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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

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
• • New! Sequences of congruence transformations: choose the sequence
• 15 Identify congruent figures
• 16 Congruence statements and corresponding parts
• • New! Determine if two figures are congruent: justify your answer
• 17 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
• • New! 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
• • New! Interpret lines of best fit: word problems
• 10 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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Printable 8th Grade Math Worksheets

Graph the frequency of each digit in the first 100 digits of pi in this data and graphing worksheet!

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• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
• Multiplication
• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
• More Number Sense Worksheets
• Size Comparison
• Measuring Length
• Metric Unit Conversion
• Customary Unit Conversion
• Temperature
• More Measurement Worksheets
• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
• Box-and-whisker Plot
• Permutation and Combination
• Probability
• Venn Diagram
• More Statistics Worksheets
• Shapes - 2D
• Shapes - 3D
• Lines, Rays and Line Segments
• Points, Lines and Planes
• Transformation
• Quadrilateral
• Ordered Pairs
• Midpoint Formula
• Distance Formula
• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
• Surface Area
• Pythagorean Theorem
• More Geometry Worksheets
• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
• Direct and Inverse Variation
• Order of Operations
• Squaring Numbers
• Square Roots
• Scientific Notations
• Speed, Distance, and Time
• Absolute Value
• More Pre-Algebra Worksheets
• Translating Algebraic Phrases
• Evaluating Algebraic Expressions
• Simplifying Algebraic Expressions
• Algebraic Identities
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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!

Select Grade 8 Math Worksheets by Topic

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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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.

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8th Grade Mathematics Worksheets: FREE & Printable

Looking for free printable Math worksheets and exercises to help your 8th-grade students prepare for the 8th Grade Mathematics test?

Need 8th Grade Mathematics Practice exercises and activities to measure your students’ exam readiness? want great 8th Grade Math worksheets to help your students review and master math concepts? If so, then look no further.

Here is a comprehensive and perfect collection of FREE 8th Grade Mathematics worksheets that would help your students in 8th Grade Math preparation and practice.

You can download free 20+ 8th grade math worksheets from Bytelearn.

Download our free Mathematics worksheets for the 8th Grade test.

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Related Topics

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The BEST Prep Book to Help Your Student ACE the Grade 8 Math!

Mastering Grade 8 Math The Ultimate Step by Step Guide to Acing 8th Grade Math

8th grade mathematics concepts, whole numbers.

• Whole Number Addition and Subtraction
• Whole Number Multiplication and Division
• Rounding and Estimates

Fractions and Decimals

• Simplifying Fractions
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions
• Adding and Subtracting Mixed Numbers
• Multiplying and Dividing Mixed Numbers
• Adding and Subtracting Decimals
• Multiplying and Dividing Decimals
• Comparing Decimals
• Rounding Decimals
• Factoring Numbers
• Greatest Common Factor
• Least Common Multiple

Real Numbers and Integers

• Adding and Subtracting Integers
• Multiplying and Dividing Integers
• Order of Operations
• Ordering Integers and Numbers
• Integers and Absolute Value

Proportions, Ratios, and Percent

• Simplifying Ratios
• Proportional Ratios
• Similarity and Ratios
• Ratio and Rates Word Problems
• Percentage Calculations
• Percent Problems
• Discount, Tax and Tip
• Percent of Change
• Simple Interest

Algebraic Expressions

• Simplifying Variable Expressions
• Simplifying Polynomial Expressions
• Translate Phrases into an Algebraic Statement
• The Distributive Property
• Evaluating One Variable Expressions
• Evaluating Two Variables Expressions
• Combining like Terms

Equations and Inequalities

• One-Step Equations
• Multi-Step Equations
• Graphing Single–Variable Inequalities
• One-Step Inequalities
• Multi-Step Inequalities

Systems of Equations

• Systems of Equations Word Problems
• Quadratic Equation

The Best Math Study Guide for 8th-Grade Students!

Grade 8 Math for Students The Ultimate Step by Step Guide to Preparing for the Grade 8 Math Test

Linear functions.

• Finding Slope
• Graphing Lines Using Line Equation
• Writing Linear Equations
• Graphing Linear Inequalities
• Finding Midpoint
• Finding Distance of Two Points

Exponents and Radicals

• Multiplication Property of Exponents
• Zero and Negative Exponents
• Division Property of Exponents
• Powers of Products and Quotients
• Negative Exponents and Negative Bases
• Scientific Notation
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Polynomials

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Geometry and Solid Figures

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Statistics and Probability

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Class 8 Mathematics Assignments

We have provided below free printable Class 8 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 8 Mathematics . These Assignments for Grade 8 Mathematics cover all important topics which can come in your standard 8 tests and examinations. Free printable Assignments for CBSE Class 8 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 8 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 8 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 8. Students can click on the links below and download all Pdf Assignments for Mathematics class 8 for free. All latest Kendriya Vidyalaya Class 8 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 8 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 8 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 8th. Our expert faculty have covered Class 8 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 8 Mathematics and CBSE Assignments for Mathematics Class 8 will be really helpful for standard 8th students to prepare for the class tests and school examinations. Class 8th students can easily free download in Pdf all printable practice worksheets given below.

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• All Mathematics assignments for Class 8 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
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• Class 8 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

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At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 8 which you can download in Pdf

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You can click on the links above and get assignments for Mathematics in Grade 8, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

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• NCERT Solutions
• NCERT Class 8
• NCERT 8 Maths

NCERT Solutions for Class 8 Maths

Ncert solutions for class 8 maths cbse 2023-24 edition – free pdf download.

NCERT Solutions for Class 8 Maths includes all the questions provided in the textbook that is prescribed in accordance with the CBSE Board. The syllabus given for all the classes is completely based on the NCERT curriculum. Hence, preparing for exams using NCERT Solutions will definitely provide students with an advantage.

BYJU’S NCERT Class 8 Solutions for Maths has been designed to help students solve problems with ease. The CBSE 8th Class Solutions for Maths provided here come with well-prepared exercises along with detailed explanations given by our expert teachers that further make learning and understanding concepts an easy task. So, if students have been looking for the most detailed and accurate Class 8 NCERT Solutions for Maths,  which is also free, this is the right place.

Chapter-Wise NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8th Maths provided here are very beneficial for students. They can use these  NCERT Solutions for Class 8 as a reference while practising the problems and developing better skills along with preparing efficiently for the exams. The exercises are given at the end of every chapter to practise the concepts learned in the chapter.

