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Change recurring decimals into their corresponding fractions and vica versa.

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Check that you know what inequality signs mean and how they are used to compare two quantities.

Choose the correct inequality or equals sign from the dropdown box between the two numbers.

If you make a mistake, click on the inequality/equals sign to make another choice.

Description of Levels

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Level 1 - Comparing positive integers

Level 2 - Comparing positive and negative decimal numbers

Level 3 - Comparing positive and negative fractions

Level 4 - Comparing metric measures

Level 5 - Matching statements to number line diagrams.

Level 6 - Solving linear inequalities.

Level 7 - Solving linear two part inequalities.

Level 8 - Matching statements to graphs.

Level 9 - Quadratic Inequalities

Linear Programming - A selection of linear programming questions with an interactive graph plotting tool.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

More on this topic including lesson Starters, visual aids and investigations.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Help

> means greater than (the number on the left of this sign must be more than the number on the right).

< means less than (the number on the left of this sign must be less than the number on the right).

= means equals (the number on the left of this sign must have the same value as the number on the right).

It is easier to compare two (fractions with quite different denominators) by converting them both to decimals. Do this by dividing the top (numerator) by the bottom (denominator).

1 kilometre (km) = 1000 metres (m)

1 metre (m) = 100 centimetres (cm)

1 centimetre (cm) = 10 millimetres (mm)

1 kilogram (kg) = 1000 grams (g)

1 litre (l) = 1000 millilitres (ml)

1 hour = 60 minutes

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Check that you know what inequality signs mean and how they are used to compare two quantities.

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Place the numbers in the correct sets in this concentric circles Venn diagram.

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Determine the upper and lower bounds when rounding quantities used in calculations.

This is level 2: quantities rounded to the nearest multiple. You can earn a trophy if you get at least 7 questions correct.

Description of Levels

Close

Level 1 - Numbers truncated or rounded up or down to a given multiple.

Level 2 - Quantities rounded to the nearest multiple.

Level 3 - Numbers rounded to a number of decimal places.

Level 4 - Discrete and continuous quantities rounded to a number of significant figures.

Level 5 - Mixed calculations involving upper and lower bounds.

Level 6 - Upper and lower bounds of algebraic expressions.

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Extension

Students who are also studying Physics may want to investigate a topic called Propagation of Uncertainties that uses these formulas.

$$ \text{If} \quad y= a \pm b \quad \text{then} \quad \Delta y = \Delta a + \Delta b $$ $$ \text{If} \quad y= \frac{ab}{c} \quad \text{then} \quad \frac{\Delta y}{y} = \frac{\Delta a}{a} + \frac{\Delta b}{b} + \frac{\Delta c}{c} $$ $$ \text{If} \quad y= a^n \quad \text{then} \quad \frac{\Delta y}{y} = \begin{vmatrix} n \frac{\Delta a}{a} \end{vmatrix} $$

The triangular symbols are the Greek letter delta and represent the errors or, more accurately, uncertainties.

Help Video

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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Determine the upper and lower bounds when rounding quantities used in calculations. This is level 2: quantities rounded to the nearest multiple. You can earn a trophy if you get at least 7 questions correct. Close Level 1 - Numbers truncated or rounded up or down to a given multiple.

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Spiral method of showing irrational numbers on number line, nth roots etc

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Use the concept to find 16th root of a number

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https://flexbooks.ck12.org/cbook/ck-12-cbse-math-class-9/section/1.2/primary/lesson/irrational-numbers/

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Year 2025: A Mathematical Marvel! 🤩✨ #2025 #mathlover #numbergame #cubequantumacademy

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A superb way for finding fractions of amounts including fractions of measures: cm, grams and ml. This teaching resource is ideal for mental maths sessions using an interactive whiteboard. It requires knowledge of tables. Ideal for SATs.

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A superb way for finding fractions of amounts including fractions of measures: cm, grams and ml. This teaching resource is ideal for mental maths sessions using an interactive whiteboard. It requires knowledge of tables. Ideal for SATs.

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Online Bingo number picker. Choose to show the numbers picked or mathematical expressions representing them.

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https://byjus.com/maths/quotient/

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Place the numbers in the rings so that the sum of the numbers in each ring is the same. Four numbers are already in the correct place and the ring sum is 11.

Olympic Projects and Investigations for the Keen Mathematical Athlete.

Optimal Running Strategy

Investigate different running strategies for a 400m race. Compare the times if an athlete starts fast and slows down, starts slow and speeds up, or maintains a constant speed. Use data from past Olympic races to support your analysis.

Cumulative Medals

For each day of the Olympics, record the total number of medals earned by your country. For each day work out the cumulative frequency and use these numbers to draw a cumulative frequency chart. Describe the features of your chart.

Impact of Altitude on Performance

Investigate how altitude affects athletic performance. Compare performances of athletes in high-altitude venues versus sea-level venues. Analyse data from events held in cities like Mexico City and compare it to events held in London.

