader practice graphing skills by applying them to real life at home. For instance, track your child's growth over the course of the year. On a graph, label the x-axis as the months that go by and label the y-axis as height in inches. Each month, your child can plot how tall she is using an ordered pair. If she is 48 inches after four months, then the coordinate would look like this: (48, 4).

Math Problems by Concept


In 5th grade, students learn to interpret numerical relationships that are expressed by equations. For instance, in the equation 2x = y, students learn that x is two times greater than y. In the following problems, ask your child to write a numerical expression based on the written instructions.

1. A number, y, is three times greater than five added to a number, x.

For this problem, the equation should look like this: y = 3 (5 + x). It can be helpful if you point out to your child that the word 'is' often indicates an equality sign (=).

As an additional challenge, have your child solve the problem by providing a number for one of the variables. For instance, if x = 1, what is y? In this case, y would equal 18.

2. Six less than a number, b, is four.

The equation for this problem is: b - 6 = 4. Your child can continue to solve this problem because it has only one variable. For this problem, b equals ten.

3. Twice a number, t, and fifteen more is 3.

The equation looks like this: 2t + 15 = 3. Solving this problem is extra challenging because it includes negative numbers. In this case, t = -6.


Your child will benefit most from graphing practice if you provide graphing paper. On the paper, you can create a graph with the four quadrants created by the x and y-axes. Then, give your son or daughter a list of coordinates to plot on the graph. Include both positive and negative numbers. After the points have been plotted, your child can draw a line that connects the slope of these points.

Remember, graphing can present opportunities for real-world application. Ask your son to graph how many weeks it will take him to save up $100. He can then create a table that will track the growth. On the left side of the table are the x-axis coordinates, which represent the amount of money he has. The right side of the table has the y-axis coordinates, which keep track of the time that elapses. After collecting his data, he can plot the coordinates on a graph.

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