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

In this chapter, students will be learning properties related to real numbers, integers, whole numbers, rational numbers and natural numbers – independent, associative and closure. The chapter deals with the role of zero and one, multiplication over addition, representation of rational Numbers on the number line , and searching for rational numbers between two rational numbers. The topics of additive identity (0) and multiplicative identity (1) are also covered in this chapter. There are 2 exercises in this chapter, which contain questions from all the topics present in the chapter.

Also, access the following resources for Class 8 Chapter 1 Rational Numbers  at BYJU’S:

• Rational Numbers Class 8 Notes – Chapter 1
• NCERT Exemplar Class 8 Maths Solutions for Chapter 1 – Rational Numbers
• RD Sharma Solutions for Class 8 Maths Chapter 1 – Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 2 Linear Equations in One Variable

The chapter, Linear Equations in One Variable, deals with linear expression in one variable alone. Such equations are known as linear equations in one variable . There are six exercises in this chapter with a total of 65 questions in them. The chapter includes different concepts, including solving linear equations in one variable, some of its applications, reducing equations to a simpler form and word problems related to linear equations in one variable.

Also, access the following resources for Class 8 Chapter 2 Linear Equations in One Variable  at BYJU’S:

• Linear Equations In One Variable Class 8 Notes- Chapter 2
• NCERT Exemplar Class 8 Maths Solutions for Chapter 4 – Linear Equations In One Variable
• RD Sharma Solutions for Class 8 Maths Chapter 9 Linear Equation in One Variable

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals

The chapter Understanding Quadrilaterals of Class 8 Maths provides the students with a proper understanding of the quadrilaterals . The chapter also covers different kinds of polygons, including triangles, quadrilaterals, pentagons, hexagons, etc. The chapter contains 4 exercises which aid the students in understanding these shapes properly.

Also, access the following resources for Class 8 Chapter 3 Understanding Quadrilaterals  at BYJU’S:

• Understanding Quadrilaterals Class 8 Notes – Chapter 3
• Important Questions for Maths Class 8 Chapter 3 Understanding Quadrilaterals
• NCERT Exemplar Class 8 Maths Solutions for Chapter 5 – Understanding Quadrilaterals Practical Geometry
• RD Sharma Solutions for Class 8 Maths Chapter 16 Understanding Shapes- II (Quadrilaterals)

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

The chapter, Practical Geometry, includes the method of constructing a quadrilateral with various parameters given. The chapter consists of 5 exercises, each dealing with different methods of constructing the quadrilateral. For instance, the first exercise deals with the construction of quadrilaterals when the length of four sides and a diagonal are given; similarly, the second exercise involves the method of construction of quadrilaterals when two diagonals and three sides are given, and so on. Hence, we can conclude that learning this chapter will make the students well-versed in all the concepts of quadrilateral for further classes.

Also, access the following resources for Class 8 Chapter 4 Practical Geometry  at BYJU’S:

• Practical Geometry Class 8 Notes – Chapter 4
• Important Questions Maths Class 8 Chapter 4: Practical Geometry
• RD Sharma Solutions for Class 8 Maths Chapter 18 Practical Geometry (Constructions)

NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

The collection of information that can be used for analysis is known as data. In this chapter, students learn about the organisation and representation of data. Organising the data in a systematic method is referred to as data handling . In this chapter, students learn to represent these data diagrammatically as a pictograph, a bar graph, a double bar graph, a pie chart and a histogram. During the course of this chapter, students will be briefed about the concept of probability or likelihood. There are 3 exercises in this chapter that deal with all the concepts covered in the chapter.

Also, access the following resources for Class 8 Chapter 5 Data Handling  at BYJU’S:

• Data Handling Class 8 Notes- Chapter 5
• Important Questions Class 8 Maths Chapter 5 Data Handling
• NCERT Exemplar Class 8 Maths Solutions for Chapter 2 – Data Handling
• RD Sharma Solutions for Class 8 Maths Chapter 23 Data Handling – I (Classification and Tabulation of Data)

NCERT Solutions for Class 8 Maths Chapter 6 Square and Square Roots

This chapter, Squares and Square Roots, helps the students learn about the concept of square numbers and the square root of a number. The chapter deals with properties of square numbers, interesting patterns that could be learnt using square numbers, finding the square of a number, Pythagorean triplets , finding square roots through various methods, square roots of decimals and much more.

Also, access the following resources for Class 8 Chapter 6 Square and Square Roots  at BYJU’S:

• Squares and Square Roots Class 8 Notes: Chapter 6
• RD Sharma Solutions for Class 8 Maths Chapter 3 – Squares and Square Roots
• NCERT Exemplar Class 8 Maths Solutions for Chapter 3 – Squares And Square Roots Cubes And Cube Roots
• Important Questions Class 8 Maths Chapter 6- Squares and Square Roots

NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots

In the chapter, Cubes and Cube Roots, students learn about numerous strategies to find out the cubes and cube roots of a number. The chapter discusses finding the cubes of different numbers, some interesting patterns that could be learnt using cubes and finding the cube roots . There are 2 exercises in the chapter that will help the students understand the basics of cubes and cube roots in depth.

Also, access the following resources for Class 8 Chapter 7 Cube and Cube Roots  at BYJU’S:

• Cubes and Cube Roots Class 8 Notes: Chapter 7
• Important Questions Class 8 Maths Chapter 7: Cubes and Cube Roots
• RD Sharma Solutions for Class 8 Maths Chapter 4 – Cubes and Cube Roots

NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities

The chapter, Comparing Quantities, helps the students in learning the comparison between the rise and decrease of percentages, market value, sales value, discount, etc. The chapter deals with an important concept that can be used in day-to-day life, Interest. Students learn about simple interest , compound interest calculated half-yearly, quarterly, monthly or yearly, and much more. There are 3 exercises in this chapter which help the students in learning the concept of comparing quantities.

Also, access the following resources for Class 8 Chapter 8 Comparing Quantities  at BYJU’S:

• Important Question Class 8 Maths Chapter 8: Comparing Quantities
• NCERT Exemplar Class 8 Maths Solutions for Chapter 9 – Comparing Quantities
• Comparing Quantities Class 8 Notes: Chapter 8

NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities

This chapter, Algebraic Expressions and Identities, helps the students understand the concepts like terms, factors and coefficients related to algebraic expressions. A brief on the basics of monomials , binomials and polynomials is also given in the chapter. Students learn the addition, subtraction and multiplication of algebraic expressions. The concept of identity is also covered in the chapter. The 5 exercises in the chapter cover all the concepts present in algebraic expressions and identities.

