The Number Gym (KS1,2,3)

NEW: Exploring Fractions

Use this activity to explore the functionality of both the numerator and the denominator. Click on the blue triangular buttons to increase or decrease either of these and instantly see the effects. Explore top-heavy or improper fractions too.

Optionally toggle between fraction strip and pie-chart styles. See the User Guide for more teaching ideas.

NEW: Mr G's Place Value Chart

The inspiration for this chart comes from Caleb Gattegno (1911-1988) whose writings on teaching and learning have been hugely influential. His original chart had the numbers in rows, but we believe that there is much to be gained by arranging them into columns to reflect the way we show the place values of our numbers when they are written.

Just drag the green counters up or down to add or subtract. But what happens if you slide them horizonally to the left or right by one column? See the User Guide for more teaching ideas.

NEW: Mr G's Place Value Challenge

This challenge follows on from the Gattegno Exploration. Select the type of challenge and set the columns required to display. Then press Go. When you think you have the right answer, hover over the tick to check - then click the tick.
Challenge Types:
Single column add or subtract: This option involves adjusting a counter in just one column up or down a few places.
Two columns add or subtract: As above but adjusting the values in two columns.
Rounding add or subtract: So, +19 involves moving the tens counter up two places (+20) and the units counter down one place (-1).
Multiply or divide by 10: This time move the counter or counters horizontally to the left for multiplication or to the right for division.

NEW: Mounds and unMounds - Exploring Negative Numbers

This activity illustrates why subtracting a negative number is the same as adding a positive one.

Using a virtual sand-tray we can make sand-castles or mounds by 'piling up sand' but for each pile we make we've left a hole or un-mound so the total sums to zero. But then there's the funnel. With this we can truly add sand to or take it away from the tray. See the User Guide for more details.

NEW: How Many Stones are in each Bag? - an introduction to algebra

"It is a defect of most algebra books that they begin by developing a lot of machinery, and it is a long time before the learner sees what he can do with all this machinery." W.W. Sawyer 1964

This activity is inspired by the writings or W. W. Sawyer (1911 - 2008), especially his book "Visions in Elementary Mathematics". The idea here is to present 'real' problems to solve before introducing their representation in the language of algebra. See User Guide for more details.

NEW: Healthy Eating Algebra

This activity, too, owes much to Sawyer's book "Visions in Elementary Mathematics".

It presents a progressive set of problems, each based on calculating the cost of a banana and an apple. Each problem contains two statements and may naturally lead to their formal representation as simple simultaneous equations. A 'Show Algebra?' checkbox is available for toggling between formats if required.

Improved: In the Zone! - a Game for Two Players

This favourite has been modified to allow the game to be played with just two or three zones as well as the original four.

As before, each player is given three counters which they have to place in the appropriate zones to make a total as close as possible to the displayed target.

Spinner Games

Choose your game from the variations on 3 in a line and 4 in a line. Spin the spinners and add the numbers.

Then place your counter over the right answer but choose carefully to find the best place to get your line and to block your opponent.

User-defined Spinner Games

Consult the User Guide for a whole range of ideas or invent your own games with two spinners where you can choose how many segments in each and define the text in each segment.

Guess my Number

You can play Guess my Number at just about any level: from 0 to10 integers up to 0 to 1000 or a random 100 with or without decimals and/or negative numbers.

What Fraction of the Shapes are...

...triangles or stars or pentagons or NOT red?

This game for 2 teams or players allows you to group the shapes by the relevant attribute before inputting your answer. Reducing the fraction to a simpler form will earn you more points!

Shape Builder

ShapeBuilder offers another powerful way to investigate shape. Akin to stretching elastic bands over pinboards, but with far more flexibility, shapes can be simply generated by defining their colour and number of vertices. They can then be dragged across the 'canvas' where they will click to the selected grid style. Each vertex can then be dragged to change the shape as required. Labels and lines can also be added. From free expression to specific investigations, ShapeBuilder provides a very powerful but simple to use shape generator.

Route Pathways - improved for 2.6

Pupils need to be given opportunities to use directional language and consider alternative options when solving problems.This program allows you to create a network of pathways and then to consider what instructions would be necessary to send a turtle on a journey along the tracks.

For v2.6 this activity now supports a 3x3 grid as well as the original 6x6 grid.

