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Free Math Worksheets — Over 100k free practice problems on Khan Academy

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• Addition and subtraction
• Place value (tens and hundreds)
• Addition and subtraction within 20
• Addition and subtraction within 100
• Addition and subtraction within 1000
• Measurement and data
• Counting and place value
• Measurement and geometry
• Place value
• Measurement, data, and geometry
• Add and subtract within 20
• Add and subtract within 100
• Add and subtract within 1,000
• Money and time
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• Intro to multiplication
• 1-digit multiplication
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• Understand fractions
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• Units of measurement
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• Add decimals
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• Multi-digit multiplication and division
• Divide fractions
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• Divide decimals
• Powers of ten
• Coordinate plane
• Algebraic thinking
• Converting units of measure
• Properties of shapes
• Ratios, rates, & percentages
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• Negative numbers
• Properties of numbers
• Variables & expressions
• Equations & inequalities introduction
• Data and statistics
• Negative numbers: addition and subtraction
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• Fractions, decimals, & percentages
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• Foundations
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• Expressions with exponents
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• Algebra foundations
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• Study design
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• Scatterplots
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• Inference comparing two groups or populations
• Chi-square tests for categorical data
• More on regression
• Prepare for the 2020 AP®︎ Statistics Exam
• AP®︎ Statistics Standards mappings
• Polynomials
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• Limits and continuity
• Derivatives: definition and basic rules
• Derivatives: chain rule and other advanced topics
• Applications of derivatives
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• Applications of integrals
• Differentiation: definition and basic derivative rules
• Differentiation: composite, implicit, and inverse functions
• Contextual applications of differentiation
• Applying derivatives to analyze functions
• Integration and accumulation of change
• Applications of integration
• AP Calculus AB solved free response questions from past exams
• AP®︎ Calculus AB Standards mappings
• Infinite sequences and series
• AP Calculus BC solved exams
• AP®︎ Calculus BC Standards mappings
• Integrals review
• Integration techniques
• Thinking about multivariable functions
• Derivatives of multivariable functions
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• Integrating multivariable functions
• Green’s, Stokes’, and the divergence theorems
• First order differential equations
• Second order linear equations
• Laplace transform
• Vectors and spaces
• Matrix transformations
• Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

Math Worksheets	Khan Academy
Math worksheets take forever to hunt down across the internet	Khan Academy is your one-stop-shop for practice from arithmetic to calculus
Math worksheets can vary in quality from site to site	Every Khan Academy question was written by a math expert with a strong education background
Math worksheets can have ads or cost money	Khan Academy is a nonprofit whose resources are always free to teachers and learners – no ads, no subscriptions
Printing math worksheets use up a significant amount of paper and are hard to distribute during virtual learning	Khan Academy practice requires no paper and can be distributed whether your students are in-person or online
Math worksheets can lead to cheating or a lack of differentiation since every student works on the same questions	Khan Academy has a full question bank to draw from, ensuring that each student works on different questions – and at their perfect skill level
Math worksheets can slow down student learning since they need to wait for feedback	Khan Academy gives instant feedback after every answer – including hints and video support if students are stuck
Math worksheets take up time to collect and take up valuable planning time to grade	Khan Academy questions are graded instantly and automatically for you

What do Khan Academy’s interactive math worksheets look like?

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Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

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Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

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Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