Also access the following resources for  Class 8 Chapter 9 Algebraic Expressions and Identities  at BYJU’S:

• Algebraic Expressions and Identities Class 8 Notes: Chapter 9
• RD Sharma Solutions for Class 8 Maths Chapter 6 – Algebraic Expressions and Identities
• NCERT Exemplar Class 8 Maths Solutions for Chapter 7 – Algebraic Expressions And Identities Factorisation
• Important Questions Class 8 Maths Chapter 9 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

In this chapter, with the help of 3 exercises present, students learn to visualize solid shapes in different dimensions. The chapter is very interesting since it deals with viewing 3D shapes, mapping the space around us, and learning about faces, edges and vertices. The chapter also discusses Euler’s formula , which states that F + V – E = 2, where F is Faces, V is Vertices, and E is Edges, along with its application.

Also, access the following resources for Class 8 Chapter 10 Visualizing Solid Shapes  at BYJU’S:

• Visualising Solid Shapes Class 8 Notes: Chapter 10
• Important Questions Class 8 Maths Chapter 10 Visualising Solid Shapes
• RD Sharma Solutions for Class 8 Maths Chapter 19 Visualising Shapes
• NCERT Exemplar Class 8 Maths Solutions for Chapter 6 – Visualising Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration

Students in lower classes must have learnt about the area and perimeter of various closed plane figures such as triangles, rectangles, circles, etc. In this chapter, Mensuration , students will learn to solve problems related to the perimeter and area of other plane closed figures like quadrilaterals. Eventually, the students will learn about the surface area and volume of different solid shapes such as a cube, cuboids and cylinders. A total of 4 exercises are present in this chapter.

Also, access the following resources for Class 8 Chapter 11 Mensuration  at BYJU’S:

• Mensuration Class 8 Notes- Chapter 11
• Important Questions Class 8 Maths Chapter 11 Mensuration
• RD Sharma Solutions for Class 8 Maths Chapter 20 Mensuration – I (Area of a Trapezium and a Polygon)
• NCERT Exemplar Class 8 Maths Solutions for Chapter 11 – Mensuration

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

In the chapter, Exponents and Powers, students learn different concepts, including powers with negative exponents, laws of exponents , use of exponents to express the numbers in standard form and comparison of extremely large numbers with small numbers. The chapter consists of 2 exercises to help the students learn about the topics of exponents and powers.

Also, access the following resources for Class 8 Chapter 12 Exponents and Powers  at BYJU’S:

• NCERT Exemplar Class 8 Maths Solutions for Chapter 8 – Exponents And Powers
• Important Questions Class 8 Maths Chapter 12 Exponents And Powers
• RD Sharma Solutions for Class 8 Maths Chapter 2 – Powers

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

This chapter contains 2 exercises with questions based on the concepts of direct proportion and inverse proportion. Two quantities, x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. On the other hand, two quantities, x and y, are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.

Also, access the following resources for Class 8 Chapter 13 Direct and Inverse Proportions  at BYJU’S:

• Direct and Inverse Proportions Class 8 Maths Notes – Chapter 13
• NCERT Exemplar Class 8 Maths Solutions for Chapter 10 – Direct And Inverse Proportions
• Important Questions Class 8 Maths Chapter 13 Direct and Inverse Proportions
• RD Sharma Solutions for Class 8 Maths Chapter 10 Direct and Inverse Variations

NCERT Solutions for Class 8 Maths Chapter 14 Factorization

In this chapter, students learn to perform Factorization. The topics covered in this chapter include factors of natural numbers and algebraic expressions , factorisation by regrouping terms and factorisation using identities. The chapter also deals with the division of algebraic expressions that, includes division of a monomial by another monomial, division of a polynomial by a monomial, etc. There are 4 exercises in this chapter that contain questions covering all the topics present in the chapter.

Also, access the following resources for Class 8 Chapter 14 Factorization  at BYJU’S:

• RD Sharma Solutions for Class 8 Maths Chapter – 7 Factorization
• Factorisation Class 8 Notes- Chapter 14
• Important Questions Class 8 Maths Chapter 14 Factorization

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

In the chapter, Introduction to Graphs, students learn to represent different types of data with various kinds of graphs. The different types of graphs include bar graphs , pie graphs, line graphs and linear graphs. The chapter will help the students in learning how to locate a point and coordinate in a graph. A total of 3 exercises are present in the chapter that will help the students understand the concepts of Graphs.

Also, access the following resources for Class 8 Chapter 15 Introduction to Graphs  at BYJU’S:

• Introduction To Graphs Class 8 Notes- Chapter 15
• Important Questions Class 8 Maths Chapter 15: Introduction to Graphs
• NCERT Exemplar Class 8 Maths Solutions for Chapter 12 – Introduction To Graphs
• RD Sharma Solutions for Class 8 Maths Chapter 27 Introduction to Graphs

NCERT Solutions for Class 8 Maths Chapter 16 Playing with Numbers

Students, so far, have studied various types of numbers, such as natural numbers, whole numbers, integers and rational numbers . They might have also studied a number of interesting properties of these numbers, finding factors, multiples and the relationships among them. Likewise, in this chapter, students can explore the vast genres of numbers in detail. These ideas can help the students in justifying tests of divisibility. There are 2 exercises in this chapter that covers the topic of playing with numbers.

Also, access the following resources for Class 8 Chapter 16 Playing with Numbers  at BYJU’S:

• Playing With Numbers Class 8 Notes- Chapter 16
• Important Questions Class 8 Maths Chapter 16: Playing with Numbers
• NCERT Exemplar Class 8 Maths Solutions for Chapter 13 – Playing with Numbers
• RD Sharma Solutions for Class 8 Maths Chapter 5 – Playing with Numbers

CBSE Class 8 Maths Solutions of NCERT Book

We are providing chapter-wise NCERT Maths Solutions for Class 8. The solutions provided on this page will help students understand and solve all the NCERT Class 8 mathematics book questions. These solutions are free, and students can view them online on the website or download the PDF.

Solving NCERT Maths question papers and sample papers will also help the students to understand different types of questions as well as the marking scheme. Also, students can learn from NCERT Exemplar Class 8 to practise exemplar problems.

