Introduction

Century Box can be used by the teacher as a teaching aid and by pupils as a way to both investigate numbers and to reinforce concepts.

It is ideal for use with an Interactive Whiteboard, but can be used by individuals or groups to explore number relationships.

It can show from 1 to 256 consecutive numbers in a range bigger than you will ever need (from -2,147,483,648 to 2,147,483,648) in steps of 0.001 to 1000.

Grids can be altered at any time, but teachers can define all aspects of the number grid and save as a Configuration for a quick start.

Getting started

This is a brief instructional on how to use the main display.

There are four things you can do from the main menu screen:

The main screen shows a menu of configurations:

Green buttons are Folders: these can be opened to reveal further Configurations or Folders.

Cream buttons are Configurations: a single click will open the program with the grid defined by the Configuration settings.

Click on the Basic Configuration to reveal a standard 10 x 10, 1 to 100 number grid.

Click the 2 (or press 2 on the keyboard) to instantly fill the cells of all the multiples of 2. Click 2 again (or press 2) to turn off the highlights.

Click 3 and 4 to show multiples of both numbers (and, where the two highlights meet in the same cells, the multiples of 12). In this grid the numbers are incremented by 1. You can highlight the multiples of any number between 2 and 10. If your increment value is 0.01, you can click to show multiples of numbers between 0.02 and 0.1, provided these numbers appear on your grid, or you can use the keyboard keys 2-0.

Right-click any number to make it invisible: right-click again to show it.

Click on the cream arrow in the bottom-left corner of the screen to reveal the menu panel (or press the Menu key). All controls can always be implemented by keystroke combinations. Controls in the menu panel can be turned off individually: the menu panel will not appear if all controls are off.

Click Reset numbers to turn off any highlights and to show any hidden numbers. Click twice on the Up arrow against Width (or press SHIFT + W twice) to use a different method of showing the 12-times table. You can reduce the width by pressing CTRL + W.

Click the Reset all button to restore the original configuration.

Fill modes

There are four fill modes to set the highlights. In this configuration the default is Grid, in which all multiples of the chosen number are immediately coloured. Click the Up arrow against Fill mode (SHIFT + F) to switch to Line fill mode and a button will appear against each row. Click the 3 and 4 cells again and only these numbers are highlighted. Click the line button of row 1 (ALT + 1) to highlight the multiples of these two numbers in that row. Rows can be highlighted in any order. If you are working from the keyboard and have more than 10 rows, hold down the SHIFT key to add 10 to your number selection (SHIFT + ALT + 4 = Row 14).

In Manual Fill mode you are given a Paint pot. Click any cell in the grid to fill it with the current colour. Click the Paint pot (or press C) to cycle through the four available colours.

Century Box remembers colour fills if you change mode, so you can switch between modes without loss. The Reset numbers command only removes colouring for the displayed mode. This feature can be used to your advantage. You can’t save a pre-coloured grid, but you can prepare a grid to illustrate a point and then switch to another fill mode showing an unfilled grid to discuss the point and ask for predictions. At an appropriate point, switch to your prepared grid.

Select Fill mode: None to turn off all options.

Step rates and start numbers

Click the Up arrow against Increment (SHIFT + I) to increase the step rate. Both the increment and the start number will by multiplied by 10. If the Down arrow is clicked (CTRL + I), both numbers will be divided by 10. You can only move the decimal point three places in either direction and the result will depend on your start number and your initial step rate. You can never show a numbers smaller than thousandths.

If you wish to keep the same start number while increasing or decreasing the incremental step rate, you must return to the main menu and choose a different Configuration.

You can start your grid from 0 if you click on the Down arrow against Start number (CTRL + N). Keep clicking and you enter the realm of negative numbers.

For the advanced pupils in the Maths Club, Century Box can show counting in other number bases. Click Reset all and then click the Up arrow against Number base (SHIFT + B) to show a base 11 sequence. 10 is represented by 0A and 11 by 10. Click the Down arrow (CTRL + B) three times to show how we might count if we had only eight fingers. You can show number bases from 2 to 16.

Keyboard shortcuts

The Configurations Editor

Press CTRL + F2 from the main menu screen to open the Editor.

On the left side of the screen is a tree view of the Folders and Configurations available to you. To open a Folder, click on the + next to the Folder’s name.

