Short-Term Memory Workout

Give your brain a memory workout using this fun app. Short-term Memory Workout is designed provide activities to help improve short-term memory capabilities.

Daily training activities will help improve memory capabilities. The Short-term Pattern Recall activity provides a workout for your ability to remember patterns that you see and hear. Choose the dice icon to generate a random pattern. Pay close attention while the pattern is shown. After seeing the pattern you will be asked to repeat the pattern by tapping the circular buttons on the hexagon. 

The Shape and Location Sensory Recall activity focuses on the sensory recall aspect of memory. Use this activity to provide a workout that involves remember the shape and position of randomly placed on a 3×3 grid. Choose the dice icon to generate a random set of shapes placed at random locations on a 3×3 grid. After the shapes disappear, you are challenged to drag shapes from below the grid to show where the shapes were on the grid. 

Challenge yourself to see how high of a score you can get on the Short-term Memory Workout activities. The scoreboard feature automatically keeps track of your scores. 

Short-Term Memory Workout is available with a volume discount for educational institutions. This app can be purchased worldwide exclusively through the AppleApp Store.  The apps are also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of any of these apps. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

Virtual Learning Amid School Closures for Corona Virus (COVID-19)

Experienced educators who are familiar with the challenges associated with responding to national emergencies know that school closures can affect children’s academic progress, safety and social lives.  Parents and teachers are now faced with extended school closures due to the threat of the corona virus (COVID-19).

According experts at this time more than 30,000 schools in the U.S. are being closed and this leaves more than 20 million students being asked to shift to online learning activities to keep their academic progress on target. Currently entire states have shutdown schools and some of the nation’s largest school districts have recently announced closures.

Ventura Educational Systems is offering five free apps to help elementary students to keep up their math skills:

Addition Puzzles


Addition Puzzles is an exciting, interactive math game to help kids practice addition skills. Use logic to select the numbers that will solve the puzzle. Puzzles are randomly generated so the app offers an almost infinite number of puzzles at six different levels. Puzzles can be selected that involve just whole numbers from 0 to 20 or integers from -10 to 10.

Math Spin-o-Rama


Use Math Spin-o-Rama to help your students practice and improve math skills.

Math Spin-O-Rama provides practice with two and three place addition with a new twist. The numbers in the problem are in the wrong place and must be rotated to be in the right place to fit the answer.

The app has four levels and includes practice in doing both two-place and three place addition. Math Spin-O-Rama makes learning fun. As students answer correctly they earn gold stars. Once they have earn five gold stars they get a chance to spin the wheel to earn a prize. The prizes are collected in a table.

Make learning fun with Math Spin-O-Rama.

Addition Blockmania


Help Kids Learn Addition Facts and Improve Basic Math Skills!

Use Addition Blockmania to help your students practice and improve math skills.  This game challenges students to think quickly and be accurate. The object is to find a set of blocks in the stacks whose sum is equal to the given number.

The app offers four levels of activity. Larger numbers are used at the higher levels. Animation, sound effects and speech help to make this curriculum-based math activity exciting for young mathematicians. Elementary school teachers and parents with young students will find that kids enjoy practicing math skills when they are given this app to use.

On Target Math Skills

Help Kids Practice Arithmetic Skills and Problem Solving Abilities with On Target Math Skills.

The On Target Math Skills app generates an almost infinite number of puzzles where the challeng is to make a specific number given four other numbers. Students can use any of the four basic arithmetic operations, addition, subtraction, multiplication or division to try to solve the puzzle. In coming up with a solution, students will need to use the problem order of operations.

The app challenges the player to find 10 solutions in order to earn a trophy. The app offers 5 different levels of difficulty. The On Target Math Skills app is designed to be a quick math exercise that teachers can use to provide a quick basic arithmetic and problem solving activity.

Interactive Multiplication Chart

Help Kids Learn Multiplication Facts and Improve Basic Math Skills!

The Interactive Multiplication Chart app uses a grid to help students see the patterns in the addition table.