Historical Performance Trends

Investigate the trends in world records over the past century in events like the 100m sprint and the long jump. Analyse how the records have improved and predict future records based on historical data.

Economics of Hosting the Olympics

Investigate the costs and benefits of hosting the Olympic Games. Compare the economic impact on cities that have hosted the games in the past 30 years. Analyse data on infrastructure spending, tourism revenue, and long-term benefits to the local economy.

Gender and Performance

Investigate the performance gap between male and female athletes in various Olympic events. Analyse data to see if the gap has been closing over the years and explore potential reasons for these trends.

Predicting Medal Counts

Use statistical models to predict the medal counts for different countries in the upcoming Olympics. Analyse factors such as past performance, current world rankings, and investment in sports programs.

Medals Pie Charts

Choose five countries that have had a wide range of success in the last Olympics. For each country manually draw a pie chart showing the proportion of gold, silver and bronze medals they won. Comment on what can be seen when comparing the pie charts.

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Arrange the digits one to nine to make a number which is divisible in the way described.

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Match the values and the units to the world records

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Match the values and the units to the world records

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The number of digits that are meaningful: they have an accuracy matching our measurements, or are simply all we need.

Example: we measure the garden to within 1 meter.
Our calculations give an area of 58.37215 m ²
But that is way more digits than our accuracy of measurement, so we decide to use 2 significant digits.
Our final result is (the two significant digits are 5 and 8).

More Examples:
* when we show a result like 4.500 we are saying we know it isn't 4.499 or 4.501
* but a number like 300 suggests we know it isn't 200 or 400

We can add a "plus/minus" (±) value to show our level of accuracy:
Example: 300 ± 10 says we know it is between 290 and 310

Have a play:

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The number of digits that are meaningful: they have an accuracy matching our measurements, or are simply all we need. Example: we measure the garden to within 1 meter. Our calculations give an area of 58.37215 m 2 But that is way more digits than our accuracy of measurement, so we decide to use 2 significant digits.

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https://www.mathsisfun.com/algebra/standard-form.html

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Use the exponent rules to prove logarithmic properties like Product Property, Quotient Property and Power Property. Learn the justification of these properties with ease!

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Practise using the quick ways to spot whether a number is divisible by the digits 2 to 9.

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Absolute and Relative Error and How to Calculate Them

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Absolute and Relative Error and How to Calculate Them

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Absolute, relative, and percent error are ways to measure the error of a measurement or calculation.

Absolute, relative, and percent error are the most common experimental error calculations in science. Grouped together, they are types of approximation error. Basically, the premise is that no matter how carefully you measure something, you'll always be off a bit due to the limitations of the measuring instrument. For example, you may be only able to measure to the nearest millimeter on a ruler or the nearest milliliter on a graduated cylinder. Here are the definitions, equations, and examples of how to use these types of error calculations.

Absolute Error

Absolute error is the magnitude (size) of the difference between a measured value and a true or exact value.
Absolute Error = |True Value - Measured Value|
Absolute Error Example:
A measurement is 24.54 mm and the true or known value is 26.00 mm. Find the absolute error.
Absolute Error = |26.00 mm - 25.54 mm|= 0.46 mm
Note absolute error retains its units of measurement.

The vertical bars indicate absolute value. In other words, you drop any negative sign you may get. For this reason, it doesn't actually matter whether you subtract the measured value from the true value or the other way around. You'll see the formula written both ways in textbooks and both forms are correct.

What matters is that you interpret the error correctly. If you graph error bars, half of the error is higher than the measured value and half is lower. For example, if your error is 0.2 cm, it is the same as saying ±0.1 cm.

The absolute error tells you how big a difference there is between the measured and true values, but this information isn't very helpful when you want to know if the measured value is close to the real value or not. For example, an absolute error of 0.1 grams is more significant if the true value is 1.4 grams than if the true value is 114 kilograms! This is where relative error and percent error help.

Relative Error

Relative error puts absolute error into perspective because it compares the size of absolute error to the size of the true value. Note that the units drop off in this calculation, so relative error is dimensionless (unitless).

Relative Error = |True Value - Measured Value| / True Value
Relative Error = Absolute Error / True Value

Relative Error Example:
A measurement is 53 and the true or known value is 55. Find the relative error.
Relative Error = |55 - 53| / 55 = 0.034
Note this value maintains two significant digits.

Note: Relative error is undefined when the true value is zero. Also, relative error only makes sense when a measurement scale starts at a true zero. So, it makes sense for the Kelvin temperature scale, but not for Fahrenheit or Celsius!

Percent Error

Percent error is just relative error multiplied by 100%. It tells what percent of a measurement is questionable.

Percent Error = |True Value - Measured Value| / True Value x 100%
Percent Error = Absolute Error / True Value x 100%
Percent Error = Relative Error x 100%

Percent Error Example:
A speedometer says a car is going 70 mph but its real speed is 72 mph. Find the percent error.
Percent Error = |72 - 70| / 72 x 100% = 2.8%

Mean Absolute Error

Absolute error is fine if you're only taking one measurement, but what about when you collect more data? Then, mean absolute error is useful. Mean absolute error or MAE is the sum of all the absolute errors divided by the number of errors (data points). In other words, it's the average of the errors. Mean absolute error, like absolute error, retains its units.