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There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Problem Solving. In the right column below are links to related online activities, videos and teacher resources. A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.
: Add up a sequence of consecutive numbers. Can you find a quick way to do it? : Can you write an ex : How many different shapes with an area of 2 square units can you make by joining dots on this grid with straight lines? : Use only the 1, 5 and 0 keys on a calculator to make given totals. : By how much would the area of this triangle increase if its base was enlarged to 8cm? : Work out the contents and the cost of the Christmas boxes from the given clues. : A game in which players take turns to add a single-digit number to what is already in the calculator. The winner is the player who makes the display show 30. : Calculate the total cost of four cars from the information given. : Work out the number of chin ups the characters do on the last day of the week give information about averages. : Work out the total cost of five Christmas presents from the information given. : Can you use the digits on the left of this clock along with any mathematical operations to equal the digits on the right? : A puzzle about the number of coins on a table given information about fractions of them. : Three consecutive numbers multiplied together give a given product. Pupils are asked to figure out what the numbers are. : Which three consecutive numbers multiplied together give the given answer. : How did the clock break if the numbers on each of the pieces added up to the same total? : What numbers should be on each face of the two cubes to make this perpetual calendar? : Determine whether the given nets would fold to produce a dice. : Arrange the digits 1 to 6 to make a three digit number divided by a two digit number giving a one digit answer. : Fit families onto eleven seater buses without splitting up the families. : Find out which of the calculator keys is faulty from the given information. A mathematical puzzle requiring good problem solving strategies. : Add up the answers to the four real life questions. : An activity involving a broken calculator which is missing the four button. Can you evaluate the given expressions without using the four? : Which of the numbers from one to twenty can you make with the digits 4, 5, 6 and 7? : A clock face containing only the number 4. Can you make a clock face containing any other single number? : Figure out which numbers will complete the sentences in the frame correctly. : Find symmetric words in this ancient cipher. : The height of this giraffe is three and a half metres plus half of its height. How tall is the giraffe? : If all the students in this room shook hands with each other, how many handshakes would there be altogether? : A little lateral thinking will help you solve this number puzzle. : How many Triangles can you find in the diagram? : How many triangles are hidden in the pattern? What strategy might you use to count them all to ensure you don't miss any out? : Find a systematic way of counting the number of triangles in the given diagram. : Find a word whose letters would cost exactly ninety nine pence. : Find the weight of one cuboid (by division) of each colour then add your answers together. : Work out what the calculations might be from the letter clues. : A lamp and a bulb together cost 32 pounds. The lamp costs 30 pounds more than the bulb. How much does the bulb cost? : A classic matchstick puzzle designed to challenge your spacial awareness. : Find which digits are missing from the randomly generated calculations. : A puzzle about a restaurant bill. Exactly where did the missing pound go? : Arrange the digits one to nine to make a correct addition calculation. : Arrange the numbers 1-9 to make three 3 digit numbers that add up to 999. : This activity requires eight students to sit non consecutively on a grid of chairs. : How many ways can you write an expression for 100 which only uses the same digit repeated and any operations? : Work out the least amount of time for four people to walk through a tunnel? : Two questions involving estimating a quantity. : Five numbers are added together in pairs and the sums shown. What might the five numbers be? : Arrange numbers on the plane shaped grid to produce the given totals : If six girls can plant 90 trees in a day. How many trees can ten girls plant in a day? The unitary method. : Arrange the numbers to produce the largest product. : Arrange numbers at the bottom of the pyramid which will give the largest total at the top. : There are some rabbits and chickens in a field. Calculate how many of each given the number of heads and feet. : Use the weights of the trains to work out the weight of a locomotive and a coach. A real situation which produces simultaneous equations. : Find a calculation for the current year which uses all of the digits 1 to 9. : Go around the roundabout performing each of the operations. Which starting point gives the largest answer? : Can you draw 4 straight lines, without taking your pencil off the paper, which pass through all 9 roses? : Work out the number of clowns and horses given the number of heads and feet. : A question which can be best answered by using algebra. : Make sums from the three digit numbers given. : Allow two trains to pass by using the limited amount of siding space. : Can you work out what each of the strange symbols represents in these calculations? : The classic game of Nim played with a group of pens and pencils. The game can be extended to the multi-pile version. : A problem which can best be solved as a pair of simultaneous equations. : An activity involving a calculator which is missing the six button. Can you evaluate the given expressions without using the six? : Arrange the digits one to nine in the grid so that they obey the row and column headings. : How many different ways can you spell out the word snowman by moving from snowflake to snowflake. : Arrange the numbers on the grid of squares so that the totals along each line of three squares are equal. : Arrange the numbers on the cards so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even. : Arrange the numbered trees so that adjacent sums are square numbers. : Separate three rows of three animals using three squares. : Use the information implied in the diagram to calculate the perimeter of this shape. : Which of the coloured stencils will fit over the numbered card to produce correct calculations? : Is it possible to work out the perimeter of this shape if not all the side lengths are given? : Interactive number-based logic puzzle similar to those featuring in The Times and Telegraph newspapers. : What are the numbers if their sum equals their product? : Each traffic sign stands for a number. Some of the sums of rows and columns are shown. What numbers might the signs stand for? : Arrange the numbers one to eight into the calculations to make the totals correct.. : Work out who is in which team from the information given. : How can you put the dice into the tins so that there is an odd number of dice in each tin? : In how many different ways might Tran decide to wear his hats in one week? : A tricky problem set on a coordinate grid. : Arrange the numbers 1 to 9 in a 3 by 3 grid so that none of the line totals are the same. : Each letter stands for a different digit. Can you make sense of this word sum?   ::  : Use a biased coin to obtain a fair result : Find the easy way to solve this kinematics problem involving a fly and two rhinos. : Use a process of elimination to work out the correct date from the clues given. : Find the dimensions of a cuboid matching the description given : Find the mathematical word from the cipher : Find the length of a rectangle enclosing the largest possible area. : The classic Fermi problem using standard estimation techniques : The hands of a clock are together at midnight. At what time are they next together? : What number is six times the sum of its digits? : Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads. : Find an arithmetic series and a geometric series that have the same sum of the first five terms. : Find ex Questions on the areas and perimeters of rectangles which will test your problem solving abilities. The short web address is: Pupils should be taught to solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why Pupils should be taught to use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling Pupils should be taught to solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes Pupils should be taught to solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign Pupils should be taught to solve problems involving number up to three decimal places Pupils should be taught to solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates Pupils should be taught to solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts Pupils should be taught to solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison Pupils should be taught to solve problems involving unequal sharing and grouping using knowledge of fractions and multiples. Pupils should be taught to find pairs of numbers that satisfy an equation with two unknowns Pupils should be taught to solve problems involving addition, subtraction, multiplication and division Pupils should be taught to use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. Pupils should be taught to solve problems which require answers to be rounded to specified degrees of accuracy 'Starter of the Day' page by Fiona Bray, Cams Hill School: "This is an excellent website. We all often use the starters as the pupils come in the door and get settled as we take the register." Comment recorded on the 'Starter of the Day' page by M Chant, Chase Lane School Harwich: "My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million." Comment recorded on the 'Starter of the Day' page by Mike Sendrove, Salt Grammar School, UK.: "A really useful set of resources - thanks. Is the collection available on CD? Are solutions available?" Comment recorded on the 'Starter of the Day' page by Inger Kisby, Herts and Essex High School: "Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work." Comment recorded on the 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it! Thanks" Comment recorded on the 'Starter of the Day' page by Mr Stoner, St George's College of Technology: "This resource has made a great deal of difference to the standard of starters for all of our lessons. Thank you for being so creative and imaginative." Comment recorded on the 'Starter of the Day' page by Angela Lowry, : "I think these are great! So useful and handy, the children love them. Could we have some on angles too please?" Comment recorded on the 'Starter of the Day' page by Julie Reakes, The English College, Dubai: "It's great to have a starter that's timed and focuses the attention of everyone fully. I told them in advance I would do 10 then record their percentages." Comment recorded on the 'Starter of the Day' page by S Johnson, The King John School: "We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory." Comment recorded on the 'Starter of the Day' page by Judy, Chatsmore CHS: "This triangle starter is excellent. I have used it with all of my ks3 and ks4 classes and they are all totally focused when counting the triangles." Comment recorded on the 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School: "My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions." Comment recorded on the 'Starter of the Day' page by L Smith, Colwyn Bay: "An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!" Comment recorded on the 'Starter of the Day' page by Mr Jones, Wales: "I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!" Comment recorded on the 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast: "My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please." Comment recorded on the 'Starter of the Day' page by S Mirza, Park High School, Colne: "Very good starters, help pupils settle very well in maths classroom." Comment recorded on the 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 'Starter of the Day' page by Carol, Sheffield PArk Academy: "3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!" Comment recorded on the 'Starter of the Day' page by Busolla, Australia: "Thank you very much for providing these resources for free for teachers and students. It has been engaging for the students - all trying to reach their highest level and competing with their peers while also learning. Thank you very much!" Comment recorded on the 'Starter of the Day' page by Ros, Belize: "A really awesome website! Teachers and students are learning in such a fun way! Keep it up..." Comment recorded on the 'Starter of the Day' page by Peter Wright, St Joseph's College: "Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities. Thanks for such a great resource!" Comment recorded on the 'Starter of the Day' page by Liz, Kuwait: "I would like to thank you for the excellent resources which I used every day. My students would often turn up early to tackle the starter of the day as there were stamps for the first 5 finishers. We also had a lot of fun with the fun maths. All in all your resources provoked discussion and the students had a lot of fun." Comment recorded on the 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks." Comment recorded on the 'Starter of the Day' page by Greg, Wales: "Excellent resource, I use it all of the time! The only problem is that there is too much good stuff here!!" Comment recorded on the 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon: "Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated." Comment recorded on the 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun." Comment recorded on the 'Starter of the Day' page by Amy Thay, Coventry: "Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils. Thanks again" Comment recorded on the 'Starter of the Day' page by Mrs Johnstone, 7Je: "I think this is a brilliant website as all the students enjoy doing the puzzles and it is a brilliant way to start a lesson." Comment recorded on the 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy: "I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson." Comment recorded on the 'Starter of the Day' page by Mr Smith, West Sussex, UK: "I am an NQT and have only just discovered this website. I nearly wet my pants with joy. To the creator of this website and all of those teachers who have contributed to it, I would like to say a big THANK YOU!!! :)." Comment recorded on the 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull: "Dear Transum, I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"	What good is being a master of calculation if you cannot apply your skills to problem solving? This topic provides lots of examples, activities and situations in which pupils can practise their problem solving skills. : How many two-scoop ice creams can you make from the given flavours? : How close can you get to the target by making a calculation out of the five numbers given? : A step by step guide showing how to solve a Word Sum where each letter stands for a different digit. : This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers. : Questions on the areas and perimeters of rectangles which will test your problem solving abilities. : Online, interactive jigsaw puzzles of grids of numbers. : How many two-scoop ice creams can you make from the given flavours? : Interactive jigsaw puzzles of different types of grids containing prime numbers. : Arrange the given number tiles to make two 2 digit numbers that add up to the given total. : A puzzle requiring the arrangement of numbers on the function machines to link the given input numbers to the correct output. : Some of the buttons are missing from this calculator. Can you make the totals from 1 to 20? : Use the pieces of the tangram puzzle to make the basic shapes then complete the table showing which shapes are possible. : Find the consective numbers that are added or multiplied to give the given totals : Arrange the given digits to make three numbers such that the third is the product of the first and the second. : Arrange the given digits to make three numbers such that two of them add up to the third. : An online interactive jigsaw puzzle of a grid of Roman numerals. : Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible. : Use the number clues to answer the seasonal questions about the five festive figures. : Find the expression from a series of guesses and clues. : Find the missing numbers in these triangular, self-checking puzzles and discover the wonders of these fascinating structures. : Ten balance puzzles to prepare you for solving equations. : Work out how many items were bought from the information given. : A self marking set of ten mathematical questions about a clock which cracked! : Arrange the given digits to make six 3-digit numbers that combine in an awesome way. : A drag and drop activity challenging you to arrange the digits to produce the largest possible product. : Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams. : Arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same. : Each row, column and diagonal should produce the same sum. : Arrange the digits 1 to 9 on the triangle so that the sum of the numbers along each side is equal to the given total. : The students numbered 1 to 8 should sit on the chairs so that no two consecutively numbered students sit next to each other. : Use the pieces of the T puzzle to fit into the outlines provided. A drag, rotate and drop interactive challenge. : The Transum version of the traditional sliding tile puzzle. : Divide the grid into rectangular pieces so that the area of each piece is the same as the number it contains. : Arrange the cards to create a valid mathematical statement. : Solve multi-step problems in contexts, deciding which operations and methods to use and why. : Can you determine the unique digits that will complete these factor trees? : A self marking step by step approach to calculating the number of triangles in a design. : Use the digits 1 to 9 to make three 3 digit numbers which add up to 999. : Can you arrange all of the counters on the grid to form 10 lines of three counters? : Arrange the numbers from 1 to 9 to make an expression with a value of 100. : Find a strategy to figure out the values of the letters used in these calculations. : Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills. : Help the cops catch the robbers by finding the vectors that will end the chase. : Can you make four litres if you only have seven and five litre jugs? : Can you get your car out of the very crowded car park by moving other cars forwards or backwards? : Find expressions using only one digit which equal the given targets. : Move the trams to their indicated parking places in the shunting yard as quickly as possible. : Calculate the missing numbers in these partly completed pyramid puzzles. : Find where the mines are hidden without stepping on one. : Find the five numbers which when added or multiplied together in pairs to produce the given sums or products. : A different way to complete a Sudoku puzzle with clues available at every stage. : If you were to pick up the sticks from this pile so that you were always removing the top stick what calculation would you create? : Solve this deduction logic puzzle to find who, where and what. : Arrange numbers on the plane shaped grid to produce the given totals : The traditional River Crossing challenge. Can you do it in the smallest number of moves? : Arrange the numbered footballs on the goal posts to make three, 3-number products that are all the same. : A number arranging puzzle with seven levels of challenge. : Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target? : Toss the pancakes until they are neatly stacked in order of size. Find how to do this using the smallest number of moves. : Arrange the twelve pentominoes in the outline of a rectangle. : Find the hidden wallaby using the clues revealed at the chosen coordinates. : Arrange the nine pieces of the puzzle on the grid to make different polygons. : Ten questions which can be solved using the unitary method. : The six button has dropped off! How could these calculations be done using this calculator? : The classic hourglass puzzle; Time the boiling of an egg using only the two egg timers provided. : Arrange the numbers on the squares so that the totals along each line of three squares are equal. : An online interactive jigsaw puzzle of a grid of Thai number symbols. : Arrange the digits one to nine to make the four calculations correct. : Interactive number-based logic puzzles similar to those featuring in daily newspapers. : Find your way through the maze encountering mathematical operations in the correct order to achieve the given total. : Arrange the digits one to nine on the spaces provided to make two division calculations containing multiples of three. : A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid. : Arrange the sheep in the field according to the instructions. An introduction to loci. : An online interactive jigsaw puzzle of a grid of Chinese number symbols. : Partition numbers in different ways according to the clues given. The higher levels are quite hard! : Arrange the given numbers in a three by three grid to obtain the diagonal, row and column products. : This is an interactive version of the puzzle described by Henry Ernest Dudeney in The Canterbury Puzzles : Quite a challenging number placing puzzle involving fractions. : In how many different ways can the numbers be arranged to give the same totals? : Place the nine numbers in the table so they obey the row and column headings about the properties of the numbers. : Arrange the sixteen numbers on the four by four grid so that groups of four numbers in a pattern add up to the same total. : A jumbled moving-block puzzle cube is shown as a net. Can you solve it? : Like the magic square but all of the totals should be different. : An adventure game requiring students to solve puzzles as they move through the old mansion. : Decide which mathematical operation is required then use it to find the answers. : Arrange the numbers on the cards so that each of the three digit numbers formed horizontally are square numbers and each of the three digit numbers formed vertically are even. : Arrange the twelve numbers in the triangles on the hexagram so that the numbers in each line of five triangles add up to the same total. : Crack the code by replacing the encrypted letters in the given text. There are lots of hints provided about code breaking techniques. : Move the pieces of the tower from one place to another in the minimum number of moves. : Arrange the twelve numbers on the hexagram so that the numbers in each line add up to the same total. : Click on six fleur-de-lis to leave an even number in each row and column. : Drag the numbers into the red cells so that the sum of the three numbers in each row and each column is a prime number. : Arrange the numbers from 1 to 6 in the spaces to make the division calculation correct. : This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers. : Arrange the digits to make three 3 digit numbers such that the second is double the first and the third is three times the first. : A puzzle to find four different ways of making 900 by multiplying together three different numbers. : Solve the problem of getting four people through a tunnel with one torch in the minimum amount of time. : Arrange the sixteen numbers on the octagram so that the numbers in each line add up to the same total. : Some picture grid puzzles which can be solved by using simultaneous equations. : Figure out which numbers will complete the sentences in the frame correctly. A drag and drop activity. : Make a schedule for the 24-hour Darts Marathon which will take into account everyone's requests and keep everyone happy. : A mini adventure game containing maths puzzles and problems. Find your way through the maze of tunnels to find Goldberg's magic harpsicord. : Arrange the given numbers as bases and indices in the three-term sum to make the target total. : Solve the number puzzles drawn on the pavement of Trafalgar Square in London. : Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house. : Arrange a rota for the Scouts to travel in boats so that they are with different people each day. : Arrange the dominoes in seven squares. The number of dots along each side of the square must be equal to the number in the middle Finally there is , a set of 10 randomly chosen, multiple choice questions suggested by people from around the world. : Choose the amount of liquid from each bottle needed to make the watermelon grow as big as possible. : Two men and two boys want to cross a river and they only have one canoe which will only hold one man or two boys. : Investigate the ways of making up various postage amounts using 3p and 8p stamps. An online stamp calculator is provided for you to check your working. : Can you make four litres if you only have seven and five litre jugs? : Investigate the number of rectangles on a grid of squares. What strategies will be useful in coming up with the answer? : The classic hourglass puzzle; Time the boiling of an egg using only the two egg timers provided. : A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid. : Move the pieces of the tower from one place to another in the minimum number of moves. : Investigate the possibility of redesigning the Braille alphabet to make it easier to learn. : Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house. : Manipulate the Lissajou curve to produce a perfectly symmetrical (vertically and horizontally) infinity symbol. : A puzzle about a two digit number divided by the sum of its digits. : The Simpson's 26th season finale. 'Mathlete's Feat' is full of mathematical problems that Presh solves. : This video from Mind Your Decisions teaches a trick so you can solve the puzzle quickly. : Dividing by zero, zero divided by zero and zero to the power of zero - all pose problems! : A printable grid containing many copies of the design used in the shape counting Starter. : A printable grid containing many copies of the design used in the second shape counting Starter. : Six line drawings that may or may not be able to be traced without lifting the pencil or going over any line twice. : Can you find the solution to these Lemon Law challenges using a spreadsheet? : A worksheet containing many copies of the How Many Rectangles Starter diagram allowing students to record their findings. : Work out which digit each of the ten symbols represents from the six given calculations. : This worksheet extends the puzzle in the July 21st Starter of the Day. : A worksheet containing the grids to fill in for the Tools puzzles. : Each box represents a missing operation (add, subtract, multiply or divide). Can you work out what they are? : Put the numbers 1 to 5 in the bottom row of the pyramid then each other brick is the sum of the two below. Links to other websites containing resources for Problem Solving are provided for those logged into ' '. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below: The activity you are looking for may have been classified in a different way from the way you were expecting. You can search the whole of Transum Maths by using the box below.   Is there anything you would have a regular use for that we don't feature here? Please let us know. Arrange the dominoes in seven squares. The number of dots along each side of the square must be equal to the number in the middle The short web address is:
Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the page. A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.
Have today's Starter of the Day as your default homepage. Copy the URL below then select Tools > Internet Options (Internet Explorer) then paste the URL into the homepage field.   Wednesday, March 29, 2023 "This month we ran our puzzle and problem solving team competition amongst the different grades. We decided to improve from the traditional "hard maths" questions and have inquiry and thinking stations. This wasn't about who was the best at just Maths, it was about who was the best at doing Maths using all the MYP ATL Skills. Thanks again to the fantastic Transum.org site for the puzzles I used to create the stations. To mention a few brilliant aspects about using this site for Maths stations. On refreshing you get a new but similar puzzle, points are often generated, instructions included for staff to read and creative interactive levels you can adjust depending on the grade...Completely FREE!" Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. to enter your comments.