This app challenges the player to find an intersection on a grid where the product of the two multipliers fits the randomly selected problem description. Complete the activities by finding 10 correct answers. The Interactive Multiplication Chart app is designed to be a quick math exercise that teachers can use to provide practice with basic multiplication facts.

In addition to the free apps listed above Ventura Educational Systems offers a huge library of inexpensive apps focus on math, science and reading development. Our most recent releases are Hundreds Chart Deluxe, Math Connections I and II, and Phonics Connections.

Please visit our website for more information.

Pioneers in Math and Science

New apps for iOS and tvOS Devices:

Aristotle • Ancient Greek Philosopher
Rachel Carson – Environmental Scientists
Bonaventura Cavalieri • Mathematician
Nicolaus Copernicus • Astronomer
Marie Curie – Chemist & Physicist
Charles Darwin  • The Science of Evolution
René Descartes • Philosopher • Mathematician
Albert Einstein • Theoretical Physicist
Euclid • The Father of Geometry
Leonhard Euler • Mathematician
Michael Faraday • Chemist & Physicist
Fibonacci • Mathematician
Leonardo Fibonacci • Mathematician
Galileo Galilei • The Father of Modern Science
Carl Gauss • Physicist • Mathematician • Astronomer
Johannes Kepler • Astronomer & Mathematician
Sofia Kovalevskaya • Mathematician
Ada Lovelace • The First Coder
James Maxwell – Physicist • Mathematician
Lise Meitner – Nuclear Physicist
Gregor Mendel • Botanist
Isaac Newton – Mathematician • Physicist • Astronomer
Blaise Pascal – Mathematician • Scientist • Philosopher
Louis Pasteur – • Microbiologist • Chemist
Cecilia Payne – Stellar Astronomer • Astrophysicist
Pythagoras • Mathematician & Philosopher
Ernest Rutherford • Nuclear Physicist

It is reported that Newton once said , “If I have seen further than others, it is by standing upon the shoulders of Giants”.  The Pioneers in Math and Science series of apps for iOS and tvOS devices explores the lives and contributions of several giants in astronomy, physics, philosophy, biology and mathematics who lived before and after Newton.


In Galileo Galilei • The Father of Modern Science, a timeline feature is used to introduce students to the fascinating life of Galileo.  It discusses his early education and explains that as a young man Galileo’s father moves the family to Florence which at the time was a major center for artistic, literary and scientific studies.


The timeline feature is interactive and students can request more information about any of the highlighted years but tapping the year.  The arrows at either end of the time allow students to scroll through the time period.

Illustrated information screens pop up to help students learn about Galileo’s accomplishments.  Students will find it inspirational that many of the things that fascinated Galileo as a young man became a major focus of his studies and lead to mathematical and scientific breakthroughs for him later in his life.


In Isaac Newton – Mathematician • Physicist • Astronomer, students explore the many Newton’s achievements including those related to the nature of white light.  Newton discovered that sunlight was actually made up of many different colors.  He should this by holding up a prism near a window in his laboratory and projecting a spectrum of colors.


René Descartes • Philosopher • Mathematician presents the work of the man who linked algebra and geometry and laid the foundation for modern mathematics.


Descartes work in philosophy formed the basis for the modern scientific method.  He wrote about his skepticism regarding what he could experience through his senses and encourage people to seek knowledge through reason, mathematics and science.

In Charles Darwin • The Science of Evolution a map of the world is used to show the voyage of exploration of the HMS Beagle.  This five year journey around the world gave Darwin the information he needed to develop his Theory of Evolution.Screen2.png

Each of the apps in this series feature a quiz so that student can demonstrate comprehension of the reading material and other special features such as a speech where the text from the diagrams, quizzes or scrolls can be read aloud to students.