Mean Absolute Error Example:
You weigh yourself three times and get values of 126 lbs, 129 lbs, 127 lbs. Your true weight is 127 lbs. What is the mean absolute error of the measurements.
Mean Absolute Error = [|126-127 lbs|+|129-127 lbs|+|127-127 lbs|]/3 = 1 lb

References

Hazewinkel, Michiel, ed. (2001). "Theory of Errors." Encyclopedia of Mathematics. Springer Science+Business Media B.V. / Kluwer Academic Publishers. ISBN 978-1-55608-010-4.

Helfrick, Albert D. (2005). Modern Electronic Instrumentation and Measurement Techniques. ISBN 81-297-0731-4.

Steel, Robert G. D.; Torrie, James H. (1960). Principles and Procedures of Statistics, With Special Reference to Biological Sciences. McGraw-Hill.

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Absolute and Relative Error and How to Calculate Them

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Learn about absolute and relative error. See their formulas and get examples of how to calculate them in science.

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https://www.cuemath.com/commercial-math/inverse-proportion/

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Geometric sequence example

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Times Tables

Learn a Times Table in only 5 days! Here are some free online activities (including Tablesmaster) to help you achieve your goal. There are games, exercises and speed tests designed to improve your recall of multiplication facts.

It is important to learn the times tables from 2 to 12. You should learn then as you'd learn a song or a dance. In fact you need to know your times tables forwards, backwards and all mixed up. Spend time learning them well and you'll reap the benefits in future.

Here are some printable forms on which you can record your progress: Personal Best Reverse Bar Chart | Tips For Remembering Multiplication Facts. Keep practising and one day you will be able to answer multiplication questions as fast as this:

The state of pupils' numeracy is always in the news and in particular politicians have pledged that every child in England will know their 12 times table before they leave primary school as part of a "war on innumeracy". They argue that there is still a case for learning your twelve times table, even though there are no longer 12 pence in a shilling, but the reason is to do with discovering patterns and building a confidence in handling numbers.

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math maths mathematics times tables mental arithmetic

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Learn a Times Table in only 5 days! Here are some free online activities (including Tablesmaster) to help you achieve your goal. There are games, exercises and speed tests designed to improve your recall of multiplication facts.

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One pixel on that display is defective. It could be either on or off. Find that pixel and fix the problem.

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One pixel on that display is defective. It could be either on or off. Find that pixel and fix the problem.

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Students are encouraged to reason about square roots and to reinforce the idea that square roots are numbers on a number line. This lesson continues students’ progression from geometric to algebraic characterizations of square roots.

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Which light switches on? (factor pattern)

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Which light switches on? (factor pattern)

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Drag the numbers onto the grey squares so that the percentage statements are true.

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How many seeds in one? Estimate how many seeds in all?

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How many seeds in one? Estimate how many seeds in all?

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If you can picture in your mind what a percentage looks like you may be better able to preform mental calculations with that percentage.

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What do you know about the fraction

Stand up if it is a whole number.

Put a hand up if it can be simplified.

Nod your head if it is equal to a recurring decimal.

Hum if it is an improper fraction.

Sway from side to side if it is greater than a half.

This is a visual aid designed to be projected onto a whiteboard for whole class exposition. It also works well for use in remote teaching via video link. Click on the blue buttons to hide statements which would not be appropriate for your class.

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What do you know about the fraction Stand up if it is a whole number. Put a hand up if it can be simplified. Nod your head if it is equal to a recurring decimal. Hum if it is an improper fraction. Sway from side to side if it is greater than a half.

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This is a team picking game. The first to pick a team with three members that total 15 is the winner.

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A Maths Starter Of The Day

Numbered trees
Consider each pair
Adjacent sums
Must be square

Topics: Starter | Arithmetic | Number | Problem Solving | Puzzles

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

Answers

Sign in to your Transum subscription account to see the answers

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon link. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Educational Technology on Amazon

Teacher, do your students have access to computers such as tablets, iPads or Laptops? This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:

Transum.org/go/?Start=March20

However it would be better to assign one of the student interactive activities below.

Here is the URL which will take them to a similar activity.
Transum.org/go/?Start=January8
Here is the URL which will take them to another activity involving square numbers.
Transum.org/go/?to=Square

Here is the URL which will take them to the interactive version of this activity called Square Pairs Game
Transum.org/go/?to=SqPG

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Numbered trees Consider each pair Adjacent sums Must be square Topics: Starter | Arithmetic | Number | Problem Solving | Puzzles How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments?

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Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.

A two player game requiring 18 numbers to be arranged in a similar adjacent-pairs-must-be-prime way is at Prime Pairs Game.

Here's a reminder of what defines a prime number:

The solutions to this and other Transum puzzles, exercises and activities are available here 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 Sign Up 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.

