2 Kids – 1 iPad, Lots of Frogs…

Hop to It Math

In an ideal world schools would be able to provide an iPad for every student, but in many cases a one-to-one ratio is just not feasible.  I have developed several learning apps that are designed to be used by two students at the same time.  Hop to It Math is one game designed to help kids improve math skills and can be used with two students simultaneously.



The board is layed out like a traditional board game where players move markers along a path to reach a goal.  In this case the markers are frogs and the goal is the finish line.

The game begins by displaying a problem.  Below the problem a calculator style number pad to use for entering the answer.


A wide range of problems can be selected by the players:

Level 1:
Addition – Whole Numbers (1-10)
Subtraction – Whole Numbers (1-18)
Multiplication – Facts (1-5)
Division – Facts (up to 25 ÷ 5)

Level 2:
Addition – Whole Numbers (0-20)
Subtraction – Whole Numbers (1-40)
Multiplication – Facts (0-12)
Division – Facts (up to 144 ÷ 12)

After a correct answer is entered, a spinner appears on the screen.  The player taps the spinner and the player’s frog hops to the next position.

Hop to It Math - tvOS

The Apple TV version of the game (shown above) offers a 1920 x 1080 pixels version of the game.  By swiping the Siri Remove players enter answers, operate the spinner and move their frog.  My goal in developing this game is to provide elementary students with a fun way to practice and improve math skills.


Another two player game that is based on the frog theme is FrogGo.  FrogGo is designed to support S.T.E.M objectives and introduce student to basic programming concepts. Science, Technology, Engineering and Mathematics are critically important 21st Century skills and I wanted to support these objectives by providing a fun learning experience.

Six commands are available to control the player’s frog:  Forward (FD), Right  90° (RT), Left 90° (LT), Jump (JMP), Double Move (2X) and Triple Move (3X).  The goal is to program your frog to move and capture the rewards that are randomly placed on the game board.  Players need to avoid moving out of bounds.


The scorecards are used to track the number of rewards each player has accumulated.  The winner is the player who has accumulated the most rewards at the end of the game.  Computational thinking is an essential process that is used in most careers and it can be introduced at a very early age with tools like FrogGo. In FrogGo each player’s turn begins with analyzing a problem, breaking it down into components parts or steps and then describing a path to a solution using algorithmic thinking. A programming sequence is defined by choosing from a list of functions. Sequences of commands are successful if they lead to one of three goals (flies, stars or trophies). Programs that don’t work need to be ‘debugged’ by the player.  I hope that FrogGo will provide teachers with a way to interest kids in learning more about computer programming and realize that designing computer games can be even more fun than playing them.


Math Bingo

If you’ve ever had the joyful experience of trying to teach a four-year-old how to play Tic-Tac-Toe you hopefully have witnessed the excitement that a child feels when they suddenly learn that games involve strategy.  Instantly games become more interesting.  Now there is a reason to hide your cards when playing Old Maid.  Math Bingo is a bit like Tic-Tac-Toe in that players can develop a strategy.  Regular Bingo involves calling out randomly balls,  B-13, I-24, and so on.  Each number only appears once on a typical bingo card.  Math Bingo involves a strategy because the same answer might occur a couple of times on the card and therefore the player must strategically decide which answer to pick.

Math BIngo 1

Math Bingo is designed for iPad and Apple TV.  It is a two player game.  On the iPad version players sit opposite each other so the playing surface looks something like this.  The bingo cards are rotated 180° so the orientation is correct for each user.


When designing the Apple TV version of Math Bingo, I thought it would be fun for kids to use slightly scary looking critters as markers in the game, so play begins after each player has selected which marker to use.

Math BIngo 2.png

Using the settings option, players can select the skill level that they would like to practice. The app provides 20 levels, all keyed to the Common Core Standards.  Level 1 is beginning addition facts so it’s a good place for K-1 students to start.

Math BIngo 3

When they are ready each player taps the Go! icon and the game begins.  The app will generate a set of 25 problems at the skill level selected using the settings option.  Every game is unique.

Here, two addition problems are presented 9+5 and 9+2.  During the game each player will be given the same problems but not in the same order.  Players take turns and move the yellow highlight to designate their answer choice.  When using the Apple TV version, the highlight is moved by swiping the Siri Remote or using a joystick.  On the iPad the player just taps the screen.  The goal is to select an appropriate answer with a strategy of trying to get 5 markers in a line.

Math BIngo 4.png

When the correct answer is chosen the game marker appears and an audible reward is given.  Play continues until one player gets a BINGO, five markers in a horizontal, vertical or diagonal line.  Let me know if you would like a free download code so you try this app to see if it would be useful to your students.

Math BIngo 5

And, oh, by the way if you are interested in a fun way to introduce Tic-Tac-Toe try my Tic-Tac-Tarantula for iPad, especially if you are into creepy crawly things.  Tic-Tac-Tarantula is a one or two player game — match wits against the computer or play with a friend.