Galileo Galilei • The Father of Modern ScienceIsaac Newton – Mathematician • Physicist • AstronomerRené Descartes • Philosopher • Mathematician and Charles Darwin  • The Science of Evolution and other  apps in this series are available with a volume discount for educational institutions. These apps can be purchased worldwide exclusively through the Apple App Store.  The apps are also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of any of these apps. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

Math Decoder

Most people who are involved in education and have studied educational psychology know the name, Jean Piaget.  Piaget’s Theory of Cognitive Development, defined and described stages of development: sensorimotor, pre-operational, concrete operational and formal operational.  Many math curriculum materials are designed to fit with these developmental stages that roughly correspond to age groups:  sensorimotor (0-2), pre-operation stage (2 to 7), concrete operational (7 to 11), and formal operational (11+ and adulthood).  The availability of computers and educational software may have shifted some of these age groupings toward the younger ages since very young children are often using iPads and other devices to explore and learn concepts with assistance of highly interactive educational games and experiences.  Apps can be very engaging and often create multimedia learning environments that motivate students through positive reinforcements such as praise, points, stars, trophies or virtual stickers.

The manipulative approach to teaching math is based on the cognitive development theories of Piaget, Bruner and others.  Software designed to support these theories, for example my Hands-On Math Series, brings the manipulative approach to the computer screen by creating interactive representations of mathematical objects.  Math Decoder is designed in a similar way so that the student is able to move numbered tokens into place to show his or her answer.

Math Decoder presents random numbers in a grid that is similar to the familiar tic-tac-toe board.  Problems are given using shapes that reference the position of the numbers in the grid.  To give an answer students must determine which numbers are referenced by the shapes and then perform the arithmetic operation.


Using Math Decoder helps build mental math skills.  It involves abstract thinking because the symbols are used to represent numbers in way that is similar to how variables are used in algebra.  I designed Math Decoder to be a quick exercise that teachers and parents can assign to students when they have a few minutes of time.  Challenge students to earn a trophy.  It’s fun!

Math Decoder is available with a volume discount for educational institutions. Algebra Portal AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Algebra Portal AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

Algebra Portal AR

Algebra Portal AR

Apple’s new ARKit has opened the door to new kinds of app experiences.  My new app, Algebra Portal AR, creates virtual rooms filled with information about important terms and key concepts related to the Algebra I curriculum.  What is really exciting about the Algebra Portal is students stand up, walk around and experience a totally immersive environment that is filled with illustrated examples that are used to explain some of the fundamental ideas of algebra.


The floor Algebra Portal is a standard Cartesian plane with the x and y axes labelled.  Teachers could develop lesson experiences that involve students walking into the portal and then moving to a specific (xy) position to learn about a particular topic from the algebra curriculum.

When a wall inside the Algebra Portal is tapped a menu of terms is displayed.  If a term is selected detailed information about the topic is displayed with examples.algebra_portal_4

Students and teachers will be amazed when they create virtual rooms filled with information about key terms and concepts from the middle school and high school algebra curriculum.

Explore algebra in a new way with the Algebra Portal AR. Use the camera view on your iPad to detect a flat surface and then tap the screen. Instantly a portal opens to a world filled with information about the terms and concepts that are part of the algebra curriculum.


In an nutshell, to use the app, students walk around in the augmented reality algebra portal where they can tap on the walls and other objects in the rooms to get more information and to hear Siri read aloud information about the selected item. Students can scroll through an extensive list of terms related to the information on the walls of the rooms, walls and objects in the portal.

Algebra Portal AR creates virtual rooms that are approximately 4 meters by 7 meters. It is best used in a well-lit open space, perhaps in a school’s auditorium or multi-purpose room. If the Algebra Portal sounds interesting to you, you might also like the Geometry Portal AR.

Algebra Portal AR is available with a volume discount for educational institutions. Algebra Portal AR can be purchased worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Algebra Portal AR. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.


Target 10 – Like a Word Search but with Numbers


It is great fun when you have precocious grandchildren who have creative and inventive minds.  One of my grandkids is really into word search puzzles.  He loves finding the names of states, or capitals, or astronomy words, or anything else that might be the theme of a word search puzzle.  But the gears in that creative mind started spinning one day and he created a search type of puzzle with numbers.  The gist of the idea was to write an array of random numbers on graph paper and then pick a random target number and try to find numbers in the array that add up to the target number.  This concept gave birth to an iOS and tvOS app named Target 10.