There is a printable game board for this and some of the other Transum Maths games.

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Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.

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The Martian | "Do The Math" Clip [HD] | 20th Century FOX

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The Martian Hexadecimal Scene - Modcasts.com

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Players take turns arranging their cards to make a single digit number, a two digit number, a three digit number and a four digit number. They should do this while the other player is not looking.

The player with the largest single digit number wins one point, the largest two digit number wins two points, the largest three digit number wins three points and the largest four digit number wins four points.

The game can be played many times as strategies are developed and the first player to earn 50 points is the winner.

The concept for the game Manifest comes from the mathematician and creative talent, Frank Tapson, and was mentioned in Don Steward's excellent blog.

If you like this game idea there are similar activities called Great Expectation, Nevertheless and Superior on the Transum Mathematics website.

For more online fun go to Transum's extensive Maths Games page.

There is a printable game board for this and some of the other Transum Maths games.

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Players take turns arranging their cards to make a single digit number, a two digit number, a three digit number and a four digit number. They should do this while the other player is not looking.

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Imagine you are on a desert island with nothing but a pack of playing cards. Do you have to stop learning mathematics? Of course not, there are many fascinating mathematical activities you can enjoy and here are some ideas.

Long Line Make a line of cards so that consectutive card totals are odd, even, prime or square;

Make 15 Take turns to select a card. The first person to make a sum of 15 with their cards wins;

Card Tower Find the rule for the number sequence created while building a tower or bridge of cards;

Squares Use nine playing cards to form a magic, unmagic, prime or sum square;

Snap! There are many ways to play snap and include numeracy facts in the rules;

Times Tables The more ways you can practice your times tables the better. Here are some ideas;

Greater A really interesting way to explore probability while having fun at the same time;

More ... There is an ever-growing list of other activities for learning Mathematics with cards;

If you are not familiar with standard playing cards here is a guide.

There are 52 cards in a pack (usually called a deck). The cards are grouped into four suits of 13 cards each. these suits are called clubs, diamonds, hearts and spades. Click on a tab below to see the cards in each of these suits.

Hearts ♥Diamonds ♦Clubs ♣Spades ♠

Do you have any wonderful ideas for using playing cards to help learn mathematics? Please share your ideas here.

Playing cards have been around since the ninth century. They were invented in China and spread across Europe in the fourteenth century. Though the designs on the cards have changed over the years the basic number properties have not.

Because they are so popular the manufacture of high quality cards is not expensive and makes them an ideal tool for learning mathematics.

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Imagine you are on a desert island with nothing but a pack of playing cards. Do you have to stop learning mathematics? Of course not, there are many fascinating mathematical activities you can enjoy and here are some ideas.

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The traditional game of Snap powered by the computer. A snap is a pair of numbers which round to the same whole number.

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Yes this is a very strange game. "It" is the number in the circle. Students obey the instructions given.

The small button at the bottom right of the red panel will give a new number.

A Mathematics Lesson Starter Of The Day

Topics: Starter | Games | Number

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

Answers

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items I have chosen and recommend to get you started. As an Amazon Associate I earn a small amount from qualifying purchases which helps pay for the upkeep of this website.

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=March29
Here is the URL which will take them to a fast-reaction game based on the properties of numbers.
Transum.org/go/?to=Watsadoo

Extension Activity

Devise another strange game like today's Starter. Use a spreadsheet to produce a table showing the properties of each number up to 100

Curriculum Reference

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Yes this is a very strange game. "It" is the number in the circle. Students obey the instructions given. The small button at the bottom right of the red panel will give a new number. Topics: Starter | Games | Number How did you use this starter?

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Instructions

Make your own bingo card using the same format as the one above. It can easily be sketched in your exercise book or you could print these Two Dice Bingo Cards. Select your own numbers to go on the card.

If you are in a class you can play against your classmates. If you are alone you can play against the computer.

For the whole class game, when everyone has made a card the teacher begins the game by rolling the dice. Each person should cross a number off their card if it matches the total of the two dice. The first person to cross off all ten of their numbers should call out 'Bingo' and they are declared the winner.

The strategy for this game is to choose numbers which will get crossed off before anyone else has called out 'Bingo'. You may repeat a number on your card as many times as you wish but you can only cross off one instance of that number each time it appears as a total. Is it wise to fill your bingo card with the most likely total or should you aim for a selection of numbers?

The computer has chosen numbers for the card above but the dice are quite fair and will generate random numbers unknown to the computer in advance.

This activity can be developed by constructing a table showing the possibility space s for addition, subtraction and multiplication of the numbers on two dice.

There are more online probability activities to spice up your Maths lessons.

See also Maths Bingo for a numeracy practice game.

Extension: If 7 is the total that is most likely to occur when adding the numbers on two dice together, why is filling your bingo cards with sevens not the best strategy?

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Make your own bingo card using the same format as the one above. It can easily be sketched in your exercise book or you could print these Two Dice Bingo Cards. Select your own numbers to go on the card. If you are in a class you can play against your classmates.