Key Features of BYJU’S NCERT Class 8 Maths Solutions

• These solutions cover all the chapters that are included in the Class 8 Maths book.
• The solutions are given in easy steps to help students understand the concepts better.
• These solutions can be downloaded and referred to at any time and at any place.
• These CBSE 8th Class Maths solutions are available for free, and any student can access them.

These are just a few benefits of using the Solutions of Maths NCERT 8th Class . Students can register with BYJU’S and get the opportunity to learn topics of CBSE or NCERT syllabus for Class 8 Maths or any other Class more effectively. They can learn different topics right from their homes using the internet, where they can browse content on their PCs. Moving on, students can customize their learning experience, and they can do it all at their own pace without worrying about deadlines or any stress. Further, we are providing the best subject experts or mentors who will guide students to learn the subject and its concepts in a more simple and fun manner.

Another benefit that students can experience with BYJU’S is that they can opt to learn NCERT subjects by accessing our solutions anywhere and at any time of the day. In addition, BYJU’S is keen on tracking the progress that students make. Feedback and counselling are provided via periodic assessments. In case students face any doubts while going through the CBSE Class 8 Maths NCERT Solutions , they can always approach our BYJU’S support team to clear all their doubts. Besides, students can bring in all their queries regarding Maths as well as other subjects, including Physics, Chemistry, and Biology. Our responsive team is always ready to answer all types of questions.

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What do 8th graders learn in math?

reviewed by Jo-ann Caballes

Created on Jun 19, 2024

Updated on June 19, 2024

As 7th graders transition to 8th grade, children start to deal with multi-step word problems that use whole numbers, decimals, fractions, and percentages simultaneously. While this can be pretty frustrating, parents and teachers should ensure that kids know that 8th-grade math concepts teach them not only problem-solving but also how to be independent thinkers.

What do you learn in 8th-grade math?

Essential 8th-grade math skills your child should know include:

• Using linear equations in one and two variables
• Creating graphs and other diagrams to illustrate those relationships
• Understanding functions, where students learn to interpret and analyze functional relationships
• Understanding irrational numbers and comparing them to rational numbers
• Understanding measures of central tendency and variability and applying them to real-life scenarios
• Operating with rational numbers and the applications of percentage, rate, and proportion
• Applying the Pythagorean Theorem to find unknown lengths in right triangles and explaining why it works
• Computing square roots and their opposite exponents

The skills students learn in 8th grade aren’t easy, especially in math. Kids who had troubles in previous years may have some difficulties keeping up, so it’s important to build confidence in math by eighth grade.

By the end of the academic year, children should have a solid foundation in these areas. That prepares them for more complex math concepts in high school, including  Algebra I and Geometry. The main focus of 8th-grade level math is not on mechanical calculation but on really understanding math concepts so they can be applied in real-life day-to-day situations. This approach aims to build a strong mathematical mindset that is vital for future academic and career success, especially in fields that require quantitative analysis (STEM disciplines).

What to do to help your kid conquer 8th-grade math topics?

Strategies that help your kid mastering 8th-grade math include providing emotional support, establishing routines, and maintaining open communication. 

But what if your child faces more serious emotional challenges during puberty that interfere with a healthy family dynamic? 8th grade can be a real hassle for a family, especially since your child is actively going through puberty. Emotional, physical, and cognitive changes can sometimes impact their academic performance, leading to bad grades and frustration both on the kid’s and parents’ side.

Children aren’t always open about what’s going on in school, let alone discussing what is not going well. Asking your kid about the possible challenges is not helping either, as you might get tears or angry outbursts as an answer. After all, it is not easy to be your child’s best friend, especially in moments like this. Supporting your child’s learning at home can be ineffective because of these mood swings, so seeking additional resources that encourage a positive attitude toward math can be a good idea.

Seeking additional resources 

Doesn’t it feel, at times, that school math teaching methods are designed to make your children suffer? It seems like complaints from your 13-year-old never end, and a confusing school math curriculum isn’t helping at all. Studies have shown that game-based learning environments (exactly the ones that are not being practiced at traditional schools) can support significant improvements in students’ mathematical skills, especially when games are designed with educational purposes in mind. As children explore this world through play, real-life math games with real rewards will help them master complex concepts much faster. 

How do 8th graders learn math with Brighterly

If your child is falling behind in math in 8th grade, online math tutoring that incorporates game-based math learning can be a solution. Platforms like Brighterly can boost your child’s math skills with the help of professional math tutors who take into consideration each kid’s needs and temper.

And the best thing, Brighterly doesn’t just load kids with facts without explaining the real world behind them. It helps them understand how math can be utilized in their everyday life. 

Find the perfect math tutor here

Say goodbye to your child’s struggles with math.

What math is taught in 8th grade

Math in 8th grade sets the stage for what children will learn in high school and typically covers these basic programs: 

• Pre-Algebra 

8th-grade Pre-Algebra

Pre-Algebra is normally taught in middle school math and prepares children for more advanced math concepts of Algebra I. It’s the first step toward complex math problems and helps kids lay a good foundation for Algebra I. 

Pre-Algebra explores topics like: 

• Scientific notations, exponents, and roots
• Expressions and variables
• Rational number word problems and percents
• Percentages
• Proportional relationships
• Functions and linear models
• Factors and Multiples
• One-step and two-step equations and inequalities
• Exponents Intro and Order of Operations
• Equations and inequalities – introduction
• Ratios and Rates
• Multi-step equations
• System of equations

8th-grade Algebra I

Algebra I is typically introduced in 9th grade. However, students who excel in math are offered more advanced courses like Algebra I as well. A report by the U.S. Department of Education in 2018 says children who take Algebra I in 8th grade perform better in high school and college. 

Algebra I includes the following topics: 

• Exponents and radicals
• Inequalities
• Absolute value and piecewise functions
• Exponential growth and decay
• Forms of linear equations
• Linear equations and graphs
• Creativity in algebra
• Solving equations and inequalities
• Quadratic functions and equations
• Working with units
• Irrational numbers

8th-grade Geometry

Geometry in 8th-grade math creates the setting for future understanding of more difficult geometry concepts. For instance, this is the first year that children make proofs to prove that something is true. As this is a pivotal year for geometry class, kids who fail to grasp these concepts will more likely struggle in future math classes.