The screen above shows the main game board for Target 10.  The object of Target 10 is to earn 10 stars by finding sets of numbers in the grid that add up to the target number.

Target 10 offers four levels. On an iPad simply tap the Settings icon and then from a screen similar to the one show below, choose a level.  If you are using Apple TV you swipe to get to the Settings Icon and then swipe and click to choose a level.


Automatically a new puzzle is generated at the level you selected.  Study the puzzle to find chains of numbers that add up to the target number.  There’s a fun little twist.  The position of any two numbers can be switched.  When you can’t find any more sets of numbers to make the target sum, try using the Switch icon to move numbers.  To do a switch tap the Switch icon and then navigate to the two numbers whose positions you want to switch. If you are still stuck, you can tap the New Board icon for a new grid.

Switch Icon                                                            New Board Icon

icon_switch            icon_dice

Continue finding sets of numbers that add up to the target number until you have earned 10 stars.


In designing this app I wanted to motivate elementary age students to get quicker at mental math.  It is my intention that by using Target 10 on your iOS device or Apple TV you will be able to engage students problem solving and strategic thinking activities that they will enjoy. The tvOS version of Target 10 offers the same great features as the iOS version, and additionally can be controlled using tvOS compatible game controllers so maybe the kids will think they are playing a video game.

Target 10 is available with a volume discount for educational institutions.  Target 10 is available worldwide exclusively through the Apple App Store.  It also available through Apple’s volume purchase program. Schools get a significant discount when purchasing multiple copies of Target 10. Contact Apple Education for more information about the volume purchase program.  Please visit Ventura Educational Systems’ website for more information about this and other iOS and tvOS apps for education.

More Widgets

Once I got started designing the Math Widgets series I realized it was going to be a lot of fun.  The study of mathematics is an immensely broad topic and for kids who are really into math it is wonderful if a teacher can provide enrichment experiences that introduce new ideas and concepts that go beyond “what’s on the test”.  The Math Widgets series is a collection of tools with these kids and teachers in mind.


Math Widgets III explores some special concepts in number theory.  For example, the Multibase Abacus piques one’s interest in alternative number systems.  What if we only had 8 fingers instead of 10?  Would we use a base 8 system?  With the Multibase Abacus students can investigate base 8 and any other base from 2 to 10.


On the Multibase Abacus, numbers are represented by tapping beads to add or subtract values from the columns of various place value systems.  In the example below we are showing a base 5 system.  Starting on the right we have the ones place labeled with 50.  Moving to the left we have 5’s, 25’s, 125’s, 625’s etc.  Tapping one of the column labels results in a bubble showing the value of the place in base 10.  In the quiz mode students are challenged to represent randomly selected numbers in randomly selected bases.  Quite a few skills come into play when trying to answer the questions posed by the Multibase Abacus, including: estimation, addition, subtraction, multiplication and using exponents.


Clock Arithmetic is another topic in math that is perfect for an enriched curriculum.  Whenever we divide two integers there is always a remainder (sometimes it’s zero).  Clock Arithmetic is a widget that encourages student’s to explore this concept which is known as Modular Arithmetic.  In programming languages there is a special operator used to signify the modulus function.  If a=7 and b=3 then in computer code a%b returns 1 since one is the remainder when 7 is divided by 3.  Sometimes the word ‘mod’ is used instead of the “%” symbol to describe this calculation, for example 15 mod 12 is equal to 3.  In the example below, tapping the 2 is the correct response.


Once in a while, but rarely, you might find a newspaper article about a mathematician solving a problem or finding a proof that has been elusive for hundreds of years.  For example, the conjecture  that no three positive integers ab, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known to have infinitely many solutions since antiquity.  First conjectured by Pierre de Fermat in 1637, this theorem had been the focus of study by mathematician for centuries and was finally proven in 1995 by Andrew Wiles.  Goldbach’s Conjecture has never been proven. It was first posed in a letter from Goldbach to Euler in 1742.  The conjecture posits that every even integer greater than 2 can be expressed as the sum of two primes.  Use the Goldbach’s Conjecture widget to explore this idea by finding the primes whose sum is the given even numbers.


