30 8th Grade Math Problems: Answers With Worked Examples

8th Grade math problems build upon the basic algebraic reasoning and number system knowledge formed in prior grades. They help prepare students for more challenging math concepts that lay ahead of them in high school. 

In this blog, middle school math teacher, Erin, provides educators with 30 8th grade math problems to use in the classroom to strengthen learners’ math skills. Teachers can use these 8th grade math problems as warm-ups, competitive partner games, individual practice, or review before a test.

What are 8th grade math problems?

8th grade math problems are math problems specifically for 8th grade students focusing on the math skills and concepts learned in 8th grade. 

Many 8th grade math problems typically focus on algebraic reasoning to strengthen the foundations of solving for an unknown variable early on in the year. The majority of 8th grade math builds upon this skill. 

For example, when learning geometric concepts such as angle measures, surface area, volume, arc length, and sector area, formulas with an unknown variable are used to solve for measurement quantities.

8th grade math problems: Math curriculum

6th grade math problems and 7th grade math problems build the foundations for the 8th grade math curriculum. In 7th grade, students work with rational numbers and are introduced to simplifying algebraic expressions and solving algebraic equations. 

As students progress to 8th grade, a quick review of 7th grade material leads to a deeper dive into Algebra at a much faster pace.

The math curriculum in 8th grade hones in on linear functions and systems of equations where there are two variables rather than one. 

Perhaps, one of the biggest reasons 8th grade students struggle with the Common Core Math Standards is that they don’t have strong algebraic knowledge before introducing more than one variable.

30 8th grade math problems 

Here are 30 8th grade middle school math problems to help students practice and secure their knowledge of the core math concepts needed to succeed in high school and beyond. 

8th grade math problems: Rational number operations

Question 1 

(-2)+(-5)=

Answer: -7

Add the values, then keep the negative sign when adding two negative numbers.

Question 2 

(-\frac{3}{8})-(\frac{7}{9})=

Answer:  -1\frac{11}{72} \text{ or } -\frac{83}{72}

This is another example of adding two negative numbers. Students must add the two fractions and then keep the negative sign.

Question 3 

(\frac{3}{8}) ^{2} +3(0.025)=

Answer: \frac{53}{320}

Squaring a fraction means both the numerator and denominator are squared. Therefore: 

3^{2} = 9 8^{2} = 64 (\frac{3}{8})^{2} = \frac{9}{64}

Show students how to enter fractions and exponents on their calculators. Calculators automatically reduce answers to the lowest terms and can help save students time.

8th grade math problems: Quotients of exponents, decimals, roots, and scientific notation

Question 4 

Approximate the non-perfect root \sqrt{10} to the nearest tenth without using a calculator.

Answer: 3.2

The non-perfect root of 10 falls between the two perfect roots of 9 and 16.

Question 5 

Write the product of   \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} using the exponential form.

Answer: (\frac{2}{3})^{4}

Question 6 

Apply the Product of Powers Rule to simplify 4^{2} \times 4^{6} without using a calculator.

Answer: 4^{8}

The Produce of Powers Rule states that when the operation between to like bases raised to different powers is multiplication, keep the base and add the exponents.

8th grade math problems: Combining like terms and distributive property

Question 7 

-7x+2+3x-5

Answer: -4x-3

For struggling learners, circling one term and boxing the other works well. Additionally, using color to separate the terms is effective when several terms are used.

Question 8

14-2x+3x-1

Answer: x+13

Explain to students that answers should often be reported with the variable listed before the constant.

Question 9

3(2x+6-5x+3)

Answer: -9x+27

Drawing arrows to visualize which terms are multiplied together can be very effective.

Teach students they can use negative signs and subtraction signs interchangeably in algebra. 

For example, 14-2 x means the 14 is positive and the 2 x is negative, even though the operation before the 2 x is a subtraction sign.

8th grade math problems: Solving one-step and two-step equations

Question 10 

-4 + x = 10

Answer: x =14 

Visual aids and drawings of a vertical line through the equal sign improve some students’ understanding. This clearly indicates the “left” and “right” sides and the need to balance them. 

Other students do not like the vertical line, and I typically leave it off when showing my work.

Question 11

\frac{x}{120} =3

Answer: x= 360

Question 12 

\frac{3}{4}x-\frac{1}{8}=\frac{1}{4}

Answer: x=\frac{1}{2}

8th grade math problems: Solving multi-step equations with the variable on both sides

Question 13 

3(2x+1)+x= -39

Answer: x = -6 

Question 14 

-3x+2=10-x

Answer: x= -4

Choose a side to move the x term to. I often told students to try and avoid working with negative numbers if they can, but it’s not necessary.