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A game for two players who take turns to select two numbers that add up to a square number.

Enter the names of the players.

Player 1:

Player 2:

Start

Each adjacent pair of numbers on the line must add up to a square number.
Play Again

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

https://www.Transum.org/go/?Num=669

Teachers' Notes

Log in and refresh this page to see the answers.

See Square Pairs for the related lesson Starter.

Close

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A game for two players who take turns to select two numbers that add up to a square number.

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Instructions

Player 1 has seven red counters and player 2 has seven blue counters. The objective of the game is for a player to get all seven of their counters around the game board before the other player does.

Player 1 begins by rolling two dice and choosing one of them.

Player 1 then chooses a counter to be moved. The number of squares the counter is moved is either equal to the chosen dice number (if the counter is not yet on the board) or equal to the remainder when the number in the square is divided by the number on the chosen dice.

If a counter ends its move on a square already containing a counter the latter is knocked off the board and returns to its starting position.

This game is an adaption of The Royal Game of UR which gets its name from two game boards which were found in tombs in Iraq by Sir Leonard Wooley, who was carrying out excavations in the ancient city of Ur in the 1920s. The two boards date from before 2600 BCE.

The Royal Game of UR original board photographed at the British Museum by Transum in April 2018

A Babylonian tablet written in the ancient cuneiform language describing the game was discovered by Irving Finkel, a curator at the British Museum in London. The tablet dates from 177-176 BCE.

Photographed by Transum in April 2018

The game board and the instructions on the Babylonian tablet are displayed in this cabinet in gallery 56 of the museum.

Photographed by Transum in April 2018

There are a couple of other board games derived from the Royal Game of Ur on display at the British Museum in London. Here is an ivory senet board with a drawer for storing the glazed gaming pieces.

Photographed by Transum in April 2018

The photograph below shows another variation of the game. The British Museum describe the item as follows: Ivory gaming box, 1250-1050 BC. This ivory gaming box was used to play a game similar to the Egyptian 'Game of Twenty Squares'. Board games on Cyprus were enjoyed by all classes, and crossed cultural boundaries. The box was buried with a wealthy inhabitant of a major trading and manufacturing town near Enkomi in eastern Cyprus. The carving style is a mix of Canaanite, Egyptian and Aegean motifs, showing the cosmopolitan nature of Cypriot society at this time.

Photographed by Transum at the British Museum in April 2018

Transum's Remainder Race differs from The Royal Game of UR in a number of important ways. Determining the number of squares to be moved as being the remainder of a division calculation is specifically included as a required skill for this educational activity. Although the game board is the same shape as the ancient version, requiring the exact number to finish the game is not a feature of this version.

If playing this game as part of a class lesson there may not be time for one of the players to get all seven counters to the end. A suggestion is for all to agree that whover has got the most counters to the end by the time the bell goes (or after 15 minutes for example) is the winner. Furthermore, to reduce the possibility of a draw, each player could be awarded points based on how many squares their counters had passed in total. The following table shows the points for the current game:

CURRENT SCORE

Player 1

Player 2

0

0

So if you wish to go for the limited time version of the game a hidden timer can be set up here. When the time has expired the board is frozen and the winner declared.

Timer: 00:00

The two-digit numbers on the squares are generated randomly every time the page is loaded. They could be anything from 11 to 99 with one notable exception. Can you work out what that exception is? It is the only two digit number that would not allow the counter to move whatever the dice number.

If you have chosen to play against the computer rest assured that the computer does not know how to play the perfect game so you stand a reasonable chance of winning the game.

Additional resources are available 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 Sign Up 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.

Frank Skinner was fascinated by the Royal Game of UR in the British Museum and talked about it on his comedy podcast.

See Transum's ever-growing collection of Probability lesson starters, activities, exam-style questions and and investigations.

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Player 1 has seven red counters and player 2 has seven blue counters. The objective of the game is for a player to get all seven of their counters around the game board before the other player does. Player 1 begins by rolling two dice and choosing one of them.

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Answer: https://youtu.be/WdL1EBNZvQ4

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In Transum prison there are 50 prisoners in cells numbered 1 to 50.

On day 1, the guard turns the key in every lock to open every cell.

On day 2, the guard turns the key in every cell which is a multiple of 2. This locks all the even numbered cells.

On day 3, the guard turns the key in every cell which is a multiple of 3, locking or unlocking them.

On day 4, the guard turns the key in every cell which is a multiple of 4, locking or unlocking them.

This continues for fifty days. The prisoners whose cells are open after the 50th day are set free. Which prisoners will be set free?

Click on the cells above to open and close the doors. When you have worked out what the situation will be after 50 days click the 'check' button to see if you are correct.

Recently Updated

Puzzle Cube Net

A jumbled moving-block puzzle cube is shown as a net. Can you solve it? So far this activity has been accessed 20102 times and 1858 Transum Trophies have been awarded for completing it.

Prison Cell Problem

Can you work out which prisoners will be set free?