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The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

The problem	How to act out the problem
Gia has 6 apples. Jordan has 3 apples. How many apples do they have altogether?	Two students use counters to represent the apples. One student has 6 counters and the other student takes 3. Then, they can combine their “apples” and count the total.
Michael has 7 pencils. He gives 2 pencils to Sarah. How many pencils does Michael have now?	One student (“Michael”) holds 7 pencils, the other (“Sarah”) holds 2 pencils. The student playing Michael gives 2 pencils to the student playing Sarah. Then the students count how many pencils Michael is left holding.

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE :

• 8 Common Core math examples
• Tier 3 Interventions: A School Leaders Guide
• Tier 2 Interventions: A School Leaders Guide
• Tier 1 Interventions: A School Leaders Guide

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

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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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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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The links below take you to a selection of short problems based on UKMT junior and intermediate mathematical challenge questions. We have chosen these problems because they are ideal for consolidating and assessing subject knowledge, mathematical thinking and problem-solving skills. You may wish to use these as lesson starters, homework tasks, or as part of internal assessment exercises. Longer NRICH problems can be found on the Secondary Curriculum page.

Number - Short Problems

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Thinking Mathematically - Short Problems

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x^{\msquare}

\log_{\msquare}

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\nthroot[\msquare]{\square}

\le

\ge

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\cdot

\div

x^{\circ}

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\left(\square\right)^{'}

\frac{d}{dx}

\frac{\partial}{\partial x}

\int

\int_{\msquare}^{\msquare}

\lim

\sum

\infty

\theta

(f\:\circ\:g)

f(x)

▭\:\longdivision{▭}

\times \twostack{▭}{▭}

+ \twostack{▭}{▭}

- \twostack{▭}{▭}

\left(

\right)

\times

\square\frac{\square}{\square}

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x^{\msquare}

\log_{\msquare}

\sqrt{\square}

\nthroot[\msquare]{\square}

\le

\ge

\frac{\msquare}{\msquare}

\cdot

\div

x^{\circ}

\pi

\left(\square\right)^{'}

\frac{d}{dx}

\frac{\partial}{\partial x}

\int

\int_{\msquare}^{\msquare}

\lim

\sum

\infty

\theta

(f\:\circ\:g)

f(x)

- \twostack{▭}{▭}	\lt	7	8	9	\div	AC
+ \twostack{▭}{▭}	\gt	4	5	6	\times	\square\frac{\square}{\square}
\times \twostack{▭}{▭}	\left(	1	2	3	-	x
▭\:\longdivision{▭}	\right)	.	0	=	+	y

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Word Problems Teaching Resources

Browse maths word problems and word problem worksheets created by teachers for Australian teachers like you! This vast collection covers all four maths operations with problem-solving tasks that allow students to apply their maths skills to real-world problems!