Route Tiles Challenge

New activity for version 2.4 Using the same tiles from the Route Paths activity, this time we're providing a set of challenges. Each one presents a different combination of tiles which have to be placed jig-saw like so that only continuous circuits are built - no loose ends allowed. Finally, we explore the traversability of the circuit - can you program the turtle to walk around the entire circuit without going over any section twice?

Good for developing lateral thinking.

Turtle Tracks

New activity for version 2.4. Using the same turtle from the Route Paths activity, this time we've dispensed with the tiles and have extended the drawing possibilities by allowing a variable angle of turn and choice of trail colours.

Good for free-expression and for drawing complex geometric shapes (see image) from iterations of pentagons to dodecagons. You can also pre-program the turtle and replay the program multiple times to develop these images.

NumberGym's "Turtling & ShapeBuilder" package

Although the above four activities are already included in The Number Gym, they may also be purchased as a separate package: Site Licence: £85. To order this package please email your order to sales@numbergym.co.uk or call us on 01727 759 439.

Same Difference

New activity for version 2.4. A mind-friendly method of subtraction as featured in Ian Sugarman's recent article in MATHEMATICS TEACHING.

72 - 47 may look daunting for mental arithmetic but 75 - 50 isn't nearly so bad. With a little practice on this activity you'll soon be able to simplify those tricky subtractions.

Tables Challenge

New activity for version 2.4. This flexible table-tester allows you to select which tables to test and whether you want them presented in order or randomly. With on-screen keypad and arrow keys this is ideal for Whiteboards. When finished the tables are marked and corrected. Results are stored for your last three attempts.

Exploring Equivalent Fractions

Now with a drop-down box to select the base denominator. Using the Number Gym's special chocolate bars, click on the squares to uncover halves, thirds, quarters and much more. Printed matter can't compete with the interactivity available here. Hide the answer, then see if you were right. Excellent for whiteboards with whole-class or small-group work.

Exploring Fraction Addition

Now with a drop-down box to select the base denominator. Explore the addition of fractions with buttons to hide both the answer and the resulting chocolate bars. Excellent for whiteboards with whole-class or small-group work. Click on the image to try it out.

Smile Arrays (very punny!)

This program allows you to display an array of smiley faces of any size up to 10 by 10. You can highlight the array as a multiplication fact – the product will be the total number of smiley faces in the array - or as a division fact. The array can be separated into either its rows or its columns.

Rod Trains

Rods can be placed along a number line to make a train. Each carriage can be the same length/colour of rod. When this happens the commutative aspect of multiplication can be displayed simultaneously e.g. 10 can be 5 of the red (2) rods or 2 of the yellow (5) rods.
Other lengths can be investigated e.g. 12 can be seen to be built with multiples of 2, 3, 4 and 6 rods.
Also good for visual demonstration of division with remainer.

Chance Statements

This activity is a fun way to introduce pupils to the language of probability – the different levels of chance or likelihood that an event will happen. It makes sense to do this in the context of real or imaginary events from everyday life rather than go straight into mathematical contexts. Click Spin to generate a random statement - then drag it onto the probability line on the right. Click Spin for more statements.

Toss a Coin

This activity allows you to demonstrate and discuss the idea that when there is an even chance of one of two events happening, this does not mean that the events will be alternate – HEAD/TAIL/HEAD/TAIL etc. There can be runs of the same one several times, because the coin doesn’t “remember” what it did last time.

Toss 2 Coins

This simulation allows you to see very clearly that there are really 4 rather than 3 different possibilities when you toss two coins. The repeated higher frequency of the BOTH column is rather counter-intuitive and running this simulation after pupils have had a chance to discuss and predict the outcome should prove highly effective

Sum of 2 Dice

Following on from the two coin activity, the sum of two dice graph pattern clearly demonstrates that the number of combinations for each total increases towards the central value of 7.
Pupils might want to document these combinations
eg. 2 = 1,1
3 = 1,2 or 2,1
4 = 1,3 or 2,2 or 3,1

Spinners

The most effective way of using this simulation is as a follow-up to pupils discussing their predictions of the likely outcome of a certain number of spins on any particular board. Can be used in real time or high-speed mode.

About Time!

