8th grade math problem solving activities

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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.

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8th Grade Math Worksheets

First things first, prioritize major topics with our printable compilation of 8th grade math worksheets with answer keys. Pursue conceptual understanding of topics like number systems, expressions and equations, work with radicals and exponents, solve linear equations and inequalities, evaluate and compare functions, understand similarity and congruence, know and apply the Pythagorean Theorem, find volume and surface area, develop an understanding of statistics and probability and much more. Our free math worksheets for grade 8 students make sure they start right!

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Explore 2,400+ Eighth Grade Math Worksheets

Converting Fractions to Decimal

Convert each fraction with a multiple of 10 as its denominator into a decimal number by placing the decimal point at the right spot.

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Finding the Square Roots of Perfect Squares

Apply prime factorization and determine the square roots of the first fifty perfect squares offered as positive integers.

Slope of a Line passing through Two Points

Use the formula, m = (y 2 - y 1 ) / (x 1 - x 1 ) to find the slope(m) of a line passing through two points: (x 1 ,y 1 ) and (x 2 ,y 2 ).

Solving Multi-Step Equations

Follow the order of operations, rearrange to make the unknown variable the subject, and solve for its integer value.

Identifying Functions from Ordered Pairs

Observe each set of ordered pairs given in Part A, figure out ordered pairs from graphs in Part B, and state if they represent a function.

Translation on Graphs | Writing Coordinates

Slide each figure in the said direction: up or down, left or right. Write the coordinates of the shifted image.

Congruence | Congruent Parts

Complete the congruence statement for each pair of triangles by writing the corresponding side or corresponding angle.

Finding the Interior Angle

Find the measure of the indicated interior angle by subtracting the sum of the known angles from 180.

Interior Angles - Finding the Unknown

Observe whether the interior angles lie on the same side or opposite sides of the transversal and find the unknown angle.

Identifying Right Triangles

Square the adjacent and opposite sides of the triangle; take the root of their sum; if you arrive at the hypotenuse, then it's a right triangle.

Volume of Cones

Plug the given radius(r) and height(h) in the formula V = 1/3πr 2 h and find the volume of the cone.

Mean, Median, Mode, and Range

Read each word problem with a real-life scenario and find the mean, median, mode, and range for each data set.

Converting Fractions to Percent

Switch each fraction to percent by multiplying the numerator by 100, dividing the product by the denominator, and adding the % symbol.

Finding the Square of Square Roots

The square of a square root is the radicand. So, simply multiply the radicand with the square of the number outside the root.

Convert to the Standard Form

Isolate the x and y-terms to one side and the constant to the other side of the equation and rewrite it in the form: ax + by = c.

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LIST OF TOPICS

TOPICS INCLUDE:

BODMAS Expanding Brackets Factorising Indices Inequalities Linear Functions Real Life Graphs Rearranging Equations Sequences Simplification Solving Equations Substitution

Calculator Methods Decimals Fractions Fractions Decimals Percentages Mental Methods Negative Numbers Percentages Place Value Powers Proportion Ratio Rounding Time Types of Number Written Methods

2D Shapes 3D Shapes Area and Perimeter Bearings Scale and Loci Circles Compound Measures Constructions Coordinates Lines and Angles Polygons Pythagoras Similarity and Congruence Transformations Volume and Surface Area

Histograms and Frequency Polygons Mean Median Mode Pie Charts and Bar Charts Probability Scatter Graphs Stem-and-Leaf Diagrams Two-Way Tables and Pictograms

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Printable 8th Grade Math Worksheets

Grade 8 Math Worksheets

8th grade math is a pivotal year that prepares students for the challenges of high school mathematics and beyond. The curriculum is designed to provide a deep and thorough understanding of key mathematical concepts, including algebra, functions, geometry, statistics, probability, number systems, and proportional relationships. The emphasis on problem-solving, critical thinking, and mathematical reasoning ensures that students are not only able to perform mathematical operations but also to understand and apply mathematical concepts in real-world situations.

Data Analysis and Statistics

Mean, Median, Mode, and Range | Answer Key Probability Word Problems | Answer Key Grade 8 Problem Solving Word Problems | Answer Key Proportional Relationships | Answer Key

Equations and Systems of Equations | Answer Key Functions | Answer Key Graphing Linear Equations | Answer Key Quadratic Functions | Answer Key Systems of Equations | Answer Key

Exponents and Scientific Notation | Answer Key Real Number Operations | Answer Key

Shapes and Transformations | Answer Key Pythagorean Theorem Word Problems | Answer Key Making Transformations | Answer Key Volume and Surface Area Word Problems | Answer Key

What Math Skills Do Students Learn in 8th Grade?

In 8th grade math, students delve into a comprehensive curriculum designed to build a strong foundation for high school mathematics and beyond. The year is typically divided into several key units that encompass a wide range of mathematical concepts, each aiming to enhance the students’ understanding, problem-solving skills, and logical thinking. Here’s an in-depth look at what students learn in 8th grade math:

The journey begins with an in-depth exploration of algebraic expressions and equations. Students learn to manipulate algebraic expressions, including simplifying, expanding, and factoring them. They work with linear equations and inequalities, learning to solve them using various methods such as graphing, substitution, and elimination. This unit also introduces them to systems of linear equations, where they find the point of intersection between two lines, representing the solution to the system. This foundational knowledge is crucial as it prepares students for more complex algebraic concepts in high school.

Next, students delve into the world of functions, a critical concept in algebra. They learn to understand and interpret functions as relationships between two variables, typically represented as f(x). The curriculum covers different types of functions, including linear, quadratic, and exponential functions. Students learn to graph these functions, identify their key characteristics such as slope and intercepts for linear functions, and analyze their behavior. This unit emphasizes the real-world applications of functions, helping students see the relevance of what they are learning.

Geometry is another significant component of the 8th grade math curriculum. Students deepen their understanding of geometric concepts, starting with the basics of points, lines, and angles. They explore the properties of various geometric shapes, including triangles, quadrilaterals, and other polygons, as well as three-dimensional figures like prisms, cylinders, cones, and spheres. The curriculum includes a thorough examination of the Pythagorean theorem, teaching students to apply it in different contexts to find missing side lengths in right triangles. They also learn about transformations, including translations, rotations, reflections, and dilations, and how these affect the coordinates of shapes on the coordinate plane. This unit often incorporates proofs, where students learn to justify their reasoning and demonstrate the logical progression of their thoughts.

The study of statistics and probability is also a key aspect of 8th grade math. Students learn to collect, organize, and interpret data using various methods. They explore different types of graphs and charts, such as histograms, box plots, and scatter plots, and learn to use them to represent data effectively. Measures of central tendency (mean, median, and mode) and measures of variability (range, interquartile range, and standard deviation) are also covered, helping students to analyze and summarize data sets. In probability, students learn about simple and compound events, using tools such as probability trees and the fundamental counting principle to determine the likelihood of different outcomes. This unit helps students understand how to make informed decisions based on data, a skill that is increasingly important in the modern world.

Another important area of focus is number systems and their properties. Students extend their understanding of the real number system, including rational and irrational numbers. They learn to perform operations with integers, fractions, and decimals, and explore the relationships between these different forms of numbers. This unit also covers exponents and roots, teaching students to simplify expressions involving powers and to solve equations involving square roots and cube roots. Scientific notation is introduced as a way to represent very large or very small numbers, a skill that is particularly useful in science and engineering.