Geometry in 8th grade focuses on:

• Exploring different types of triangles and their properties
• Using the Pythagorean Theorem to solve problems 
• Calculating the volume and surface area of solid figures
• Using the coordinate plane to solve geometric problems

Students also get introduced to important geometry vocabulary like: 

• Line Segment
• Translation

A basic understanding of these terms is crucial for later understanding of high school geometry class. 

What does 8th-grade math look like?

The primary focus for an 8th-grade math curriculum is algebra, number sense and operations, geometry, and measurement and spatial sense. Data analysis and probability are also included. While these math topics might be a surprise, they are vital for 8th-grade math skills your child should know.

What to do to succeed in 8th-grade math?

• Build a schedule

Practice like a pro

• Find a reliable tutor

As your child transitions to 8th grade, setting some rules and routines is recommended. Doing well in 8th-grade math is important to build a strong foundation for high school, as well as for future academic and career success. Here is a more detailed breakdown of how to  succeed in 8th-grade math:

Build a schedule 

Planning is important, especially at the delicate age of adolescence, when every minor inconvenience can disrupt the normal pace of the day. Creating a study schedule and setting realistic goals will help your kid tackle 8th-grade head-on.

Practicing like a champion does not require your kid to overwork. Regular and conscious practice is enough to stay on the right track. 

Also, practicing with worksheets is a great way to test their understanding and identify areas of improvement. 

Find a reliable tutor 

Having difficulties in school math is completely normal. For some kids, it can be a temporary setback, while for others, handling 8th-grade math may be a serious challenge. Getting help from supportive math tutors who take into account math knowledge gaps your kid might have is advisory. Online tutoring at platforms like Brighterly is the perfect solution for children who don’t feel much confidence in math. 1:1 sessions foster a more supportive environment, making it easier for your kid to catch up with complex math problems. 

Improve your child’s math skill today with Brighterly

Let them be at the top of their class.

What should 8th graders know in math?

First and foremost, your child has to understand that 8th-grade math focuses on how to approach complex problems by breaking them down into smaller parts. This teaches them problem-solving, an essential skill across all disciplines and everyday life.

But generally, 8th-grade math objectives include defining and differentiating between different types of sampling techniques, using technology to determine the mean, median, and mode, identifying rational and irrational numbers, and describing meanings, solving problems in two variables using linear equations, calculating and approximate principal square roots, and identifying and perform transformations of a figure on a coordinate plane.

To wrap things up, 8th-grade math covers algebra, geometry, and data analysis, which are essential foundations for high school. Providing support with game-based learning and professional tutoring is an optimal choice for kids who struggle in math. Additionally, encouragement and open communication between parents and children help navigate 8th grade effectively in order to prepare children for later grades.

Claim a free trial lesson with Brighterly to create a positive and supporting environment for your kids —  and make sure your child succeeds in math in 8th grade and later academic years.

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

Poems make learning easier, so why not use them to teach math? Especially when you need to explain number formation in kindergarten.  When hidden in catchy poems, number formation rhymes help kids memorize how to write numbers while having some fun. So check this article out to see the best number formation poems — and […]

Jun 18, 2024

Math programs from 1st to 12th grade

Online summer math camp for kids and teens.

Choose kid's grade

Summer Math Program Boost Your Child's Math Abilities! Ideal for 1st-12th Graders, Perfectly Synced with School Curriculum!

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STEP Support - Assignment 8

Introduction

This STEP support module introduces the AM-GM inequality and the intersections of circles and ellipses. Previous assignments can be found here , but you can do this one without having done the others first.

STEP questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck").

About this assignment

The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise.

The warm up for this assignment proves the AM-GM inequality for 2, 3 and 4 values. The AM-GM inequality states that the arithmetic mean of a set of values is greater than or equal to the geometric mean of those values and is a very useful and powerful result.

The main STEP question (2002 STEP 1 Question 1) is about the intersections of a circle and an ellipse; you don't need to know anything about ellipses to tackle the question but once you have done it you might like to visit Desmos to draw the graphs and see what is happening.

The final question revisits the "Socks" problem first seen in assignment 5 , but this time there are three colours to consider.

A nice result connecting the arithmetic mean, the geometric mean and the harmonic mean is discussed here . There is a discussion of some of the different ways of proving the $n$ value case here .

Ellipses and other "conic sections" are discussed in this Plus maths article .

Some more hints and tips for solving Geometry STEP questions can be found in this Advanced Problem Solving module .

Hints, support and self evaluation

The “Hints and partial solutions for Assignment 8” file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.

Here is a Worked Video Solution to the STEP question from this assignment.

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)

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Mathematical Association of America

American mathematics competitions.

Founded in 1950, the AMC is the preeminent math competition for students K-12. Today, over 300,000 students in 50 states and over 30 countries take the AMC to bolster their confidence and passion for math.

Empowering the next generation of problem solvers.

The AMC program is more than just a competition; it’s a national effort to strengthen the mathematical capabilities of our next generation of innovators. By challenging students with engaging problems, the AMC sets the stage for lifelong mathematical exploration, discovery, and achievement.

Who can participate in the AMC?

The AMC proudly engages with a dedicated group of participants, each crucial to the success of our mathematical community:

• Students: Young mathematicians from middle and high schools are at the heart of the AMC. Their curiosity, passion, and problem-solving skills shape the future of mathematics.
• Competition Managers: Educators and math circle teachers play a pivotal role in developing students’ mathematical abilities and ensuring the smooth operation of the AMC.
• Parents: Their support and encouragement are essential as their children navigate their journey of mathematical discovery and growth.

The AMC aims to create a more inclusive and empowered math community. Through examinations and curriculum materials, we support educators in fostering the analytical skills to drive future innovations.

Get Involved

Eager to dive into the AMC? Here's how you can become a part of this transformative experience:

Students : Discover how to register for the AMC, access preparation materials, and begin tackling challenges. Competition Managers : Find out how to organize an AMC competition at your school or institution, providing a platform for students to shine. Parents : Explore registration details for your child and learn how you can support their mathematical journey.

Together, we're not just solving mathematical problems - we're preparing for a brighter future. Join the AMC community in advancing the understanding and appreciation of mathematics. Let’s embark on this exciting journey together.

For more information on registration, preparation resources, and upcoming competition dates, [explore our site further].

Dive into mathematics with the AMC 8, a 25-question, 40-minute competition designed to promote developing and enhancing problem-solving skills. Start your mathematical journey today and register for the AMC 8, where curiosity meets challenge!