Question  15 

-2x-34=98-5x

Answer: x = 44

When starting, it is helpful if all answers result in an integer. Students can then determine that something has gone wrong if they receive a fraction or decimal answer. 

For high-level learners, incorporate square roots of perfect squares and cube roots where applicable.

8th grade math problems: Special cases and determining the number of solutions

Question 16 

6(2x+4)=4(3x+6)

Answer: All real numbers; infinite solutions

When the resulting statement is true (24=24) , any number can be used for x .

Question 17 

4(x-3)=4x+2

Answer: Undefined; no solution

When the resulting statement is false (-12=2) , this means no number can be used for x

Question 18 

-3(x+5)= -(3x+15)

Answer: All real numbers; infinite solutions

Explain to students they should treat a negative sign (sometimes a subtraction sign) outside parentheses as a negative value that needs to be distributed.

8th grade math problems: Applying linear equations to word problems and real-world application

Question 19 

Susie spent 2.75 hours on homework last night. She spent \frac{1}{4} hour longer on math than she did on reading. How much time did she spend studying both subjects?

Answer: Susie spent 1.25 hours reading and 1.5 hours on math.

Question 20 

In 5 years, Johnny will be twice as old as he is now. How old is Johnny now?

Answer: Johnny is 5 years old.

Challenge students to read simpler word problems and write their own equations to represent the scenarios.

8th grade math problems: Linear functions

Question 21

Is there a proportional relationship in this table of values? If so, find slope.  

Answer: Yes; slope = -1

The definition of slope is the change in y (dependent variable) divided by the change in x (independent variable).

Question 22

Graph the function y=3x+4

Answer:

Have students use a t-chart to help identify coordinates before graphing. Later on, show students how to graph simply using the rules of y-intercepts and slopes.

Question 23

Write the equation of the line that passes through (1, -19) and (-2, -7)  in slope-intercept form.

Answer: y= -4x-15

8th grade math problems: Scatter plots

Question 24

Give a possible scenario to relate the data in the graph provided.

Answer: There are many possible solutions to this question. Here is one possible answer: 

Question 25

Make a scatter plot from the data chart provided. Then, describe the correlation, if any.

Answer:

The correlation shows a positive linear relationship between the x and y axis as both variables increase.

Question 26

Both graphs display the same data points. Write the equation of the trend line in the graph on the left, as it fits the data better than the trend line in the graph on the right.

Answer: y= -0.37x+7.46 

Extension: After students write the equation of the line of best fit on paper, challenge the students to plot the points on an online graphing calculator. 

Then, have students type y_{1} \sim mx_{1}+b  to see how close their equation matches the true linear regression.

8th grade math problems: Pythagorean Theorem, angles of triangles, surface area, volume

Question 27 

Solve for the missing dimension in the right triangle.

Answer: x=8.1 \text{ feet} 

Question 28 

Calculate the measure of exterior angle A by solving for x . Use algebraic reasoning and apply the Exterior Angle Theorem.

Answer: A=108^{\circ}

Question  29

Calculate the surface area and volume for the given triangular prism.

Answer: \text{Surface area } = 68cm^2 ; \text{ Volume } = 30cm^3

Question 30 

Calculate the surface area and volume for the given cone. Round to the nearest hundredth.

Answer: \text{Surface area } = 75.40cm^2 ; \text{ Volume } = 37.70cm^3  

Top Tips for Teaching 8th Grade Math Problems

For success in teaching 8th grade math problems, educators should incorporate:  

• Visuals
• Technology
• Rote skills
• Real-world application

Combining these teaching strategies is crucial for young learners. In my 15 years of experience as a math educator, students are more motivated to pay attention and power through lectures, note-taking, assignments, projects, and assessments if the educator figures out how to make the learning relevant and special to individuals. 

Simple things such as having students hand-write notes made a huge impact. Switching assignments between digital and paper frequently helped reduce groaning about the mundane. Incorporating art into math projects brought joy and opened students’ eyes to all the ways and places math is used in everyday life.

8th grade math worksheets

Looking for more resources? Please see our selection of eighth grade math worksheets covering grade 8 key math topics and more:

• Solve Equations With Fractions Worksheet
• Adding and Subtracting Scientific Notation Worksheet
• Solving Inequalities Worksheet
• Ratios Problem Solving Worksheet
• Negative Exponents Worksheet

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