The key is turned for each factor in the prison cell number. Does that give you a clue? You can use the grid of cells above to simulate the 50 days of activity or you could think of the problem more analytically.

There are many more fascinating maths puzzles on Transum.org:

The solutions to this and other Transum puzzles, exercises and activities are available in this space when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher or parent you can apply for one here.

A Transum subscription also gives you access to the 'Class Admin' student management system and opens up ad-free access to the Transum website for you and your pupils.

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In Transum prison there are 50 prisoners in cells numbered 1 to 50. On day 1, the guard turns the key in every lock to open every cell. On day 2, the guard turns the key in every cell which is a multiple of 2. This locks all the even numbered cells.

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This is a simplified list of mathematical skills that pupils should have. It has been designed so that each idea has five levels making it visually easy to see where a pupil is now and what they need to do to improve.

Please note that the main objective of creating this inventory grid was to produce something that provided visual impact. Each of the ideas or concepts has been broken down into five levels. This has been done for consistency so the differences in the difficulty between levels is not the same in all cases. Please let us know if you have any suggestions for improvement.

The activity buttons will take you to the nearest match activity on the Transum website. The activity is not always an exact match for the statement but is the closest available.

This page should print nicely for you records or can be used online. The page should remember your ticks from one visit to the next. It does this by using Local Storage so the information is saved only on the computer you are working on right now.

Transum subscribers can use this page as part of the Class Admin system keeping a record of progress for each and every student in the class.

See also the Formal Written Methods examples.

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This is a simplified list of mathematical skills that pupils should have. It has been designed so that each idea has five levels making it visually easy to see where a pupil is now and what they need to do to improve.

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Drag the jigsaw pieces onto the frame so that the prime numbers are in order from smallest to largest.

Description of Levels

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Level 1 - 6 by 5 grid of prime numbers starting at 1

Level 2 - 6 by 6 grid of prime numbers starting at a number between 3 and 9

Level 3 - 7 by 7 grid of prime numbers starting at a number between 33 and 49

Level 4 - 8 by 7 grid of prime numbers starting at a number between 70 and 88

Level 5 - 6 by 5 grid of numbers (composites hidden) starting at 1

Level 6 - 6 by 6 grid of numbers (composites hidden) starting at a number between 3 and 9

Level 7 - 7 by 7 grid of numbers (composites hidden) starting at a number between 33 and 49

Level 8 - 8 by 7 grid of numbers (composites hidden) starting at a number between 70 and 88

Level 9 - 8 by 8 grid of numbers (composites hidden) starting at a number between 450 and 470

Level 10 - 8 by 8 grid of numbers (composites hidden) starting at a number between 599 and 900

Note that the higher levels are quite a challenge because they include a range of numbers in which the prime numbers are more spaced out. You will get jigsaw pieces that contain only hidden composite numbers but you still have to correctly guess the intended positions of these pieces. It is not sufficient to fit all the pieces on the rectangle with no gaps; all the pieces need to be in the position I designed for them!

Roman Numerals Jigsaw - If you enjoyed this jigsaw there are others you can try.
Chinese Numbers Jigsaw Thai Numbers Jigsaw

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Video

Note that the higher levels are quite a challenge because they include a range of numbers in which the prime numbers are more spaced out. You will get jigsaw pieces that contain only hidden composite numbers but you still have to correctly guess the intended positions of these pieces. It is not sufficient to fit all the pieces on the rectangle with no gaps; all the pieces need to be in the position I designed for them!

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

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Interactive jigsaw puzzles of different types of grids containing prime numbers.

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This a game for one or two players. Take it in turns to drop the counters into the grid. The winner is the first to line up four numbers with a common factor other than one.

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Flabbergasted Game

This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.

The computer does not play the 'perfect' game so you stand a good chance of beating it.

A Transum virtual trophy is available to the winner of a game lasting more than turns.

The numbers used in this game are recorded below:

Challenge: In two-player mode you could try to make the longest sequence possible.

The solution to the challenge is available here 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 Sign Up page.

This game was inspired by the Flabbergasted Lesson Starter.

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This game for one or two players is an exciting challenge to demonstrate an understanding of factors and multiples.

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Answer: https://nrich.maths.org/4793/solution

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Base 12 - Why Counting In Twelves Would Make Life Easier

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Base 12 - Why Counting In Twelves Would Make Life Easier

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Base 12 - Why Counting In Twelves Would Make Life Easier

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"A psychic is a person who has the abilities of extra-sensory perception, such as clairvoyance, psychometry, premonition and precognition, or other paranormal abilities such as psychokinesis. The study of such paranormal abilities is called parapsychology. The issue of whether or not psychic abilities actually exist is still controversial within science; however, recent polls do show a high instance of support amongst scientists and academics." Wikepedia

"This widely used word, which can be an adjective or a noun, derives from the Greek psyche, meaning 'mind' or 'soul'. As an adjective, psychic is often used synonymously with paranormal. Any event that appears to challenge conventional assumptions regarding the limits of possibility is designated a psychic phenomenon. Paranormal. Literally, "beside the normal," a paranormal event is one that violates the boundaries of space and time, or cause and effect, as they are normally understood. ...' hyponoesis.org

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psychic mind reading reader magic online numbers

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Let the psychic read the cards and magically reveal the number you have secretly chosen. What is the mathematics that makes this trick work?