From worksheets to task cards, this collection is full of Australian maths curriculum-aligned resources, ready for your classroom, your lesson plans and your students!

Curious about using word problems in your classroom? Read on for a primer from our teacher team, including a kid-friendly definition of the concept and tips to ensure your students succeed with word problems!

What Is a Word Problem? A Kid-Friendly Definition

No doubt you know the answer to this question, but would you know how to answer if a student asked? Here's a handy definition that you can use!

A word problem is a kind of maths problem that is presented in words instead of just numbers. Word problems require us to use our maths skills to solve real-life scenarios or situations.

A word problem usually includes a question or a scenario that needs to be solved using one of the four maths operations like addition, subtraction, multiplication or division.

How to Help Students Succeed With Word Problems

Word problems are a fantastic tool to help students build their problem-solving skills. So how do you set them up for success?

Our teacher team has a few tricks up our sleeve to ensure your students are able to translate their maths skills into real-world problem-solving situations.

1. Teach Key Word Problem Vocabulary

Word problems are full of, well, words that serve as cues for students to help them know which operations to apply. Make sure to explicitly teach students the words so they know the appropriate actions.

For example, if a student sees the term 'take away' in a word problem, they should know that subtraction is involved. Here are just a few other key word problem vocabulary terms:

• Increased by
• How much longer

You may want to create anchor charts as a class with some of these keywords so students have a handy reference.

2. Hand Out Highlighter Pens

Teach students to work through a word problem and highlight or underline the important information (such as what is being asked for), while they cross out redundant information and other bits that are not necessary.

This can help them focus on the key points that matter.

3. Teach the CUBES Strategy

This handy strategy is a favourite amongst our teacher team (you'll even find CUBES resources on our site!). CUBES stands for:

• C ircle all the numbers
• U nderline the question
• B ox the key words
• E valuate and write the equation
• S olve & check

4. Practise Creating Word Problems As a Class

Before you hand already crafted word problems to your students to solve, why not work together as a class to create some?

Take regular addition or subtraction problems from the many worksheets on Teach Starter, and turn them into word problems together so students can reverse engineer the process. Students can also draw a picture to illustrate the problem.

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Multiplication and Division Word Problems Task Cards (Facts of 2, 5 and 10)

Use a range of strategies ​​to solve multiplication and division problems with 2, 5 and 10 times tables.

Multi-Step Word Problem Cards (Division and Multiplication) - Year 5-6

Solve multi-step multiplication and long division word problems with a set of printable maths task cards.

Multiplication and Division Word Problems Task Cards (2-Digit by 1-Digit)

Use a range of strategies ​​to solve 2-digit by 1-digit multiplication and division problems that exceed the facts of the 12 times tables.

Money Task Cards - Multi-Step Word Problems

Practise solving money word problems with a printable set of multi-step word problem task cards.

Multi-Step Addition and Subtraction Word Problem Cards – Middle Primary

Solve multi-step addition and subtraction word problems with a set of printable maths task cards.

Open-Ended Maths Problem Solving Cards - Upper Primary

Boost your students’ problem-solving skills with rigorous open-ended maths problems for Year 5 and 6 students.

Maths Word Problem Match-Up Game - 0- 50 Division and Multiplication

Twenty word problem cards for division and multiplication using numbers 0-50.

Daily Problem-Solving - Multistep Word Problems for Year 2-3

Boost your students’ problem-solving skills with rigorous daily review of multi-step word problems for Years 2 and 3.

Daily Maths Word Problems - Year 5

A set of 20 problem solving questions suited to year 5 students.

Multiplication and Division Word Problems Task Cards (Facts of 1-12)

Use a range of strategies ​​to solve multiplication and division problems for times tables facts 1-12.

Soccer-Themed Maths Problem Solving Worksheets

Practise multiplication, division and problem solving skills with a high-interest soccer-themed scenario activity.

Word Problem Worksheets - Year 5 and Year 6

4 mixed operations word problem worksheets with answers.

Daily Maths Word Problems – Year 3

A set of 20 problem solving questions suited to year 3 students.

Maths Brain Teasers - Year 2 Word Problems

Challenge your year 2 students to solve these brain teasers with a set of 24 maths word problems.

Addition and Subtraction Word Problems - Match Game

Practise reading, modelling, and solving addition and subtraction word problems with a matching activity.

Addition and Subtraction Word Problem Task Cards (Numbers 10-50)

Use a range of addition and subtraction strategies to solve twenty word problems that contain numbers 10–50.

Daily Maths Word Problems - Year 6 (Worksheets)

A set of 20 problem-solving questions suited to year 6 students.

Daily Maths Word Problems - Year 4 (Worksheets)

A set of 20 problem-solving questions suited to year 4 students.

Word Problem Worksheet - Money

Money word problem worksheet with answers.

CUBES Classroom Display and Bookmark Set

Tackle word problems with this CUBES problem-solving classroom display and bookmark set.

Addition and Subtraction Word Problem Task Cards (Numbers 1-50)

Use a range of addition and subtraction strategies to solve twenty word problems that contain numbers 1–50.

Multiplication and Division Interactive PowerPoint

An engaging 64 slide interactive PowerPoint to use when learning about multiplication and division.

Open-Ended Maths Problem Solving PowerPoint - Lower Primary

A PowerPoint with 20 open-ended problem solving questions covering a range of mathematical concepts.

Class Carnival – Probability STEM Challenges

A set of four carnival-themed STEM challenges where students create fun games that incorporate probability.

Data Maths Investigation – Line Up the Coins

A mathematics investigation about data, embedded in a real-world context.

Pandora's Party Palace Maths Activity – Middle Years

16 mathematics problem solving task cards involving money in a real-world context.

Mixed Operations - Length Word Problems Worksheets

Solve multi-step length word problems with a printable pack of 3-act Maths Word Problem Worksheets.

Pandora's Party Palace Maths Activity – Lower Years

Pandora's Party Palace Maths Activity – Upper Years

Sixteen mathematics problem-solving task cards involving money in a real-world context.

Length Word Problems - Year 3 Maths Worksheet

Help your students relate addition and subtraction with length using a printable Measurement Word Problems Worksheet for Year 3.

Open-Ended Maths Problem Solving PowerPoint - Middle Primary

Open-ended Maths Problem Solving Cards - Middle Primary

A set of 20 open-ended problem solving cards covering a range of mathematical concepts.

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80 Math Riddles with Answers for All Ages

Math riddles are a delightful way to challenge your mind and have fun while learning. These clever puzzles combine logic and numbers, making you think outside the box to find the solution. Whether you’re a math enthusiast or simply enjoy a good brain teaser, this article has math riddles for everyone.

Solving math riddles offers numerous benefits beyond mere entertainment. They enhance problem-solving skills, critical thinking, and creativity. Regular engagement with riddles can boost your cognitive abilities, improving memory, attention, and overall mental agility. I’ve organized the 80 math riddles with answers for kids and adults in this article from easy to hard, allowing you to gradually increase the challenge and build your confidence. So get ready to explore these math riddles with answers and enjoy!

Easy Math Riddles

These easy math riddles are perfect for beginners or anyone looking for a quick mental exercise. They involve simple calculations and logical thinking.

Riddle 1: I am a number that is greater than 10 but less than 15. I am an odd number, and when you add my digits together, the sum is 6. What number am I?

• Explanation: 13 is greater than 10 and less than 15. It’s odd, and 1 + 3 = 4.

Riddle 2: If you have 5 apples and take away 2, how many apples do you have left?

• Explanation: This is a simple subtraction problem: 5 – 2 = 3

Riddle 3: What number do you get when you multiply all the numbers on a telephone’s number pad?

• Answer: Zero
• Explanation: A telephone’s number pad includes the number 0. Any number multiplied by 0 equals 0.

Riddle 4: If there are 6 oranges in a basket and you take away half, how many oranges are left?

• Explanation: Half of 6 is 3.

Riddle 5: I am the smallest two-digit number that is even. What number am I?