The concept of ratios and proportional relationships is reinforced and expanded in 8th grade. Students learn to solve problems involving proportions, including those related to scale drawings and similar figures. They explore the concept of slope as a rate of change, using it to describe the steepness of a line and to solve real-world problems involving proportional relationships. This unit often includes the study of direct and inverse variation, helping students to understand different types of relationships between variables.

In addition to these core areas, 8th grade math often includes topics that prepare students for high school math courses. One such topic is introductory trigonometry, where students learn about the basic trigonometric ratios (sine, cosine, and tangent) and how to use them to solve problems involving right triangles. This introduction to trigonometry lays the groundwork for more advanced study in high school.

The curriculum also emphasizes the development of mathematical reasoning and problem-solving skills. Students are encouraged to think critically and to approach problems methodically. They learn to break down complex problems into smaller, more manageable parts, to recognize patterns, and to use logical reasoning to arrive at solutions. This process often involves writing out their thought processes and justifying their answers, helping to build strong communication skills that are essential in all areas of life.

Throughout the year, technology and hands-on activities play an important role in enhancing students’ learning experiences. Graphing calculators, computer software, and online resources are often integrated into lessons to help students visualize concepts and explore mathematical ideas in greater depth. Hands-on activities, such as building geometric models or conducting experiments to collect data, provide practical applications of mathematical concepts and make learning more engaging.

Assessment in 8th grade math is varied and ongoing, with a combination of formative and summative assessments used to gauge students’ understanding and progress. Formative assessments, such as quizzes, homework assignments, and classwork, provide regular feedback to students and teachers, helping to identify areas where additional practice or instruction may be needed. Summative assessments, such as unit tests and standardized exams, evaluate students’ mastery of the material and their readiness for high school math.

The importance of collaboration and discussion is also emphasized in 8th grade math. Students often work in pairs or small groups to solve problems, share ideas, and explain their reasoning to their peers. This collaborative approach helps to develop communication and teamwork skills, and it provides opportunities for students to learn from each other and to see different perspectives on mathematical problems.

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Eighth grade math

IXL offers hundreds of eighth grade math skills to explore and learn! Not sure where to start? Go to your personalized Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, state standards, or standardized test.

A. Integers

• 1 Compare and order integers
• 2 Integer addition and subtraction rules
• 3 Add and subtract integers using counters
• 4 Add and subtract integers
• 5 Add and subtract three or more integers
• 6 Add and subtract integers: word problems
• 7 Integer multiplication and division rules
• 8 Multiply and divide integers
• 9 Evaluate numerical expressions involving integers

B. Rational numbers

• 1 Convert between repeating decimals and fractions
• 2 Convert between decimals and fractions or mixed numbers
• 3 Compare rational numbers
• 4 Put rational numbers in order
• 5 Reciprocals and multiplicative inverses
• 6 Add and subtract rational numbers
• 7 Add and subtract rational numbers: word problems
• 8 Apply addition and subtraction rules
• 9 Multiply and divide rational numbers
• 10 Multiply and divide rational numbers: word problems
• 11 Apply multiplication and division rules
• 12 Apply addition, subtraction, multiplication, and division rules
• 13 Evaluate numerical expressions involving rational numbers
• 14 Multi-step word problems

C. Exponents

• 1 Understanding exponents
• 2 Evaluate powers
• 3 Solve equations with variable exponents
• 4 Powers with negative bases
• 5 Powers with decimal and fractional bases
• 6 Understanding negative exponents
• 7 Evaluate powers with negative exponents
• 8 Evaluate powers with negative or zero exponents
• 9 Multiply powers: integer bases
• 10 Divide powers: integer bases
• 11 Multiply and divide powers: integer bases
• 12 Power of a power: integer bases
• 13 Evaluate expressions using properties of exponents
• 14 Identify equivalent expressions involving exponents I
• 15 Identify equivalent expressions involving exponents II
• 16 Multiply powers: variable bases
• 17 Divide powers: variable bases
• 18 Multiply and divide powers: variable bases
• 19 Powers of a power: variable bases

D. Scientific notation

• 1 Convert between standard and scientific notation
• 2 Scientific notation on calculators
• 3 Compare numbers written in scientific notation
• 4 Add and subtract numbers written in scientific notation
• 5 Multiply numbers written in scientific notation
• 6 Divide numbers written in scientific notation

E. Square roots and cube roots

• 1 Square roots of perfect squares
• 2 Estimate positive square roots
• 3 Positive and negative square roots
• 4 Estimate positive and negative square roots
• 5 Relationship between squares and square roots
• 6 Solve equations using square roots
• 7 Cube roots of positive perfect cubes
• 8 Cube roots of positive and negative perfect cubes
• 9 Solve equations using cube roots
• 10 Estimate cube roots

F. Rational and irrational numbers

• 1 Identify rational and irrational square roots
• 2 Identify rational and irrational numbers
• 3 Classify numbers
• 4 Irrational numbers on number lines
• • New! Compare and order rational and irrational numbers

G. Proportions

• 1 Solve proportions
• 2 Solve proportions: word problems
• 3 Estimate population size using proportions
• 4 Scale drawings: word problems
• 5 Scale drawings: scale factor word problems

H. Percents

• 1 Convert between percents, fractions, and decimals
• 2 Compare percents to fractions and decimals
• 3 Find what percent one number is of another
• 4 Find what percent one number is of another: word problems
• 5 Estimate percents of numbers
• 6 Percents of numbers and money amounts
• 7 Percents of numbers: word problems
• 8 Compare percents of numbers
• 9 Solve percent equations
• 10 Percent of change
• 11 Percent of change: word problems
• 12 Percent of change: find the original amount word problems

I. Consumer math

• 1 Price lists
• 2 Unit prices
• 3 Unit prices with unit conversions
• 4 Unit prices: find the total price
• 5 Percent of a number: tax, discount, and more
• 6 Find the percent: tax, discount, and more
• 7 Sale prices: find the original price
• 8 Multi-step problems with percents
• 9 Estimate tips
• 10 Simple interest
• 11 Compound interest

J. Units of measurement

• 1 Convert rates and measurements: customary units
• 2 Convert rates and measurements: metric units
• 3 Mixed customary units
• 4 Convert between customary and metric systems
• 5 Convert between Celsius and Fahrenheit

K. Expressions

• 1 Write variable expressions: one operation
• 2 Write variable expressions: two or three operations
• 3 Write variable expressions from diagrams
• 4 Write variable expressions: word problems
• 5 Evaluate one-variable expressions
• 6 Evaluate multi-variable expressions
• 7 Evaluate absolute value expressions
• 8 Evaluate radical expressions
• 9 Evaluate rational expressions
• 10 Identify terms and coefficients
• 11 Sort factors of variable expressions

L. Equivalent expressions

• 1 Properties of addition and multiplication
• 2 Multiply using the distributive property
• 3 Write equivalent expressions using properties
• 4 Add and subtract like terms
• 5 Add and subtract linear expressions
• 6 Factors of linear expressions
• 7 Identify equivalent linear expressions I
• 8 Identify equivalent linear expressions II
• 9 Identify equivalent linear expressions: word problems

M. One-variable equations

• 1 Which x satisfies an equation?
• 2 Write an equation from words
• 3 Model and solve equations using algebra tiles
• 4 Write and solve equations that represent diagrams
• 5 Properties of equality
• 6 Identify equivalent equations
• 7 Solve one-step equations
• 8 Solve two-step equations
• 9 Solve two-step equations: complete the solution
• 10 Solve one-step and two-step equations: word problems
• 11 Solve equations involving like terms
• 12 Solve equations with variables on both sides
• 13 Solve equations with variables on both sides: fractional coefficients
• 14 Solve equations with variables on both sides: word problems
• 15 Solve equations with the distributive property
• 16 Solve multi-step equations
• 17 Solve multi-step equations with fractional coefficients
• 18 Solve equations: mixed review
• 19 Solve multi-step equations: complete the solution
• 20 Find the number of solutions
• 21 Create equations with no solutions or infinitely many solutions