For : Middle school students, typically in grades 6-8, though younger students may also participate.

What : A 25-question, 40-minute multiple-choice examination designed to promote the development of problem-solving skills.

When : Held annually in January.

Elevate your mathematical skills with the AMC 10/12, challenging competitions that are the gateway to further opportunities, including the AIME and USAMO. Take the next step in your mathematical odyssey and sign up for the AMC 10/12, paving your way to mathematical excellence!

For : High school students in grades 10 and below, with a maximum age of under 17.5 years on the day of the competition.

What : A 25-question, 75-minute multiple-choice examination focused on high school mathematics up to the 10th-grade level.

When : Held annually in November.

For : High school students in grades 12 and below, with a maximum age of under 19.5 years on the day of the competition.

What : A 25-question, 75-minute multiple-choice examination that covers high school mathematics up to the 12th-grade level.

When : Also held annually in November.

Your Mathematical Journey: AMC to IMO

AMC 8, AMC 10/12 : Begin your adventure with the AMC 8 for an introductory challenge or the AMC 10/12 for a chance to advance further in competitive mathematics. [Register for the AMC] and take the first step.

AIME : Excel in the AMC 10/12 to qualify for the AIME, a more challenging examination that tests your problem-solving prowess and mathematical ingenuity.

USAMO/USAJMO : Achieve high scores in the AIME and AMC 10/12 to earn an invitation to the USAMO or USAJMO, where the nation's top mathematical talents compete in proof-based problems.

MOP : Outstanding performance in the USAMO or USAJMO could lead to participation in the MOP, an intensive training camp designed to prepare the best young mathematicians for international competition.

IMO : Excel at the MOP to join the elite team representing the United States at the IMO, the pinnacle of pre-college mathematics competition, where you'll challenge yourself against the world's best.

What is the history of the AMC?

In 1950, the first Mathematical Contest, sponsored by the New York Metropolitan Section of the Mathematical Association of America (MAA), took place. It was given in approximately 200 schools to around 6,000 students in the New York area only. Today, the competition has grown to over 300,000 students participating annually, in over 4,000 schools.

Where can I take the MAA AMC?

This search page can assist in finding a school where you could take one of the AMC contests, displaying those who registered for the past or upcoming contest. You are responsible for contacting the school to see if they are willing to accept you to take the contest at their location.

All contest results and qualifying awards will be sent to the hosting school.

Search here

When is the MAA AMC happening this year?

The 2024-25 MAA AMC dates are:

AMC 10/12 A  – Wednesday, November 6, 2024

AMC 10/12 B  – Tuesday, November 12, 2024

AMC 8  – January 22-28, 2025

Lesson Plan

June 17, 2024, 6:05 a.m.

Lesson plan: History of Juneteenth and why it became a national holiday

A Juneteenth celebration in Richmond, Virginia, 1905. Library of Congress

This lesson was originally published on June 16, 2021, and was updated on June 16, 2024.

For a Google version of this lesson plan, click here . (Note: you will need to make a copy of the document to edit it).

In this lesson, students will explore and discuss the history and context around the Juneteenth holiday in the United States. Topics explored will include the history of racial injustice in the U.S., the Civil War and the limitations of the Emancipation Proclamation. Additionally, students will be encouraged to explore the modern significance of Juneteenth and its long-term impact.

Estimated time

One 50-60 minute class period

Grade Level

Grades 6-12

On June 15, 2021, the Senate unanimously approved a bill approving June 19 as a federal holiday for “Juneteenth National Independence Day.” The House passed the bill one day later. Still, many Americans are still unaware of the history and significance of June 19.

On Jan. 1, 1863, President Abraham Lincoln issued the Emancipation Proclamation declaring “that all persons held as slaves” in the Confederacy “shall be free.” While this may have freed some enslaved people on paper, the reality was much more complicated.

Source: PBS NewsHour via Associated Press

For instance, the Emancipation Proclamation only freed those slaves held under the Confederacy, not in border states loyal to the Union, including Kentucky, West Virginia and Delaware, where slavery was still legal after the Emancipation Proclamation. In fact, slavery was still legal in Kentucky until Dec. 1865, when the 13th Amendment was passed, though Kentucky voted against ratifying the amendment.

Confederate states and slaveholders also resisted emancipation, and many people remained enslaved in Confederate states after the proclamation, even as many enslaved people fought for their freedom or escaped behind Union lines. On June 19, 1865, Major General Gordon Granger of the Union issued an order in Galveston, Texas, alerting all enslaved persons that they were legally free.

At this point in 1865, Texas was the westernmost state in America and one of the last Confederate states to be occupied by the Union. Many slaveholders had fled Union advances in other parts of the South to Texas, along with the people they had enslaved.

While it took time for the logistics of “freeing” enslaved people to come into effect, the importance of June 19, or “Juneteenth” lived on. Considering how complicated emancipation was, many dates were considered for holding celebrations of emancipation, but over 150 years later, June 19 remains.

What originally was a holiday mainly observed by Texans has grown to be recognized all over the country. Each year on “Juneteenth,” (or more formally Juneteenth National Freedom Day), communities all around the United States gather and celebrate and reflect on the history of slavery and struggle for civil rights and equality, including the work that still remains after conditional advances such as the Emancipation Proclamation.

Warm up activity

As a class, watch the BrainPop video (8 minutes) below found here introducing Juneteenth. While watching the video, answer the following discussion questions.

Source: BrainPop

Discussion questions:

• What is “Juneteenth”? What does it celebrate?
• Why did it take so long for enslaved peoples in Texas to finally be free? What obstacles existed?
• What were some of the forms of discrimination against newly freed people mentioned in the video?
• What is the Great Migration?
• How did Juneteenth become a national, not just regional, celebration?

After watching the video, separate into groups of 3-4 to discuss the focus questions (5 minutes).