• Explanation: The smallest two-digit number is 10, and it’s even.

Riddle 6: If a train leaves New York at 9 AM and travels at 60 miles per hour, how far will it have traveled by 11 AM?

• Answer: 120 miles
• Explanation: The train travels for 2 hours (from 9 AM to 11 AM). Distance = Speed x Time, so 60 miles/hour x 2 hours = 120 miles.

Riddle 7: A farmer has 10 sheep, and all but 9 die. How many sheep are left?

• Explanation: This is a trick question. “All but 9 die” means 9 sheep survive.

Riddle 8: What is the next number in this sequence: 2, 4, 6, 8, …?

• Explanation: This is a sequence of even numbers, increasing by 2 each time.

Riddle 9: If you have 3 quarters, 2 dimes, and 1 nickel, how much money do you have in total?

• Answer: 95 cents
• 3 quarters = 3 x 25 cents = 75 cents
• 2 dimes = 2 x 10 cents = 20 cents
• 1 nickel = 1 x 5 cents = 5 cents
• Total = 75 + 20 + 5 = 95 cents

Riddle 10: If you cut a pizza into 8 slices and eat 3, what fraction of the pizza is left?

• You started with 8/8 (the whole pizza).
• Remaining pizza: 8/8 – ⅜ = ⅝

Intermediate Math Riddles

These riddles require a bit more brainpower and might involve some basic algebra or logical reasoning. Get ready to stretch your mathematical muscles!

Riddle 11: A man is twice as old as his son. In 20 years, the man will be 1.5 times as old as his son. How old are they now?

• Answer: The man is 40, and his son is 20.
• Let the son’s current age be “s” and the man’s current age be “m.”
• We know m = 2s
• In 20 years, the son will be s + 20, and the man will be m + 20
• We also know that in 20 years, m + 20 = 1.5(s + 20)
• Now we have two equations and two unknowns, so we can solve for s and m.
• Substitute m = 2s into the second equation: 2s + 20 = 1.5s + 30
• m = 2s = 40

Riddle 12: If a clock takes 5 seconds to strike 6 o’clock, how long will it take to strike 12 o’clock?

• Answer: 11 seconds
• Explanation: There are 5 intervals between 6 strikes. If it takes 5 seconds for 5 intervals, each interval is 1 second long. There are 11 intervals between 12 strikes, so it will take 11 seconds.

Riddle 13: Two numbers add up to 10 and multiply to give 24. What are the two numbers?

• Answer: 4 and 6
• Solve for x and y to find the answer.

Riddle 14: A lily pad doubles in size every day. If it takes 48 days for the lily pad to cover the entire pond, how long would it take to cover half the pond?

• Answer: 47 days
• Explanation: Since the lily pad doubles in size every day, it was half the size the day before it covered the whole pond.

Riddle 15: If you’re running a race and you pass the person in second place, what place are you in now?

• Answer: Second place
• Explanation: If you pass the person in second place, you take their position.

Riddle 16: A farmer has 17 sheep, and all but 8 die. How many sheep are left?

• Explanation: “All but 8 die” means 8 sheep survive.

Riddle 17: What is the next number in the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, …?

• Explanation: In the Fibonacci sequence, each number is the sum of the two preceding ones. 5 + 8 = 13

Riddle 18: If 3 cats can catch 3 mice in 3 minutes, how long will it take 100 cats to catch 100 mice?

• Answer: 3 minutes
• Explanation: If 3 cats catch 3 mice in 3 minutes, it means each cat can catch one mouse in 3 minutes. So, 100 cats can catch 100 mice simultaneously in 3 minutes.

Riddle 19: I am a three-digit number. My tens digit is 6 more than my ones digit, and my hundreds digit is 3 less than my tens digit. What number am I?

• Answer: 393
• Let the ones digit be represented by the variable “o.”
• The tens digit is “o + 6.”
• The hundreds digit is “(o + 6) – 3” which simplifies to “o + 3.”
• The three-digit number is represented as: 100(o + 3) + 10(o + 6) + o
• You can use trial and error or further algebraic manipulation to find the value of “o” that satisfies the conditions.

Riddle 20: There are 12 apples in a basket. You take away 3, your friend takes 4, and your sister takes 2. How many apples are left in the basket?

• Start with 12 apples.
• You take 3: 12 – 3 = 9
• Your friend takes 4: 9 – 4 = 5
• Your sister takes 2: 5 – 2 = 3

Challenging Math Riddles – Push Your Limits

Prepare to be truly challenged! These riddles demand advanced problem-solving skills, abstract thinking, and a deep understanding of mathematical concepts.

Riddle 21: A snail is at the bottom of a 30-foot well. Each day it climbs 3 feet, but at night it slips back down 2 feet. How many days will it take the snail to reach the top of the well?

• Answer: 28 days
• The snail makes a net progress of 1 foot each day (3 feet up – 2 feet down).
• After 27 days, it will have climbed 27 feet.
• On the 28th day, it climbs 3 feet and reaches the top before it can slip down at night.

Riddle 22: You have 12 identical-looking balls. One of them is either slightly heavier or lighter than the others. You have a balance scale and can only use it three times. How do you find the odd ball and determine if it’s heavier or lighter?

• Answer: This requires a strategic approach involving dividing the balls into groups and carefully analyzing the results of each weighing. The full solution is a bit lengthy to explain here, but you can find detailed explanations online by searching for “12 balls puzzle.”

Riddle 23: A man has to cross a river with a fox, a chicken, and a bag of grain. He can only take one item across at a time. If left unattended, the fox will eat the chicken, and the chicken will eat the grain. How can he safely transport everything across the river?

• Take the chicken across.
• Return alone.
• Take the fox across.
• Bring the chicken back.
• Take the grain across.
• Explanation: This is a classic logic puzzle. The key is to ensure that the fox and chicken, or the chicken and grain, are never left alone on either side of the river.

Riddle 24: What is the angle between the hour and minute hand of a clock at 3:15?

• Answer: 7.5 degrees
• At 3:15, the hour hand is a quarter of the way between 3 and 4.
• Each number on the clock represents 360/12 = 30 degrees.
• A quarter of the distance between 3 and 4 is 30/4 = 7.5 degrees.
• The minute hand is pointing directly at 3.
• The angle between the hands is 7.5 degrees.

Riddle 25: You have two ropes, each of which takes one hour to burn completely. They don’t burn at a consistent rate. How can you measure 45 minutes using only these two ropes and a lighter?

• Light both ends of rope #1 and one end of rope #2 simultaneously.
• When rope #1 burns out completely (after 30 minutes, since it’s burning from both ends), immediately light the other end of rope #2.
• Rope #2 was already half burned, and now with both ends lit, it will take 15 more minutes to burn completely.
• This gives you a total of 30 + 15 = 45 minutes.

Riddle 26: If you have 8 coins and one of them is counterfeit (slightly lighter than the others), how can you find the counterfeit coin using a balance scale only twice?

• Divide the coins into three groups: 3, 3, and 2
• If they balance, the counterfeit is in the group of 2
• If they don’t balance, the counterfeit is in the lighter group of 3
• Take the group that contains the counterfeit and divide it into 1, 1, and 1 (or 1 and 1 if you started with the group of 2)
• If they balance the remaining coin is the counterfeit
• If they don’t balance, the lighter coin is the counterfeit

Riddle 27: A train leaves Chicago traveling west at 50 mph. Another train leaves Los Angeles traveling east at 60 mph. If the distance between Chicago and Los Angeles is 2100 miles, how long will it take for the two trains to meet?

• Answer: 15 hours
• The combined speed of the two trains is 50 + 60 = 110 mph
• Time = Distance / Speed
• Time = 2100 miles / 110 mph = 19.09 hours (approximately)

Riddle 28: You have 5 bags of gold coins. One bag contains counterfeit coins that weigh slightly less than the real coins. You have a digital scale (not a balance scale). How can you determine which bag has the counterfeit coins in one weighing?

• Label the bags 1 through 5
• Take 1 coin from bag #1, 2 coins from bag #2, 3 coins from bag #3, and so on.
• Weigh all these coins together
• Calculate the expected weight if all coins were real
• Subtract the actual weight from the expected weight
• For example if the difference is 0.3 grams and each counterfeit coin is 0.1 grams lighter, then bag #3 has the counterfeit coins

Riddle 29: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?  

• Answer: 47 days  
• Explanation: If the patch doubles in size every day, it was half the size the day before it covered the entire lake

Riddle 30: There are five houses in a row, each of a different color. The five homeowners each drink a different beverage, smoke a different brand of cigarette, and keep a different pet.