This activity provides fully functional analogue and digital clocks as well as a time sentence. The hands of the analogue clock can be dragged to change the time. As the minute hand is dragged, the hour hand moves accordingly. When the hour hand is dragged, it jumps an hour at a time, ensuring a valid time. The time can also be set from the digital clock using the up/down buttons. Whichever clock you change, the others are synchronised with it. Optionally various elements of the clocks can be hidden to set challenges for the class or group. Finally, the clocks can be changed from 'Drag the hands' mode to 'Real Time' with a second hand which actually ticks (if your sound is turned on!)

The Decimal Driller Challenge!

Drag the pointer along the ruler until it points to the target decimal number. Then click the tick to see if you're right. Use the keys at the end of the ruler to slide it left or right to change the visible range of numbers. In addition you can click on part of a ruler to expand that section into a new ruler showing more detail. Playing modes include 1, 2 or 3 fixed decimal positions or alternatively choose 'automatic' and let the computer adjust to your level. You can optionally include negative numbers to increase the challenge.

Percentages Made Easy

Just type the answer and press ENTER or use the on-screen keypad. Groups of five questions. Seven levels of difficulty. Starts off easy but quickly adjusts to the student's own level. Self-marking with helpful hints.

Exploring Place Value

Using this number generator, you can make any number but only with buttons to add or subtract 1 and 10, multiply or divide by 10 or 100. Scale the heights to astronomical numbers like a hundred billion and then drill down to a microscopic hundred thousandth!! Or just firm up your knowledge of hundreds, tens and units.

In its Place! - a Place Value Challenge

An original game to build on the Place Value exploration above. Using the same buttons from the exploration, you have to make the target number within the number of clicks provided? Get three in a row correct to move up a level. How far can you go?

Doubling and Near-doubling with Integers and Decimals

There are two challenge activities: near-doubling with integers or with decimals. Each activity has five levels of difficulty, which automatically adjust to the student's success rate. The aim here is to encourage the student to make the link and see the patterns between simple integer doubling and more complex variations.

Near-multiples of 10 Addition and Subtraction

This activity has had a make-over for v2.5.

Learn to add and subtract multiples and near-multiples of 10 in your head using a graded set of activities on a 10x10 number grid with helpful popups along the way.

Flexible Geometry

Position over the circle, hold down the mouse button and drag the handle across the screen. Watch the angles change before your eyes - ah, but they always add up to the same number - strange that! Use the drop-down box to explore angles in a triangle, angles when 2 lines crossing, angles in a parallelogram and angles in a quadrilateral.

Exploring Angles

Create angles using the buttons provided, clockwise and counter-clockwise. Watch as the correct angle type is displayed: from acute to full turn. Then explore the angles between the points of the compass and the digits on a clock-face. With an angle already set, click on a compass point or click digit to transpose the angle.

Exploding Number Words!

Can you translate numbers into words? No spelling required. Just drag and drop the words onto a sentence bar. When the answer's right, watch it explode.

Exploring Area & Perimeter of Rectangles

This first activity uses an animation to demonstrate each concept. With Perimeter selected, click on the Show button. The perimeter will be drawn, unit by unit, around the rectangle. The total of each side is displayed as we go and finally the length of the perimeter is displayed along with its breakdown into the sum of its four sides. The animation for area, involves colouring and counting each row of small squares which make up the rectangle.

Exploring Area & Perimeter of Irregular Shapes

In the second activity, we start to look at the perimeter and area of more complex shapes. To do this we initially build a rectangle as before but then we can click on the small squares to hide or show them. This technique allows us to construct our shapes and also to notice what happens to the area and perimeter of the shape as we go.

Equivalent Fractions Challenge

Following on from the exploration, this activity allows the student to practice and improve their knowledge of equivalent fractions. For variation, this activity uses pie-charts instead of chocolate bars. Type the answers using either set of number keys but, if using the number pad on the right, be sure to have the Num-Lock key on. There are four levels; use the drop-down box to select. Sound effects are also used.

Estimating Money - now with 'real' coins for v2.5

Display a set of coins in random positions for a few seconds, then ask the students to write down the value of the coins. Then redisplay the coins and ask a student to group the coins for counting. User-defined parameters for range of coins and number of seconds to display. Based on an original idea from Ian Sugarman, Senior Lecturer in Primary Education, Manchester Metropolitan University. See extract from Ian's article: Reasons for Counting.

On the Number Track - makeover for v2.5

A game involving a range of counting on and back activities on a movable number track. Use the '<' and '>' buttons to move along the track to find the right answer. Then click on the answer to score points.