N. One-variable inequalities

• 1 Solutions to inequalities
• 2 Graph inequalities on number lines
• 3 Write inequalities from number lines
• 4 Solve one-step inequalities
• 5 Graph solutions to one-step inequalities
• 6 Solve two-step inequalities
• 7 Graph solutions to two-step inequalities
• 8 Solve multi-step inequalities
• 9 Graph solutions to multi-step inequalities
• 10 Solve inequalities with integers: variables on both sides
• 11 Solve inequalities with decimals: variables on both sides

O. Coordinate plane

• 1 Coordinate plane review
• 2 Quadrants and axes
• 3 Follow directions on a coordinate plane
• 4 Find the distance between two points

P. Lines and angles

• 1 Identify complementary, supplementary, vertical, adjacent, and congruent angles
• 2 Find measures of complementary, supplementary, vertical, and adjacent angles
• 3 Write and solve equations using angle relationships
• 4 Identify alternate interior and alternate exterior angles
• 5 Transversals of parallel lines: name angle pairs
• 6 Transversals of parallel lines: find angle measures
• 7 Transversals of parallel lines: solve for x
• 8 Find lengths and measures of bisected line segments and angles

Q. Two-dimensional figures

• 1 Identify and classify polygons
• 2 Classify triangles
• 3 Identify trapezoids
• 4 Classify quadrilaterals I
• 5 Classify quadrilaterals II
• 6 Graph triangles and quadrilaterals
• 7 Find missing angles in triangles
• 8 Find missing angles in triangles using ratios
• 9 Triangle Angle-Sum Theorem
• 10 Find missing angles in quadrilaterals I
• 11 Find missing angles in quadrilaterals II
• 12 Exterior Angle Theorem
• 13 Interior angles of polygons
• 14 Parts of a circle

R. Transformations and congruence

• 1 Identify reflections, rotations, and translations
• 2 Describe a sequence of transformations
• 3 Translations: graph the image
• 4 Translations: find the coordinates
• 5 Translations: write the rule
• 6 Reflections over the x- and y-axes: graph the image
• 7 Reflections over the x- and y-axes: find the coordinates
• 8 Reflections: graph the image
• 9 Reflections: find the coordinates
• 10 Rotations: graph the image
• 11 Rotations: find the coordinates
• 12 Reflections and rotations: write the rule
• 13 Describe transformations
• 14 Sequences of congruence transformations: graph the image
• 15 Sequences of congruence transformations: choose the sequence
• 16 Identify congruent figures
• 17 Congruence statements and corresponding parts
• 18 Determine if two figures are congruent: justify your answer
• 19 Side lengths and angle measures of congruent figures

S. Transformations and similarity

• 1 Similar and congruent figures
• 2 Dilations: graph the image
• 3 Dilations: find the coordinates
• 4 Dilations: find the scale factor
• 5 Identify similar triangles
• 6 Angle-angle criterion for similar triangles
• 7 Side lengths and angle measures of similar triangles
• 8 Side lengths and angle measures of similar figures
• 9 Similar triangles and indirect measurement
• 10 Find missing side lengths in proportional triangles

T. Pythagorean theorem

• 1 Pythagorean theorem: find the length of the hypotenuse
• 2 Pythagorean theorem: find the missing leg length
• 3 Pythagorean theorem: find the missing leg or hypotenuse length
• 4 Pythagorean theorem: find the perimeter
• 5 Pythagorean theorem: word problems
• 6 Converse of the Pythagorean theorem: is it a right triangle?

U. Three-dimensional figures

• 1 Parts of three-dimensional figures
• 2 Nets of three-dimensional figures
• 3 Front, side, and top view
• 4 Similar solids

V. Perimeter and area

• 1 Perimeter
• 3 Area and perimeter: word problems
• 4 Area and circumference of circles
• 5 Circles: word problems
• 6 Area and perimeter of semicircles and quarter circles
• 7 Area between two shapes
• 8 Perimeter and area: changes in scale

W. Surface area and volume

• 1 Volume of cubes, prisms, and pyramids
• 2 Surface area of cubes, prisms, and pyramids
• 3 Volume of cylinders
• 4 Volume of cones
• 5 Surface area of cylinders
• 6 Surface area of cones
• 7 Volume of spheres
• 8 Surface area of spheres
• 9 Volume and surface area of similar solids

X. Proportional relationships

• 1 Find the constant of proportionality from a table
• 2 Write equations for proportional relationships from tables
• 3 Identify proportional relationships by graphing
• 4 Find the constant of proportionality from a graph
• 5 Write equations for proportional relationships from graphs
• 6 Identify proportional relationships from graphs and equations
• 7 Identify proportional relationships from tables
• 8 Identify proportional relationships: word problems
• 9 Graph proportional relationships and find the slope
• 10 Interpret graphs of proportional relationships
• 11 Write and solve equations for proportional relationships
• 12 Compare proportional relationships represented in different ways

Y. Direct variation

• 1 Find the constant of variation
• 2 Identify direct variation
• 3 Write direct variation equations
• 4 Write and solve direct variation equations
• 1 Find the slope from a graph
• 2 Find the slope from two points
• 3 Find the slope from a table
• 4 Find a missing coordinate using slope
• 5 Graph a line using slope

AA. Linear equations

• 1 Is (x, y) a solution to the linear equation?
• 2 Relate the graph of an equation to its solutions
• 3 Slope-intercept form: find the slope and y-intercept
• 4 Graph a line from an equation in slope-intercept form
• 5 Graph a line from an equation in point-slope form
• 6 Write a linear equation from a slope and y-intercept
• 7 Write a linear equation from a graph
• 8 Write a linear equation from a slope and a point
• 9 Write a linear equation from two points
• 10 Convert a linear equation in standard form to slope-intercept form
• 11 Graph a line from an equation in standard form
• 12 Graph a horizontal or vertical line
• 13 Equations of horizontal and vertical lines
• 14 Slopes of parallel and perpendicular lines

BB. Function concepts

• 1 Identify functions
• 2 Identify functions: graphs
• 3 Identify independent and dependent variables
• 4 Find values using function graphs
• 5 Complete a table for a function graph
• 6 Domain and range of functions

CC. Linear functions

• 1 Evaluate a linear function
• 2 Complete a table for a linear function
• 3 Complete a table and graph a linear function
• 4 Interpret points on the graph of a linear function
• 5 Rate of change of a linear function: graphs
• 6 Interpret the slope and y-intercept of a linear function
• 7 Write a linear function from a table
• 8 Compare linear functions: graphs and equations
• 9 Compare linear functions: tables, graphs, and equations
• 10 Write linear functions: word problems
• 11 Evaluate a linear function: word problems

DD. Nonlinear functions

• 1 Identify linear and nonlinear functions: graphs and equations
• 2 Identify linear and nonlinear functions: tables
• 3 Is (x, y) a solution to the nonlinear equation?
• 4 Evaluate a nonlinear function

EE. Interpret functions

• 1 Rate of change: tables
• 2 Rate of change: graphs
• 3 Identify graphs: word problems

