problem solving grade 8

Grade 8 Algebra Word Problems

These lessons cover some examples and solutions for algebra word problems that you will commonly encounter in grade 8.

Related Pages More Math Word Problems Algebra Word Problems

How to write algebra word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods?

Grade 8 Algebra Word Problems How to solve algebra word problems using systems of linear equations?

Example: Devon is going to make 3 shelves for her father. He has a piece of lumber 12 feet long. She wants the top shelf to be half a foot shorter than the middle shelf, and the bottom shelf to be half a foot shorter than twice the length of the top shelf. How long will each shelf be if she uses the entire 12 feet of wood?

Grade 8 Algebra Word Problems - Line Segments

Example: If JK = 7x + 9, JL = 114 and KL = 9x + 9. Find KL.

Grade 8 number word problems - common core How to write word problems into systems of linear equations and solve systems of linear equations using elimination and substitution methods?

Example 1: The sum of two numbers is 361 and the difference between the two numbers is 173. What are the two numbers?

Example 2: There are 356 Grade 8 students at Euclid’s Middle School. Thirty-four more than four times the number of girls is equal to half the number of boys. How many boys are in Grade 8 at Euclid’s Middle School? How many girls?

Example 3: A family member has some five-dollar bills and one-dollar bills in their wallet. Altogether she has 18 bills and a total of $62. How many of each bill does she have?

Example 1: A friend bought 2 boxes of pencils and 8 notebooks for school and it cost him $11. He went back to the store the same day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much would notebooks cost?

• A farm raises cows and chickens. The farmer has a total of 42 animals. One day he counts the legs of all of his animals and realizes he has a total of 114. How many cows does the farmer have? How many chickens?
• The length of a rectangle is 4 times the width. The perimeter of the rectangle is 45 inches. What is the area of the rectangle?
• The sum of the measures of angles x and y is 127". If the measure of angle x is 34° more than half the measure of angle y, what is the measure of each angle?

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Common Core - State Standards Initiative

Students learn the basic concepts of algebra, geometry, and graphing before entering high school and learning more complicated topics. It is crucial that students completely grasp these concepts before going on to harder topics like trigonometry or calculus. With our on-demand videos students have the opportunity to go over math problems with a math teacher who knows how to break it down in an easily digestible format.

• Teachers go over definitions along with multiple problems for the skills so that students fully grasp the concepts.
• Skills available for statistics, time, ratios, and other eighth grade skills.
• Students learn how to use the scracthpad to better understand how to tackle the problems.

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Virginia Standards Of Learning (sol) Curriculum

Students learn the basic concepts of algebra, geometry, and graphing before entering high school and learning more complicated topics. It is crucial that students completely grasp these concepts before going on to harder topics like trigonometry or calculus. With our on-demand videos students have the opportunity to go over math problems with a math teacher who knows how to break it down in an easily digestible format.

• Teachers go over definitions along with multiple problems for the skills so that students fully grasp the concepts.
• Skills available for statistics, time, ratios, and other eighth grade skills.
• Students learn how to use the scracthpad to better understand how to tackle the problems.

Quiz 8th-Graders With These Math Word Problems

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Solving math problems can intimidate eighth-graders . It shouldn't. Explain to students that you can use basic algebra and simple geometric formulas to solve seemingly intractable problems. The key is to use the information you are given and then isolate the variable for algebraic problems or to know when to use formulas for geometry problems. Remind students that whenever they work a problem, whatever they do to one side of the equation, they need to do to the other side. So, if they subtract five from one side of the equation, they need to subtract five from the other.

The free, printable worksheets below will give students a chance to work problems and fill in their answers in the provided blank spaces. Once the students have completed the work, use the worksheets to do quick formative assessments  for an entire math class.

Worksheet No. 1

 Deb Russell

Print the PDF :   Worksheet No. 1

On this PDF, your students will solve problems such as:

"5 hockey pucks and three hockey sticks cost $23. 5 hockey pucks and 1 hockey stick cost $20. How much does 1 hockey puck cost?"

Explain to students that they'll need to consider what they do know, such as the total price of five hockey pucks and three hockey sticks ($23) as well as the total price for five hockey pucks and one stick ($20). Point out to students that they'll start with two equations, with each providing a total price and each including five hockey sticks.