Main activities:

• Why was June 19th chosen as the date to celebrate the freedom of all Americans? What were some of the drawbacks to other dates? Can you make an argument for why you think a different date might have been better and/or worse?
• Gates describes several reasons why Juneteenth struggled to be remembered at times, and why it was able to endure. Compare and contrast what the BrainPop video included as reasons why Juneteenth struggled and endured with what Gate’s emphasizes. What do you think were the most important factors in Juneteenth’s momentum and remembrance continuing?
• “When did they start recognizing Juneteenth, if at all?”
• “What was the process of Juneteenth becoming a holiday in my state?”
• If Juneteenth isn’t recognized in your state, see if you can answer, “Why is Juneteenth not recognized?”
• This search engine for state and local government websites
• The Library of Congress

Additional activities

• Brainstorm or plan a Juneteenth celebration activity. This can be decorating a common area, bringing in a relevant local speaker or planning a refreshment break for your school. Juneteenth celebrations can be in the home, at school or in community locations. For more inspiration see these resources:
• “ How to Celebrate ” from Juneteenth.com
• See how others are celebrating Juneteenth on Twitter .
• Some activists feel ambivalent about Juneteenth becoming a national holiday, or reject the idea. To learn more about the nuances surrounding making Juneteenth a federal holiday, watch this NewsHour interview with Dr. Mark Anthony Neal recorded in 2020 amid the George Floyd protests.

• The day now known as Juneteenth was formally recognized as a national holiday in 2021, due in large part to the activism of retired teacher Opal Lee. Learn more about Lee's activism and the message of Juneteenth in this NewsHour interview with Opal Lee.

If classrooms finish and plan a celebratory activity, please share your ideas with us on social media @NewsHourEXTRA on Twitter.

This lesson was written by Cecilia Curran, NewsHour Classroom intern, while she was a rising sophomore at Amherst College. This lesson was edited by NewsHour Classroom's education producer and former history teacher Vic Pasquantonio.

Fill out this form to share your thoughts on Classroom’s resources. Sign up for NewsHour Classroom’s ready-to-go Daily News Lessons delivered to your inbox each morning.

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Injured Detroit Tigers SS Javier Báez begins hitting drills in rehab

ATLANTA — Detroit Tigers shortstop Javier Báez has been cleared for baseball activities.

The 31-year-old, who hasn't played in a game since June 8 because of a lower back injury, completed light hitting drills Tuesday in Lakeland, Florida, home of the Tigers' spring training facility, as part of his return-to-play program. He will return to Lakeland on Wednesday for fielding drills.

"That was the plan all along," manager A.J. Hinch said before Tuesday's game against the Atlanta Braves at Truist Park. "That's a good first step to get a little bit more active. It's just step by step, put some building blocks together to get him back doing some baseball things, so that's good."

FOR THE FAM: Tigers' Reese Olson bounces back, gives family and friends a show in homecoming

The Tigers placed Báez on the injured list June 11 , retroactive to June 9, with lumbar spine inflammation. The 11-year MLB veteran received an injection last Friday to treat his lower back injury , an issue that has lingered for a couple of seasons. The Tigers haven't shared a timeline for when he's expected to return, but Báez seems to have avoided long-term injury.

When Báez landed on the injured list, he discussed returning for the second half of the season . The halfway point for the Tigers is June 27; the All-Star Game is July 16.

The Tigers need Báez for his defense.

TIGERS NEWSLETTER: The shortstop problem is even worse than you think

Fellow infielders Ryan Kreidler and Zach McKinstry have handled the workload at the shortstop position in Báez's absence, but Kreidler — in particular — has struggled on defense, making multiple mistakes within the past week.

Kreidler, 26, is hitting .167 (2-for-12) with two walks and four strikeouts in six games; McKinstry, 29, is hitting .183 (20-for-109) with 10 walks and 33 strikeouts in 48 games.

Báez is hitting .183 (34-for-186) with one home run, six walks and 42 strikeouts in 53 games, spanning 196 plate appearances. He has been worth minus-4 defensive runs saved and minus-3 outs above average, but he is by far the most fundamentally sound defender in the infield.

"He's a veteran guy who has played in every situation," Hinch said of Báez's defense. "The good version of him is incredibly competitive to the day to day, especially on the defensive side, but we don't have him. I don't really spend a lot of time thinking about what could have been when he's not here. We can make the plays while he's gone and getting better."

Báez is making $25 million this season ahead of $73 million in 2025-27 to complete a six-year, $140 million contract he signed with the Tigers in December 2021.

[ MUST LISTEN: Make "Days of Roar" your go-to Detroit Tigers podcast, available anywhere you listen to podcasts ( Apple , Spotify ) ]

Alex Faedo ready for rehab assignment

Right-handed reliever Alex Faedo (right hip inflammation) is scheduled to begin a rehab assignment Wednesday with Triple-A Toledo. The 28-year-old landed on the injured list June 5 , then completed bullpen sessions last Wednesday and Sunday to set him up for his first rehab outing.

The Mud Hens are playing against the St. Paul Saints, an affiliate of the Minnesota Twins, in St. Paul, Minnesota.

BOYS OF SUMMER: Tigers fans complete journey across the country that began in 1992: 'We've done it'

Faedo has a 3.38 ERA with 13 walks and 29 strikeouts across 34⅔ innings in 21 relief appearances this season. He recently implemented new exercises to keep his pelvis in a neutral position and avoid further injury.

#Tigers medical update: Javier Báez (lumbar spine inflammation) has initiated light hitting drills as part of his return-to-play program. pic.twitter.com/pB4b92BU6H — Evan Petzold (@EvanPetzold) June 18, 2024

Contact Evan Petzold at  [email protected]  or follow him  @EvanPetzold .

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European Championship

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Portugal vs Czech Republic live updates: Francisco Conceicao scores injury-time Euro 2024 winner

The Briefing: Lacking, lucky and look who’s burst onto the scene

All eyes were on Ronaldo — but instead it was Czech Republic who took the lead, with yet another strike from outside the box; the 11th of this tournament.

Portugal were handed a huge slice of luck when Robin Hranac turned into his own net seven minutes after going behind.

And then arrived Francisco Conceicao .

Our own Tim Spiers , Tom Burrows and Sam Lee take us through all the key talking points.

Portugal 2 Czech Republic 1: Dramatic late winner boosts Cristiano Ronaldo and Co

Disappointment for dogged Czechs

Getty Images

In a defensive display, the physically imposing Czech Republic soaked up Portuguese pressure for much of the contest played in the pouring rain at Leipzig.

Ivan Hasek, who only returned to manage his country for a second spell in January, set his team up in a conservative 5-3-2 formation against their opponents filled with a cast of stellar names.

Although Portugal dominated possession, they were never banging on the door and in the end, Portugal’s equaliser came via a huge slice of luck as goalkeeper Jindrich Stanek parried the slippery ball onto the knee of Robin Hranac and into the net.