FF. Sequences

• 1 Identify arithmetic and geometric sequences
• 2 Arithmetic sequences
• 3 Geometric sequences
• 4 Sequences: mixed review
• 5 Sequences: word problems
• 6 Evaluate variable expressions for sequences
• 7 Write variable expressions for arithmetic sequences

GG. Systems of equations

• 1 Is (x, y) a solution to the system of equations?
• 2 Solve a system of equations by graphing
• 3 Solve a system of equations by graphing: word problems
• 4 Find the number of solutions to a system of equations by graphing
• 5 Find the number of solutions to a system of equations
• 6 Classify a system of equations by graphing
• 7 Classify a system of equations
• 8 Solve a system of equations using substitution
• 9 Solve a system of equations using substitution: word problems
• 10 Solve a system of equations using elimination
• 11 Solve a system of equations using elimination: word problems
• 12 Solve a system of equations using any method
• 13 Solve a system of equations using any method: word problems

HH. One-variable statistics

• 1 Calculate mean, median, mode, and range
• 2 Interpret charts and graphs to find mean, median, mode, and range
• 3 Mean, median, mode, and range: find the missing number
• 4 Changes in mean, median, mode, and range
• 5 Calculate mean absolute deviation
• 6 Calculate quartiles and interquartile range
• 7 Box plots
• 8 Identify an outlier
• 9 Identify an outlier and describe the effect of removing it

II. Two-variable statistics

• 1 Interpret line graphs
• 2 Create line graphs
• 3 Interpret scatter plots
• 4 Create scatter plots
• 5 Identify trends with scatter plots
• 6 Make predictions with scatter plots
• 7 Outliers in scatter plots
• 8 Identify lines of best fit
• 9 Write equations for lines of best fit
• 10 Interpret lines of best fit: word problems
• 11 Identify representative, random, and biased samples

JJ. Probability

• 1 Probability of simple events
• 2 Probability of opposite, mutually exclusive, and overlapping events
• 3 Experimental probability
• 4 Find probabilities using two-way frequency tables
• 5 Make predictions
• 6 Compound events: find the number of outcomes
• 7 Compound events: find the number of sums
• 8 Identify independent and dependent events
• 9 Probability of independent and dependent events
• 10 Counting principle

Eighth grade lessons

These lessons help you brush up on important math topics and prepare you to dive into skill practice!

• Additive inverses
• Adding and subtracting integers
• Multiplying and dividing integers

Rational and irrational numbers

• Rational numbers
• Adding and subtracting rational numbers
• Multiplying and dividing rational numbers
• Irrational numbers

Exponents, scientific notation, and roots

• Properties of exponents
• Scientific notation
• Adding and subtracting numbers in scientific notation
• Multiplying and dividing numbers in scientific notation
• Square roots
• Proportional relationships
• Constant of proportionality
• Simple interest
• Percent change

Two-dimensional figures

• Parts of a circle
• Area of circles
• Circumference of circles
• Complementary angles
• Supplementary angles
• Adjacent angles
• Vertical angles
• Transversals of parallel lines
• Interior angles of triangles
• Exterior angles of triangles
• The Pythagorean theorem
• The converse of the Pythagorean theorem
• Distance formula

Transformations, congruence, and similarity

• Transformations
• Translations
• Reflections
• Similar triangles

Three-dimensional figures

• Surface area formulas
• Volume formulas
• Volume of prisms
• Volume of cylinders
• Volume of pyramids
• Volume of cones
• Volume of spheres

Expressions

• Writing algebraic expressions
• Evaluating expressions
• Simplifying expressions
• The distributive property
• Expanding expressions
• Factoring expressions

Equations and inequalities

• Solving equations
• Multi-step equations
• Equations with infinitely many or no solutions
• Solving inequalities
• Linear equations
• Slope-intercept form
• Point-slope form
• Standard form of linear equations
• Equations of parallel and perpendicular lines
• Systems of equations
• Relations and functions
• Independent and dependent variables
• Linear functions
• Domain and range

Data and graphs

• Box and whisker plots
• Scatter plots
• Correlation
• Line of best fit
• Two-way tables

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8th Grade Math Games: Fun, Free Math Activities For Your Grade 8 Students (No Screens Required!)

Vanessa Sipple-Asher

8th grade math games and math activities are a useful tool to ensure valuable math practice whilst keeping students engaged in math class. In their last year of middle school, 8th graders face increasingly challenging classes as they prepare for the transition into high school. Eighth grade math games can bring some lightness to the math classroom. 

During eighth grade, students continue to build upon the key skills from 6th grade and 7th grade. One of the other key procedures and formulae they investigate is Pythagoras’ theorem. The games in this section will build a pupil’s understanding of Pythagoras’ theorem and enable them to practise other skills learnt during their time in middle school math.

Math Games For 8th Grade

15 fun math games and activities for your 8th grade students to complete independently or with a partner.

When to use eighth grade math games

Fun math games and math problems are a useful thing for any math teacher to have up their sleeve. When a class is losing focus a fun math game can help to shake things up compared to just assigning math worksheets. Math games can also be a great way to start a lesson and end a lesson. 

Letting students get on with a math game can also allow teachers the time to walk around the classroom and observe each student to see how they are understanding the concepts. 

• 3rd grade math games
• 4th grade math games
• 5th grade math games
• 6th grade math games
• 7th grade math games

How to use these 8th grade math games

The math games below are designed to be versatile and allow for adaptations to different topics and different levels of ability so feel free to adapt the games to the needs of your class. 

All games are also quite simple and require few resources. We hope that these math resources are enjoyed by your students.

Number game: how many steps?

This game encourages students to look at multiple steps they can use to get from one number to another number. It also encourages the use of inverse operations/checking of calculations to check whether answers are correct – one of the most valuable math skills they’ll learn! 

What you need to play:

• One or more players
• Scorecard 
• Pen and paper

How to play:

• Each player is given the same starting number and answer to use (e.g. starting number of 6, answer of 17).
• Each player has 1 minute to write down the steps they would take to get from 6 to 17.
• Players can use any numbers they wish.
• Players are allowed to repeat an operation to get to an answer (e.g. for getting from 6 to 17, players can just do 6 +1, +1, +1 etc. until they get to 17), but will only score 1 point for each different operation.
• The number of different steps used is the score (e.g. 5 different steps = 5 points).
• E.g. to get from 6 to 17 in the time given: 6 (x3) = 18 (+9) = 27 (+8) = 35 (/5) = 7 (+10) = 17 . This would score 5 points.
• Each player scores their number of different steps taken for each round.
• The player with the most points after the number of rounds played is the winner.
• Players are encouraged to check each other’s answers and the steps taken.
• If any stage is incorrect, the player scores 0 points for that round.

Number game: take five

This is a number game to encourage students to think carefully about strategies needed to get an answer within a range of totals. The more individual numbers used to get an answer, the more points the player gets. Students need to decide whether a strategy of getting maximum points for each answer or using fewer numbers to get each answer is the best method.

• Playing cards can be used to generate numbers to be used by player(s) in the game
• 5 numbers are selected at random.
• A consecutive set of 10 answers is agreed to work towards (e.g. 21-30, 41-50).
• Players are given a 5-minute time limit to get the answers to as many of the totals as possible.
• Players cannot repeat the use of a number for a single answer (unless it is part of the ones they have).
• The more individual numbers used for an answer, the more points can be awarded.
• E.g. the selected numbers are 9 5 2 7 1 and consecutive totals are from 21-30.
• For 23, the player could get to it using the following calculations: ( 7 x 5 ) = 35, ( 9 + 2 + 1 ) = 12, 35 – 12 = 23. Because 5 different numbers were used, the score is 5 points.
• For 28, the player could get to it using the following calculations: ( 5 – 1 ) = 4, 4 x 7 = 28. Because 3 different numbers have been used, the score is 3 points.
• If a player has two of the same answer (eg: two methods for getting 23), whichever one used more of their numbers is the points they score.

