Numerical understanding builds in students a deep knowledge base of reasoning that extends beyond symbolic representation to a full understanding what those symbols represent.

Instructive Apps that involve simple drill and practice activities may seem mathematical but are usually very low in educational value. They are also the most abundant, the apps here have been chosen because they go beyond that and provide richer educational experiences through problem solving and fluency in numerical thinking. Open ended creative apps mentioned in other sections, such as Puppet Pals and Explain Everything, can be powerful tools for students to display their numerical knowledge.

Number and Algebra
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1 2 3 Sheep - $1.99 (I-M)
Best for : early skip counting and grouping
Age range : 6 - 8 years
Features : Help the farmer round up sheep on an Australian farm. Three counting games that give young learners practice in basic counting. Helicopter involves counting small groups of sheep, Round Up requires herding sheep into even groups in pens and Jump uses skip counting to help the dog get the sheep into the ute. Detailed instructions and colourful graphics make this an engaging app. Activities are well paced the maintain engagement.
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100s Board - $2.99 (M-C)
Best for : counting, place value
Age range : 6 - 12 years
Features : A very flexible digital 100s board. Show and hide numbers, change their colour, hide rows and columns. Has 10 different draggable counters (solid and transparent) to cover numbers. Its open endness allows for use with a multitude of counting activities and operations. YouTube video.
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Aussie Kids Count Coins - $2.49 (M)
Best for : financial literacy, grouping, place value. money
Age range : 8 - 12 years
Features : Also available as Kids Count Money USA and Kids Count Money NZ. This App provides students with 6 different game modes around the various ways that money can be used: buying things, giving change, counting and comparing amounts. The game play is engaging with excellent graphics and challenging activities. Contains an option to enable notes as well as coins.
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Friends of Ten - $1.29 (I-M)
Best for : number recognition, counting, subitising
Age range : 5 - 8 years
Features : Contains six activities that concentrate on building the essential early learning skill of numbers to 10 and their combinational relationships. Counting. Whilst the focus is on understanding the relationships of the numbers up to ten, building patterns and groups are other concepts introduced in the process. YouTube video
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Mathstorm - $2.49 (I-M)
Best for : operational fluency
Age range : 8 - 12 years
Features : Builds operational fluency through challenging game play in a variety of storm themed games. The graphics and game play are engaging but what sets this App apart from the many others of this kind is the customisation controls. This allows for easy adjustment of the game play to suit the ability level of the user.
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MyScript Calculator - Free (M)
Best for : calculating
Age range : All ages
Features : Just write what you want to know on the screen and it is converted into a printed mathematical equation. Supports all basic and many advanced operations. Displaying the entire number sentence is a powerful feature as students can see the path taken to get to the answer. As well as calculating answers, if a compete equation is written and it is incorrect, rather than replace the incorrect section then the required adjustment is shown alongside the original equation. Equations can easily be manipulated and recalculated. YouTube video
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Number Pieces - Free (M)
Best for : place value, computational skills
Age range : 5 - 12 years
Features : Once added to the screen, units, tens and hundreds blocks can be freely manipulated, rotated 90ยบ, recoloured, deconstructed, regrouped and annotated over. The blocks can be used to represent multi digit numbers that are subject to manual manipulation using mathematical operations. A resizable ruler can also be added to the screen, very useful when working with arrays. There is also Number Pieces Basic version which lacks the ruler and uses different default colours for the blocks.
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Measurement and Geometry
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3 Snakes - $0.99 (I-M)
Best for : measurement, estimation
Age range : 8 - 12 years
Features : Make the length of the 3 snakes match the given criteria. Tap the arrows to change either the front or back sections of the snakes until they match the target length. This process requires the user to continually evaluate each set presented against the criteria. Very useful for introducing the metalanguage longer/longest and shorter/shortest. Early demo video
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Geoboard - Free (M)
Best for : space, measurement, geometry
Age range : 6 - 12 years
Features : Never lose another elastic band with this Geoboard that always has a plentiful supply in 8 different colours. Create line segments and polygons by stretching coloured bands around the pegs on the board. Can be used to explore geometric shapes, perimeter, area, congruence, fractions and more.
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Symmetry Shuffle - $1.99 (M)
Best for : spacial awareness
Age range : 8 - 12 years
Features : An excellent app for spatial reasoning and developing the concepts of flip, slide and turn. Very well presented on colourful backgrounds with 12 different objects on 4 different sized boards with easy and difficult modes. The puzzles require users to explore line and rotational symmetry and develop spacial sense to create strategies to solve problems. YouTube video
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Statistics and Probability

Roundom
Problem Solving
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Cargo-Bot - Free (I)
Best for : sequencing events
Age range : 10 - 16 years
Features : Create a series of instructions that, when run in a single sequence, directs the cargo crane to move all blocks from their current positions to the target positions. The solutions require increasingly complex programming to reach a solution and will certainly challenge the problem solving ability of students and introduce them to object oriented programming.
Watch a YouTube review.
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Thinking Blocks - Addition and Subtraction - Free (I)
Best for : solving word problems
Age range : 8 - 12 years
Features : A series of instructional apps that step the user through the process of how to organise the appropriate information to solve word problems. The others cover Multiplication and Division, Ratio and Proportion and Fractions. The user is asked to identify the components of the word problem and then input the appropriate numerals, with assistance given throughout the process.
Math Playground Website . . . One of many YouTube videos on Thinking Blocks.
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App Categories
I - very directed or purely for information
I-M - mostly instructive but allows for some response to user input
M - fairly even mix of instruction and creativity, produces a predetermined outcome
M-C - mostly creative but within a framework, allows for varied output
C - very open ended allowing full user control of the content created, usually starts with a black page

Prices are in $AUS and were correct at time of publication but are subject to change.