The Hexagon Arithmetic Widget is a six number system that uses emojis as the symbols.  Counting moves in a clockwise direction around the hexagon.  The object is to complete the addition table using logic to figure out the pattern.


Math Widgets I, II and III are offered exclusively by the iTunes App Store and sell for $1.99 each.  Educational discounts are available for schools.  Please visit our website for more information about these and other apps for education.


Math Widgets & Math Widgets II

There are two definitions for the term widget.  First, a widget is a small gadget or mechanical device that performs a useful function. In this context, the term is often applied to a device where the actual name is unknown or unspecified.  Second, a widget is an application, or component of an interface, that enables a user to do something special, for example perform a useful function or access special information.  Math Widgets fit both definitions.  The Math Widgets apps are collections of math tools that provide opportunities to explore a variety of important math concepts.  Some of the concepts extend the K-8 math curriculum laterally and therefore these apps are particularly useful for teachers who are looking to provide enrichment.

Let’s take a look and the first Math Widgets app.  This app is available for both iPad and Apple TV and includes four widgets: Slide Rule, Fraction Action, Integers and Coordinate Grid.

screen_1With the advent of calculators and computers, obviously the need for a slide rule has diminished, if not, virtually vanished, but what fun for kids to learn the basic idea of a slide rule by manipulating a virtual slide rule on their iPad or Apple TV.  In addition to representing the meaning of two fundamental math concepts: adding and subtracting,  the slide rule gives teachers an opportunity to discuss some of other historical tools used to help people do math for example the abacus or Napier’s Bones.  (See Abacus Deluxe and Napier’s Bones)

screen_2The operation of the Slide Rule widget is straightforward. The widget presents a problem in the middle of the screen and challenges the student to show the answer using the slide rule.  Addition and subtraction problems are presented.

screen_4The Integers widget uses a number line to help students understand operations with positive and negative numbers.  A problem is presented and the student is challenged to slide the marker to show the answer.  When slid in a positive direction a blue bar appears on the number line.  A red bar is used to show movement in the negative direction.  By using this app student will develop a better understanding of basic operations with integers.

screen_3Fraction Action provides an interactive widget for learning about equivalent fractions.  A fraction is randomly selected and displayed as a numerator over a denominator. It is also shown as parts of a circle.  The challenge for the student is to move the indicator along the fraction ruler to select the equivalent fraction.

screen_5The Coordinate Grid widget is designed to help students learn to locate points on a standard Cartesian plane.  The x and y axes and the quadrants are labelled.  The student is given a coordinate pair and is challenged to find the corresponding point on grid by moving a slider.

The first Math Widgets app seemed so useful that I thought I would do another one so I developed Math Widgets II.


Math Widgets II has 4 widgets:  Multibase Chart, Arrow Math, Tinker Totals and Peg Puzzle Party.  While studying number systems other than Base 10 might not be a critical part of the standard elementary curriculum, it is a fun enrichment idea for teachers who are looking to extend the curriculum for certain students. Multibase Chart provides an interesting experience in representing numbers using different bases.

screen_2In this example the computer has challenged the student to represent 19 in Base 8.  The red slider has be moved to isolate all the possible two digit numbers in Base 8.  Since 2 x 8 + 3 = 19, the correct answer is 23.   The correct answer is located at column D, row C.  Tapping this cell results in a positive reinforcement message and increase in score.

screen_3Success in mathematics and many other areas of study involves the skill of being able to follow a specific set of instructions.  Arrow Math provides an opportunity to practice two skills, the ability to carefully follow a set of instructions and also the meaning of an inverse operation.  Arrow Math provides teachers with a visual way to talk about inverse operations which are important in the study of mathematics.  When using this widget ask students questions such as ‘What is the inverse of moving to the right?’ or ‘What is the inverse of moving down and left?’.

screen_4The Tinker Totals widget creates number puzzles where the object is to arrange number given into the cells of a pattern so that the numbers along each line add to the same sum.

screen_5Peg Puzzle Party is a logical thinking puzzle where the challenge is to end up with the least number of pegs on the board.  A move consist of pick a peg and jumping over another peg to land in an open space.  When a peg is selected the available moves are highlighted in green.  Peg Puzzle Party is a fun way to exercise your brain and can be used to help students develop strategic thinking skills.