Fractions game: countdown

This is a more challenging version of the standard, whole number game of countdown and requires players to carry out the 4 operations using fractions and whole numbers. To make it more challenging, you can also include decimal cards. 

To make this game easier, consider giving students a number line. 

What you will need to play:

• 2 or more players
• Whole number cards (see printable resource pack)
• Fraction cards (see printable resource pack)
• 10-sided dice or 1-10 digit cards
• Paper and pen

• Place the whole number and fraction cards into 2 piles.
• Players take it in turns to select a card from the whole number or the fraction card pile.
• Once 6 cards have been selected, place them face-up on the table.
• A target number then needs to be generated (either using a 10-sided dice or 1-10 digit cards to generate the numerator and denominator).
• Players have 2 minutes to try and reach the target number using any of the 6 fraction/whole number cards and any of the 4 operations.
• The winner is the first to reach the target number or the player who is closest after 2 minutes.

PEDMAS game: 4 in a row

This is a great game for practising the rules of PEDMAS alongside strategy skills. It can be played individually or against other players.

• 1 or more players
• Number grid 1-50
• 2 coloured pens
• The first player throws the 4 dice to generate 4 numbers. 
• Using PEDMAS, they write a number sentence and colour in the square on the 1-50 grid, which contains the answer.
• The next player does the same.
• The aim of the game is to be the first player to colour in 4 squares in a row. 

Number game: nifty fifty

This game is good for developing logical thinking and problem solving.

• Set of playing cards – Ace to 10 (Ace is worth 1)
• Both players select 4 playing cards.
• With the 4 cards, they have 2 minutes to make a 2-digit + 2-digit number sentence which is closest to 50.
• The number sentence closest to 50 scores 1 point. If the player creates a calculation with exactly 50 as the answer, they earn 2 points.
• The winner is the player with the most points after 5 rounds.
• To add further complexity to this game, you could give each player 6 cards and then add a ‘wild’ negative number card into the game which both players have to use in their round. 

Subtraction game: sub-zero

This is a simple mental subtraction game, which doesn’t require any resources. An easy interactive game to play when there are a spare few minutes.

• Starting with the number 123, the first player chooses an amount to subtract.
• The number subtracted must contain one digit from the previous answer.
• The player could choose to subtract 22, so the new number would be 101.
• A zero cannot be subtracted, so the next number has to contain a 1. 
• The next player could subtract 11, so the new number is 90.
• The only number that can be subtracted now is 9.
• The game continues. The first player to get to zero is the winner. 
• The game can be played with a different starting number each time.

Number game: countdown

This mental math game is popular for any age. Younger children can access it on a more basic level, whereas older children can use more complex multi step equations. It works well in small groups, or as a whole class activity, and encourages players to think deeply to identify calculations that will get them to the target number.

• 4 ‘large number’ cards – 25, 50, 75, 100
• 2 sets of 1-10 cards 
• Set out the large number cards face down in one pile and the small number cards face down in another pile.
• Players take it in turns to choose a card from either the small or the large number piles and place it face down on the table.
• Once there are 6 cards face-up on the table, the target number needs to be generated.
• The target number can be generated by picking 3 number cards from a pile of 0-9 cards.
• Once the number has been generated, children have 2 minutes to try and reach that total using the 6 cards selected.
• Children can use any calculation using the 6 numbers, but each number can only be used once.
• The winner is the first person to reach the target number or the person to have the closest answer after 2 minutes.

Number game: target 24

This game is a great problem solving and ‘low floor, high ceiling game’, as players search for a solution. They can use only the basic calculations to reach the target number, or they can utilise much more complex mathematical calculations.

• A pack of cards (number cards only)
• Shuffle the pack of cards and lay face down on the table.
• Each player picks a card and turns it face-up on the table until there are 4 cards displayed.
• The aim of the game is to make ‘24’ using only the cards on the table and any of the 4 operations.
• For example, if they have a 6, 10, 2 and 6, the solution could be very simple, such as basic addition i.e. 6 + 10 + 2 + 6 = 24.
• Older children may include more complex operations involving brackets, for example, they may have 9, 5, 6 and 9 and solve it by 5 – (9 ÷ 9) x 6 = 24.
• If nobody is able to reach 24, the player who is the closest wins.

Number game: wild jack

This is another great game for practising mental maths and numeracy skills using all four operations.

• Playing cards with all picture cards (other than the Jacks removed)
• In this game, the 1-10 cards represent their numbers, and the Jacks can represent any number from 1-10.
• The aim of the game is to reach the target number. To make the target number, shuffle the pack and turn over the top 2 cards. If either is a 10 or Jack, put them to the bottom.
• The 2 cards turned over make the target number. For example, if you turn over a 6 of spades and a 4 of hearts, your target number will be 64.
• Each player is dealt 5 cards, which are set out face up. Players can then add, subtract, multiply and divide to try to reach the target number. 
• If a target number is reached using all 5 cards, 10 points are scored. If 4 cards are used, 8 points are scored. If 3 cards are used, 6 points are scored, and so on.
• The winner is the player with the most points at the end of the game.

Number game: game of six

This is a number game to encourage children to think carefully about strategies needed to get an answer within a range of totals. The more individual numbers used to get an answer, the more points the player gets. Children need to decide whether a strategy of getting maximum points for each answer or using fewer numbers to get each answer is the best method.

• 6 numbers are selected at random.
• E.g. the example numbers given are: 4 8 6 3 5 9 and consecutive totals are from 31-40.
• For 31, the player could carry out the following calculations: ( 4 x 8 ) = 32, ( 6 – 5 ) = 1, 32 – 1 = 31. Because 4 different numbers were used, the score is 4 points .
• For 37, the player could carry out the following calculations: ( 4 x 9 ) = 36, ( 8 + 3 ) = 11, ( 6 + 5 ) = 11, 36 + (11 / 11) = 37. Because 6 different numbers were used, the score is 6 points .
• If a player has two of the same answer (e.g. two methods for getting 31), whichever one used more of their numbers is the points they score.

Number game: 5 of a kind

This problem-solving game is quite a challenging math activity. It requires players to think deeply about the calculations they use and how they can use quite complex calculations to achieve solutions.

• A set of cards numbered 2-9
• Shuffle the number cards and place them face down on the table.
• The first player picks one of the cards. 
• This is their ‘5 of a kind’ number. For example, if they selected a 6, they would have 6, 6, 6, 6 and 6 to use.
• The aim of the game is to use one or more of the 5 digits to get an answer between one and ten.
• If for example, the player chose a 7, they would then need to use one or more of the digits to make the answer 1, 2, 3 up to 10. To make 1, they could do 7 ÷ 7. To make 2 they could do (7 ÷ 7) + (7 ÷ 7) etc.
• This is a challenging game, but the winner is the player to achieve the most answers between 1 and 10.

Square root match

This activity can be done whole-class or in partners/small groups and allows students to practice finding square roots.

• Match cards (shown below)
• Shuffle match cards and distribute one to each student
• Have students walk around the classroom and find their match (i.e., the student with “5” would partner up with the student whose card says “√25”
• Option 1: Students can work together to match up the cards 
• Option 2: Students can flip all cards face down on a table and play “memory” – players take turns flipping over two cards. If they have a match, they keep the two cards. If they aren’t a match, they flip the cards back over and the next person goes. The winner is the player who ends up with the most matches at the end.