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How many significant figures are used and why?

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How many significant figures are used and why?

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ONLY 8.5 SECONDS GAP ON THE LAST LAP! - F1 meme

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Which one is correct?

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Can you change this to an improper fraction?

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The professor begins her lecture on number theory with a little game.  First she writes a gigantic number on the blackboard.  Then she counts the students present out loud.  Each person should remember the number given to them.  The professor comes up to the number 200 – that’s how many students are in the lecture hall.  Now the professor asks everyone present to divide the number on the blackboard by their own number.  If this is possible without a remainder, the person concerned should say "yes", otherwise "no".

The students come in the order of their numbers.  The young man in the front left says "Yes."  Logically, it's number one, and every natural number is divisible by one.

The professor always hears a "yes" afterwards - with two exceptions: Two people sitting next to each other with consecutive numbers say "no".

What are the numbers of these two people?

Answer

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Answer

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Shoot the numbers as they appear but don't shoot any square numbers.

Press the Start button to begin. The game lasts for 30 seconds. As the numbers appear click on them to earn points but do not click on any square numbers as you will lose five points.

Win a Transum virtual trophy if you score 10 or more.

This is Don't Shoot the Square! level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10

© Transum Mathematics 1997-2023
Scan the QR code below to visit the online version of this activity.

https://Transum.org/go/?Num=251

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Shoot the numbers as they appear but don't shoot any square numbers.

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Each box represents a missing operation (add, subtract, multiply or divide). What are they?

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Memorise the digits of pi with help from some musical notes.

Are you ready to concentrate? Look and listen to the first digit of π: Begin

Now it is your turn to copy that. Click on the first digit of π.

That's the wrong number - Start Again

Now it is your turn to copy that. Click on the first digits of π.

Now look and listen to the first digits of π.

© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=1017

World Record

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Example

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Are you ready to concentrate? Look and listen to the first digit of π: Begin Now it is your turn to copy that. Click on the first digit of π. That's the wrong number - Start Again Now it is your turn to copy that. Click on the first digits of π.

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Learn the mathematics required to adapt recipes to serve a different number of people.

Cow Pad Gung.

Fried Rice with Shrimp (Serves 2)

Ingredients

2 Eggs
2 and half cups of steamed rice
1 tbsp diced carrot
1 medium onion diced
2 tsp sugar
2 tsp fish sauce
120g shrimps cut in half
2 tbs chopped spring onion
2 tbsn vegetable oil

Ingredients

Method

Heat a frying pan or wok, add 1 tbsn veg oil and when oil is hot add the eggs and stir until the eggs are cooked.

Add the rice and mix well with the eggs. Put in a dish on one side.

Add 1 tbsn of veg oil to the same pan. When it's hot add carrot and onion until cooked then add the shrimp.

Stir fry until the shrimp is cooked than add the rice/egg mixture seasoning with sugar and soi sauce. Taste and if too plain add more seasoning.

Add chopped spring onion, stir fry briefly then serve

© Transum Mathematics 1997-2023
Scan the QR code below to visit the online version of this activity.

https://Transum.org/go/?Num=759

Description of Levels

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Level 1 - Cow Pad Gung (Fried Rice with Shrimp) Increase quantities by integer multiplication

Level 2 - Massaman Gai (Chicken and Potato Curry) Increase quantities by multiplication

Level 3 - Gai Gorae (Spicy Grilled Chicken) Decrease quantities

Level 4 - Gwittyo Tom Yam Gung (Spicy Lemon Shrimp Soup with Noodles) Mixed questions

Level 5 - Tom Yam Gung (Spicy Lemon Shrimp Soup) Hardfer mixed questions

Level 6 - Geng Jute Jang Ngok (Glass Noodle Soup With Pork) Puzzling questions

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

The recipes used in this exercise are from Hot Sak's.

Example

This video is from Jonathan Robinson

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

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Learn the mathematics required to adapt recipes to serve a different number of people.

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Imaginary Numbers Are Real [Part 1: Introduction]

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From Quadratic equations to Imaginary numbers

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From Quadratic equations to Imaginary numbers

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How much would the original price without discount be?

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How much would the original price without discount be?

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https://mammothmemory.net/maths/numbers/multiplication-fractions/dividing-fractions-think-kentucky-chicken-fried.html

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https://en.m.wikipedia.org/wiki/Chinese_remainder_theorem

https://youtu.be/LInNgWMtFEs

https://youtu.be/KwxslifHITg

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Self-marking exercises on evaluating logarithms and using them to solve equations.

