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’s 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.

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.


Pete the Penguin’s Math Game

titlePractice, Practice, Practice!  When it comes to building basic math skills most teachers will agree that kids need a lot of practice.  The app for iPad and Apple TV creates an interactive learning environment where student’s get to practice basic math skills. One of four skills can be selected: addition, subtraction, multiplication or division. Within each skill there are five levels of difficulty.

The goal is to get 10 problems correct for each skill and for each level.


To begin the student selects a skill and then a marker to move along the trail. Sound effects and positive auditory feedback encourages the students to do their best.

• Single-Digit Addition
• Adding Multiples of 10
• Addition – Two-Digit
• Addition – Three-Digit Plus Two-Digit
• Make a 10 Addition Practice

• Single-Digit Subtraction
• Subtracting 10
• Subtraction – Two-Digit Subtraction (No Regrouping)
• Subtraction -Two-Digit (with Regrouping)
•Three-Digit Minus a Two-Digit Number

• Multiplication Facts (0-9)
• Multiplication Facts (5-12)
• Multiplication by 10 or 100
• Multiplication – Two-Digit
• Multiplication – Three-Digit by One-Digit

• Division Facts (0-9)
• Division Facts (5-12)
• Division by 10 or 100
• Division -Two-Digit by Single-Digit
• Division – Three-Digit by Single-Digit

I hope teachers will enjoy using Pete the Penguin’s Math Game 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.

The app is offered exclusively by the iTunes App Store and sells for $0.99.  Please visit our website for more information about this 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.

Just in Time for Halloween

What could be more fun that having your monster be chased by three other monsters?  Well that’s the theme of my latest math game.title

Ziggy, Spot and Pete are the three monsters that you want to avoid.  Harry is your monster and is controlled by tapping arrows on the iPad version or swiping the Siri Remote on the tvOS version.  The tvOS version also supports the use of a game controller so Harry can be moved using a compatible gaming device.


The object of the game is to move Harry to the correct answer for a math problem shown at the bottom of the screen.  Anytime that  Ziggy, Spot or Pete run into Harry as they bounce around the screen, Harry loses a unit of energy.  Fortunately when Harry gets an answer correct he gets a unit of energy back.  The goal is to score ten points before running out of energy.



Teachers and parents will like the wide range of problems.  Problems are randomly generated so the game is different every time it is played.  Skills are organized and defined using the Common Core Standards.  Look Out! Monsters! is a fast-paced game specifically designed to help kids get quicker at doing mental arithmetic.  A limited number of free promotional codes are available by request.  The app is offered exclusively by the iTunes App Store and sells for $0.99.  Please visit our website for more information about this and other apps for education.

Skills Chart

Operations and Algebraic Thinking Add within 20 Integers from 1 to 10 
Operations and Algebraic Thinking Add within 20. Integers from 5 to 20
Operations and Algebraic Thinking Add within 20. Integers from 10 to 20
Operations and Algebraic Thinking Add within 20. Integers from 1 to 20 
Operations and Algebraic Thinking Subtract within 20. Integers from 1 to 10
Operations and Algebraic Thinking Subtract within 20. Integers from 1 to 20 
Operations and Algebraic Thinking Determine the unknown whole number in an addition equation. Integers from 1 to 20
Numbers and Operations in Base Ten Add within 100, including adding a two-digit number and a one-digit number. Integers from 1 to 100 and 1 to 10
Numbers and Operations in Base Ten Given a two digit number mentally find 10 more or 10 less. Integers from 10 to 100 and 10
Numbers and Operations in Base Ten Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences) Integers from 10 to 90
Operations and Algebraic Thinking Fluently add and subtract within 20 using mental strategies. Integers from 0 to 20
Numbers and Operations in Base Ten Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Integers from 0 to 100
Numbers and Operations in Base Ten Add up to four two-digit numbers using strategies based on place value and properties of operations. Number Range: Integers from 0 to 1000
Numbers and Operations in Base Ten Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Number Range: Integers from 10 to 100 and 100 to 900
Operations and Algebraic Thinking Fluently multiply within 100. Factors from 0 to 10
Operations and Algebraic Thinking Fluently divide within 100. Divisors and Quotients from 0 to 10
Number and Operations in Base Ten Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. Dividends from 10 to 1000 and Divisors of 10 or 100
Operations and Algebraic Thinking Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Integers 1 to 10
Expressions and Equations Evaluate expressions at specific values of their variables. Integers 1 to 10
Expressions and Equations Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Integers 1 to 10


Critter Mates


You know the feeling when you get that “aha” moment and want to run through the streets shouting “Eureka!”. What is it about solving puzzles that is so satisfying?

There is some evidence that early people had an interest in problem solving. Major breakthroughs like the invention of the wheel and learning to control fire happened rarely, but finding solutions to small problems probably occurred on a regular basis.

Recently researchers have investigated the urge to solve puzzles and have attempted to explain the brain mechanisms involved. Different types of puzzles require different skills.  Crossword puzzle solvers obviously need to have a good vocabulary, memory and pattern recognizing ability.  While much more research is need, there does seem to be some evidence to suggest that a high level of experience with some times of puzzles, crosswords, for example, in older subjects helps to attenuate the negative effects of age on memory and some perceptual speed tasks.  Other types of puzzles require spatial reasoning skills.  For example, Rubik’s Cubes, pentominoes, tangrams, soma cubes and other similar puzzles are involve spatial reasoning as well as logical sequencing skills.  Critter Mates is a little bit like a crossword puzzle in that the puzzle format is a grid.  Logical sequential skills are also involved.

In children with brain damage research has shown positive effects from puzzle solving activities.  In particular children who had a weak visual symbol memory that impaired their ability to spell and read words benefitted from unscrambling puzzles where mixed-up letters were paired with pictures.  But knowing just how these mechanism work has yet to be explained.

One thing that many educators know is that problem solving skills can be taught.  Some of the methodologies that are part of a comprehensive problem solving curriculum can be taught in relation to puzzles like Critter Mates.  Many educators employ a five-stage model to teaching problem solving:

  1. Understand the problem.
  2. Describe any barriers.
  3. Identify various solutions.
    1. Create visual images.
    2. Guesstimate.
    3. Create a table.
    4. Use manipulatives.
    5. Work backward.
    6. Look for a pattern.
    7. Create a systematic list.
  4. Try out a solution.
    1. Keep accurate records.
    2. Persist with a strategy until is proven to not work.
    3. Monitor the steps.
    4. Step away from the problem for a while.
  5. Evaluate the results.

Some people like to solve puzzles and others like to design them. Which one are you? Math ability and music seem to be related to problem solving ability. So if you have talent in these areas you might also be a great puzzle solver or creator.  In many cases puzzle solving ability requires synthesizing several different pieces of information and the ability to see patterns which are also skills that are fundamental to mathematics and music.  Activities like solving the Critter Mates puzzles may help to develop or strengthen these skills.


When I designed the Critter Mates I wanted to create a problem solving challenge where kids would be motivated to solve visual puzzles using ‘critters’ as a virtual manipulative.  Understanding the puzzle is fairly simple.  The goal is to move all the critters so that they are next to each other.  One way to approach the problem might be to work backward.  Visualize the solution and then try to figure out the steps needed to get to the solution.  The Critter Mates puzzle definitely has barriers.  The critters need to navigate the walls and will often get logically stuck. Keeping notes as an accurate record of what has been tried might help to avoid pitfalls in future attempts.  I hope that you will find that Critter Mates is intrinsically motivating and useful in teaching kids to be better problem solvers.


For more information about Critter Mates app for iOS and tvOS please visit our website.  The app is available at iTunes for $0.99