Example cards for printable resource:

Exponent Game

This math game is similar to the card game “War,” but students use their cards to create and calculate exponents.

• A partner (or a small group)
• Variation: Face cards can be used as an added challenge: A=1, J=11, Q=12, K=13
• The cards should be shuffled and dealt evenly among the players
• Players should keep their stack of cards face down
• Each player flips two cards at the same time. The first card they flip is their base number and the second card flipped is the exponent. So, for example, if player 1 flips a 2 and then a 3, their number will be 2³ which equals 8. If their opponent flips a 4 and then a 2, their number will be 4² which equals 16. So player 2 wins that round.
• The player who wins each round collects all cards played during that round
• Whoever collects the most cards, wins!
• A challenging variation to this game would be to include four operation cards. These can be written on an index card or small piece of paper. As students create their two exponents, they can also draw an operation card. Then, students take turns adding, subtracting, multiplying, or dividing the two numbers.

Positive and negative cards game

This card game provides students with an opportunity to increase their understanding of positive and negative numbers during some friendly competition.

• Variation: add in face cards A=1, J=11, Q=12, K=13
• A partner or small group
• In this game, the red cards represent negative numbers and the black cards are positive numbers
• Players shuffle the cards and deal them equally between themselves, keeping them face down
• All players place one card from their stack face-up at the same time
• Players can work together or take turns determining which card has the highest value. (Example: if there is a red 8 and a black 2, the black 2 has the highest value.)
• The player with the highest value card collects the four cards from that round
• When a player’s stack runs out, they should shuffle their collected cards and continue playing with those cards
• The first player to collect all the cards, wins!

Algebra Shop

During this activity, you will turn your classroom into a “market” and give students an opportunity to “buy” classroom items by writing algebraic expressions to represent their purchases.

• Examples/ideas: 
• book, b , $4 
• pen, p , $0.25 
• desk, d, $8.25
• A piece of paper & pencil for each student
• One die for partners or small groups
• Students will “shop” for the labeled items in the classroom market.
• Taking turns with their partner(s), each student will roll the dice. The dice will tell them how many of each item they will purchase. Then, students will write an algebraic equation representing each item. For example: if a student rolls a 5 for a book, they would write the expression 5b.
• Students should calculate their expressions: 5b = 5 ($4) = $20
• When they have purchased at least one of each item, they should write an expression representing their whole purchase. 5b + 4d, etc.
• Students roll two dice to include higher quantities
• Students go around the market twice (or more) and therefore, roll the dice more than one time per item. Therefore, if they rolled a 5 for the book on the first round, then a 3 on the second round, instead of 5b their expression would be 5b + 3b = 8b = 8($4) = $32

READ MORE : 26 Whole Class Math Games

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The content in this article was originally written by content team Vanessa Sipple-Asher and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.

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Free Printable Solving Equations Worksheets for 8th Grade

Solving Equations just got more exciting! Discover an extensive collection of free printable Math worksheets for Grade 8 students, created by Quizizz. Enhance learning and master skills with ease.

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Solving Equations worksheets for Grade 8 are an essential resource for teachers looking to help their students master the fundamentals of algebra. These worksheets focus on one-variable equations, a crucial concept in Grade 8 Math curriculum. By providing a variety of problems and scenarios, these worksheets allow students to practice and hone their skills in solving algebraic equations. Teachers can use these resources to supplement their lesson plans, provide additional practice for struggling students, or even as a form of assessment to gauge students' understanding of the material. With the right set of Solving Equations worksheets for Grade 8, teachers can ensure that their students are well-prepared for the challenges of algebra and future math courses.

In addition to Solving Equations worksheets for Grade 8, Quizizz offers a comprehensive platform for teachers to create engaging and interactive quizzes, polls, and other activities to enhance their students' learning experience. Quizizz allows teachers to choose from a vast library of pre-made quizzes or create their own, tailored to their specific lesson plans and objectives. These quizzes can be assigned as homework, used for in-class review, or even as a form of assessment. With Quizizz, teachers can track their students' progress and identify areas where they may need additional support or practice. By incorporating Quizizz into their teaching strategies, teachers can not only supplement their Solving Equations worksheets for Grade 8 but also provide a dynamic and engaging learning environment for their students.

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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.

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8th Grade Math Worksheets

8th Grade Math Worksheets feature helpful and enjoyable activities based in algebra, statistics, arithmetic, and geometr y. Students can complete worksheets at their own pace to help them acquire an in-depth knowledge of the diverse mathematical concepts and equations taught in the eighth grade. The Grade 8 Math Worksheets for students are designed to reinforce their math knowledge through engaging questions. These worksheets use a stepwise learning model that allows the students to understand core concepts and equations in a competent manner, and subsequently determine a strategy to rectify their mistakes and solve complex problems correctly. ...Read More Read Less

Benefits of Grade 8 Math Worksheets

Math curriculum starts to get more complex in eighth grade. A lot of parents might not be equipped with the knowledge needed to guide their children through their homework and support their learning process at this stage. Printable 8th Grade Math Worksheets can help. By adding in some extra practice, children will become well-versed in all the math concepts needed to do well on their exams. Grade 8 Math Worksheets also help parents track their child’s overall learning process. There are many benefits to using these printable worksheets. 

Most importantly, the Grade 8 Math Worksheets: 

• Instill math confidence

As students face more difficult concepts and equations in the eighth grade, their confidence might start to shake, and they can become overwhelmed. Grade 8 Math Worksheets are designed to help students learn complex topics with ease. Students can start with the basics of various equations and concepts through these worksheets, and eventually work through other computational logic to hone their knowledge. Mastering the concepts will allow students to take their math exams without anxiety. 

• Provide Comprehensive Coverage

You can find 8th Grade Math Worksheets online that include a diverse mix of math questions covering a multitude of topics. This comprehensive coverage allows students to become acquainted with different ways to approach problems. Moreover, learning math becomes engaging and exciting for them as the monotony associated with learning the subject is eased through specially designed worksheets.

• Interactive Worksheets
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8th Grade Linear Equations Worksheets

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Choose Math Worksheets by Grade

Choose math worksheets by topic, 8th grade math worksheets explained.

Grade 8 Math Worksheets  enable students to learn and practice various types of equations, problems, theorems and more, so that they are ready to progress to high school. These math worksheets help develop problem-solving skills in students, and can be effective in enabling them to grasp math concepts quicker and apply them in real life.

Grade 8 Math Worksheets cover concepts that students learn throughout the course of the entire 8th grade year. Students can start the year with worksheets featuring activities on comparing exponents, Venn diagrams, math operations and reasoning, surface area, irrational numbers, and scientific notation. They can move on to evaluating and writing expressions, rewriting fraction equations, and determining the slope of a line, which are important topics to prepare them for the math they’ll be learning towards the end of the year. The most advanced concepts students will learn in 8th grade, including probability as a fraction, simultaneous linear equations, monomial, binomial, and polynomial operations, graphing linear inequalities, logarithms, using Pythagorean Theorem, and midpoints and equations of straight lines can all also be found on printable Grade 8 Math Worksheets. Many students have difficulty understanding these last few concepts, making  Grade 8 Math Worksheets crucial.