If you right-click in this area a pop-up menu shows you that you can:

The right-hand side of the screen shows the configuration. Information boxes are greyed until a Configuration is selected.

Clicking on most information boxes will toggle through available settings. The main exceptions go up with a left-click and down with a right-click.

Show/Hide numbers

If pupils are using Century Box for their own explorations, you may wish to disable this facility. If you have elected to turn number in the grid on and off with a right mouse-click, you have the further option of having the grid appear with no numbers at all when it first appears.

Highlight zero

If you are using Century Box to cover multiplication, then highlighting 0 as a multiple of another number may not cause problems; after all, 3 x 0 = 0. If you are exploring divisibility, the idea of sharing nothing can create difficulties with some pupils, so we have given you the choice between both approaches.

Print

A grid can be printed with Ctrl + P if this is on. No highlights will be printed.

The Menu control options on the remaining settings determine whether any control appears in the popup control panel. If all Menu controls are set to Off, the control menu will not appear in the main work area, although all keystrokes can always be used to adjust the display.

Fill mode

The options available are:

Grid – Automatically fills in multiples of the selected number.

Line – Lines will only show multiples after the line button has been clicked, giving children the opportunity to predict which multiples in that will be highlighted.

Manual - In Manual Fill mode you are given a Paint pot showing one of four colours. Click any cell in the grid to fill it with the current colour.

None – With this option selected, there is no opportunity to colour any cells.

Width

The minimum is 1, the maximum 16. Left-click to go up, right-click to go down.

Height

The minimum is 1, the maximum 16. Left-click to go up, right-click to go down.

Start number

In base 10 only, numbers may start at 0.001 and go up to any number. Although the size of the cells and the numbers they contain automatically adjust to make best use of space, no account is taken of readability – large number may be too small to read. In number bases other than 10 the Start and Increment numbers must be integers. Left-click to go up, right-click to go down.

Increment

The minimum is Thousandths, the maximum Thousands. Left-click to go up, right-click to go down.

Number base

The minimum is 2, the maximum 16. Left-click to go up, right-click to go down.

Using Century Box in the classroom

Century Box has been designed primarily as a tool for whiteboards and most of the suggestions given here are in support of this role. But with a suitable Configuration and a carefully designed workcard, a child or small group can use the program to explore numbers. For instance, they could be challenged to find out how many grids can be made with 24 cells, and then how many can be made with 23. Can they predict which will be the first cell to have all three colours when multiples of 3, 5 and 7 are all selected? If you start a grid at –5 and colour in the first 6 cells, what number do you finish on?

Introducing numbers

Century Box does not show number patterns exclusively: it can be used to give practice in number recognition and show addition and subtraction.

The demonstration Configuration in the Samples folder, Up to 10, can be used to count. In Manual Fill mode, colour can be used to show how ten can be made up of two or more other numbers.

The Single number Configuration shows just that – there’s no menu and no colouring. SHIFT + N will show the next number, CTRL + N the previous. Try setting up a similar Configuration but with the number hidden until you right-click the cell.

Odd and even; counting in twos

The Basic Configuration can be used in a number of ways. Century Box grid can be used to show counting on in twos from and back to zero (or any small number). The teacher can automatically highlight all even numbers by clicking on 2. Alternatively, colour in each number manually (CTRL + F/SHIFT + F to change mode), clicking on each even number as each new step is taken. A pattern will emerge and can be pointed out. Don’t forget, the number grid can be set to begin with 0 (or any other number – CTRL + N to go down, SHIFT + N to go up). Counting on

The program can be used to help children count on in steps of 3, 4 or 5 from any small number to 50 or beyond, then back again. It can also be used to show minus numbers so that they can count back in tens or hundreds.

Negative numbers; number sequences

Century Box can be set to begin with negative numbers so that pupils can begin to recognise and extend number sequences formed by counting from any number in steps of constant size, extending beyond zero when counting back.

Similarly, you can count on in steps of 3, 4 or 5 and see how the pattern changes.

You can set the program to Line Fill mode and colour a line at a time after, perhaps, asking pupils to predict which numbers will be coloured.

Using Manual Fill mode, odd and even numbers can be coloured in contrasting ways and the grid displayed in different arrangements up to ten, twenty and then thirty.