Worksheet No. 1 Solutions

Print the PDF :   Worksheet No. 1 Solutions

To solve the first problem on the worksheet, set it up as follows: 

Let "P" represent the variable for "puck"

Let "S" represent the variable for "stick"

So, 5P + 3S = $23, and 5P + 1S = $20

Then, subtract one equation from the other (since you know the dollar amounts):

5P + 3S - (5P + S) = $23 - $20. 

5P + 3S - 5P - S = $3. Subtract 5P from each side of the equation, which yields: 2S = $3. Divide each side of the equation by 2, which shows you that S = $1.50

Then, substitute $1.50 for S in the first equation:

5P + 3($1.50) = $23, yielding 5P + $4.50 = $23. You then subtract $4.50 from each side of the equation, yielding: 5P = $18.50.

Divide each side of the equation by 5 to yield:

P = $3.70

Note that the answer to the first problem on the answer sheet is incorrect.  It should be $3.70 . The other answers on the solution sheet are correct.

Worksheet No. 2

Print PDF : Worksheet No. 2

To solve the first equation on the worksheet, students will need to know the equation for a rectangular prism (V = lwh, where "V" equals volume, "l" equals the length, "w" equals the width, and "h" equals the height). The problem reads as follows:

"Excavation for a pool is being done in your backyard. It measures 42F x 29F x 8F. The dirt will be taken away in a truck that holds 4.53 cubic feet How many truckloads of dirt will be taken away?"

Worksheet No. 2 Solutions

Deb Russell

Print PDF : Worksheet No. 2 Solutions

To solve the problem, first, calculate the total volume of the pool. Using the formula for the volume of a rectangular prism (V = lwh), you would have:

V = 42F x 29F x 8F = 9,744 cubic feet

Then, divide 9,744 by 4.53, or:

9,744 cubic feet ÷ 4.53 cubic feet (per tuckload) = 2,151 truckloads

You can even lighten up the atmosphere of your class by exclaiming: "You are going to have to use quite a few truckloads to build that pool."

Note that the answer on the solution sheet for this problem is incorrect. It should be 2,151 cubic feet. The rest of the answers on the solution sheet are correct.

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Free Printable Algebra Worksheets for 8th Grade

Algebra-focused resources for Grade 8 math teachers! Discover a variety of free printable worksheets to help students master essential algebra concepts and skills. Enhance your lessons with Quizizz.

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Explore printable Algebra worksheets for 8th Grade

Algebra worksheets for Grade 8 are an essential resource for teachers looking to help their students master the fundamental concepts of algebra. These worksheets provide a variety of problems and exercises that cover topics such as linear equations, quadratic equations, and systems of equations. Teachers can use these worksheets to supplement their lesson plans, provide extra practice for struggling students, or as a review before exams. With a wide range of difficulty levels, Grade 8 math teachers can easily find algebra worksheets that cater to the specific needs of their students. By incorporating these worksheets into their curriculum, teachers can ensure that their students develop a strong foundation in algebra, setting them up for success in higher-level math courses.

Quizizz is an excellent platform for teachers to access a vast library of algebra worksheets for Grade 8, as well as other math resources. This platform offers a variety of interactive quizzes, games, and activities that can be used to reinforce and assess students' understanding of algebra concepts. Teachers can easily search for and assign specific worksheets or quizzes based on the topics they are covering in class, making it simple to integrate Quizizz into their existing lesson plans. In addition to algebra worksheets, Quizizz also offers resources for other Grade 8 math topics such as geometry, statistics, and probability. By utilizing Quizizz in their classrooms, teachers can provide their students with engaging and effective learning experiences that will help them excel in their Grade 8 math courses.

8TH GRADE MATH PROBLEMS WITH ANSWERS

Question 1 :

What is the smallest number by which 256 may be divided so that the quotient is perfect cube? 

(A) 2               (B) 3               (C) 4

To find the number required to divide 256 such that the quotient is a perfect cube, we have to decompose 256 into prime factors.  

Question 2 :

How many digits are there in the square root of 4456321?

(A) 2 digits        (B) 4 digits      (C) 3 digits

Square root of 1 digit and 2 digit number contains 1 digit.