Online Grade 8 Math Worksheets are effective in helping students reach a conceptual understanding of topics like number systems, expressions, and equations. They allow the students to work with radicals and exponents, gain better knowledge of statistics and probability, and master solving linear equations and inequalities. With the help of 8th Grade Math Worksheets, students will be able to clearly know and apply the Pythagorean Theorem as well.

Printable 8th Grade Math Worksheets are readily available online. Parents or the students themselves can print them at their convenience, and start solving math problems of varying difficulty levels. With consistent practice using these worksheets, students can confidently face their math exams.

How difficult is it to solve the math worksheets for 8th graders?

The  online 8th grade math worksheets have been categorized in three levels – easy, medium and hard for every 8th grader to easily chose depending their comfort with the concept without feeling overwhelmed. The students have the freedom to choose through the different levels and once they feel confident of their math skills, can always upgrade themselves with the difficulty level.

What are the math topics covered in the grade 8 math worksheets?

The eighth grade interactive worksheets consist of topics such as simple and multi-step equations, understanding transformations and congruent figures, angles of triangles and polygons, parallel lines and transversals, graphing linear equations in various forms, systems of linear equations, understanding data displays, representations of functions, exponents and scientific notation, finding square roots, problems around Pythagoras theorem, surface area and volume of cylinders, cones and spheres.

Are the grade 8 math worksheets helpful?

The eighth grade math worksheets are ideal for 8th graders as these worksheets give students a better scope to improve their math concepts while solving engaging problem sums. These printable grade 8 math worksheets have been designed with utmost precision to prepare students for their high school years, solidifying their understanding of the math concepts.

Are the 8th grade math worksheets timed?

Yes, the eighth grade interactive math worksheets have been timed. This will encourage children to participate more in such time-bound activities and acquire a solid understanding of math by self regulating their attempts.

In what all formats are the 8th grade math worksheets available?

The 8th grade interactive worksheets are available for the students in two different formats. The pdf based printable worksheets can be completed offline once downloaded while the other formats are tech based interactive worksheets which are solved in online mode.

Can I solve the grade 8 math worksheets more than once?

Yes, you can. Students can practice different math concepts using the BYJU’s free online math worksheets by attempting them more than once. In fact, after every new submission, a new set of questions appear for the students to practice and consolidate their knowledge.

8th Grade Algebra Worksheets

8th Grade Algebra worksheets can help students understand different algebraic identities and practice questions based on them. Algebra might seem a complex topic at first but solving algebra worksheets can help students get used to the topic and strengthen their concept.

Benefits of Pre Algebra Worksheets for 8th Graders

The benefits of 8th grade algebra worksheets are that they contain examples of problems and vital algebraic formulas that are required to practice different types of problems. These 8th grade math worksheets represent problems like equations, word problems, long format questions, etc. in the simplest visual manner where students can understand the concepts clearly and in a detailed step-by-step procedure. Algebra worksheets for grade 8 by Cuemath provide answer keys as well for students to refer to for help as and when they feel they missed out on a step or need more clarity on a particular problem.

Printable PDFs for 8th Grade Algebra Worksheets

Algebra worksheets for 8th grade can be easily downloaded in PDF formats for free. Cuemath worksheets come with answer keys to provide stepwise support to students while solving problems.

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If your student or child is struggling with a specific math concept, you can provide extra support and resources such as math worksheets. Sometimes, visual aids like charts, graphs, and manipulatives can help children understand abstract concepts better.

How can I make math fun?

Students learn best when they're engaged! Sprinkle a little fun into your math lessons by using educational games, videos, puzzles, and real-life scenarios. If your class seems to find math boring or uninteresting, you can also try connecting lessons to their interests or hobbies. Encourage them to ask questions and explore mathematical concepts in different ways.

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Problem Solving Activities: 7 Strategies

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Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Quiz 8th-Graders With These Math Word Problems

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• Solving 8th-grade math word problems can be intimidating, but it shouldn't be. 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 on 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 on 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 8th-grade word math 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 8th-grade word math 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 8th-grade word math 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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What are teachers saying about Khan Academy’s interactive math worksheets?

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Want to get even more out of Khan Academy?

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20 Best Math Puzzles to Engage and Challenge Your Students

Written by Maria Kampen

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• 1. Math crossword puzzles
• 2. Math problem search
• 3. Math riddles

It’s time for math class, and your students are bored.

It might sound harsh, but it’s true -- less than half of 8th grade students report being engaged at school according to this Gallup survey , and engagement levels only drop as students get older.

Math puzzles are one of the best -- and oldest -- ways to encourage student engagement. Brain teasers, logic puzzles and math riddles give students challenges that encourage problem-solving and logical thinking. They can be used in classroom gamification , and to inspire students to tackle problems they might have previously seen as too difficult.

Math puzzles for kids

Puzzles to Print

Take a crossword, and make it math: that’s the basic concept behind this highly adaptable math challenge. Instead of words, students use numbers to complete the vertical and horizontal strips. Math crossword puzzles can be adapted to teach concepts like money, addition, or rounding numbers. Solutions can be the products of equations or numbers given by clues.

Have students practice their addition, subtraction, multiplication and division skills by searching for hidden math equations in a word search-style puzzle . It can be adapted to any skill you want students to practice, and promotes a solid understanding of basic math facts.

My PreCalc students love riddles... can you figure out where the other dollar went?? #MathRiddles pic.twitter.com/BclqW9nq98 — Rachel Frasier (@MsFrasierMHS) January 8, 2019

Do your students love word problems ? Try giving them some math riddles that combine critical thinking with basic math skills. Put one up on the board for students to think about before class begins, or hand them out as extra practice after they’ve finished their work.

Prodigy is an engaging, game-based platform that turns math into an adventure! While it’s not a math puzzle in the traditional sense, Prodigy uses many of the same principles to develop critical thinking skills and mathematical fluency.

Students complete standards-aligned math questions to earn coins, collect pets and go on quests. Teachers can deliver differentiated math content to each student, prep for standardized tests and easily analyze student achievement data with a free account.

See how it works below!

KenKenKenKen

is a “grid-based numerical puzzle” that looks like a combined number cross and sudoku grid. Invented in 2004 by a famous Japanese math instructor named Tetsuya Miyamoto, it is featured daily in The New York Times and other newspapers. It challenges students to practice their basic math skills while they apply logic and critical thinking skills to the problem.

6. Pre-algebraic puzzles

Pre-algebraic puzzles use fun substitutions to get students ready to perform basic functions and encourage them to build problem-solving skills. They promote abstract reasoning and challenge students to think critically about the problems in front of them. As an added bonus, students who suffer from math anxiety might find the lack of complicated equations reassuring, and be more willing to attempt a solution.

7. Domino puzzle board

Games 4 Gains

There are hundreds of ways to use dominoes in your math classroom, but this puzzle gives students a chance to practice addition and multiplication in a fun, hands-on way. You can have students work alone or in pairs to complete the puzzle.

This online game and app challenges players to slide numbered tiles around a grid until they reach 2048. It’s super fun and not as easy as it sounds, so consider sending it home with students or assigning it after the rest of the lesson is over. It encourages students to think strategically about their next move, and it’s a great tool for learning about exponents.

Math in English

Kakuro , also called “Cross Sums,” is another mathematical crossword puzzle. Players must use the numbers one through nine to reach “clues” on the outside of the row. Decrease the size of the grid to make it easier for younger players, or keep it as is for students who need a challenge. Students can combine addition and critical thinking and develop multiple skills with one fun challenge.

10. Magic square

Magic squares have been around for thousands of years, and were introduced to Western civilization by translated Arabic texts during the Renaissance. While magic squares can be a variety of sizes, the three by three grid is the smallest possible version and is the most accessible for young students.