It will also be possible to count on in ones and tens from any two-digit number. The grid can be set to start at, for example, 10, and you can use the 10 x 10 grid to show that the column on the right side of the grid does count on in tens (Configuration Count tens). To make it more of a challenge, the grid could be set to 12 x 12 (SHIFT + W, SHIFT + H to increase the height and width) and the pupils asked to fill the appropriate cells.

Multiples

The program can be used to help pupils recognise two-digit multiples of 2, 5 or 10. To take 5 as an example, the teacher might begin with a 5 x 5 box (Configuration 5 x 5) and ask pupils to look at the numbers in the column on the extreme right. The box can be expanded a row at a time to see if their predictions are right.

Simple fractions

Pupils can learn to recognise halves and quarters, e.g. by setting the grid to 2 x 2. Colour 1 to show one quarter or 1 out of 4; colour 1 and 2 to show half or 2 out of 4; colour 1 2 and 3 to show three quarters or 3 out of 4. This will help them to see that two halves or four quarters make one whole and that two quarters and one half are equivalent. They can then carry this out themselves on screen or on printed grids.

Multiplication and division

To help to understand that multiplication is repeated addition, so that the columns equal the multiplier under discussion, 3 for example, and the vertical axis goes up to, say, 10. All of the numbers in the right column will be multiples of 3, of course.

You can also begin by showing just the first row: 1 2 3 and then reveal the next row, 4 5 6 and so on (Configuration 2 x 3 Hidden – right-click hidden numbers to reveal).

Century Box will also “help children to learn by heart the multiplication facts for the 2 and 10 times-tables and to begin to know the multiplication facts for the 5 times-table.”

The program can also assist pupils in developing their mental calculation strategies for multiplication and division by allowing them to remember or visualise the Century Box layout.

Century Box will also be useful with reference to:

Century Box will aid general understanding of multiplication and division, including a grasp of the concept that multiplication is repeated addition (see above) and division as repeated subtraction. It will help pupils to learn by heart the multiplication facts for the 2, 5 and 10 times-tables and to begin to know the 3 and 4 times-tables. This is turn will help in grasping division facts corresponding to the 2, 5 and 10 times-tables.

It is a simple matter to recognise two-digit multiples of 2, 5 or 10 simply by clicking on these numbers in Grid mode. Further reinforcement can be achieved by asking pupils to colour in the multiples using the whiteboard, their own copies of the program and/or printed grids.

Pairs of multiples of 10 that make 100 can be shown in different ways, including a number line set up at intervals of ten.

Odd and even

The programme can be set up to help children recognise odd and even numbers up to 1000 by setting the grid to begin at any number up to 1000.

Multiplication facts

It will also help children to recognise multiples of 2, 3, 4, 5 and 10, up to the tenth multiple.

The program can be used to reinforce and revise multiplication facts for 2, 3, 4, 5 and 10 times-tables (and corresponding division facts derived from 2, 3, 4, 5 and 10 times-tables) and to help pupils to know multiplication facts for 6, 7, 8 and 9 times-tables.

Pupils can learn to use a number grid as a simple calculator. Asked to multiply 4 by, say, 6, they click on 4 and then count the coloured squares, starting with the 4. They can be asked to count aloud as they point to each one, “One four is four; two fours are eight…”

At this level the program can be used to establish all multiplication facts up to 10 x 10 and to assist pupils in deriving division facts corresponding to tables up to 10 x 10.

Negative integers

The Century Box display can be used to find the difference between a positive and a negative integer, or two negative integers.

Number sequences

The program will allow teachers and pupils to recognise and extend number sequences, such as the sequence of square numbers (start with a 4 x 4 grid which will show the square – literally – to be 16, and then increase row and column by 1 to get the square of 5 and so on up to 16 x 16.

Century Box will help pupils to recognise prime numbers by noticing which numbers remain unmarked as the integers from 2 to 10 are successively selected. For example, when 2 and 3 are selected, 5 and 7 remain blank. It will also assist in factorising numbers up to 100 into prime factors.

Small steps – Big steps

The program will enable pupils to count on in steps of 0.1, 0.01 or 0.001 – or of 10s, 100s or 1000s, depending on the ‘Increment Step’ chosen.

It will also allow any base to be chosen from binary to hexadecimal (base 16).