This is level 1 ? Use the ^ key to type in a power or index, the underscore _ to type in a subscript and use the forward slash / to type a fraction. Press the right arrow key to end the power, subscript or fraction.

© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=802

Description of Levels

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Level 1 - Writing logarithm statements in exponential format and vica versa

Level 2 - Evaluating logarithms without a calculator

Level 3 - Laws of logarithms

Level 4 - Solving equations containing logarithms

Level 5 - Natural logarithms

Level 6 - Solving exponential equations using logarithms

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on Exponents including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Logarithms

$$ \text{If} \; \log_a b = c \quad \text{then} \; a^c = b$$

Tutorial

The video above is from Khan Academy

Laws of Logarithms

$$ \log a + \log b \equiv \log ab$$ $$ \log a - \log b \equiv \log \frac{a}{b}$$ $$a \log b \equiv \log b^a $$

Changing Base

$$ \log_a b = \frac{ \log_c b}{ \log_c a}$$

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Self-marking exercises on evaluating logarithms and using them to solve equations. This is level 1 ? Use the ^ key to type in a power or index, the underscore _ to type in a subscript and use the forward slash / to type a fraction.

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Easy Math Trick No One Taught You - How Ancient Egyptians Divided Numbers

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The Penny Problem That Breaks Your Brain

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Answer: https://www.transum.org/software/SW/Starter_of_the_day/starter_January8.asp

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Design your Christmas light display: Pattern:

Every: Starting at: Colour: Add

Run Light Show Clear Instructions

There are many wonderful patterns in Pascal's triangle and they make excellent designs for Christmas tree lighting. Choose a number pattern from the drop-down box above, set the timing and colour then add it to the instructions for the lighting display. Press the Run Light Show button to see your creation.

During your display each light will stay on for one second so setting a light to come on every 1 second effectively means that light stays on for the whole display time.

Patterns chosen further down the drop-down list may overwrite some of the lights in the patterns chosen higher up the list.

Don't miss out on other great Festive mathematical activities. Click the link below.
CHRISTMATHS

© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=775

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Design your Christmas light display: Pattern: Every: Starting at: Colour: Add Run Light Show Clear Instructions There are many wonderful patterns in Pascal's triangle and they make excellent designs for Christmas tree lighting. Choose a number pattern from the drop-down box above, set the timing and colour then add it to the instructions for the lighting display.

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Instructions: Use the arrow keys (or swipe) to move the tiles. When two tiles with the same number touch, they merge into one tile to make a double. What is the largest double you can make?

Trophies are available for creating tiles of the following values:

128 - Level 1 trophy
256 - Level 2 trophy
512 - Level 3 trophy
1024 - Level 4 trophy
2048 - Level 5 trophy

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Instructions: Use the arrow keys (or swipe) to move the tiles. When two tiles with the same number touch, they merge into one tile to make a double. What is the largest double you can make?

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Test your understanding of angles with this ten question, self-marking multiple choice exercise.

Here are 10 Angles multiple choice questions written by people from around the world while using the main Pentransum activity. You can earn a Transum Trophy for answering at least 9 of them correctly.

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Test your understanding of angles with this ten question, self-marking multiple choice exercise. Here are 10 Angles multiple choice questions written by people from around the world while using the main Pentransum activity. You can earn a Transum Trophy for answering at least 9 of them correctly.

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If you can picture in your mind what a percentage looks like you may be better able to preform mental calculations with that percentage.

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Arrange the numbers on the snake in order from the largest on the head to the smallest at the tail.

Largest

This is Fraction Order level 2. You can also try

Recently Updated

HCF and LCM

Practise finding the highest common factor (H.C.F), sometimes called the greatest common divisor, and the lowest common multiple (L.C.M) of two numbers. So far this activity has been accessed 35533 times and 15471 Transum Trophies have been awarded for completing it.

Fraction Order

A Fraction Sorting Challenge

This activity provides practice ordering vulgar and decimal fractions. Drag the fractions onto the snake so that the smallest fraction is at the tail and the largest is at the head.

There are 4 levels for this activity and for each one you can earn a Transum Trophy.

Fractions can be compared by considering the meaning of the numerator and denominator values. A Fraction Wall may help. Alternatively the fractions could be converted to decimals for easier sorting with the help of the Decimals Line . A spreadsheet could also be used to help manage the conversion and sorting.

There are many more fraction activities on the Fraction Topic page.

The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher or parent you can apply for one here.

A Transum subscription also gives you access to the 'Class Admin' student management system and opens up ad-free access to the Transum website for you and your pupils.

Video

This video is from MathsWatch

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don't yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

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Arrange the numbers on the snake in order from the largest on the head to the smallest at the tail.

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Find the matching pairs of cards. A drag and drop self marking activity.

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Ganesh Pai: Can you solve the passcode riddle?

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In a dystopian world, your resistance group is humanity's last hope. Unfortunately, you've all been captured by the tyrannical rulers and brought to the ancient coliseum for their deadly entertainment. Will you be able to solve the passcode riddle and get everyone out safely? Ganesh Pai shows how.