• The Brit lives in the red house
• The Swede keeps dogs as pets
• The Dane drinks tea
• The green house is immediately to the left of the white house
• The green homeowner drinks coffee
• The person who smokes Pall Mall rears birds
• The owner of the yellow house smokes Dunhill
• The man living in the center house drinks milk  
• The Norwegian lives in the first house  
• The man who smokes Blends lives next to the one who keeps cats
• The man who keeps the horse lives next to the man who smokes Dunhill
• The owner who smokes Bluemasters drinks beer  
• The German smokes Prince
• The Norwegian lives next to the blue house
• The man who smokes Blends has a neighbor who drinks water  
• Question: Who owns the fish?  
• Answer: The German
• Explanation: This is a classic logic puzzle known as the Zebra Puzzle or Einstein’s Riddle. It requires careful deduction and organization of the clues to arrive at the solution. You can find various online resources and solvers to help you work through this puzzle.

Advanced Math Riddles – For the Math Masters

Prepare to be truly challenged! These riddles demand exceptional problem-solving skills, advanced mathematical knowledge, and the ability to think creatively. Good luck!

Riddle 31: You have a 3-gallon jug and a 5-gallon jug. You need to measure exactly 4 gallons of water. How can you do this using only these two jugs and an unlimited supply of water?

• Fill the 5-gallon jug completely.
• Pour water from the 5-gallon jug into the 3-gallon jug until it’s full. This leaves 2 gallons in the 5-gallon jug.
• Empty the 3-gallon jug.
• Pour the 2 gallons from the 5-gallon jug into the 3-gallon jug.
• Fill the 5-gallon jug completely again.
• Carefully pour water from the 5-gallon jug into the 3-gallon jug (which already has 2 gallons) until the 3-gallon jug is full. This will use 1 gallon from the 5-gallon jug.
• You are now left with exactly 4 gallons in the 5-gallon jug.

Riddle 32: What is the next number in this sequence: 1, 11, 21, 1211, 111221, …?

• Answer: 312211
• 1 is read as “one 1” which becomes 11
• 11 is read as “two 1s” which becomes 21
• 21 is read as “one 2, then one 1” which becomes 1211
• 1211 is read as “one 1, then one 2, then two 1s” which becomes 111221
• 111221 is read as “three 1s, then two 2s, then one 1” which becomes 312211

Riddle 33: Three friends are sharing a hotel room that costs $30 a night. They each pay $10. Later, the hotel manager realizes there was a discount and the room only costs $25. He gives the bellhop $5 to return to the friends. The bellhop keeps $2 for himself and gives each friend $1 back. Now each friend has paid $9, for a total of $27. The bellhop has $2. Where is the missing dollar?

• Answer: There is no missing dollar. This is a wordplay trick designed to create confusion.
• Explanation: The incorrect calculation adds the bellhop’s $2 to the $27 the friends effectively paid. The correct way to think about it is that the room cost $25, and the bellhop has $2, accounting for the original $27.

Riddle 34: A circular table has a radius of 5 feet. You want to place a circular tablecloth on it that hangs over the edge by 1 foot all around. What should be the diameter of the tablecloth?

• Answer: 12 feet
• The table’s diameter is 2 * radius = 2 * 5 feet = 10 feet
• The tablecloth needs to hang over by 1 foot on all sides, so add 2 feet to the diameter
• Tablecloth diameter = 10 feet + 2 feet = 12 feet

Riddle 35: You are given a chessboard with two opposite corners removed. You also have 31 dominoes, each of which can cover exactly two squares on the chessboard. Can you cover the entire modified chessboard with the dominoes? If not, why?

• Answer: No, you cannot.
• A standard chessboard has an equal number of black and white squares (32 each).
• Removing opposite corners removes two squares of the same color.
• Now you have an imbalance, for example 32 black squares and 30 white squares
• Each domino must cover one black and one white square
• You cannot cover the modified chessboard because there aren’t enough squares of one color to match the other
• What is the sum of all the numbers from 1 to 100?
• Answer: 5050
• Sum of 1 to n = n * (n + 1) / 2
• In this case, n = 100
• Sum = 100 * (100 + 1) / 2 = 5050

Riddle 37: You have a balance scale and 9 identical-looking coins. One of the coins is counterfeit and is slightly heavier than the others. What is the minimum number of weighings required to guarantee you can find the counterfeit coin?

• Divide the coins into three groups of three.
• If they balance, the counterfeit is in the third group
• If they don’t balance, the counterfeit is in the heavier group
• Take the group with the counterfeit coin and divide it into three individual coins
• If they don’t balance, the heavier coin is the counterfeit

Riddle 38: A clock loses 10 minutes every hour. If it is set correctly at 12:00 PM, what time will it show when the actual time is 3:00 PM?

• Answer: 2:30 PM
• From 12:00 PM to 3:00 PM, there are 3 hours
• The clock loses 10 minutes every hour, so in 3 hours it will lose 3 * 10 = 30 minutes
• Therefore it will show 3:00 PM – 30 minutes = 2:30 PM

Riddle 39: If you roll two standard six-sided dice, what is the probability of getting a sum of 7?

• There are 6 possible outcomes for each die, resulting in 6 * 6 = 36 total possible combinations
• The combinations that result in a sum of 7 are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
• There are 6 favorable outcomes
• Probability = Favorable outcomes / Total possible outcomes = 6 / 36 = ⅙

Riddle 40: A ladder 10 feet long leans against a vertical wall. The base of the ladder is 6 feet away from the wall. How high up the wall does the ladder reach?

• Answer: 8 feet
• c = hypotenuse (the ladder) = 10 feet
• a = distance from the wall = 6 feet
• b = height on the wall (what we need to find)
• 6² + b² = 10²
• 36 + b² = 100
• b = √64 = 8 feet

Expert-Level Math Riddles – Only for the True Masters

Brace yourself for the ultimate challenge! These riddles require exceptional mathematical prowess, a deep understanding of complex concepts, and the ability to think outside the box. Are you ready?

Riddle 41: You have 100 doors in a row that are all initially closed. You make 100 passes by the doors. On the first pass, you visit every door and toggle its state (if it’s closed, you open it; if it’s open, you close it). On the second pass, you visit every second door and toggle its state. On the third pass, you visit every third door, and so on. After 100 passes, which doors are open?  

• Answer: The doors that are open are those corresponding to perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
• Explanation: A door’s final state (open or closed) depends on how many times its state is toggled. A door is toggled once for each of its factors. Perfect squares have an odd number of factors, so they end up toggled an odd number of times, resulting in an open state.

Riddle 42: What is the smallest positive integer that is divisible by all the numbers from 1 to 10?

• Answer: 2520
• Explanation: This is the least common multiple of the numbers from 1 to 10. You can find it by prime factorizing each number and taking the highest power of each prime that appears in any of the factorizations.

Riddle 43: A group of friends went to a restaurant and agreed to split the bill equally. However, two of them forgot their wallets, so each of the remaining friends had to pay an extra $3. If the original bill was $60, how many friends were in the group initially?

• Let ‘x’ be the original number of friends.
• The original cost per person was 60/x.
• When two friends couldn’t pay, the cost per person increased to 60/(x-2).
• This increase was $3, so 60/(x-2) – 60/x = 3
• Solve for x to get x = 8

Riddle 44: If you have a rope that is long enough to wrap around the Earth’s equator (approximately 24,901 miles), and you want to raise the rope 1 foot off the ground all the way around, how much additional rope would you need?

• Answer: Approximately 6.28 feet (or 2π feet)
• The circumference of a circle is 2πr, where r is the radius
• Increasing the radius by 1 foot increases the circumference by 2π * 1 foot
• 2π * 1 foot ≈ 6.28 feet

Riddle 45: You are in a dark room with a deck of 52 cards. 13 cards are face up, and the rest are face down. You can’t see the cards, but you can rearrange them however you like. How can you divide the cards into two piles so that each pile has the same number of face-up cards?

• Count out 13 cards from the deck without looking at them.
• Flip all the cards in this pile over.
• Now you have two piles. The original pile and the new pile of 13 cards
• The new pile of 13 will now have 13-x face-up cards (since we flipped them all) and x face-down cards
• Both piles now have the same number of face-up cards (x and 13-x)

Riddle 46: What is the sum of the infinite series: ½ + ¼ + ⅛ + 1/16 + … ?

• The sum of an infinite geometric series is a / (1 – r) if |r| < 1
• Sum = (½) / (1 – ½) = 1

Riddle 47: A clock chimes once at 1 o’clock, twice at 2 o’clock, and so on. How many times will the clock chime in a 12-hour period?

• Sum = 12 * (12 + 1) / 2 = 78

Riddle 48: You have a 3-liter bottle and a 5-liter bottle. You need to measure exactly 4 liters of water. How can you do it?