Happy Pi Day 3.14.16

Well, this is it, the big one.  Pi Day 3.14.16 won’t happen again for 100 years.  I hope you had some mathematical fun today or at least had a piece of pie.  I’ve been working on a simulation of Napier’s Bones for iOS.  The iPad app is functionally similar to Napier’s calculating tool which, of course, in the history of computing devices, was one of the earliest calculators.   The app is designed using a table top or wooden box metaphor.


Rods are picked up by tapping a number on the left and dragging it into position on the right.  Each rod is etched with the multiplication table for the specific number. I am hoping that using the app will help kids better understand the meaning of multiplication.

A slider moves up and down highlighting the multiplier and showing how the partial products are used to generate the product.

The app also includes a bit of historical information about John Napier, the Scottish mathematician who lived in Edinburg from 1550 to 1617.


I included a quiz function so that the app will challenge kids to use the device to find the answers to multiplication problems.  It starts out with two-digit number multiplied by single digit number.  Problems then get progressively more challenging.


If all goes well the app should be available from the Apple iTunes store soon, hopefully by April Fools Day.😀


Hands-On Math Hundreds Chart

Hands-On Math Hundreds Chart

When I was teaching elementary math in Southern California one of my favorite teaching aids was the hundreds chart.  I would burn up my photocopying budget reproducing hundreds charts so my students could color patterns showing the multiples of 2, 3, 5 or 7.  It really comes as no surprise to me that Hands-On Math Hundreds Chart is one of my favorite apps.  No longer is necessary to provides students with paper hundreds charts.  Using the app students just pick a color and a marker and then away they go marking patterns on the chart.


The interface is intuitive.  The markers function like objects and can picked up and moved.  To complete remove an object simply drag it off the chart.

A Teaching Tool

So what can you do with a hundreds chart?  Which concepts can you teach?  One of the first activities to do with young students is skip counting.  Pick a color and a type of marker.  To count by 3’s, for example, begin by tapping the cell labelled ‘3’ and then continue to 6, 9, 12, 15, etc.  Eventually a pattern begins to emerge.  Perhaps some of your students will discover that the pattern for 3 creates diagonal lines.  Encourage students to use math vocabulary in describing their hundreds chart explorations.

But more can be done with a hundreds chart.  Marking patterns to show multiples of a given number is a great way to practice and learn multiplication tables and it is easy for teachers to check students work with just a glance at the iPad screen.  But there must be more that can be done with a hundreds chart.

Least Common Multiple

The reason the Hands-On Math Hundreds Chart app has 8 colors and 6 shapes is so that overlapping patterns can be created on the chart.  When kids start overlapping patterns things get really interesting, mathematically speaking.  Understanding Least Common Multiple, in my mind, is an essential skill for success in mathematics.  Using Least Common Multiple (LCM) students can reduce fractions to simplest terms.  LCM is the smallest positive integer that is evenly divisible by two other numbers, a and b.

Let’s define a as 3 and b as 5 (which also happen to be two prime numbers, but more on that later).  Here’s what the chart will look like after a pattern for 3 has been marked with a red square.


Now let’s overlay the pattern for 5 with a blue circle.  Things are starting to get interesting…


At this point a teacher would want to ask the students to find all the numbers that got both marks, the red square and the blue circle.  I would recommend that the students mark these numbers with a yellow highlight (transparent yellow square).


Wow! Look at that the yellow highlighted numbers also make a pattern.  This numbers are the common multiples of 3 and 5.  Now study the chart and find the smallest number in this set.  15 is the LCM of 3 and 5.

Find the LCM of other numbers.  Just tap the eraser to completely erase the chart. Oh, and remember, if you only want to remove one marker just slide it off the chart.

A Classic Lesson

The first 4 prime numbers are 2, 3, 5, and 7.  In mathematics, the sieve of Eratosthenes is a pattern that reveals the prime numbers.  To investigate the pattern on the Hands-On Math Hundreds Chart, begin by marking the pattern for the number 2 and then we will mark 3, 5, and 7.  The procedure involves skipping the first number in the series and then marking out all the multiples.  So, skip 2 and then more out 4, 6, 8, 10, etc.  The chart should look something like this:


Use a different color for each number.  Now mark out the pattern for 3, but remember to not mark 3 since it is also prime.  Continue by marking the patterns for 5 and 7.  If a number is already marked just skip it.  Since the next prime is 11 and 11² is 121 so not on the chart and we don’t need it for this experiment.

When the marking procedures are finished, the chart should look like this:


The numbers that did not get marked are prime numbers.  All the marked numbers are composite numbers.

Get Creative!

There are lots of ways to make math fun using Hands-On Math Hundreds Chart.  Make up your own problem sets so that when the problems are answered correctly a picture is created.  For more information about this app click here.