How did Ronaldo do?

Like it or not, Cristiano Ronaldo is still the name on everyone’s lips when it comes to this Portugal team. The number of fans with his name on their shirt outnumber other players by about 10 to one, his name was roared with the volume of a goal when the line-ups were read out and they cheered his every touch in the warm up. The cult of Ronaldo is alive and well.

But now that he’s 39 years old and plays in Saudi Arabia, aka the 27th best league in the world, could he still cut it at an international tournament?

Well, he was far more involved in the game than he was during the 2022 World Cup, when he was so ineffective he was dropped. He was also, quite clearly, the team’s leader and talisman.

Were Portugal any good?

It is nice to know that it’s not just England who seem to have problems fitting their quality players into a coherent system.

Portugal picked up a morale-boosting late victory and showed that they have enough options (quality on the bench, versatility on the pitch) to find different solutions, and more will be expected of them after finding a way to get over the line.

But a little like England, it was far from the most convincing opening victory.

They dominated the game, which Czech Republic were happy enough with, but they never really clicked despite deploying an admirably fluid system.

'Fabulous' Ronald has still got it

There was also a chance for Ivan Hasek to praise the impact of Cristiano Ronaldo — just in case anyone was starting to consider the fact his powers might be waning. The Czech coach told UEFA :

💬 “It is really unbelievable how dangerous a player Cristiano is in every game, at his age. He showed his genius again, he knows how to get involved in chances.

“My hat goes off to him; he is one of the best players in football history. Truly a fabulous man.”

Hasek: 'We will need to improve'

It’s an opening defeat for Czech Republic , with games against Turkey and Georgia to come in Group F. Here’s how their head coach, Ivan Hasek , saw the result tonight, speaking to UEFA :

💬 “I have to admit it is a big pity that we did not finish our work; it was close. We made it very difficult for Portugal, one of the best teams in the world.

“We are all disappointed to have conceded in added time. We have to put it behind us very quickly, as in four days we will play a key game. We will need to improve.”

That key game coming up next is against Georgia on Saturday.

A learning experience for Czech Republic

By the way, there should be a little leeway for Czech Republic. Although the starting XI averaged 27.6 years old, the squad is actually the youngest at the tournament. Here are the five youngest squads at Euro 2024:

• 1: Czech Republic — 25.5 years
• 2: Turkey — 25.8 years
• 3: England — 26.1 years
• 4: Netherlands — 26.3 years
• 5: Ukraine — 26.3 years

And no, it’s unlikely England will get any leeway for featuring third in that list. As for the five oldest squads, they are:

• 1: Germany — 28.6 years
• 2: Scotland — 28.3
• 3: Poland — 27.8
• 4: Denmark — 27.7
• 5: Switzerland — 27.7

Those who brought the experience

The Athletic

I know what you’re thinking…

"But Michael, who were the other golden oldies to feature in European Championships of yore?"

Well, we’ve got a graphic for that. And here it is.

A first look at Group F

And with that, we’ve now had a look at every team at Euro 2024. I’ll let you think on which team impressed you most and who left you cursing their unconvincing start.

Today it was Group F ’s turn. Here’s how the table looks after those opening games today, with Turkey beating Georgia 3-1 in Dortmund earlier.

Pepe celebrates record as the Euros' best

The omnipresent Portugal defender, Pepe . All hail another landmark.

Tonight, Pepe became the oldest player to appear at a European Championship. He's 41 years old.

How did he celebrate? He won possession 11 times, which was more than any other player during the opening group games of Euro 2024.

Who knows when he'll stop playing. You wouldn't catch me guessing.

This is why Bruno shone

X/OptaAnalyst

This is a great one from Opta Analyst . No player in the opening round of Euro 2024 group games was involved in more open-play shot sequences than Bruno Fernandes tonight.

That means taking a shot, creating a chance or having a role in the build-up to a shot.

Fernandes had 11 of them, and this shows the breakdown.

Another landmark substitution

Not only did Francisco Conceicao score after just 111 seconds of coming on.

He also became the first Portugal player to score as a substitute at the European Championship since Eder… who won the 2016 final against France.

Nice stuff, Chico.

No taking Provod's big moment away

It was overtaken in the end, but it really was a lovely moment for Slavia Prague midfielder Lukas Provod , when he opened the scoring tonight.

He missed Euro 2020 with an ACL injury, studied for an economics degree during his recovery, and put his country ahead in their Euro 2024 opener with a fabulous goal.

Full-time stats zone

It's hard to look at these numbers and think Portugal deserved anything but to win tonight. Here they are...

FT: Portugal 2-1 Czech Republic

• Possession: 74% — 26%
• Shots: 19 — 5
• On target: 8 — 1
• XG: 1.74 — 0.43
• Big chances: 4 — 0
• Blocked shots: 7 — 2
• Duels won: 49 — 38
• Dispossessed: 6 — 4

We did think Portugal would come through in the end, and they did. But on that showing, I would probably have a couple of others squads ahead of them in the pecking order to win Euro 2024 (he says, getting completely ahead of himself).

Ronaldo still a chief threat

Cristiano Ronaldo was involved too. He had the highest individual xG of any player and more shots than anyone else (5). Although the latter can clearly influence the former.

But it was Chico Conceicao who had the largest xG. A whopping 0.72 in fact, for just a few minutes of action — and becoming the matchwinner as a result.

That's what it meant

He may be getting on a bit, but it is fair to say Cristiano Ronaldo enjoyed that finale.

How to win it in a matter of seconds

Francisco Conceicao was on the pitch for 111 seconds, and scored with just his second touch.

How about that for efficiency?

A double sub for the ages

Incredible impact from the two subs - Pedro Neto's cross, Francisco Conceicao's finish.

There were SIX attacking players - Diogo Jota, Pedro Neto, Francisco Conceicao, Cristiano Ronaldo, Bruno Fernandes and Bernardo Silva - on the pitch at the end there.

And that’s it. The final whistle goes and Portugal find a way. Just about.

How Portugal finally took the lead

90+2' Portugal 2-1 Czech Republic

It’s a fabulous touch and a composed finish from Francisco Conceicao and made by Pedro Neto, who had only come on a few minutes earlier too.

But there is also big help from Hranac again, as he slips and Neto’s cross is popped on a plate for Conceicao.

The scorer is booked for his celebrations, as the shirt swiftly comes off.