• Fill the 5-liter bottle completely.
• Pour water from the 5-liter bottle into the 3-liter bottle until it’s full. This leaves 2 liters in the 5-liter bottle
• Empty the 3-liter bottle
• Pour the 2 liters from the 5-liter bottle into the 3-liter bottle
• Fill the 5-liter bottle completely again
• Carefully pour water from the 5-liter bottle into the 3-liter bottle (which already has 2 liters) until the 3-liter bottle is full. This will use 1 liter from the 5-liter bottle
• You are now left with exactly 4 liters in the 5-liter bottle

Riddle 49: What is the largest prime number less than 100?

• Explanation: A prime number is a whole number greater than 1 that has only two factors (divisors): 1 and itself

Riddle 50: You are given 12 balls and a balance scale. One of the balls is slightly heavier or lighter than the others, but you don’t know which. You are allowed to use the balance scale three times. How can you find the odd ball and determine whether it’s heavier or lighter?

Special Topics in Math Riddles – Explore New Dimensions

Delve into the fascinating world of specialized math riddles, where geometry, probability, and other captivating areas come into play. These riddles will expand your horizons and challenge your understanding of mathematical concepts.

Riddle 51: You have a square cake. How can you cut it into 8 equal pieces with only three straight cuts?

• Make two cuts across the cake, dividing it into 4 equal quadrants.
• Stack the 4 pieces on top of each other
• Make one cut through the center of the stack, dividing all 4 pieces in half
• Explanation: By stacking the pieces, you’re essentially treating them as a single entity, allowing you to divide them all in half with a single cut.

Riddle 52: You are given two hourglasses: one that runs for 4 minutes and one that runs for 7 minutes. How can you measure exactly 9 minutes using only these two hourglasses?

• Start both hourglasses simultaneously
• When the 4-minute hourglass runs out, immediately flip it over
• When the 7-minute hourglass runs out, flip the 4-minute hourglass over again (it will have 1 minute of sand remaining in the bottom)
• Let the 4-minute hourglass run out completely (this takes 1 minute)
• At this point, 8 minutes will have passed (7 minutes from the first run of the 7-minute hourglass + 1 minute from the second run of the 4-minute hourglass)
• Immediately flip the 7-minute hourglass over (it will have 1 minute of sand remaining in the bottom bulb)
• Let the 7-minute hourglass run out completely (this takes 1 minute)
• You have now measured a total of 9 minutes

Riddle 53: A man is looking at a portrait and says, “Brothers and sisters have I none, but that man’s father is my father’s son.” Who is in the portrait?

• Answer: His son
• Explanation:
• “Brothers and sisters have I none” means he’s an only child
• “My father’s son” must refer to himself, as he has no siblings
• So the statement simplifies to “That man’s father is me”
• Therefore the portrait is of his son

Riddle 54: You have a bag containing 5 red balls and 3 blue balls. You draw two balls from the bag without replacement. What is the probability that both balls are red?

• Answer: 5/14
• Probability of the first ball being red = 5 (red balls) / 8 (total balls)
• After taking out one red ball, there are 4 red balls and 7 total balls left
• Probability of the second ball being red = 4/7
• Probability of both events happening = (⅝) * (4/7) = 5/14

Riddle 55: A room has 4 corners. Each corner has a cat. Each cat sees 3 other cats. How many cats are there in the room?

• Explanation: This is a trick question designed to create confusion. Each cat in a corner sees the other 3 cats in the other corners

Riddle 56: You are given three boxes. One contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes are mislabeled so that no label accurately describes the contents of the box it’s on. You can open one box and, without looking inside, take out one piece of fruit. By looking at this piece of fruit, how can you immediately label all the boxes correctly?

• Open the box labeled “Apples and Oranges”
• Take out one piece of fruit without looking inside
• (since it’s mislabeled and can’t contain only oranges)
• The box labeled “Apples” must contain only oranges
• This box actually contains
• The box labeled “Oranges” must contain only apples
• Explanation: The key is to open the box labeled “Apples and Oranges” because it’s guaranteed to be mislabeled. The fruit you pick will reveal the true contents of that box, allowing you to deduce the contents of the other two boxes based on the mislabeling.

Riddle 57: A boat is traveling upstream on a river at a speed of 10 mph. The river’s current flows at a speed of 2 mph. How long will it take the boat to travel 24 miles upstream?

• Answer: 3 hours
• The boat’s effective speed upstream is its speed minus the current’s speed: 10 mph – 2 mph = 8 mph
• Time = 24 miles / 8 mph = 3 hours

Riddle 58: You are given a 1-meter-long ribbon, and each day you cut half of it away. How many days will it take for the ribbon to be shorter than 1 centimeter?

• Answer: 7 days
• Day 1: 1 meter / 2 = 0.5 meters (50 centimeters)
• Day 2: 0.5 meters / 2 = 0.25 meters (25 centimeters)
• Day 3: 0.25 meters / 2 = 0.125 meters (12.5 centimeters)
• Day 4: 0.125 meters / 2 = 0.0625 meters (6.25 centimeters)
• Day 5: 0.0625 meters / 2 = 0.03125 meters (3.125 centimeters)
• Day 6: 0.03125 meters / 2 = 0.015625 meters (1.5625 centimeters)
• Day 7: 0.015625 meters / 2 = 0.0078125 meters (0.78125 centimeters)

Riddle 59: In a group of 100 people, 90 people drink coffee, 80 people drink tea, and 75 people drink both. How many people drink neither coffee nor tea?

This can be solved using the Principle of Inclusion-Exclusion:

• Total = Coffee + Tea – Both + Neither
• 100 = 90 + 80 – 75 + Neither
• Neither = 100 – 90 – 80 + 75
• Neither = 5

Riddle 60: Imagine you’re standing at the center of a circular field. You walk halfway to the edge of the field and stop. You then turn 90 degrees to your right and walk in a straight line until you reach the edge of the field. How far did you walk in total (in terms of the field’s radius, ‘r’)?

• Answer: 1.5r
• You first walk halfway to the edge, covering a distance of r/2
• Then you walk along a radius of the circle, covering a distance of r
• Total distance = r/2 + r = 1.5r

Application-Based Riddles – Math in the Real World

These riddles put your mathematical thinking to the test in practical scenarios. Can you solve problems related to everyday situations and real-world applications of math?

Riddle 61: You’re planning a road trip that’s 500 miles long. Your car gets 25 miles per gallon, and gas costs $4 per gallon. How much will you spend on gas for the entire trip?

• Answer: $80
• Gallons needed = Total distance / Miles per gallon = 500 miles / 25 miles/gallon = 20 gallons
• Total cost = Gallons needed * Price per gallon = 20 gallons * $4/gallon = $80

Riddle 62: You have a recipe that calls for 2 cups of flour to make 12 cookies. How much flour would you need to make 30 cookies?

• Answer: 5 cups
• Flour per cookie = Total flour / Number of cookies = 2 cups / 12 cookies = ⅙ cup/cookie
• Flour for 30 cookies = Flour per cookie * Number of cookies = (⅙ cup/cookie) * 30 cookies = 5 cups

Riddle 63: A store is having a 30% off sale on all items. If you buy a shirt that originally costs $20, how much will you save?

• Discount = Original price * Discount percentage = $20 * 0.30 = $6

Riddle 64: You’re painting a rectangular wall that is 12 feet long and 8 feet high. A can of paint covers 400 square feet. How many cans of paint will you need to buy to paint the entire wall with two coats?

• Answer: 1 can
• Wall area = Length * Height = 12 feet * 8 feet = 96 square feet
• Total area to paint (with two coats) = Wall area * 2 = 96 square feet * 2 = 192 square feet
• Cans needed = Total area to paint / Coverage per can = 192 square feet / 400 square feet/can = 0.48 cans
• Since you can’t buy fractions of cans, you’ll need to buy 1 whole can

Riddle 65: You invest $1000 in a savings account that earns 5% interest annually. How much money will you have in the account after 2 years if you don’t withdraw any money?

• Answer: $1102.50
• Interest earned = Principal * Interest rate = $1000 * 0.05 = $50
• Total at the end of year 1 = Principal + Interest = $1000 + $50 = $1050
• Interest earned = New principal * Interest rate = $1050 * 0.05 = $52.50
• Total at the end of year 2 = New principal + Interest = $1050 + $52.50 = $1102.50

Riddle 66: You’re building a fence around a circular garden with a radius of 10 feet. How many feet of fencing will you need?

• Answer: Approximately 62.8 feet
• Circumference of a circle = 2πr, where r is the radius
• Circumference = 2 * π * 10 feet ≈ 62.8 feet

Riddle 67: You’re flying a kite, and the string makes a 45-degree angle with the ground. If you’ve let out 100 feet of string, how high is the kite flying?