Math Widgets and Math Widgets II are offered exclusively by the iTunes App Store and sells for $1.99.  Please visit our website for more information about these and other apps for education.


Mouse Maze Math

Some apps are just really fun to develop.  Mouse Maze Math is one of those apps!  For me the idea of programming a mouse to run through a maze is an old one.  I used to kid my programming students that we were going to see who could build the smartest mouse.  We would set out to  write programs where we used graphics to define a maze and then added a section of the program that would control a little red blip that represented the mouse.  The object was to write a program that would navigate the maze and eventually get the red blip to move to the yellow blip that represented the cheese.

Computers have come a long way since the days that I was working with 7th and 8th graders at the first computer lab in Ventura County.  I read in the news today that Apple’s new Mac Book Pro is 6.8 million times faster than the original one.  That’s pretty amazing and Mouse Maze Math is pretty different from what was possible back in the days when floppy disk drives were a new thing.mousemaze_title

Mouse Maze Math challenges students to answer arithmetic problems as they give navigation instructions to a mouse to enable it to run through the maze. It is available for iPads and Apple TV.  In the iPad version students tap  green arrows cause the mouse move in one of four directions: left, down, right or up. In the Apple TV version a student can either use the Siri Remote by swiping and tapping or use a game controller to control the mouse.

In the maze shown below some of the pathways are blocked by arithmetic symbols.  When these symbols are encountered a calculator-like device is displayed.


If the student answers the problem correctly the mouse stays on the spot and the student can continue to solve the maze.


Mazes are randomly selected and automatically displayed when the dice icon is tapped, but mazes can also be built by the students.  By dragging elements of the maze onto the grid, student are able to construct a maze.  Mazes built by students can be saved and retrieved at a later time.


Mouse Maze Math is a fun way to practice arithmetic and also creatively use the iPad to design and construct mazes.  I’ve always believed in active teaching and active learning.  I hope teachers will enjoy using this tool with their students.  Teachers should let me know if they are interested in evaluating this app for use at their school.   I have a limited number of download codes for FREE evaluation copies of this app.   I hope that elementary students enjoy practicing basic math skills with this app and that this colorful interactive app will help them in their journey to become great problem solvers.

Fraction Builder

I submitted Fraction Builder to iTunes yesterday and it was approved in less than an hour!  It is so amazing to me what great service Apple offers to developers.  I certainly appreciate the way that the App Store provides access to my work to students and teachers all over the world.


In most of my math apps I try to make them icon-based so that language skills are not critical for working with concepts.  Fraction Builder has a series of icons across the top of the screen.  Tapping each icon results in a specific function.

For example, tapping the red dice generates a random fraction.  Denominators range from 1 to 12.  Once the denominator is set, numerators can be any number that results in a proper fraction.


When the question mark is tapped, a question is generated and displayed on a moveable note.  To answer the question students drag number tiles to make the fraction.  Usually it is best to start with the denominator.  If using this app in a classroom, the teacher should explain that the denominator represents the number of equal parts.  For this example, the student would first slide the three tile to the denominator position.  Next, the student should slide a one to the numerator position.  Once the numerator and denominator have been properly set, the students should tap the check mark.  When this icon is tapped the app compares the students answer to the correct answer for the question.


A scoreboard displays student progress as they work with the app.  It shows the topic, number of questions attempted and the percent correct.  Quiz questions are based on three main topic areas:

• Naming Fractions

• Equivalent Fractions

• Comparing Fractions

Various other functions are performed when other icons are tapped.  This chart explains the other functions.notebook

I hope that teachers will let me know if they are interested in evaluating this app for use at their school.   I have a limited number of download codes for FREE evaluation copies of this app.   For some students learning about fractions is difficult.  It is my hope that this colorful interactive app will help them in their journey to master fraction concepts.