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History of numbers: Mayan and Roman

Mayan numbers

A Mayan image
Click on me to reveal or hide numbers

A Mayan number = 38Find out about the Mayan number system: mental arithmetic problem-solving.
The Mayans wrote their numbers vertically, with each 'digit' being represented by either a set of dots and horizontal lines. They also had a symbol for zero. The value of a dot is 1, a line represents 5. The highest dots and lines represent 20s, ie one dot is 20, two dots is 40 etc.

Click underneath a number to reveal its value.

M1: Work out how the Mayan number system works by looking at these addition sums.
Mayan counting: this will reveal how the Mayan numbers work. Click on the up and down buttons to increase or decrease the number by one.
More addition sums: click underneath the number to show its value.
M4: Harder addition sums (numbers up to 50)
Random Mayan numbers less than 50 : click on the 'change' button.
Random Mayan numbers from 50 to 99
Random Mayan numbers from 100 to 399
Mayan times-tables
Mayan number sequences

Roman numerals

Find out about Roman Numerals

Click underneath a number to reveal its value.

M46: Count up or down using Roman numerals. Use the option buttons decide how much to go up or down.
Roman years: four options, years 1000-1499, 1500-1899, 1900- and 1000- current year.

SAT-type questions

Link to the activitiy

M44: Follow rules: Double the number in the square and add or subtract the number in the triangle to make the number in the circle.

Link to pattern 1
pattern 1
Link to pattern 2
pattern 2

Three bar fence

Number sequences: formulas

Use this slider to change the number of squaresA repeating pattern is made from squares and circles. How many squares will there be with 17 circles? How many circles with 20 squares?

Use the slider to determine the number of squares.

Pattern 1
Pattern 2


A fence is made from posts and bars. How many bars will there be with 20 posts?

M12: Fence 1 (two bars between each pair of posts).
Fence 2 (three bars between each pair of posts).

Link to activity

M14: Circle three numbers that add up to make....

Link to number cards

M15: Use five cards to make this sum correct

Link to worksheet

M16: Solve simple equations

Link to the activity

M17: Complete this table of values

An example of missing digits

M18: Missing digits: SAT type questions

M19: Missing numbers, SAT type questions: using a calculator

Link to resource

M20: Work out the distance from A to B
eg. If the distance from A to B is seven times as far as from B to C (see example on the left)

M45: Work out the height of a box
Work out the height of a pile of boxes and an individual box.
Click on the question mark and under each pile to reveal the answers.

Solving problems
Link to the wall puzzles
An example of a wall puzzle

M21: Wall puzzles

The number on a brick is either the sum, difference or product of the two numbers below. Drag the numbers on to the wall. When the numbers are in the right place the polygon characters will spin round. There are 6 levels of difficulty: level 1, five numbers have to be placed on the wall, level 6, all ten numbers have to be dragged to the wall.

Use these buttons to change the optionsUse these buttons to decide how the numbers are worked out.
The choices are: the sum, the difference or a mixture (product, sum, difference).

Select the level with the slider. Click on 'go'.

Click on the 'change' button to quickly generate a new wall puzzle.

An example of a shape puzzle
Example of Shape Puzzle 1

The sliders and 'check' buttonShape Puzzles
Work out the value of each shape. The total for each row and column is shown. Use the sliders to input your answers. Click on the 'check' button to see how many are correct.
The shapes will be watching you!

M22: Shape Puzzle 1
Three of the same shape can appear in a row (see the example on the left, three hexagons are in the top row.

M23: Shape Puzzle 2
Three of the same shape will not appear in a row.

M24: Shape Puzzle 3
The solutions can be negative numbers.

Link to sum puzzles
Load the resource

Number puzzles

M25: Sum puzzle
What are the numbers in the circles?


M38: Another sum puzzle
The three numbers in each line must add up to the same total. The total can be shown or hidden.
The number options are: 1. Small whole numbers 2. Multiples of ten 3. Decimals 4 Positive and negative numbers.
Use the other buttons to show a few puzzles or just one.
An example of a multiplication table

Multiplication tables
Complete this multiplication table

M26: Multiplication table 1
Multiplication table 2 more difficult

An example of a magic square

Magic Squares
Complete the magic squares

M28: 3 x 3 magic square
4 x 4 magic square

Load the activity
An example of shape equations   An example of letter equations

Solve simple equations

M39: Balancing problems: what is the weight of a gold bar?
Use the 1 ,2 and 3 buttons to generate the problems. Three levels of difficulty:
level 1: small whole number solutions

level 2: multiple of ten solutions

level 3:
gold bars on both sides
Use these buttons to generate either one problem or four problems.Generate one or four problems

M30: Work out what number each shape represents (positive numbers)
Work out what number each shape represents (positive and negative numbers)
Work out the value of each letter (positive numbers)

Solving problems: functions
Link to the functions activitiy


M33: What are the missing numbers? :see example on the left.
The same functions are used in each line. Can be used to develop algebraic thinking, for example, the numbers in the triangles are 4 times the numbers in the squares.

Load the mystery calculator
What do the mystery buttons do?


M36: Mystery calculator : what functions do the 9 mystery buttons carry out?
The buttons showing polygon people carry out different functions. Click on a button to see what it does. The results are saved in the table.
There are six 'levels':

1. Fixed add and subtract (the same operations everytime)
2. Random add and subtract
3. Fixed multiply and divide
4. Fixed multiply and add or subtract eg x 2 + 1
5. Random multiply and add or subtract
6. A variety of operations, eg rounding
Load the function machines


M37: Function machines : one or two function machines
The function machine buttonsClick on the '1' button to generate a new single function machine, click on the '2' button for a new double function machine. Click on the yellow button to hide or show the inverse functions.

Click inside the function machine to hide or show the function. The purple functions can be swapped over: drag them by the eyes!
Click on the input and outputs to hide or show them.

Change the operations used
Use these buttons to change the operations in the function machines.

Find the missing digits

Link to missing digits (horizontal sums)

Link to missing digits (vertical sums)

Two missing didigts

Missing numbers in a grid

M34: Find the missing digits (horizontal sums)

Find the missing digits (vertical sums)


M40: Two missing digits The two missing digits are given. Fill them in to make the sums correct. Click on the squares to hide or show the digits.


M41: Missing numbers in a grid The three missing numbers are given. Fill in the missing numbers to make the rows and columns add up to the given totals. Click on the grid to hid or show the numbers.

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