Square root of 3 and 4 digit number contains 2 digits.

Square root of 5 and 6 digit number contains 3 digits.

Square root of 7 and 8 digit number contains 4 digits.

So, the square root of the given number has 4 digits.

Question 3 :

Find the value of 3x 3  + 4x 2  + x - 5 when x = -3.

(A) -53                 (B) -71               (C) -32

Let f(x) = 3x 3  + 4x 2  + x - 5.

Substitute x = -3.

f(-3) =  3(-3) 3  + 4(-3) 2  + (-3) - 5

= 3(-27) + 4(9) - 3 - 5

= -81 + 36 - 3 - 5

Question 4 :

The perimeter of a rectangle is 52 cm. If its width is 2 cm more than one-third of its length, find the dimensions of the rectangle.

(A) 12 cm and 4 cm

(B) 18 cm and 8 cm

(C) 15 cm and 9 cm

Perimeter of a rectangle = 52 cm.

2(length + width)  =  52 ==>  l + w  =  26

Let x be the length. The, w idth = x/3 + 2.

x + (x/3) + 2 = 26

[(3x + x)/3] +2 = 26

Width = 18/3 + 2

So, the required dimensions are 18 cm and 8 cm.

Question 5 :

What must be added to each of the numerator and the denominator of the fraction 7/11 to make it equal to 3/4.

(A) 9                    (B) 5             (C) 12

Let x be the required number to be added to both numerator and denominator of the fraction.

(7 + x)/(11 + x)  =  3/4

4(7 + x)  =  3(11 + x)

28 + 4x  =  33 + 3x

4x - 3x  =  33 - 28

x  =  5

So, 5 is the required number to be added to make the fraction 7/11 as 3/4.

Question 6 :

A line which intersects two or more lines at a distinct points is called a ____________

(A) concurrent       (B) Intersecting     (C) Transversal

A line which intersects two or more lines at a distinct points is called a concurrent.

Question 7 :

The opposite angles of a cyclic quadrilateral are _______________

(A) Supplementary    (B) Complementary (C) None of these

The sum of opposite angles of a cyclic quadrilateral is 180 degree.

So, the answer is supplementary.

Question 8 :

In triangle ABC is inscribed in a circle with center O and BC is a diameter, if angle BAC is 50°, find angle ABC.

(A)  50°           (B)  40°           (C)  48°

In the right triangle ABC,

∠ A + ∠ B + ∠ C  =  180 °

50 ° + ∠ B + 90 °   =  180 °

140 ° + ∠ B  =  180 °

∠ B  =  40

Question 9 :

The circumference of a circle is 44 cm. Find its area (use π = 22/7) 

(A) 154 cm 2       (B) 130 cm 2       (C) 145 cm 2

Circumference of a circle =   44 cm

2 πr  =  44

2  ⋅  (22/7)  ⋅ r  =  44

r  =  7

Area of circle  =   πr 2

  =  (22/7)  ⋅  (7) 2

  =  154 cm 2

Question 10 :

The volume of a right circular cylinder is 1100 cm 3  and the radius of its base is 5 cm. Calculate its curved surface area. 

(A) 410 cm 2         (B) 125 cm 2           (C) 440 cm 2

Volume of a right circular cylinder  =  1100 cm 3

  πr 2 h =   1100 cm 3

(22/7)  ⋅ (5) 2  ⋅ h  =  1100

h  = 2/7

Curved surface area of cylinder  =  2 πrh

  =  2  ⋅ (22/7) ⋅ 5 ⋅ (2/7)

=  440 cm 2

So, the curved surface area of cylinder is  440 cm 2

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Past Contests, Solutions and Results

Problems, Solutions and Results from previous years can be found in the table below. These resources can be used by students to review and attempt past contests to gain a better understanding of the contest format and level of difficulty. Educators can use these resources to help their students prepare for contests or draw inspiration from some of these questions to create teaching materials, lesson plans or quizzes.

Below you will find resources from the last 10 years.

For the Gauss , Pascal, Cayley, and Fermat Contests, the CEMC Problem Set Generator can be used to create sets of past problems with customized topics. 

Quadratic Equations Problems with Answers for Grade 8

Grade 8 questions on quadratic equations with solutions and explanations included.

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