This is also a great math puzzle to try if your students are tactile learners. Using recycled bottle caps, label each with a number from one to nine. Have your students arrange them in a three by three square so that the sum of any three caps in a line (horizontally, vertically and diagonally) equals 15.

11. Perimeter magic triangle

This activity uses the same materials and concept as the magic square, but asks students to arrange the numbers one to six in a triangle where all three sides equal the same number. There are a few different solutions to this puzzle, so encourage students to see how many they can find.

Sudoku is an excellent after-lesson activity that encourages logical thinking and problem solving. You’ve probably already played this classic puzzle, and it’s a great choice for your students. Sudoku puzzles appear in newspapers around the world every day, and there are hundreds of online resources that generate puzzles based on difficulty.

13. Flexagon

There’s a pretty good chance that by now, fidget spinners have infiltrated your classroom. If you want to counter that invasion, consider challenging your students to create flexagons. Flexagons are paper-folded objects that can be transformed into different shapes through pinching and folding, and will keep wandering fingers busy and focused on the wonders of geometry.

14. Turn the fish

This puzzle seems simple, but it just might stump your students. After setting up sticks in the required order, challenge them to make the fish swim in the other direction -- by moving just three matchsticks.

15. Join the dots

Cool Math 4 Kids

This puzzle challenges students to connect all the dots in a three by three grid using only four straight lines. While it may sound easy, chances are that it will take your class a while to come up with the solution. (Hint: it requires some “out of the box” thinking.)

16. Brain teasers

While they don’t always deal directly with math skills, brain teasers can be important tools in the development of a child’s critical thinking skills. Incorporate brain teasers into a classroom discussion, or use them as math journal prompts and challenge students to explain their thinking.

Bonus: For a discussion on probability introduce an older class to the Monty Hall Problem, one of the most controversial math logic problems of all time.

17. Tower of Hanoi

This interactive logic puzzle was invented by a French mathematician named Edouard Lucas in 1883. It even comes with an origin story: According to legend, there is a temple with three posts and 64 golden disks.

Priests move these disks in accordance with the rules of the game, in order to fulfill a prophecy that claims the world will end with the last move of the puzzle. But not to worry -- it’s going to take the priests about 585 billion years to finish, so you’ll be able to fit in the rest of your math class.

Starting with three disks stacked on top of each other, students must move all of the disks from the first to the third pole without stacking a larger disk on top of a smaller one. Older students can even learn about the functions behind the solution: the minimum number of moves can be expressed by the equation 2n-1, where n is the number of disks.

18. Tangram

Tangram puzzles -- which originated in China and were brought to Europe during the early 19th century through trade routes -- use seven flat, geometric shapes to make silhouettes. While Tangrams are usually made out of wood, you can make sets for your class out of colored construction paper or felt.

Tangrams are an excellent tool for learners who enjoy being able to manipulate their work, and there are thousands of published problems to keep your students busy.

Similar to Sudoku, Str8ts challenges players to use their logic skills to place numbers in blank squares. The numbers might be consecutive, but can appear in any order. For example, a row could be filled with 5, 7, 4, 6 and 8 . This puzzle is better suited to older students, and can be used as a before-class or after-lesson activity to reinforce essential logic skills.

20. Mobius band

Is it magic? Is it geometry? Your students will be so amazed they might have a hard time figuring it out. Have them model the problem with strips of paper and see for themselves how it works in real life. With older students, use mobius bands to talk about geometry and surface area.

Why use math puzzles to teach?

Math puzzles encourage critical thinking.

Critical thinking and logic skills are important for all careers, not just STEM-related ones. Puzzles challenge students to understand structure and apply logical thinking skills to new problems.

A study from the Eurasia Journal of Mathematics, Science and Technology Education found that puzzles “develop logical thinking, combinatorial abilities, strengthen the capacity of abstract thinking and operating with spatial images, instill critical thinking and develop mathematical memory.”

All these skills allow young students to build a foundation of skills they’ll draw on for the rest of their lives, no matter what kind of post-secondary route they pursue.

They help build math fluency

Math games can help students build a basic understanding of essential math concepts, and as another study shows, can also help them retain concepts longer .

In the study, early elementary students gradually moved from using the “counting” part of their brains to complete math problems to the “remembering” part that adults use, suggesting math puzzles and repeated problems can help build the essential skill of math fluency .

Many of the math puzzles above allow students to practice essential addition, subtraction, multiplication and division skills, while advanced or modified problems can be used to introduce pre-algebraic concepts and advanced logic skills.

Math puzzles connect to existing curricula

No matter what curriculum you’re using, there’s a good chance it emphasizes problem-solving, critique and abstract thinking. This is especially true of Common Core math and similar curricula.

How Math Skills Impact Student Development

Math puzzles allow students to develop foundational skills in a number of key areas, and can influence how students approach math practically and abstractly. You can also tie them into strategies like active learning and differentiated instruction.

Instead of just teaching facts and formulas, math puzzles allow you to connect directly with core standards in the curriculum. You can also use them to provide a valuable starting point for measuring how well students are developing their critical thinking and abstract reasoning skills.

Tips for using math puzzles in the classroom

View this post on Instagram A post shared by Sarah Werstuik (@teach.plan.love)

Now that you’ve got some great math puzzles, it might be tricky to figure out how to best incorporate them into your classroom. Here are some suggestions for making the most of your lesson time:

Make sure the puzzles are the right level for your class

If the problems are too easy, students will get bored and disengage from the lesson. However, if the problems are too difficult to solve, there’s a good chance they’ll get frustrated and give up early.

There’s a time and a place

While fun math puzzles are a great way to engage your students in developing critical thinking skills, they’re not a tool for teaching important math concepts. Instead, use them to reinforce the concepts they’ve already learned.

Kitty Rutherford , a Mathematics Consultant in North Carolina, emphasizes that math puzzles and games shouldn’t be based solely on mental math skills , but on “conceptual understanding” that builds fluency over time. Math puzzles help build the essential balance between thinking and remembering.

Give them space to figure it out

Rachel Keen , from the Department of Psychology at the University of Virginia, conducted a study about problem-solving skills in preschoolers. She found that “playful, exploratory learning leads to more creative and flexible use of materials than does explicit training from an adult.”

Give your students space to struggle with a problem and apply their own solutions before jumping in to help them. If the problem is grade-appropriate and solvable, students will learn more from applying their own reasoning to it than just watching you solve it for them.

Model puzzles for your students

Use problems like the mobius strip to awe and amaze your students before drawing them into a larger discussion about the mathematical concept that it represents. If possible, make math puzzles physical using recycled craft supplies or modular tools.

Afterward, have a class discussion or put up math journal prompts. What methods did your students try? What tools did they use? What worked and what didn’t? Having students explicitly state how they got to their solution (or even where they got stuck) challenges them to examine their process and draw conclusions from their experience.

Final thoughts on math puzzles

Be aware that it might take a while to get all your students on board -- they could be hesitant about approaching unfamiliar problems or stuck in the unenthusiasm that math class often brings. Consider creating a weekly leaderboard in your classroom for the students that complete the most puzzles, or work through a few as a class before sending students off on their own.

Instead of yawns and bored stares , get ready to see eager participants and thoughtful concentration. Whether you choose to use them as an after-class bonus, a first day of school activity or as part of a targeted lesson plan, math puzzles will delight your students while also allowing them to develop critical skills that they’ll use for the rest of their lives.

What are you waiting for? Get puzzling!

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