• Answer: Approximately 70.7 feet
• This involves trigonometry. The height of the kite is the opposite side to the 45-degree angle
• sin(45 degrees) = Height / String length
• Height = sin(45 degrees) * 100 feet
• Height ≈ 0.707 * 100 feet ≈ 70.7 feet

Riddle 68: A train leaves Station A at 8:00 AM and travels at 40 mph towards Station B. Another train leaves Station B at 9:00 AM and travels at 60 mph towards Station A. If the distance between the two stations is 240 miles, at what time will the two trains meet?

• Answer: 10:24 AM
• The first train travels for one hour before the second train leaves, covering a distance of 40 miles
• The remaining distance is 240 – 40 = 200 miles
• The combined speed of the two trains is 40 + 60 = 100 mph
• Time to meet = Remaining distance / Combined speed = 200 miles / 100 mph = 2 hours
• The second train left at 9:00 AM, so they will meet 2 hours later at 11:00 AM
• However, we need to account for the fact that the first train had a 1-hour head start
• In that one hour, the first train covered ¼ of the remaining distance (40 miles out of 200 miles)
• So the trains will actually meet ¼ of the 2-hour duration earlier
• ¼ * 2 hours = 30 minutes
• Therefore they will meet at 11:00 AM – 30 minutes = 10:30 AM

Riddle 69: You have a rectangular garden that is 12 meters long and 8 meters wide. You want to create a diagonal path across the garden. How long will the path be?

• Answer: 4√13 meters (approximately 14.42 meters)
• The diagonal path divides the rectangle into two right-angled triangles
• The diagonal is the hypotenuse of these triangles
• Use the Pythagorean theorem: a² + b² = c²
• a = length = 12 meters
• b = width = 8 meters
• c = diagonal (what we need to find)
• 12² + 8² = c²
• 144 + 64 = c²
• c = √208 = √(16 * 13) = 4√13 meters

Riddle 70: You flip a fair coin three times. What is the probability of getting at least two heads?

• Probability = Favorable outcomes / Total possible outcomes
• Probability = 4 / 8 = ½

Real-Life Scenarios – Putting Math to Work

Math isn’t just about numbers and equations; it’s a powerful tool we use to solve problems and make sense of the world around us. These riddles will challenge you to apply your mathematical thinking to real-life situations.

Riddle 71: You’re planning a pizza party for 15 people, and you estimate each person will eat 3 slices. If a large pizza has 12 slices, how many large pizzas should you order?

• Total slices needed: 15 people * 3 slices/person = 45 slices
• Number of pizzas: 45 slices / 12 slices/pizza = 3.75 pizzas
• Since you can’t order fractions of pizzas, round up to the nearest whole number: 4 pizzas

Riddle 72: You want to tile a square bathroom floor that is 10 feet by 10 feet. Each tile is 1 foot by 1 foot. How many tiles will you need?

• Answer: 100
• Area of the bathroom floor: 10 feet * 10 feet = 100 square feet
• Number of tiles: Total area / Area per tile = 100 square feet / 1 square foot/tile = 100 tiles

Riddle 73: You’re driving at a speed of 60 miles per hour. How long will it take you to travel 300 miles?

• Answer: 5 hours
• Time = 300 miles / 60 miles/hour = 5 hours

Riddle 74: You have a rectangular garden that’s 20 meters long and 15 meters wide. You want to build a fence around it. How much fencing will you need?

• Answer: 70 meters
• Perimeter of a rectangle = 2 * (Length + Width)
• Perimeter = 2 * (20 meters + 15 meters)
• Perimeter = 2 * 35 meters = 70 meters

Riddle 75: You have a budget of $500 for groceries each month. You’ve already spent $320. How much money do you have left for the rest of the month?

• Answer: $180
• Money left = Total budget – Money spent
• Money left = $500 – $320 = $180

Riddle 76: You’re baking a cake and the recipe calls for ½ cup of sugar. You only have a ¼ cup measuring cup. How many times will you need to fill the ¼ cup to get ½ cup of sugar?

• Number of times = Desired amount / Measuring cup size
• Number of times = (½ cup) / (¼ cup) = 2

Riddle 77: You’re mixing paint and the instructions say to use a ratio of 3 parts blue to 2 parts yellow. If you use 9 cups of blue paint, how many cups of yellow paint will you need?

• Answer: 6 cups
• Ratio of blue to yellow = 3:2
• This means for every 3 cups of blue, you need 2 cups of yellow
• If you have 9 cups of blue, you have 3 groups of 3 cups
• Yellow paint needed = Number of groups * Yellow paint per group
• Yellow paint needed = 3 groups * 2 cups/group = 6 cups

Riddle 78: You’re planning a party and want to buy enough soda for everyone. Each person is expected to drink 2 cans of soda, and you’re expecting 25 guests. If soda comes in packs of 12, how many packs should you buy?

• Total cans needed: 25 guests * 2 cans/guest = 50 cans
• Number of packs: 50 cans / 12 cans/pack = 4.16 packs
• Round up to the nearest whole number: 5 packs

Riddle 79: You’re building a bookshelf and need to cut a piece of wood that’s 6 feet long into 1.5-foot pieces. How many pieces can you cut from the original piece of wood?

• Number of pieces = Total length / Length per piece
• Number of pieces = 6 feet / 1.5 feet/piece = 4 pieces

Riddle 80: You’re on a train that’s traveling at 80 miles per hour. If the next station is 200 miles away, how long will it take to reach the station?

• Answer: 2.5 hours
• Time = 200 miles / 80 miles/hour = 2.5 hours

We hope you’ve enjoyed this collection of math riddles, spanning from easy warm-ups to mind-bending challenges. Remember, solving riddles is not only fun but also a fantastic way to boost your critical thinking, problem-solving skills, and overall cognitive abilities.

Key Takeaways

• Math riddles offer a playful and engaging way to learn and practice mathematical concepts.
• They encourage creative thinking and the ability to approach problems from different angles.
• Solving riddles can enhance your logical reasoning and deduction skills.
• Regular practice with math riddles can improve your mental agility and overall brainpower.

Keep Exploring

Don’t stop here! There’s a vast world of math riddles waiting to be discovered. Challenge yourself with more complex puzzles, explore different areas of mathematics, and share your favorite riddles with friends and family.

• Riddles for Adults: Challenge your mind and have fun with our collection of riddles for adults . These brain teasers will keep you entertained for hours!
• Riddles for Kids: Keep your kids entertained and engaged with our fun and educational riddles for kids of all ages . These riddles are perfect for family gatherings, classrooms, or just a fun afternoon at home!

Further Resources

• Books: Numerous books are dedicated to math riddles and puzzles. Look for titles that cater to your skill level and interests.
• Websites and Apps: Many websites and apps offer a wide variety of math riddles and brain teasers. Some popular options include Braingle, Math Riddles and Puzzles, and the MentalUP app.
• Online Communities: Join online forums and communities where math enthusiasts share and discuss riddles. You can find new challenges, get help with solutions, and connect with like-minded individuals.

Frequently Asked Questions (FAQs)

Q: Why are math riddles beneficial for learning?

A: Math riddles go beyond rote memorization and encourage you to actively engage with mathematical concepts. They help develop problem-solving skills, critical thinking, and creativity. By presenting problems in a fun and challenging way, riddles make learning math more enjoyable and memorable.

Q: How can I improve my ability to solve math riddles?

A: Practice is key! Start with easier riddles and gradually progress to more challenging ones. Don’t be afraid to try different approaches and make mistakes. The more you expose yourself to various types of riddles, the better you’ll become at recognizing patterns, applying logic, and finding solutions.

Q: Can math riddles help me in my everyday life?

A: Absolutely! Math riddles enhance your problem-solving skills, which are valuable in various real-life situations. Whether you’re budgeting your finances, planning a trip, or tackling a DIY project, the ability to think critically and logically will always come in handy.

Q: Are there math riddles for specific topics like geometry or algebra?

A: Yes, math riddles cover a wide range of topics and difficulty levels. You can find riddles specifically focused on geometry, algebra, probability, and other areas of mathematics. Explore different types of riddles to deepen your understanding of specific mathematical concepts.

Q: Where can I find more math riddles?

A: There are numerous resources available online and offline. Look for math riddle books, websites, apps, and online communities. Many educational platforms also offer math riddles as part of their learning materials.

Q: Can I create my own math riddles?

A: Definitely! Creating your own math riddles is a great way to exercise your creativity and mathematical thinking. Start with simple concepts and gradually increase the complexity. Share your riddles with friends and family to challenge them and have fun together.

Remember, math riddles are not just about finding the right answer. They’re about the journey of discovery, the thrill of the challenge, and the satisfaction of unraveling a mathematical mystery. So keep exploring, keep learning, and most importantly, keep having fun with math!

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